# Optical diagnostics of laser-produced plasmas

S. S. Harilal<EMAIL_ADDRESS>Pacific Northwest National Laboratory, Richland,
Washington 99352, USA.  M. C. Phillips  James C. Wyant College of Optical
Sciences, University of Arizona, Tucson, Arizona 85721, USA.  D. H. Froula
Laboratory for Laser Energetics, University of Rochester, Rochester, New York
14623, USA  K. K. Anoop  R. C. Issac  Department of Physics, Cochin University
of Science and Technology, Cochin, Kerala 682022, India  F. N. Beg  Center for
Energy Research, University of California San Diego, La Jolla, California
92093, USA

###### Abstract

Laser-produced plasmas (LPPs) engulf exotic and complex conditions ranging in
temperature, density, pressure, magnetic and electric fields, charge states,
charged particle kinetics, and gas-phase reactions, based on the irradiation
conditions, target geometries, and the background cover gas. The application
potential of the LPP is so diverse that it generates considerable interest for
both basic and applied research areas. The fundamental research on LPPs can be
traced back to the early 1960s, immediately after the invention of the laser.
In the 1970s, the laser was identified as a tool to pursue inertial
confinement fusion, and since then, several other technologies emerged out of
LPPs. These applications prompted the development and adaptation of innovative
diagnostic tools for understanding the fundamental nature and spatiotemporal
properties of these complex systems. Although most of the traditional
characterization techniques developed for other plasma sources can be used to
characterize the LPPs, care must be taken to interpret the results because of
their small size, transient nature, and inhomogeneities. The existence of the
large spatiotemporal density and temperature gradients often necessitates non-
uniform weighted averaging over distance and time. Among the various plasma
characterization tools, optical-based diagnostic tools play a key role in the
accurate measurements of LPP parameters. The optical toolbox contains optical
spectroscopy (emission, absorption, and fluorescence), passive and active
imaging and optical probing methods (shadowgraphy, Schlieren, interferometry,
Thomson scattering, deflectometry, and velocimetry). Each technique is useful
for measuring a specific property, and its use is limited to a certain time
span during the LPP evolution because of the sensitivity issues related to the
selected measuring tool. Therefore, multiple diagnostic tools are essential
for a comprehensive insight into the entire plasma behavior. In recent times,
the improvements in performance in the lasers and detector systems expanded
the capability of the aforementioned passive and active diagnostics tools.
This review provides an overview of optical diagnostic tools frequently
employed for the characterization of the LPPs and emphasizes techniques,
associated assumptions, and challenges. Considering most of the industrial and
other applications of the LPP belong to low to moderate laser intensities
($10^{8}-10^{15}$ Wcm-2), this review focuses on diagnostic tools pertaining
to this regime.

††preprint: APS/123-QED

###### Contents

  1. I Introduction
  2. II Optical spectroscopy
    1. II.1 Emission Spectroscopy
      1. II.1.1 Instrumentation and analysis considerations
      2. II.1.2 Electron density using Stark effect
      3. II.1.3 Measurement of temperature
      4. II.1.4 Optical time-of-flight measurements
    2. II.2 Absorption spectroscopy
      1. II.2.1 Laser absorption spectroscopy
      2. II.2.2 Absorption spectroscopy using broadband sources
      3. II.2.3 Temperature and density measurement
      4. II.2.4 Kinetics of LPP using absorption spectroscopy
    3. II.3 Laser-induced fluorescence
      1. II.3.1 Instrumentation and analysis considerations
      2. II.3.2 Temperature and density measurement
    4. II.4 Local Thermodynamic Equilibrium
  3. III Passive and active Imaging tools
    1. III.1 Fast photography
    2. III.2 LIF and absorption imaging
  4. IV Optical Probing
    1. IV.1 Shadowgraphy
    2. IV.2 Schlieren imaging
    3. IV.3 Laser Interferometry
    4. IV.4 Thomson scattering
      1. IV.4.1 Laser beam propagation
      2. IV.4.2 Thomson scattering from a Maxwellian plasma
  5. V Summary of other optical methods
    1. V.1 Moiré deflectometry
    2. V.2 Optical velocimetry
  6. VI Summary

##  I Introduction

Plasma is the fourth state of matter, and there are several ways to generate
plasmas in the laboratory. One of the methods commonly used is to focus an
intense pulsed laser on a matter of interest. Among the various laboratory
plasmas, the laser-produced plasma (LPP) may be one of the most complex
systems because of its transient nature combined with spatial inhomogeneities
[269]. LPPs are also characterized by high temperatures and high densities of
electrons and ions. Although the history of fundamental research on LPPs can
be traced back to the early 1960s with the earliest article about LPPs
appearing immediately after the invention of the laser [29, 203], most
advances in using LPPs for various applications emerged after lasers were
proposed as drivers for inertial confinement fusion. Currently, LPPs find
applications in a wide variety of fields such as material science [50],
analytical instrumentation [278], spectroscopy [242], planetary science [285],
geology [87], agriculture [249], high energy density physics (HEDP) [81],
laser ion source [334], laser ablation propulsion [262], laser processing
(micromachining, cutting, etc.) [98], and medicine [102], among others.

All LPP applications require the availability of reliable lasers with
different characteristics (laser energy, pulse width, wavelength, beam
profile) and a deeper understanding of the LPP properties by developing and
using state-of-the-art diagnostic tools in conjunction with modeling efforts.
In materials science and nanotechnology, pulsed laser deposition (PLD) is a
well-established method for fabricating thin films of complex oxides [286,
330] where a strong correlation between the dynamics of the LPP and the
quality of thin films exists [50, 187]. In spectroscopic applications, such as
in laser-induced breakdown spectroscopy (LIBS), the LPP is generated via
stoichiometric ablation, and the subsequent light emission from the plasma is
used for the qualitative and quantitative elemental and isotopic analysis of
multi-element samples [239, 61, 242, 130]. The LPP is also used as the front
end for various analytical tools such as laser ablation inductively coupled
plasma mass spectrometry (LA-ICP-MS) [193], LA inductively coupled plasma
optical emission spectroscopy (LA-ICP-OES) [311], LA time-of-flight mass
spectrometry (LA-TOF-MS) [4], LA laser-induced fluorescence (LA-LIF) [236],
and LA laser-absorption spectroscopy (LA-LAS) [304].

The LPP can produce high-brightness extreme ultraviolet (EUV) radiation, which
is currently being used as a photon source in nanolithography [119, 296, 16].
LPPs are also considered a potential radiation source for water-window
microscopy [178]. Higher harmonic generation from an LPP is a promising tool
for generating coherent EUV sources [287]. LPPs are also recognized as a
promising medium for generating intense pulsed X-ray and gamma-ray radiation
sources [254, 270, 159, 53], collimated ion beams [88, 202], and plasma-based
particle accelerators [161, 58]. The laser-plasma accelerators (LPAs) are
capable of producing fields $10^{4}$ times those of conventional accelerators,
and advanced LPAs are going to play a significant role in accelerator physics,
radiotherapy, and high-energy physics applications in the upcoming years [213,
31, 19, 299, 326]. The LPP is also a powerful and compact source of multi-MeV
ions [184]. Some of the recent scientific achievements obtained with LPPs are
neutron source development [233], extreme ionization of heavy atoms [149],
fusion reactions [189], and terahertz generation [146]. An LPP-based emission
spectroscopy system has been deployed in the Mars Curiosity and Perseverance
rovers for elemental analysis of rocks and soil [55, 214]. In addition to
these, the LPP is useful for recreating astrophysical plasmas in the
laboratory and used as a surrogate for studying plasma chemistry occurring in
high-explosion and nuclear events [198, 175, 168].

Plasmas are traditionally defined as partially ionized gaseous mediums with
total charge neutrality and are characterized and classified according to
their temperature and density. Most of the other plasma parameters, _viz._
particle kinetics, opacity, pressure, the energy of the shocks, etc., are
directly and indirectly connected to the temperature and density of the plasma
system. The laser parameters such as energy, wavelength, and pulse length turn
out to be crucial control knobs for changing the fundamental parameters of the
LPP. For example, by changing the laser power density, the initial peak
temperature of the LPP can be tuned from a few thousand Kelvin to millions of
Kelvin. The peak density of LPP systems also changes by several orders of
magnitude based on laser power density and ambient conditions. Fig. 1 shows an
approximate map of the temperature and density range of LPPs used in various
applications. Regardless of the initial conditions of the LPP, the temperature
and density decrease as the plasma expands and eventually reaches equilibrium
with the surrounding environment. Thus, the physical conditions within the LPP
can span a wide range of temperatures, pressures, and atomic/electron
densities, with a corresponding change in chemical composition (ionized atoms,
neutral atoms, molecules, clusters, etc.).

Figure 1:  Typical properties of LPPs used for various applications.

The physics of the LPP generation and subsequent evolution changes
significantly with laser intensity. The physical properties of plasmas
produced by similar laser intensities with varying pulse widths will also be
vastly different due to differences in the physics of plasma generation. For
analytical applications such as LIBS, the plasma source should provide a
copious amount of light from the excited-state population of atomic species
where the required temperature and density are in the range of 1-3 eV and
$10^{15}-10^{17}cm^{-3}$ [285], respectively, and hundreds of µJ to tens of mJ
of laser pulse energies are therefore used for plasma production [278, 46].
For LPP sources for EUV lithography, a bright plasma source emitting at a
narrow band wavelength region around 13.5 nm is needed, which requires an
optically thin plasma with temperatures $\approx$ 30 eV [296, 303, 318]. For
water-window microscopy, a bright source emitting in the spectral region of
2.2-4.4 nm is required, which necessitates a plasma with a temperature of
$\approx$100 eV. In HEDP, the temperature and density of the plasmas reaches
above 1 keV and near-solid density, respectively. Therefore, tens of kJ to MJ
pulse energies are used where plasma pressure exceeds 100 GPa [104, 19]. HEDPs
play an important role in national security applications, high-brightness
sources of gamma and X-rays, neutrons, and protons [254, 54].

Although the procedure of generating an LPP is relatively simple - focus a
pulsed laser with intensities above the laser ablation threshold ($\gtrsim
10^{8}$ Wcm-2) on a material of interest - the physics involved in such a
process is notoriously complex. Numerous interrelated processes happen during
the generation and subsequent expansion of LPP. Some of them are heating,
ionization, melting, vaporization, phase explosion, ejection of particles,
plasma creation, laser-plasma interaction, instabilities, plasma hydrodynamic
expansion, shock wave generation, and confinement, to list a few [268]. A
schematic example of various processes during a nanosecond LPP generation and
expansion into an ambient is given in Fig. 2. The lifecycle of an LPP spans
over several orders of magnitude in time, and its fundamental properties
change many orders during its lifecycle. The energy, pulse width, and
wavelength of the laser will affect both laser-target and laser-plasma
interactions [197, 300, 9]. For longer-pulsed lasers ($\sim$ ns-µs), the LPP
generation happens during the leading edge of the laser pulse, and a large
fraction of energy is used for heating the plasma. The laser-plasma heating is
absent for shorter pulsed lasers (e.g., fs laser pulses). However, prompt
ionization can occur during the ultrafast laser pulse interaction with the
target in the high-intensity regime, which is the basis of laser wakefield
acceleration [86, 199].

Nanosecond pulsed lasers are commonly used for LPP generation, but ultrashort
femtosecond LPPs have numerous advantages in material science and analytical
applications [190, 272, 130, 315]. A detailed account of laser-produced plasma
generation physics is well-documented in many review articles and textbooks
[268, 96, 121].The physics of laser-matter interactions changes with the type
of matter (solid, liquid, gas), and the laser intensity thresholds for
generating plasmas depend strongly on the medium properties [61]. Even for
solid targets, the ablation physics vary with target physical and chemical
properties [97, 248]. In metals, the laser couples with free electrons. For
semiconductors and insulators, the laser is coupled with bound electrons. The
presence of an ambient medium or external magnetic field also significantly
alters plasma properties [167, 142, 20]. So, the parameter space for
controlling the LPP properties is vast. However, many tuning variables are
also helpful for defining the LPP properties for each application. Therefore,
the broad appeal of LPP for many scientific and industrial applications can
also be related to better control of LPP properties using a wide variety of
parameters.

Figure 2:  Various physical processes happening during a nanosecond laser-
produced plasma generation and expansion into an ambient gas medium are given.

Plasma diagnostics play a vital role in understanding the physical properties
of all plasmas, including LPPs, as well as their optimization for various
applications [154, 207, 241, 156, 186]. Because of the large variation in
fundamental parameters with space and time, different diagnostic tools are
essential to capture details of the LPP during its entire lifecycle.
Considering the transient nature combined with spatial inhomogeneity of LPPs,
the diagnostics need to have high spatial and temporal resolutions. Therefore,
in addition to general issues associated with the diagnostics of traditional
steady-state plasmas, there exist certain challenges for a comprehensive
characterization of LPPs because of their small size and transient and
inhomogeneous nature. Hence, great care must be taken when collecting and
interpreting results obtained using various diagnostic tools because of the
large gradients in the physical and chemical properties of LPPs with time and
space, which may result in weighted averaging of measured properties over
certain length and time scales.

Some of the common optical diagnostics used for plasma characterization
include optical spectroscopy (emission spectroscopy, absorption spectroscopy,
and laser-induced fluorescence [LIF]), imaging and diagnostics employing an
optical probe such as shadowgraphy, Schlieren, interferometry, Thomson
scattering, deflectometry, and velocimetry. In addition to optical diagnostic
methods, charged particle analysis tools such as ion probes [76], Faraday cup
[10], electrostatic energy analyzer [34], and time-of-flight mass spectrometry
[331, 4] are also used regularly by the LPP community. Each diagnostic tool
has its pros and cons and should be considered complementary. It is not
possible to obtain complete information about the plasma from a single
diagnostic tool because each is fundamentally constrained to operate only on
certain temperature and density regimes of the plasma. Therefore, multiple
tools are essential for global insight into plasma behavior. For example,
imaging tools are very useful for understanding the hydrodynamics and
morphology of the plume. Interferometry provides density measurements during
plasma evolution. Emission spectroscopy is useful for tracking various species
in the plume as well as measuring fundamental properties of the plume at
intermediate time scales. Absorption and fluorescence methods provide valuable
information at late times during LPP evolution. Several assumptions are also
made for characterizing the LPPs using different diagnostic tools (e.g.,
homogeneous plasma, thermodynamic equilibrium, geometry and symmetry
considerations). However, these assumptions may not necessarily be valid for
complex LPP systems.

Plasma characterization employing optical methods use either photons released
by the plasma via spontaneous emission or the effects generated on/by an
external photon source (e.g., laser, arc lamp) when it interacts with a plasma
(e.g., scattering, deflection, phase shift, rotation of polarization,
absorption, excitation, etc.). Considering the experimental methodologies and
measurement assumptions, various plasma diagnostic tools can be classified
into active and passive methods and as direct or indirect methods [70, 120].
Passive methods use radiation (photons) emitted from the plasma for measuring
the parameters of interest. For example, emission spectroscopy and self-
emission imaging belong to this category. In active methods, an external
source is used for LPP characterization, and examples of this category include
all optical probing methods. Direct methods refer to obtaining plasma
parameters without making assumptions about the plasma conditions such as
thermodynamic equilibrium, electron, and ion velocity distributions, the
geometry of the plasma, etc. On the other hand, indirect methods require
certain assumptions of the conditions of the plasma for interpretation of
plasma properties. The passive and active methods can simultaneously be direct
or indirect.

For a plasma scientist, it must be mentioned that accurate diagnosis of
transient plasma systems such as LPP or pulsed power-driven plasmas (e.g.,
Z-pinch) is perhaps one of the most challenging tasks compared to other
natural and man-made plasmas. The present review provides an overview of
various optical diagnostic tools that can be used to accurately characterize
transient LPPs. It uses an integrated approach combining various optical
diagnostic tools for a comprehensive characterization by highlighting each
method’s capabilities, limitations, and unique challenges. Since optical
spectroscopy and Thomson scattering methods are capable of providing detailed
measurements of various LPP parameters (temperature, density, plasma kinetics,
etc.), further theoretical descriptions are furnished. However, this review
does not attempt to cover the details about the physics of laser-plasma
generation. Since most of the existing applications of the LPP belong to laser
intensities in the low to moderate range intensity regime ($10^{8}-10^{15}$
Wcm-2), this review focuses on diagnostic tools pertaining to this regime.
However, it must be mentioned that the fundamentals and scientific principles
of the discussed diagnostic tools are similar for all laser intensity regimes,
including HEDP plasmas.

The organization of this review is as follows. The optical diagnostics toolbox
for LPPs contains a wide variety of passive and active techniques that are
broadly separated into three categories in this review, _viz._ optical
spectroscopy, passive and active imaging tools, and optical probing. Section
II gives the details of optical spectroscopic methods such as emission
spectroscopy, absorption spectroscopy, and laser-induced fluorescence. In
section III, the details of various imaging tools for LPP characterization are
discussed, which include fast photography, and passive imaging methods.
Section IV discusses the details of various optical probing techniques which
include shadowgraphy, Schlieren, interferometry, and Thomson scattering. A
brief summary of other optical methods (e.g., deflectometry, and velocimetry)
is given in Section V. This article ends with a summary (Section VI) that
includes a table showing the pros and cons of each technique, utility of
various diagnostic tools, assumptions, and challenges. Each section is self-
contained and intended to be accessible to beginners and early career
researchers.

##  II Optical spectroscopy

The basics of optical spectroscopy include analyzing atomic and molecular line
radiations, which can be used for diagnosing the LPP through the knowledge of
plasma spectroscopy. Emission spectroscopy - a passive method - uses
spontaneously emitted light from atoms and molecules, typically excited by
electrons. Absorption and fluorescence spectroscopy belong to the active
sensing category, where an external light source is utilized for probing. In
absorption spectroscopy, the amount of light transmitted (absorbed) is
measured when the probe beam passes through the plasma. Fluorescence
spectroscopy combines absorption and emission and monitors the change in
spontaneous emission caused by the absorption of probe photons.

Compared to absorption and fluorescence spectroscopy, emission spectroscopy is
a widely utilized diagnostic tool in the LPP community because of its
experimental simplicity and non-intrusive nature. This is also partly due to
LIBS’ widespread use as an analytical tool, which inherently is a combination
of the LPP and emission spectroscopy. Therefore, significant work exists in
the literature about the characterization of the LPP using emission
spectroscopy, including some excellent reviews [12, 120, 180, 285, 339].
However, even though absorption and fluorescence spectroscopy are capable of
providing highly accurate results for the study of LPP fundamentals, they have
seen only modest use for diagnosing LPPs. This could be due to the active
nature of these techniques combined with more demanding experimental efforts
[328, 176, 237, 261, 24, 225].

All spectral lines originating from an LPP are broadened due to various
mechanisms such as Stark, Doppler, van der Waals, natural, etc. [116, 186,
130, 109]. The lineshapes provided by each broadening mechanism vary:
collisional-broadening mechanisms including Stark, resonance, and van der
Waals provide a Lorentzian profile while Doppler contributions yield a
Gaussian profile. Therefore, the recorded emission line profile from an LPP
will be a convolution of various line-broadening contributions. The theory of
various line-broadening mechanisms is given in detail elsewhere [116]. Among
the various broadening mechanisms, the Stark effect, which is caused by
charged particles, is the dominant mechanism at the early times of LPP
evolution. The Doppler effect, contributed by the thermal motion of the
species with respect to the observer, is dominant in low background pressure
environments and at late times of plasma evolution. When an LPP is expanding
into moderate to high background pressures, Van der Waals broadening may be
nontrivial [136]. Resonance broadening may be important for high atomic number
densities. Compared to other line-broadening mechanisms, the contribution of
natural line broadening is insignificant. For example, for an atomic
transition with a 10 ns spontaneous lifetime, the natural broadening width is
16 MHz.

In this section, details about the measurement of various physical parameters
of the LPP using emission, absorption, and fluorescence techniques are given.
For the sake of brevity, the details of line broadening, self-absorption,
self-reversal, and theoretical aspects of line emission are not discussed in
detail here. Instead, the experimental aspects and the application of optical
spectroscopy for the measurement of various LPP properties such as
temperature, density, kinetics, etc. are discussed with concerned equations,
but if the reader would like to get more information on the subject,
appropriate citations are given for further reading.

###  II.1 Emission Spectroscopy

Emission spectroscopy refers to the measurement of spontaneous emission of
radiation as a function of wavelength. There are different types of emission
spectroscopy: X-ray, EUV, UV, VIS, IR, etc. The experimental instrumentation
requirements change significantly with respect to the choice of the wavelength
region. Regardless of the selection of the spectral region, a spectrometer
with an appropriate wavelength dispersive element (grating, prism, crystal,
etc.) or interference-based element (etalon, interferometer) is used for the
separation of the light into its wavelength components. From the experimental
point of view, the UV-VIS-NIR spectral range is more straightforward and
widely used due to its operation in ambient air atmosphere, simple practical
alignment, and availability of cost-effective instrumentation. Because most of
the applications of LPPs are in the moderate laser intensity regime with
temperatures $\leq$ 10 eV, the focus of the diagnostic discussion here
pertains to the UV-VIS regime; however, the analysis methodologies for
inferring plasma parameters are similar regardless of the spectral region
selected for measurement.

OES is perhaps the most used diagnostic tool for LPP characterization.
Accurate information about the plasma temperature and density can be gathered
using emission spectroscopy. Apart from temperature and density, other
information such as the composition of various species in the plume (atoms,
ions, molecules), kinetic distribution, line broadening, and insight into the
plasma process or chemistry can also be gathered. OES is also a useful method
for gathering fundamental spectral parameters such as oscillator strengths and
Stark impact parameters [253, 1, 36]. Although the technique is simple because
spectra can be easily measured, interpretation or measurement of physical
parameters can be fairly complex, and the plasma conditions should meet
specific requirements such as local thermodynamic equilibrium (LTE) [115, 181,
12, 186].

In a plasma system, an atom can move from one electron configuration to
another through the absorption or emission of a photon. The wavelength
($\lambda$) or frequency ($\nu$) of a photon involved in such an emission
process corresponds to the energy difference between the two electronic
levels: $E_{j}-E_{i}=h\nu=hc/\lambda$, where $h$ is Planck’s constant, $c$ is
the speed of light, and $j(i)$ represents the upper (lower) energy level. The
emission intensity of an electronic transition depends on the number density
of the species in the upper level $n_{j}$ and the atomic transition
probability $A_{ji}$ (Einstein coefficient) or, equivalently, the oscillator
strength $f_{ji}$. All line transitions undergo broadening because of various
mechanisms, and if $\chi(\nu)$ is the area-normalized line profile function,
the spectral emission coefficient $I(\nu)_{j\to i}$ of a line with a central
frequency $\nu$ is given by

$I(\nu)_{j\to i}=\dfrac{h\nu}{4\pi}A_{ji}n_{j}\chi(\nu)$ (1)

Assuming thermal equilibrium, the Boltzmann equation provides the distribution
of the atoms in the same ionization state among the various energy levels as a
function of energy and temperature:

$n_{j}=\dfrac{g_{j}n_{tot}}{U(T)}e^{-E_{j}/{k_{b}T_{ex}}}$ (2)

where $n_{tot}$ is the total atomic number density, $g_{j}$ is the degeneracy
of level $j$, $k_{b}$ is the Boltzmann constant, $T_{ex}$ is the excitation
temperature, and $U(T)=\sum_{j}g_{j}e^{-E_{j}/{k_{b}T}}$ is the partition
function. Eq. 2 also gives the relationship between the level population,
excitation energy, and temperature.

The Saha equation provides the relative distribution of atoms among successive
ionization states as a function of temperature and electron density [186].

$\dfrac{n_{Z+1}n_{e}}{n_{Z}}=2\dfrac{U_{Z+1}(T)}{U_{Z}(T)}\left(\dfrac{2\pi
m_{e}k_{B}T}{h^{2}}\right)^{3/2}e^{-E_{IP}/k_{b}T}$ (3)

where $z$ and $z+1$ represent successive ionization stages of a given element,
$m_{e}$ is the electron mass, and $E_{IP}$ is the ionization potential from
state $z$ to $z+1$.

The following subsections provide details of emission spectroscopy
instrumentation and spectral analysis considerations, methodologies used for
density and temperature measurement, and LPP kinetics.

####  II.1.1 Instrumentation and analysis considerations

Emission spectroscopy instrumentation records the intensity of line radiation
against the wavelength. A schematic of the emission process in a two-level
system, OES experimental setup for the LPP characterization, an example of the
emission spectrum, and potential physical parameters gathered using this
technique are given in Fig. 3. A typical setup includes collection optics, a
spectrometer, and a detector. Considering spatial and temporal gradients in an
LPP, the light collection method and the specifications of emission
spectroscopic instrumentation may influence the quality of the collected
information. If one of the modalities (space or time) is integrated, only
weighted average values of the measured properties are obtained.

Figure 3:  (a) Emissions between two electronic levels in an atom, (b)
schematic of an emission spectroscopic system employing a spectrograph-ICCD
combination and/or monochromator-PMT combination, (c) an example of a spectrum
collected from an LPP, and (d) the fundamental properties of the plasma that
can be obtained from emission spectroscopy.

Because an LPP expands orthogonal to the target surface irrespective of laser
beam direction, the spatial information is gathered by imaging various
locations of the plasma parallel to the target surface and onto the entrance
slit of an imaging spectrograph. On the contrary, all plasma expansion
features can be gathered when the plume expansion axis (target normal) is
arranged parallel to the slit height. Depending on the orientation of the LPP
plume relative to the spectrograph entrance slit, image rotation using prisms
(e.g., Dove prism) [172] or folding optical systems [284] may be necessary.
Although positive lenses are commonly used for light collection and imaging,
the use of mirrors can avoid chromatic aberration. The available spatial
resolution is governed by the magnification of the optical system used to
transfer the radiation from the plasma to the spectrograph and the slit width
and height. For spatially integrated analysis, the emission from the entire
plume is collected and analyzed. The latter scenario is preferred for LIBS
analysis, especially with a standoff configuration [113].

The spectroscopic instrumentation used to analyze the LPP emission determines
spectral resolution, bandwidth, and time resolution. Moderate to high spectral
resolution spectrographs are essential for measuring lineshapes, linewidths,
shifts, and the magnitude/area of a given emission peak. There exists a trade-
off between the resolution of the spectrometer, the spectral bandwidth, and
throughput. Czerny-Turner (CT) or Echelle-type spectrographs are the most
common configurations. A CT spectrograph provides high throughput, but the
bandwidth of the detection may be limited with the use of a high-resolution
grating. As an example, a combination of a 0.5 m spectrograph and 2,400
grooves/mm grating provides a dispersion at the detector plane of
$\approx$0.66 nm/mm at 500 nm, which corresponds to a bandwidth of $\approx$10
nm when using a detector that has an 18 mm width. Instead, Echelle
spectrographs provide a large spectral range (200-900 nm) with reasonably good
spectral resolution [240, 60] though they come with reduced throughput
compared to CT spectrographs. Spatial heterodyne spectrometers provide high
spectral resolution and come with increased sensitivity and small size [110,
201].

The time resolution available from an emission spectroscopic system is
determined by the detector coupled to the spectrograph. Depending on the
selection of the detector, the wavelength dispersion instrument can be used as
a spectrograph or a monochromator. Typically, multichannel detectors such as
CCD and intensified CCD (ICCD) are used. Regular CCD or CMOS cameras can be
operated in a continuous-acquisition mode or can be triggered (synchronized)
with the LPP generation but cannot provide high-speed temporal gating for
time-resolved emission measurements. ICCD detectors provide time delay/gating
resolution down to a few ns and are preferred for time-resolved studies of
LPPs. The addition of an electron multiplier (em) to CCD (emCCD) or ICCD
(emICCD) is useful for low-light applications. The spectrograph is turned into
a single channel analyzer or monochromator when a photomultiplier tube (PMT)
is used. In this scenario, the spectral features can be obtained by wavelength
scanning, and time-resolved data is easily obtained through high-speed
digitization of the PMT signal. Compared to ICCDs, the PMTs provide a broader
dynamic range. For quantitative analysis of the LPP, spectroscopic
instrumentation (light collection system, spectrometer, and detector) should
be radiometrically calibrated. The potential origins of noise associated with
an emission spectroscopy measurement include source noise due to fluctuations
in the laser-sample or laser-plasma interaction, shot noise due to the number
of photons arriving on the detector, detector noise due to dark current, and
instrumental drift due to thermal effects.

In addition to various plasma induced line-broadening mechanisms, the spectral
lines can also be broadened because of artificial effects. For example, all
emission spectroscopy detection systems have an inherent instrumental profile.
So, knowledge of an instrumental profile is a prerequisite if its width is not
negligible (e.g., $\leq 10\times$ smaller than the contribution of other
plasma broadening contributions). The shape of the instrumental broadening
depends on several parameters associated with spectrometers (e.g., entrance
and exit slits, pixel width in the case of a multi-channel detector,
diffraction phenomena, quality of the system components, aberrations,
alignment, etc.) and therefore will be a convolution of several individual
terms that are typically neither completely Gaussian nor Lorentzian. The
instrumental profile can be experimentally measured using a narrow linewidth
laser (e.g., He-Ne) or a low-pressure discharge lamp. Because the instrumental
profile depends on the spectrometer entrance slit width, it is important to
measure the instrumental linewidth with the entrance slit used for the plasma
lineshape measurement.

By knowing the instrumental profile of the spectrometer used, the
contributions of various line-broadening mechanisms can be obtained through
deconvolution. The broadening contributed by Lorentzian profiles adds linearly
while the Gaussian profiles add quadratically, and the overall profile is a
convolution of Gaussian and Lorentzian (Voigt function). Assuming the
instrumental profile is Gaussian $(\Delta\lambda_{G(instru.)})$ and other
broadening mechanisms are negligible except the Stark effect, the Stark width
$(\Delta\lambda_{Stark})$ can be obtained from the measured full width half
maximum (FWHM) $(\Delta\lambda_{mea.})$ using the following relation

${\scriptstyle\Delta\lambda_{mea.}=\dfrac{\Delta\lambda_{Stark}}{2}+\sqrt{{\left(\dfrac{\Delta{\lambda}_{Stark}}{2}\right)^{2}+\left(\Delta{\lambda}_{G(instru.)}\right)^{2}}}}$
(4)

If the instrumental profile is Lorentzian $(\Delta\lambda_{L(instru.)})$, the
measured profile will be a simple addition of Stark and instrumental
broadening.

$\Delta\lambda_{mea.}=\lambda_{Stark}+\Delta\lambda_{L(instru.)}$ (5)

At late times of plasma evolution, the Stark effect is negligible and the
Doppler effect contributes to line broadening. If the instrumental broadening
is Gaussian, then the Doppler contribution $\Delta\lambda_{Doppler}$ can be
deduced from the following relation:

$\Delta\lambda_{mea.}=\sqrt{{\Delta\lambda_{Doppler}}^{2}+{\Delta\lambda_{G(instru.)}}^{2}}$
(6)

It is recommended to use high-resolution spectrographs with spectral
resolutions significantly better than the linewidth of the selected transition
for plasma lineshape analysis. However, even with the use of a high-resolution
spectrometer, it is challenging to separate crowded atomic transitions in a
high-Z plasma system (e.g., W, U) with many overlapping emission lines and
closely spaced molecular bands [172, 140].

The convolution or deconvolution of the spectral profiles discussed above is
for spectral lineshapes measured under optically thin conditions. In addition
to the instrumental profile, other factors such as self-absorption, self-
reversal, etc. may distort the lineshape. For example, the self-absorption
processes in the plasma may lead to the broadening of an emission line. This
is because absorption is strongest at the line center and weakest at the wings
of the spectral profile. However, it is difficult to evaluate the amount of
self-absorption in an LPP by simply observing the lineshape. For inhomogeneous
plasmas like LPPs, a central dip in the line profile can also be seen (self-
reversal) for optically thick lines, which is caused by absorption in the
cooler outer layers or coronal regions [63, 66]. Such self-absorption and/or
self-reversal in an LPP can cause artificial inflation in the measured
linewidths as well as a decrease in peak height. In such a scenario, the
correction of self-absorption is necessary for using lineshapes for plasma
diagnostics [32].

The spectral profiles recorded from an LPP are influenced by plasma physical
conditions, and are therefore useful for inferring the plasma properties. An
example of spectral features recorded at various times from an Al LPP is given
in Fig. 4 [129] and it shows significant changes in spectral properties with
time after the onset of plasma formation. Typically the continuum radiation
dominates at early times of LPP evolution because of free-free
(Bremsstrahlung) and free-bound (recombination) transitions. As time evolves,
the ionic and line radiation dominate the spectral features. Molecular species
are generated at late times of plasma evolution [69]. Since the emission
contribution from the continuum, ions, neutrals, and molecules appears at
various times after the plasma onset, their spectral features are useful for
tracking temporal evolution of plasma physical conditions. The various methods
used for measuring density and temperature of an LPP system using emission
spectroscopy are described below.

Figure 4:  Time-resolved plasma spectra recorded from a ns laser-generated Al
plasma showing continuum, ionic, atomic, and molecular emissions at various
times during its evolution. The gate delays used are marked in the spectral
features. The insets in (d) correspond to the zoomed AlO emission spectral
region. Adapted from 129.

####  II.1.2 Electron density using Stark effect

Electron density measurements using Stark-broadened line profiles is an
important spectroscopic diagnostic tool for the LPPs. Stark broadening arises
from the proximity of an ion or electron to another particle that undergoes an
optical transition. Stark broadening is mainly a density effect and does not
depend sensitively on the temperature or on the electron velocity
distribution, and it does not require the plasma to be in local thermodynamic
equilibrium (LTE). So, Stark broadening can be used for measuring electron
densities even in cases where the existence of LTE is doubtful, whereas some
other methods would then become invalid. In addition, measuring electron
density from Stark broadening does not require the knowledge of absolute
photon intensities, and just the relative lineshapes and widths are enough.
The most important experimental considerations for choosing a spectral
analysis for Stark-broadening measurements are line strength, separations from
neighboring lines, and good spectral resolution of the measuring instrument.
Because Stark broadening of a transition is significant when the densities of
the plasmas $\geq 10^{16}$ cm-3, a standard spectrograph with resolution
$(\lambda/\Delta\lambda)\geq 10000$ is adequate for the measurement. The other
factors to consider include (1) knowledge of the Stark broadening coefficient
or impact parameter of the selected line with good accuracy; (2) optically
thin lines having high intensity and good sensitivity to the Stark effect, and
(3) deconvolution of the Stark-broadening linewidth from other broadening
effects.

The theory of the Stark effect describes that the presence of an external
electrical field will cause a change in the energy of the emitting atom
because of its interaction with the permanent dipole moment (Griem, 1964). For
non-hydrogenic atoms with no permanent dipole moment, the change in energy of
the emitting atoms will be proportional to the square of the electric field
and known as the quadratic Stark effect. The broadening (FWHM) and shift of an
atom transition due to the quadratic Stark effect are given by [186, 115].

${\scriptstyle\Delta\lambda_{1/2}\approx
2W\left(\dfrac{n_{e}}{10^{16}}\right)+3.5A\left(\dfrac{n_{e}}{10^{16}}\right)^{1/4}\left[1-\dfrac{3}{4}N_{D}^{-1/3}\right]W\left(\dfrac{n_{e}}{10^{16}}\right)}\\\
$ (7) ${\scriptstyle\Delta\lambda_{shift}\approx
D\left(\dfrac{n_{e}}{10^{16}}\right)\mp
2A\left(\dfrac{n_{e}}{10^{16}}\right)^{1/4}\left[1-\dfrac{3}{4}N_{D}^{-1/3}\right]W\left(\dfrac{n_{e}}{10^{16}}\right)}\\\
$ (8)

where $W$ is the electron-impact parameter that can be incorporated at
different temperatures, $A$ is the ion broadening parameter, and $N_{D}$ is
the number of particles in the Debye sphere, which is given by

$N_{D}=1.72\times 10^{12}\dfrac{(T(eV))^{3/2}}{(n_{e}(m^{-3}))^{1/2}}$ (9)

The first and second terms in Eq. (7 and 8) correspond to electron impact and
ion correction factors, respectively. For non-hydrogenic atoms, Stark
broadening is predominantly due to electron impact, and the perturbations
caused by the ions can therefore be neglected. There exists an extensive
library for Stark-broadening parameters for selected emission lines of low-Z
and mid-Z elements [116, 181]; however, limited work is available for high-Z
elements [253, 36]. An example of a Stark-broadened line profile as well as
Stark shift for Ca I 585.74 nm transition at various times after the plasma
onset is given in Fig. 5a [35]. Previous reports showed asymmetry in the
Stark-broadened line profiles from LPPs [179], and the factors that introduce
asymmetry in the lineshapes are the ion broadening and fine structure
splitting.

Because hydrogen and hydrogen-like atoms possess finite dipole moments, Stark
broadening and shifts become very predominant, and the change in energy is
proportional to the electric field and provides a linear Stark effect. Typical
time evolution of Stark-broadened profiles of the $H_{\alpha}$ transition from
an LPP are given in Fig. 5b [35]. A set of empirical formulae are derived for
measuring the electron density of LPPs in gases and solids using Stark-
broadened $H_{\alpha}$ and $H_{\beta}$ transitions [257]:

Figure 5:  Time evolution of the Stark-broadened profile of (a) Ca I 585.74 nm
and (b) Hα 656.28 nm. The smooth curves represent the spectral fits. Adapted
from 35

$\Delta\lambda_{H_{\alpha}}(nm)\approx
1.3\left(\dfrac{n_{e}(cm^{-3})}{10^{17}}\right)^{0.64\pm 0.03}$ (10)

$\Delta\lambda_{H_{\beta}}(nm)\approx
4.5\left(\dfrac{n_{e}(cm^{-3})}{10^{17}}\right)^{0.71\pm 0.03}$ (11)

The empirical formulae for Hβ is valid for electron densities in the range of
$0.03$ to $8\times 10^{17}$ cm-3 and for Hα in the order of $0.01$ to
$100\times 10^{17}$cm-3.

The accuracy of electron density measurements of an LPP using recorded
spectral lineshapes depends on the errors of the reference Stark-broadening
parameters. Radziemski  _et al._ [269] measured the time evolution of electron
density in an aerosol plasma using several lines of multiple elements and
found that its values are significantly scattered, and this discrepancy is
attributed to the limitation in the accuracy of the theory to determine the
reference parameters.

Stark broadening becomes negligible when the electron density drops $\leq$
1016 cm-3. Therefore, determining electron density via spectral linewidths
measured in OES is limited to early times in the LPP with sufficiently high
electron density. It is also very challenging to measure other line-broadening
mechanisms such as Doppler, van der Waals, etc. using emission spectroscopy
because of their smaller contributions $(\sim$ 1-10 pm) relative to the
instrumental profile of standard spectrometers.

####  II.1.3 Measurement of temperature

Eq. 1 provided the relationship between emission intensity and excited level
population, which in turn depends strongly on temperature through the
Boltzmann relation (Eq. 2). But the definition of temperature in an LPP system
is somewhat ambiguous. In fact, several temperature nomenclature terms exist
in an LPP system, including excitation temperature, neutral, electron and ion
temperature, molecular or gas (vibrational and rotational) temperature,
kinetic, translational temperature, etc., and all these temperatures should be
similar if the LPP system is in LTE. Optical spectroscopic tools are useful
for measuring each of these temperature categories. For example, the Boltzmann
analysis is used to measure excitation (atom, ion) and molecular temperature,
and the Saha Boltzmann equation and line-to-continuum intensity ratio provide
electron temperature. Boltzmann and Saha’s methods are most commonly used by
the LPP community, and therefore, a brief account of these is given below.

#####  Boltzmann method

The Boltzmann method is used routinely for measuring the temperature of the
plasma using the spectral lines of a similar charge state [3, 339, 186]. By
combining equations (1) and (2), the spectral emission coefficient of a
transition from energy level $j$ to $i$ is written as [186]

$I(\lambda)_{j\to
i}=\dfrac{hc}{4\pi\lambda_{ji}}A_{ji}\dfrac{n_{tot}g_{j}}{U(T)}e^{-E_{j}/k_{b}T}\chi(\nu)$
(12)

Using Eq. 12, the intensity ratio of the spectral intensities of two lines (1
and 2) with the same ionization stage can provide the excitation temperature:

$\dfrac{I_{2}}{I_{1}}=\dfrac{g_{2}}{g_{1}}\dfrac{A_{2}}{A_{1}}\dfrac{\lambda_{1}}{\lambda_{2}}e^{-\left(E_{2}-E_{1}\right)/{k_{b}T}}$
(13)

However, to obtain accurate temperature measurements, it is recommended to use
several lines for constructing a Boltzmann plot with a large upper energy
difference. The natural logarithm of Eq. 12 gives

$\ln\left(\dfrac{I_{ji}\lambda_{ji}}{g_{j}A_{ji}}\right)=-\dfrac{1}{k_{b}T}E_{j}+\ln\left(\dfrac{hcn_{tot}}{4\pi
U(T)}\right)$ (14)

Eq. 14 gives a linear plot if $\ln(I\lambda/gA)$ is plotted against the energy
levels E of several transitions, and the slope of the plot corresponds to
temperature. Because a similar ionization stage is used for the Boltzmann
method, the measured temperature is typically called the excitation
temperature. If the spectral lines of a certain element with charge state
$z=0$ (neutrals) are used, it can be referred to as neutral atom excitation
temperature. Similarly, if the ions $(z\geq 1)$ are used for temperature
measurement, it is referred to as ion temperature. An example of a Boltzmann
plot is given in Fig. 6. Aguilera and Aragon [3] used several Fe I and Fe II
lines for constructing Boltzmann plots for an LPP system generated from a
Fe–Ni alloy and noticed that excitation temperatures obtained through the
spatially integrated measurement of neutrals (Fe I) and ions (Fe II) possess
different values (See Fig. 6a). However, the measured excitation temperatures
from neutral atoms and ions through a spatially resolved analysis together
with an Abel inversion showed similar temperatures within the error (Fig. 6b).
These results indicate the importance of spatially resolved analysis and Abel
inversion to account for the inhomogeneity of the LPP [180].

Figure 6:  Examples of Boltzmann plots obtained from Fe I lines and Fe II
lines are given for (a) spatially integrated measurement and (b) spatially
resolved measurement and Abel inversion. The temperature values deduced from
the linear fit are also given. From 3

.

##### Saha-Boltzmann method

The electron temperature of an LPP system can be measured using the Saha
equation by taking the intensity ratio of lines originating from successive
ionization states. Compared to the Boltzmann method that employs line
intensities of the same element and ionization state, improved sensitivity can
be obtained using this method because the effective energy difference is now
enhanced by the ionization energy, which is much larger than the thermal
energy. Therefore, the Saha–Boltzmann analysis is more reliable than the
simple Boltzmann analysis, providing a more accurate temperature [3]. Under
LTE, the intensity ratios of lines originated from successive ionization
stages is given by Saha-Boltzmann [186]:

${\scriptstyle\dfrac{I^{\prime}}{I}=\dfrac{g^{\prime}A^{\prime}\lambda}{gA\lambda^{\prime}}\left(\dfrac{2\pi
m_{e}k_{b}T}{h^{2}}\right)^{3/2}\dfrac{2}{n_{e}}e^{-(E^{\prime}-E+E_{IP}-\Delta
E)/{k_{b}T}}}$ (15)

where the primed symbols represent the line of an atom with a higher
ionization stage, $E_{IP}$ represents the ionization potential of a lesser
ionization state, and $\Delta E$ is the correction to the ionization potential
for interaction in the plasma, which is given by

$\Delta E=3z\dfrac{e^{2}}{4\pi\epsilon_{0}}\left(\dfrac{4\pi
n_{e}}{3}\right)^{1/3}$ (16)

where $z$ is the lower ionization state. Eq. 15 is suited for temperature
measurements by taking the ratio between two lines of successive ionization
states. However, the knowledge of electron density $n_{e}$ is necessary to
measure temperature. It is possible to perform the temperature measurement
without the knowledge of $n_{e}$ if two sets of equations (two lines each of
successive ionization states) are considered [126].

Similar to the Boltzmann plot (Eq. 14), a multi-line approach was suggested by
Yalcin  _et al._ [332] based on the Saha and Boltzmann equations. An example
of a Saha-Boltzmann plot employing neutrals and singly ionized lines of N is
shown in Fig. 7 [332]. Here, the x-coordinate values of the ions were modified
by a correction term that depend on the temperature and the electron density
which is given by

$\ln\left(\dfrac{I_{ji}\lambda_{ji}}{g_{j}A_{ji}}\right)^{*}=\ln\left(\dfrac{I_{ji}\lambda_{ji}}{g_{j}A_{ji}}\right)-z\ln\left(2\left[\dfrac{2\pi
m_{e}k_{B}}{h^{2}}\right]^{3/2}\dfrac{T^{3/2}}{n_{e}}\right)$ (17)

where z=1 for singly ionized atoms. Apart from these, the excitation energy
(y-axis in Fig. 7) of the ions in the Saha–Boltzmann plot should also be
modified by adding the ionization energy of the lower ionization stages.

Figure 7:  The Saha–Boltzmann plot for N lines at a delay of 0.35 µs during
LPP evolution. The LPP was generated using a frequency-doubled Nd:YAG laser in
a metal aerosol. From 332.

Spectral simulation tools are useful for measuring the excitation or
electronic temperature of an LPP system, and this is performed by comparing
the simulation with the experimentally measured spectral features . Spectral
simulation is possible by using a comprehensive collisional radiative (CR)
model with atomic codes or level populations that are calculated according to
the Boltzmann and Saha equations under the LTE assumption [144, 182]. This
method is certainly useful for measuring temperatures of complex spectral
features of high-Z plasmas [134]. However, to obtain accurate characterization
of the plasma, it is imperative to consider spatial inhomogeneity and
radiative transport simulations in the modeling tool.

#####  Molecular temperature

Similar to atomic transitions, each excited molecule emits a set of discrete
frequencies determined by the energy levels and their populations. For
molecules, each electronic level ($T_{e}$) consists of a vibrational energy
level manifold ($G_{v}$), and for each vibrational level, there is a
rotational energy level manifold ($F_{J}$). Therefore, the energy
corresponding to an optical transition ($\epsilon$) for a molecular transition
is given by the difference between the energies of the electronic, vibration,
and rotational levels in the upper and lower electronic states [145]

${\scriptstyle\epsilon=E(e^{\prime},\nu^{\prime},J^{\prime})-E(e^{\prime\prime},\nu^{\prime\prime},J^{\prime\prime})=T_{e}^{\prime}+G_{\nu}^{\prime}+F_{J}^{\prime}-(T_{e}^{\prime\prime}+G_{\nu}^{\prime\prime}+F_{J}^{\prime\prime})}$
(18)

where the upper-state and lower-state energy terms are represented by ′ and
′′, respectively. Because each electronic level for a molecule contains
vibrational and rotational manifolds, each molecular species has many more
transitions than the corresponding atoms composing the molecule.

The population of vibrational and rotational levels is related to its
temperature (vibrational and rotational) through the Boltzmann equation. For
example, in the case of vibrational transitions, the sums of the strengths of
all bands with the same upper ($\nu$) or lower ($\nu^{\prime}$) state are
proportional to the number of molecules in the respective states, and the line
intensities of various vibrational levels are related to temperature through
the following equation (Herzberg, 1950b):

$\ln(\sum_{v^{\prime}}(\lambda^{4}I_{vv^{\prime}}))=C_{1}-G(\nu)\dfrac{hc}{k_{b}T_{vib}}$
(19)

where $C_{1}$ is a constant and $G(\nu)$ is the term value corresponding to
the vibrational level in the upper electronic state, which can be estimated
using the following relation:

$\displaystyle
G(\nu)=\dfrac{E_{vib}}{hc}=\omega_{e}\left(\nu+\dfrac{1}{2}\right)-\omega_{e}x_{e}\left(\nu+\dfrac{1}{2}\right)^{2}+$
$\displaystyle\omega_{e}y_{e}\left(\nu+\dfrac{1}{2}\right)^{3}+\omega_{e}z_{e}\left(\nu+\dfrac{1}{2}\right)^{4}$
(20)

where $E_{vib}$ represents the molecule’s vibrational energy levels and
$\omega_{e},x_{e},y_{e},z_{e}$ are molecular constants. Similar to the
Boltzmann plot generated for the atomic excitation temperature, the
vibrational temperature can be obtained by plotting
$\ln(\sum_{\nu^{\prime}}(\lambda^{4}I_{\nu^{\prime}}))$ vs $G(\nu)$, and the
slope provides $1/k_{b}T_{vib}$.

Typically, spectral fits are preferred for measuring vibrational and
rotational temperatures rather than using Boltzmann plots because molecular
spectral features contain crowded rotational and vibrational energy states
compared to the atomic spectra. Spectral simulation allows the measurement of
both rotational and vibrational temperatures, and they may show significant
differences in the case of gaseous (low-temperature) plasmas [195, 342].
However, in the case of LPP, one frequently finds equal vibrational and
rotational temperatures $(T_{vib}=T_{rot})$ [150, 258, 132].

There are several molecular simulation programs available (e.g., PGOPHER
[327], SPECAIR [195], BESP [259], and LIFBASE [210]) that provide molecular
spectral features by utilizing standard molecular constants. The PGOPHER
simulation tool was used by several research groups for extracting rotational
and vibrational temperatures from the LPP system [327]. Parigger  _et al._
[259] developed the BESP simulation tool. For laser-produced atmospheric air
plasmas, SPECAIR (a commercial software) is routinely used and includes the
most important radiating atoms, ions, and diatomic molecules present in air
plasmas [195, 175, 132]. A comparison between the experimental and simulated
spectra of CN from an LPP source is given in Fig. 8 [310].

Figure 8:  Comparison of measured CN violet $\Delta v=0$ emission band and
spectral simulation. The measured emission spectrum is shown in black in the
upper part of the figure, and the inverted simulated spectrum is shown in blue
in the lower part. Adapted from 310.

Lam  _et al._ [194] compared the atomic excitation and molecular rotational
temperatures of a multi-component plasma and found a mismatch between them and
explained due to the lack of thermodynamic equilibrium. A similar study
involving laser-produced air plasma showed a good agreement between the atomic
oxygen excitation temperature and the molecular temperatures for N${}_{2}^{+}$
and CN [132]. However, they observed a discontinuity in the temperature decay
for N${}_{2}^{+}$, CN, and OH molecular temperatures, explained by changes in
plasma hydrodynamics and chemistry that lead to spatial inhomogeneity.

Because the physical properties of the LPP system vary significantly with time
and space, spatially and temporally resolved diagnostic measurement techniques
are appropriate for retrieving accurate distributions of temperature and
density [3]. Even though spatially resolved collection of the emission is
possible by 2D side-on imaging of the 3D expanding LPP system onto the slit of
the spectrometer, it must be mentioned that it only provides the line-of-sight
integrated measurements and it indicates that the collected data correspond to
the weighted average values of the spectral properties. Considering the
spatial inhomogeneity of the LPP system, this is one of the major hurdles in
using optical spectroscopy for quantitative spectroscopic measurements [180].
Abel inversion can be utilized to address these issues, and it converts the
axially and laterally resolved data into radially resolved data, assuming
cylindrical symmetry of the LPP [224]. Therefore, line-of-sight measurements
without performing Abel inversion may introduce systematic error in the
measured temperature and density values. Other approaches to account for line-
of-sight averaging through inhomogeneous LPPs may include the use of radiative
transport models or simulations [111].

####  II.1.4 Optical time-of-flight measurements

Temporally resolved spectral emissions from various species in an LPP are very
important for understanding plume kinetics [158, 129, 74]. This is typically
performed using a combination of the monochromator and a single channel
detector such as PMT (see Fig. 3). Similar information about the kinetics of
plume species can be obtained using a spectrograph-ICCD combination. However,
this requires multiple laser shots by varying gate delay [41, 312].
Considering the transient nature of the LPP, such analysis is based on
analyzing different plasmas generated by numerous laser pulses, and it would
therefore be less accurate. Instead, the combination of monochromator-PMT
provides the kinetic distribution of an emitting species in the plume using a
single laser pulse. Compared to array detectors, the PMTs also provide broad
spectral coverage with high quantum efficiency (QE) and excellent time
response and sensitivity.

For spatially resolved studies, the plasma plume from different regions is
imaged onto the monochromator slit, and the temporal evolution of the selected
transition is collected using PMT, which is then fed to a digital oscilloscope
for recording. This diagnostic method is often referred to as optical time of
flight (OTOF) and provides the delay as well as the persistence of emitting
species in the plume [288, 291, 335]. By selecting various species in the
plume (ions, atoms, molecules, etc.), the kinetic distribution of the LPP can
be mapped. An example of optical TOF from C2 molecules from laser-produced
graphite plasma at various laser fluences is given in Fig. 9a [133], and it
shows the modifications in C2 emission kinetics due to the changes in species
formation mechanisms.

The OTOF method is routinely used by the LPP community for studying plasma
chemistry [290], self-absorption [95], ion acceleration [308], 2D mapping of
various species in the plume [5], and optimizing parameters for PLD [82]. The
application of OTOF for studying the LPP plume chemistry is shown in Fig. 9b,
and it shows spatiotemporal contours of U I emission in the presence of
various background gases (air, nitrogen, and argon), and the presence of
reacting gas (air) reduces the emission persistence of U significantly [290].

Figure 9:  (a) OTOF of C2 emission at 516.5 nm recorded at 5 mm away from the
target for various laser fluences (a) 12.7 J.cm-2, (b) 26.7 J.cm-2, (c) 28
J.cm-2, and (d) 29.3 J.cm-2. Adapted from 133. (b) Spatiotemporal emission
contours for the U I 591.54 nm line under various background gases (nitrogen,
air, and argon) recorded at 100 Torr pressure, showing the effect of plasma
oxidation on emission persistence. Space- and time-resolved emission contours
were generated by combining OTOF profiles recorded at various distances from
the target. Adapted from 290.

###  II.2 Absorption spectroscopy

Absorption spectroscopy (AS) refers to the absorption of radiation as a
function of wavelength or frequency when a probe beam passes through a medium
and is a well-established technique for identifying and/or quantifying gas-
phase atomic and molecular species. Unlike emission spectroscopy, AS is an
active technique that necessitates the use of a light source (laser, arc lamp,
etc.) for probing the absorption by the LPP species. AS can be performed
across the entire electromagnetic spectrum if a suitable light source is
available, and depending on the probing spectral region, there are a wide
variety of experimental schemes (X-ray AS, UV-VIS AS, IR-AS, etc.); however,
the fundamental principles are the same.

In AS, the amount of light transmitted through the LPP is measured.For a
spatially uniform system, the relationship between the transmitted and initial
light intensity is given by:

$I(\nu,t)=I_{0}(\nu)e^{-A(\nu,t)}$ (21)

where $I(\nu,t)$ is the intensity of the probe laser at the optical frequency
$\nu$ incident on the detector at time $t$, $I_{o}(\nu)$ is the intensity of
the probe laser in the absence of absorption, and $A(\nu,t)$ is the
absorbance. Based on Eq. 21, the absorbance can be expressed as
$A(\nu,t)=-\ln[I(\nu,t)/I_{0}(\nu)]$ (note that an equivalent expression may
be defined using base-10 rather than base-e, and conventions may differ among
sub-fields). The absorbance may also be expressed as the product of an
absorption coefficient $\alpha(\nu,t)$ and an optical path length
$L:A(\nu,t)=\alpha(\nu,t)\cdot L$, which is again valid for a spatially
uniform system along the measurement path. The absorption coefficient is the
product of the absorption cross-section with the difference in population
density between lower and upper states of the probed transition and may be
expressed as:

$\alpha_{ij}(\nu)=\tilde{\sigma_{0}}\cdot
g_{i}f_{ij}\cdot\left[\dfrac{n_{i}}{g_{i}}-\dfrac{n_{j}}{g_{j}}\right]\cdot\chi(\nu)$
(22)

where $\tilde{\sigma_{0}}=e^{2}/4\epsilon_{0}m_{e}c$ is a constant equal to
$2.654\times 10^{-6}$m2 s-1, $f_{ij}$ is the transition oscillator strength,
and $n_{i}$ is the number density in the lower level (m${}^{-3})$. The
population difference term in Eq. 22 accounts for stimulated emission, but for
thermal distributions following Boltzmann statistics at temperatures typically
probed by AS in LPPs, this is often negligible for optical transitions at
visible wavelengths. Thus, it is often safe to assume $n_{j}\ll n_{i}$, in
which case Eqns. (21) and (22) may be simplified to:

$A(\nu,t)=\alpha_{ij}(\nu,t)\cdot L=\tilde{\sigma_{0}}\cdot
f_{ij}\cdot\chi(\nu,t)\cdot n_{i}(t)\cdot L$ (23)

Absorbance is a dimensionless quantity, while absorption coefficient
represents the optical attenuation per unit length of the medium. The change
in absorbance with respect to frequency provides the absorption spectrum,
which varies in time in the LPP due to differences in both the lineshape and
the atomic number density in the energy levels being probed.

Similar expressions may be derived without assumptions of spatially uniform
conditions using radiative transport theory [11]. As a simple example, in Eq.
(23) the product of the absorption coefficient with length may be replaced by
an integral along the measurement path:

${\scriptstyle A(\nu,t)=\int\alpha_{ij}(\nu,t,x)\cdot
dx=\tilde{\sigma_{0}}\cdot f_{ij}\cdot\int\chi(\nu,t,x)\cdot n_{i}(t,x)\cdot
dx}$ (24)

If the conditions in the LPP at a given time can be approximated as uniform in
temperature, pressure, and electron density such that the lineshape function
$\chi(\nu,t,x)$ does not vary with position, the spatial integral in Eq. (24)
only includes the number density over the measurement path and the resulting
integral $\int n_{i}(t,x)\cdot dx$ is known as the column density.
Furthermore, the column density is reduced to $n_{i}(t)\cdot L$ for spatially
uniform conditions along the measurement path.

The basic experimental set up for performing AS of LPPs includes (1) a pulsed
laser to generate an LPP; (2) a light source for probing the plasma; and (3) a
detector for analyzing the transmitted/absorbed intensity. Both broadband and
narrowband light sources can be used for performing AS [177]; however, the
characteristics of the probe light source (e.g., laser, arc lamps, frequency
combs, etc.) may affect the properties of the collected data, as well as the
analysis method [170, 225]. Unlike emission analysis, AS requires a certain
experimental orientation for the probe beam. For example, the probe beam
should be directed through the plasma parallel to the sample surface, and it
may be useful to keep a smaller probe beam size for reducing the interaction
region within the LPP. The following subsections provide details of
experimental schemes and analysis methods used for AS employing tunable lasers
(laser absorption spectroscopy, or LAS), broadband arc sources, and frequency
combs.

####  II.2.1 Laser absorption spectroscopy

A schematic of the absorption spectroscopy setup for LPP analysis that employs
a tunable laser source is given in Fig. 10. Examples of time-resolved
absorbance, absorption spectrum, and potential LPP parameters that can be
gathered using tunable LAS are also given in this figure. For recording the
absorption spectrum using tunable CW laser sources, the probe laser wavelength
is scanned across the selected transition, and for each ablation event the
time-resolved intensity transmitted through the LPP is recorded using a
photodiode and digitizer. The wavelength step size and total scan range may be
adjusted depending on the linewidth of the transition being probed. Typical
spectral coverage of AS using narrow linewidth lasers is limited to the
tunability of the laser, which is often $\approx$ 60 GHz ($<$ 0.1 nm) or lower
for continuous high-resolution scans. An example of time-resolved absorption
spectra obtained from an LPP source using a CW tunable laser is given in Fig.
10f [135].

Figure 10:  (a) Absorption process between two electronic levels in an atomic
system, (b) schematic of the laser absorption spectroscopy experimental scheme
for analyzing an LPP, (c) time evolution of absorbance, (d) absorption
spectrum, (e) typical fundamental properties of the plasma that can be
obtained from absorption spectroscopy, and (f) the time-resolved absorption
spectrum obtaining using tunable laser are given. The selected transition is
Al I 394.4 nm. A ns laser was used to produce plasma from an Inconel alloy
sample. From 135.

For LAS data collection and analysis, an oscilloscope or analog-to-digital
converter (ADC) is routinely used. Considering the dynamical nature of LPP
expansion and large dynamic range of measured signals, a time response
$\lesssim 1\mu$s and 16-bit ADC resolution is desirable. Signals may be
averaged over multiple ablation shots to reduce noise if desired. The
wavelength or frequency of the probe laser at each step may be measured to
high accuracy using a wavemeter or determined using other methods such as
comparison with a reference absorption cell [45], hollow-cathode lamp
absorption or opto-galvanic signal [17], or measuring transmission fringes
through an etalon with a known free-spectral range [261]. Typical tunable
lasers such as dye or Ti:Sapphire or external cavity diode lasers (ECDL)
provide linewidths in the range of $\sim$ 0.1-10 MHz, which is small compared
to major line-broadening mechanisms in an LPP (Stark, Doppler, van der Waals).
Lineshape measurements of atomic transitions in the LPP require multiple
wavelengths to be measured across the absorption profile. If Lorentzian
broadening mechanisms are dominant, determination of an accurate spectral
baseline may require that the profile be measured over a total range that is
significantly broader than the linewidth.

Spontaneous emission from the LPP reaching the detector can cause errors in
quantitative absorbance measurements [225], and it can be reduced using
filters, gratings, prisms, and by limiting the detector field of view.
Ultimately, it is not possible to completely remove the resonant spontaneous
emission at the wavelength of the transition probed by the LAS. However, if it
can be assured that the probe intensity on the detector is much higher than
the collected spontaneous emission intensity, which is usually practical for
laser-based absorption light sources, then the spontaneous emission
contribution to the signal can be neglected. This approximation becomes more
valid at later times in the LPP evolution probed by LAS. Late time analysis of
plasmas with limited spectral broadening and negligible instrumental
broadening of LAS enables high-resolution spectroscopic applications such as
isotopic splitting and hyperfine structure analysis [293, 265, 238, 39, 155].

Given the requirement to measure a large number of wavelengths in sequence for
separate LPP ablation events, combined with potential averaging over multiple
ablation shots, tunable CW measurements of absorption lines are often time-
consuming, especially for low-repetition rate (10-20 Hz) ablation lasers.
However, despite the potentially long acquisition times, the measurements
provide unparalleled spectral resolution and high-speed temporal information
over the full lifetime of the LPP, along with high SNR. Although it is
possible to scan a tunable laser at high speed to record an absorption
spectrum during a single ablation event, changes in atomic number density and
temperature during the scan make spectral analysis problematic, especially at
earlier times of LPP evolution [205].

Nonlinearities of Beer’s Law arising from the logarithmic relationship between
absorbance and measured intensities may be important for transitions with high
peak absorbance. For laser sources with a linewidth much less than the
transition linewidth, the linearity of Beer’s law is preserved to high
absorbance values. In these cases, the practical limit to the maximum
measurable absorbance is typically dictated by the dynamic range of the
measurement system and the ability to eliminate all sources of stray light and
detector offsets. Detector offsets may often be removed via:

$A(\nu,t)=-\ln\dfrac{I(t,\nu)-I_{b}}{I_{0}(\nu)-I_{b}}$ (25)

where $I_{b}$ is the detector signal in the absence of the light source used
for the absorbance measurement. As Eq. (25) makes clear, when the absorbance
is high such that $I(t,\nu)\to 0$, any errors in determining $I_{b}$ will lead
to corresponding significant errors in the calculated absorbance.

Using LAS, it is often possible to measure peak absorbance values up to $\sim
3-5$ [261, 192]. Absorption lines with higher absorbances near the peak may
still be measured accurately away from the peak center, and in some cases may
be used for spectral fitting if care is taken to exclude the inaccurate points
near the peak center [261]. However, this situation will naturally lead to
higher uncertainty in the fit parameters because the true peak center and
maximum amplitude are not measured. For absorption measurements where the
measurement resolution is broader than the actual linewidth of the measured
lines, Beer’s Law nonlinearities become more problematic [117]. In these
cases, it may be appropriate to measure only weak absorption lines or to
account properly for an instrument lineshape function in the spectral fitting
routine [177].

Potential sources of noise in LAS measurements include laser amplitude noise
due to power fluctuations, detector noise, pointing instabilities of the probe
beam, frequency fluctuations, and density fluctuations in the plasma plume
[73]. Assuming low-noise and stable CW laser sources are used, the dominant
source of noise in LPP measurements is often “flicker noise” arising from
variations in LPP conditions between each ablation event. Because the LAS
measurement is performed serially at each wavelength, each measured wavelength
may experience a plasma with slightly different physical conditions. Thus, for
each LPP, the probe beam may encounter different atomic number density,
temperature, scattering, and/or beam steering, any of which may lead to
amplitude variations in the spectral absorbance profile that are
indistinguishable from noise. Averaging over multiple ablation shots may help
reduce the amplitude of flicker noise. However, the methodology used for
signal averaging (transmitted probe beam intensity vs. absorbance) can
influence the errors in the measured absorbance signal due to its nonlinear
exponential relation with intensity. Various approaches have been developed to
reduce the effects of flicker noise in LAS measurements, including measurement
of differential absorption relative to a second co-aligned laser with a
wavelength that is not resonant with the probed transition [305]. When other
noise sources are removed, the ultimate sensitivity of the LAS method is
determined by photon shot noise.

Absorption spectral features may be distorted at early times of plasma
evolution due to inhomogeneities in the plasma. As an extreme example, at low
background pressure conditions and at early times during the LPP evolution,
Doppler splitting may be observed in the spectral absorption profiles of lines
because of the counter-propagating velocity distributions of atoms or ions
along the probe laser line of sight [38, 237]. Fig. 11 shows contour maps of
the time-resolved absorption of neutral Sr atoms formed in the ablation of
CaCO3, which shows Doppler splitting [38]. Although most distinct at low
pressures and giving rise to a dual-peaked absorption profile, similar effects
of non-thermal atomic/ionic distributions may be present at early times for
higher pressures as well, which may distort the absorption lineshape from a
simple Voigt profile.

Figure 11:  Contour map of the time-resolved optical spectra of ablated Sr
atoms in the presence of 2.5 Torr He cover gas with a probe beam at 3 mm
height. Absorbance units with the strongest absorption are indicated by the
darkest shading. Adapted from 38.

Other factors may also influence the observed lineshape in LAS measurements
and lead to errors in determined plasma parameters if not properly accounted
for. For example, high laser intensity used for probing the plasma may induce
power broadening or optical pumping effects in the probed spectral line [320],
although it has been shown that a Doppler temperature may still be obtained by
using a correction factor for power broadening [218]. Hyperfine structure in
absorption lines may often be observed in high-resolution measurements [141],
but even if not fully resolved it should be accounted for in spectral fitting
to avoid an overestimation of the true spectral linewidths [192]. Similar
considerations apply for elements with multiple isotopes such as Rb, even if
the isotope shifts are too small to resolve experimentally [176].

The absorption spectra obtained using narrowband CW tunable lasers provide
limited spectral bandwidth; however, they give high spectral resolution, time-
resolved absorbance during the entire lifetime of the plasma, and very high
signal-to-noise ratio (SNR) for each measurement because of the high source
intensity. So far, the selection of an atomic transition for performing LAS of
LPP is constrained to the availability of reliable lasers with narrow
linewidth and a large tuning range. Recent advancements in diode and
Ti:Sapphire laser technology can provide the capability to perform LAS of any
atomic transition in the UV-VIS-IR spectral range.

####  II.2.2 Absorption spectroscopy using broadband sources

AS employing broadband light sources such as arc lamps, laser plasma
continuum, etc. provide wide spectral bandwidth; however, a spectrograph is
used for measuring the absorption spectrum (Fig. 12a). In this scenario,
similar to emission spectroscopy, the spectral resolution available is
constrained by the detection system. Information about the LPP at a certain
time after ablation can be collected from a single shot, and the temporal
dynamics are generated by delaying the probe source with respect to the LPP
source or by using time-gated detection. Although broadband measurements are
made on a single shot, improvements in SNR may require averaging over multiple
shots. The use of broadband absorption methods where multiple wavelengths are
measured simultaneously may also be advantageous for reducing some effects of
flicker noise because the LPP variations affect all wavelengths uniformly.

Figure 12:  (a) Schematic of the AS setup using a BB arc lamp. (b) The
absorption spectrum from an LPP recorded using an arc lamp is given. From 324.
The absorption spectrum corresponds to the UO 593.55 nm band from a U metal
plasma, and the peak marked with a red dotted line corresponds to the UI
593.38 nm atomic transition. (c) Schematic of AS employing frequency combs.
(d) Broadband single-shot absorption measurement of the laser-induced plasma
using frequency combs. The inset shows a zoomed-in view of the
$5S_{1/2}-5P_{3/2}Rb~{}D_{2}$ line. From 24.

Weerakkody and Glumac [324] used a xenon flash lamp as a broadband light
source for performing absorption spectroscopy of LPPs. The flashlamp provided
a broadband light source with a duration of $\sim$ 10 µs, which was collected,
directed through the LPP, and then dispersed using a custom 1.5 m CT
spectrometer with gratings used in high orders similar to an echelle
configuration. An example of a uranium oxide (UO) absorption spectrum obtained
from an LPP source using an arc lamp is given in Fig. 12b. Because time
resolution was provided by the pulsed light source, a non-intensified CCD
detector was used for detecting the transmitted light, and absorption spectra
at different times after LPP generation were probed. An optical parametric
oscillator (OPO) based pseudo-continuum source was used for performing
absorption spectroscopy in conjunction with a high-resolution echelle
spectrograph with ICCD [226].

Several authors used the early-time Bremsstrahlung emission from an LPP as a
broadband pulsed light source for performing AS. For example, Ribière and
Cheron [274] performed near-UV absorption spectroscopy of various elements
including Al, Mg, Ni, Cu, and Si by employing the continuum emission from an
LPP as a source to probe a second time-delayed LPP. In a similar experiment
scheme, called dual plasma absorption spectroscopy (DP-AS), the broad VUV
continuum emission from a high-Z LPP was used to probe VUV photo-absorption
spectral features from a second LPP [43, 44, 59, 247]. Similar to a DP-AS
scheme, an extreme ultraviolet (XUV) continuum generated from a first LPP was
used to measure the XUV absorption spectra of Th [223]. A confocal
configuration of the double-pulse measurement was performed to study
Fraunhofer-type absorption lines in a cooling LPP [243].

Compared to using arc lamps and tunable laser sources as probes, the AS of
LPPs using frequency combs is a relatively new approach. The limitations of
LAS (narrow spectral range) and AS employing broadband arc lamp light sources
(spectral resolution) can be overcome with the use of frequency combs, which
provide both high spectral resolution and broadband detection [24]. A
frequency comb is a stabilized mode-locked laser, which provides a set of
narrow-linewidth frequency modes [64]. Dual-comb spectroscopy (DCS) uses
multi-heterodyne optical interference between two frequency combs with
slightly different repetition rates and provides a representation of the
optical spectrum in the radio-frequency (RF) domain, with a one-to-one mapping
of RF frequency to optical frequency [56]. A schematic of a DCS AS setup is
given in Fig. 12c.

A benefit of DCS for the measurement of absorption spectra in LPPs is that all
wavelengths are measured simultaneously. As a result, flicker noise in DCS
does not lead to spectral noise as it does in scanning CW LAS.. However, the
trade-off for measurement of all wavelengths simultaneously in DCS is that the
average power on the photodiode must be reduced well below what is typically
used for CW LAS measurements. As a result, the noise levels are typically
higher for DCS relative to CW LAS but may be reduced by averaging over
multiple LPP events. Another trade-off with DCS arises between time resolution
and frequency resolution. Because DCS measurements are based on a Fourier
transformation of an interferogram in the time domain to generate the spectral
measurement, the time and frequency resolutions are linked [323]. In Bergevin
_et al._ [24], an absorption spectrum of Rb and K was measured over an optical
bandwidth of 13 nm with sub-GHz resolution (Fig. 12d). The spectral resolution
was sufficient to measure the hyperfine and isotope splitting of the Rb D2
line. DCS AS was used for time-resolved plasma characterization and for
resolving the closely spaced absorption lines of higher-Z materials [340,
323].

####  II.2.3 Temperature and density measurement

Most of the data analysis methodologies presented for emission spectroscopy
(Section II.A) are also applicable to AS analysis. For example, by monitoring
the Stark width or shift of the absorption line, the electron density can be
inferred. Similarly, the Boltzmann plot can be constructed using absorption
lines for inferring excitation temperature. In the last three decades, several
groups have used the AS of LPPs to measure lower state populations, transition
linewidths in the plasma, and absorption-based kinetic and excitation
temperatures [234, 83, 45, 238, 226].

In the following discussions, we will use the simplified forms of the
equations without explicitly including the spatial integration along the line
of sight, but it should be understood that these conditions do not exist at
all times in the LPP. For late times of LPP evolution that are usually probed
by AS, it is often acceptable to assume spatially uniform conditions. Similar
equations can be written in units of frequency, wavelength, or wavenumber,
with corresponding changes in units for spectral integrations. Finally, it is
also possible to write the above equations using Einstein A and B coefficients
instead of oscillator strength, and conventions differ between various sub-
fields.

For LAS measurements with a tunable CW laser source, the experimental results
provide an absorbance spectrum of an optical transition for multiple times in
the LPP evolution. As shown by Eq. (23), in spatially uniform conditions, each
absorbance spectrum may be represented by
$A_{ij}(\nu,t)=\tilde{\sigma_{0}}\cdot f_{ij}\cdot\chi(\nu,t)\cdot
n_{i}(t)\cdot L$. At each time delay after ablation, the absorbance spectrum
may be fit using an appropriate lineshape function $\chi(\nu,t)$, and the
spectrally integrated area of the absorbance peak is proportional to the
column density in the lower level of the probed transition. An example of
time-resolved, path-integrated atom density for two Al I transitions (394.4 nm
and 396.15 nm) and ion density of a Ca II transition (393.37 nm) are given in
Fig. 13a [192]. This measurement was performed using a tunable laser as a
probe, and a spectral fit was performed for the experimental spectra at each
time delay to determine the column density via the peak areas. Several authors
used LAS for measuring path-integrated (column) number densities of a selected
transition and performing quasi-three-dimensional spatial mapping [83, 6, 217,
220, 107].

Figure 13:  Column density (nL) as a function of time calculated from fits to
LAS absorbance spectra for two Al transitions at 394.4 nm and 496.15 nm and a
Ca II transition at 393.37 nm. 266 nm, 6 ns pulses were used for producing LPP
on a glass target, and LAS spectra were obtained using a CW tunable laser.
Adapted from 192. Comparison of time evolution of kinetic temperatures
measured using LAS of ns and fs LPPs. An Inconel sample containing a small
amount of Al $(<0.4$ at$\%)$ was used. The large error bars at early times of
ns LPP are a result of uncertainty in the spectral line fitting due to low
absorbance. From 135.

The column density measured by LAS is determined by the number density in the
lower energy level probed by the measurement and not the total atomic number
density. This is true even for ground-state resonance transitions. Assuming a
Boltzmann distribution, the atomic populations in the energy levels are given
by Eq. (2), from which it is apparent that the ground state number density is
reduced according to the partition function at the given temperature. In
tunable LAS measurements of resonance lines, this effect can often be observed
via a reduced column density at early times in LPP evolution due to the high
excitation temperatures, as shown in Fig. 13a for Al I transitions.

The fitting of experimental absorbance lineshapes may also be used to
determine various physical properties of the LPP. As described in Section
II.A, the spectral lineshape is usually modeled as a Voigt profile, wherein
the width of the Lorentzian component is determined by collisional broadening
(Stark, resonance, van der Waals) and the width of the Gaussian component by
Doppler broadening. For LAS with CW lasers, the instrumental broadening is
negligible; however, it may be important for broadband absorption methods.
Because LAS probes the electronic lower energy state of an atomic population,
analysis of plasma evolution is possible at lower temperatures and later times
than what is accessible by emission measurements. At late times, Stark
broadening becomes negligible, and the linewidth is dominated by Doppler
broadening and possibly van der Waals broadening at higher ambient pressures.
The kinetic (Doppler, translational) temperature can be calculated from the
Gaussian linewidth according to the relation [73]

$w_{g}=7.16\times 10^{-7}\lambda_{0}\left(\dfrac{T}{m}\right)^{1/2}$ (26)

where $w_{g}$ is the Gaussian FWHM of the line in nm, $\lambda_{0}$ is the
center wavelength of the transition in nm, T is the kinetic temperature in K,
and m is the mass of the species in amu.

Examples of kinetic temperatures of ns and fs LPPs measured using LAS are
given in Fig.13b [135]. The large errors in the measured temperature at early
times of ns LPP evolution are due to low absorbance signals and therefore the
uncertainty in the spectral line fitting. LaHaye  _et al._ [192] used LAS for
measuring the time evolution of kinetic temperature by employing Doppler-
broadened Al transitions in a ns LPP and comparing to excitation temperature
determined from OES, thereby finding a discontinuity between temporal decay of
the kinetic and excitation temperature, which can be explained by the
inhomogeneous nature of the LPP. Therefore, even if the plasma is in LTE,
differences in various temperatures (neutral vs. ion vs. molecular vs.
kinetic) can be expected because of the inhomogeneous properties of LPP
systems, similar to observations using emission spectroscopy.

The absorption spectrum obtained using broadband light sources (arc, frequency
comb) can be used for excitation temperature measurement by employing
Boltzmann plot methods. Using the column density measured from absorption
$(n_{i}\times L)$ combined with the Boltzmann relation given in Eq. (2), the
electronic excitation temperature can be measured under the assumption of LTE
using the following relation

$\ln\left(\dfrac{n_{i}\cdot L}{g_{i}}\right)=\ln\left(\dfrac{n_{tot}\cdot
L}{Z(T)}\right)-\dfrac{E_{i}}{k_{b}T}$ (27)

Thus, the slope of a linear fit of $\ln\left({n_{i}\cdot L}/{g_{i}}\right)$ vs
$E_{i}$ gives the excitation temperature, while the y-intercept is related to
the total column density divided by the partition function. Boltzmann plots
from multi-line absorption spectra used to determine the absorption excitation
temperature and column density are given in Refs. [83, 340, 324]. An example
of a Boltzmann plot using Gd absorption lines measured using DCS, and the
resulting excitation temperatures are given in Fig. 14 [323].

Figure 14:  (a) An example of a Boltzmann plot generated from DCS absorption
spectroscopy of Gd plasma and using Gd lines is given. (b) The measured
excitation temperature evolution is given. From 323

.

In principle, it should be possible to determine Stark broadening at early
times of plasma evolution via an increase in the Lorentzian linewidth [28,
136]; however, these measurements are complicated due to depletion of low-
energy-level populations, leading to a low absorption strength. The high
spatial inhomogeneity at early times and non-thermal velocity distributions
may also lead to deviations in the observed lineshape from a simple Voigt
profile. Furthermore, the large density gradients present in the early times
of plasma expansion may distort the line shapes arising partly from optical
refraction [85]. The measurement of Lorentzian width at late times of plasma
evolution at various pressure levels provides van der Waals broadening [136,
305].

Merten and Johnson [227] used an OPO-based pseudo-continuum source for
performing absorption spectroscopy and reported Li isotopic shifts as well as
the time evolution of the kinetic temperature of a ns LPP. They used Abel
inversion methods to determine total number density and mass of atomic Ti in
LPPs. Weerakkody  _et al._ [325], Weerakkody and Glumac [324] used broadband,
high-resolution absorption spectra of U I and U II to determine absorption
excitation temperature via a Boltzmann plot analysis. Molecular absorption
spectra from SiO, BeH, UO, and ZrN were reported, and when possible were
compared with simulated spectra modeled using PGOPHER to estimate molecular
temperatures.

####  II.2.4 Kinetics of LPP using absorption spectroscopy

Several authors used AS for investigating the LPP spatiotemporal dynamics [99,
333, 237, 49, 183, 137]. These methods utilize a combination of temporal
dynamics of the observed absorption signal at the probe laser positions, along
with variations in the absorption spectral profile with time. As was shown in
Fig. 11, at early times of plasma evolution a dual-peaked absorption spectra
may be observed, especially at low pressure, which may be used to estimate the
velocity distributions of atoms and ions in the expanding LPP [38]. Miyabe
_et al._ [237] used similar methods to investigate plume dynamics of neutral
and ionized Ce.

Tarallo  _et al._ [304] used LAS to measure plume dynamics and kinetic
temperature of molecular BaH using Doppler-shifted absorption profiles and
inclusion of nonlinear absorption saturation effects. Examples of the time-of-
flight absorption signals recorded at various distances from the target for
BAH molecules are given in Fig. 15. Harilal  _et al._ [137] used a combination
of absorption and emission TOF profiles for comparing spatiotemporal evolution
of excited and ground state species in a laser ablation plume. They also
reported that the LAS TOF profiles are useful for studying shock propagation
into ambient gas medium. Geohegan and Puretzky [100] used a $\sim$ 1.5 µs Xe
broadband source for recording the absorption spectrum and for studying
kinetics of atoms and ions from an LPP.

Figure 15:  TOF absorption signals (blue and black curves) of BaH molecules
from an LPP are recorded at different distances from the target surface. The
smooth red lines represent the best fit to the data. From 304

.

###  II.3 Laser-induced fluorescence

Laser-induced fluorescence (LIF) combines the principles of both absorption
and emission. In LIF, the probe laser is tuned to match an atomic or molecular
transition, and the spontaneous emission resulting from the decay of the
resonantly excited atoms is measured. The following subsections provide
details of LIF instrumentation for LPP analysis, and methods employed for
plasma characterization.

####  II.3.1 Instrumentation and analysis considerations

Since LIF combines the principles of absorption and emission spectroscopy, the
instrumentation requirement is also a combination of LAS (for excitation) and
OES (light collection and analysis). A schematic of the LIF pumping and
detection schemes, an example of a time-resolved LIF emission, and an
excitation spectrum are given in Fig. 16, along with potential plasma
properties that can be measured using LIF of LPP. If the resonantly pumped
transition shares the upper energy level with more than one transition, LIF
can be monitored by selecting any of these transitions. If the LIF emission is
monitored at the same wavelength of probe radiation, it is commonly called
resonance LIF. Similarly, if other transitions that are coupled to the same
upper level are used for LIF monitoring, it is called directly coupled LIF or
non-resonance LIF (see Fig. 16a). The use of a directly coupled LIF transition
is useful in avoiding detection of the spurious scattering signals from the
probe laser. Unlike LAS, the LIF pumping scheme has fewer geometric
limitations. So, LIF can be used for standoff analysis [128, 168].

The general parameters of LIF spectroscopy for probing and sensing are the
excitation spectrum, emission spectrum, and fluorescence lifetime or decay
rate [298]. When the probe laser is tuned across the spectral range of an
absorption line, the fluorescence intensity is monitored as a function of
probe wavelength, and the spectrum obtained is called the excitation spectrum.
Under conditions of low optical density and low probe intensity, the LIF
excitation spectrum is directly proportional to the absorption spectrum
obtained from LAS. For excitation, lasers with a wide wavelength tuning range
and narrow linewidth are preferred.

Figure 16:  (a) Schematic of LIF excitation and emission; (b) typical LIF of
LPP experimental scheme; (c) time-resolved LIF emission from LPP using CW
excitation, where the early time peak seen in the temporal profile is due to
thermally excited emission; (d) excitation spectrum; and (e) potential
properties of the plasma that can be gathered using LIF.

Both pulsed lasers [252, 108] and CW lasers [294] can be used for LIF
excitation, provided that the spectral bandwidth of the laser is smaller than
the linewidth of the optical transition for efficient excitation of the
targeted transition. However, the LIF probe laser properties influence the
detection scheme, and the use of high laser intensities may affect the
recorded lineshape. At low laser intensities, the LIF signal varies linearly,
where the de-excitation rate of an atom is faster than the excitation rate. In
this scenario, most of the atoms are in the lower/ground state, and the probe
laser causes negligible depopulation. As the laser intensity of the LIF probe
laser increases, the LIF signal becomes nonlinear with respect to pump laser
intensity due to depopulation or bleaching of the lower-level population,
leading to saturation of the detected LIF signal [245]. The saturation effect
during LIF experiments will lead to spectral broadening because saturation is
strongest in the line center compared to the wings. Detailed description of
saturation and power broadening is discussed by Demtroder [72]. Compared to
the pulsed LIF excitation scheme, the laser-intensity saturation effects are
expected to be minimal with the use of a CW excitation source. The other
advantage of using CW lasers as an excitation source is that they continuously
excite the lower-state population during the entire lifetime of the LPP plume,
which may be monitored via time-resolved detection of the continuous LIF
emission signal [135].

Any traditional detectors with appropriate spectral filters can be used for
measuring the LIF signal. If the wavelength of the LIF emission is different
from the excitation wavelength (directly coupled LIF), the scattering of the
LIF probe laser can be easily eliminated by filters or monochromators. For
detection, PMTs are preferred for measurements requiring high time resolution
or small signal intensities. The potential sources of noise or interfering
signal associated with LIF measurements include thermally excited emissions
from the plasma, stray laser light, inherent noises from the detector (dark
current, shot noise), and electromagnetic pickup noises coming into detection
lines. For LPPs, the thermally excited emission is typically the dominant
signal interfering with the detection of the LIF emission signal. However, the
thermally-excited emission and LIF emission may often be separated using gated
detectors due to their different time-dependence (See Fig. 16c). LIF also
provides benefits for detection of small emission signals by virtue of being a
“background-free” detection method, in contrast to AS where small signal
variations must be detected on a large background $I_{0}$. The spectral
resolution available in LIF diagnostics of the LPP is dictated by the
linewidth of the probe laser; therefore, LIF can be utilized for recording
high-resolution spectral features. An example of the LIF spectrum is given in
Fig. 17, where a pulsed dye laser is used to record the LIF spectrum of SiO+
from a laser-produced Si plasma generated in an 80 mTorr oxygen ambient [219].

Figure 17:  The LIF spectra of the SiO+ 0-0 band recorded at 80 mTorr O2
pressure. The plasma was produced using a 1064 nm laser beam, and LIF was
performed by scanning a pulse dye laser. From 219.

Simultaneous emission and excitation spectral features can be measured using
2D-fluorescence spectroscopy (2D-FS), where a spectrograph - ICCD combination
is used. This technique can also be used for reducing effects of shot-to-shot
(flicker) noise in an LPP [261]. For recording the 2D-FS, the LIF emission
spectra are collected for each wavelength step during the excitation laser
scan using a spectrograph-ICCD detector system, giving a map of emission
intensity versus both excitation and emission wavelengths. An example of 2D-FS
is given in Fig. 18 where non-resonant LIF emissions from U I 404.275 nm was
recorded while the excitation laser beam was tuned across the U I 394.3816 nm
transition [138]. The measurement was performed on a ns LPP from a glass
target containing a trace amount of U at 45 Torr N2 ambient pressure. A one-
dimensional cross-section of the 2D-FS map at a fixed emission wavelength
gives the corresponding excitation spectrum (Fig. 18c). Similarly, a one-
dimensional cross-section at a fixed fluorescence excitation wavelength
provides the emission spectrum (Fig. 18d). The weak emissions seen at 404.4
and 404.72 nm are from K I, and the 2D-FS spectrum shows a constant emission
intensity for these transitions versus LIF probe wavelength, indicating that
the K I transitions were not pumped.

Figure 18:  (a) 2D-FS of U I and weak thermal emission from K I lines at 45
Torr N2 pressure from a ns-laser-produced plasma. (b) Zoomed-in image of 2D-FS
of UI transition. The emission and excitation spectra are given in (c) and
(d). From 138.

Pulsed LIF of LPPs is routinely used to boost the emission signal, which is
important for analytical applications such as trace detection [147, 306, 196,
163, 208]. Previous studies showed that LIF of LPP improved detection limits
and reduced matrix effects [188]. LIF of LPPs is also useful for detecting
isotopes [292, 261], analyzing hyperfine structures [141], and reducing self-
reversal effects in the spectral profiles [168]. Although the LIF provides
high sensitivity for trace element detection, it is challenging to use LIF for
quantitative measurements of bulk elements because of the inherent
nonlinearity of LIF signals with atomic number density under conditions of
high absorbance [141]. For a low-intensity LIF probe laser, the detected LIF
signal $S_{F}(\lambda_{ex},t)$ can be expressed in a simplified form as [37]:

$S_{F}(\lambda_{ex},t)=S_{0}\cdot I_{0}\cdot[1-e^{-A(\lambda_{ex},t)}]$ (28)

where $\lambda_{ex}$ is the wavelength of the laser exciting the LIF
transition, t is time, $S_{0}$ is a constant factor incorporating collection
area/efficiency and fluorescence quantum yield, $I_{0}$ is the incident laser
intensity, and $A(\lambda_{ex},t)$ is the absorbance of the LIF probe laser.
Under conditions of high absorbance, the LIF intensity is nonlinear with the
atomic number density and approaches a maximum value, which may distort the
shape of the excitation spectrum in a manner similar to self-absorption
effects observed in emission spectroscopy.

####  II.3.2 Temperature and density measurement

LIF is a very well-known technique in combustion research; fusion devices
(e.g., Tokamak); and ICR plasmas for sensitive and spatially resolved analysis
of particle behavior, density, and velocity distributions of atoms, ions, and
molecules. In theory, the LIF of LPP can provide all plasma properties
gathered using the LAS technique. However, challenges exist to perform
accurate measurement of fundamental properties of a high-density plasma source
such as LPP using LIF compared to LAS. For example, if LIF photons are
reabsorbed by the plasma, it may distort the excitation spectra. Understanding
the collisional quenching of LIF signal is also very important. Hence, a
detailed understanding of signal-generation and radiation transport processes,
which requires solving the rate equations combining both absorption and
collisional decay, is essential for using LIF for accurate plume
characterization.

Several authors use the LAS technique for calibration of LIF signatures to
measure the absolute density of particles in an LPP [251, 209, 250]. Martin
_et al._ [217] measured Mg atom density from an LPP derived from a planar LIF
image, and the calibration of the number densities was performed using the
resonance broadening of the absorption line shapes. Dutouquet and Hermann [84]
used LIF for measuring ground-state number densities of atoms and molecules
from LPPs generated from Al, C, and Ti targets in N2 or O2 low-pressure
atmospheres, and the absolute calibration of ground-state densities was
performed using additional absorption measurements. Orsel  _et al._ [255] used
LIF for studying oxidation processes in YBiO3 LPPs. They recorded Y, YO, and
Bi spatiotemporal distributions in the plasma using LIF, and calibration of
absolute density was performed using simultaneous measurement of AS (Fig. 17).
2D LIF imaging is also used by several authors for studying the dynamics of
the LPP in the presence of an ambient [245], and details about LIF imaging are
given in Section IIIB.

Figure 19:  Density distributions of Bi, Y, and YO from a YBiO3 LPP. Each
picture contains an LIF measurement in a 75 mTorr ambient environment: (left)
$O_{2}$ and (right) Ar. All pictures are normalized, with the normalization
factor shown at the bottom of each image. The densities shown are measured at
35 µs delay after ablation. From 255.

###  II.4 Local Thermodynamic Equilibrium

For the temperature and density measurement employing spectroscopic tools, it
is commonly assumed that the plasma is in LTE (except the electron density
measurement using Stark broadening). Under thermal equilibrium (TE), the
population distribution of atoms or ions at various energy levels in a plasma
is related to the temperature and the density through a Boltzmann
distribution, the population distributions of atoms of adjacent ions states
are described by a Saha-Boltzmann relation and the intensity of radiation is
given by the Planck function. However, it is challenging to establish TE in
LPPs. So, the measurement of various temperatures in the LPP is carried out
under the assumption of LTE.

The existence of LTE in a transient system such as LPP requires that the
electron-atom and electron-ion collisional processes occur sufficiently fast
and dominate the radiative processes. The radiation processes in a LTE plasma
are not following a Planck function; instead, it depends on local plasma
conditions along with population distributions and atomic transition
probabilities. LTE is a reasonably valid assumption for LPPs with relatively
high densities and low plasma temperatures. In these scenarios, the population
distributions at any time during plasma evolution are determined by the local
plasma conditions set by Boltzmann and Saha relations. Even if there is a
departure from LTE, a part of the energy levels favor collisional transitions
over radiative transitions and those plasmas are considered to in partial LTE.

There exist several articles discussing the existence of LTE in an LPP [62,
339], and still, it is a debated topic specifically when and where the LPP is
considered to be in LTE or partial LTE. One of the most commonly utilized
methods for validating the existence of LTE in LPP is the McWhirter criterion
[222], which states that the minimum density for LTE should be

$n_{e}(cm^{-3})\geq 1.4\times 10^{16}T^{1/2}(\Delta E)^{3}$ (29)

where $T$ and $\Delta E$ (the energy difference between upper and lower energy
levels) are in eV. But it must be pointed out that the McWhirter criterion,
which is derived for homogeneous and optically thin plasma, may be a necessary
condition but not a sufficient condition to ensure LTE for a transient and
inhomogeneous plasma like an LPP. In other words, the minimum electron
requirement according to the McWhirter criterion warrants that the LTE
conditions may exist in the plasma, but not with certainty. According to
Cristoforetti  _et al._ [62], the mere use of the McWhirter criterion alone to
assess the existence of the LTE in laser-induced plasmas should not be
encouraged. Considering the existence of large gradients in fundamental
parameters of the LPP with space and time, a significant deviation from LTE
can be expected if the measurements were performed in a spatially and
temporally integrated manner. Instead, the assumption of partial LTE may be
valid for spatially and temporally resolved spectral analysis.

The LTE is not a valid assumption for plasmas with low densities and/or high
temperatures, which are typically called non-equilibrium plasmas or non-LTE
plasmas. Examples of non-equilibrium plasmas include inertial and magnetic
confinement fusion plasmas, as well as astrophysical and processing plasmas.
The collision-radiative (CR) model is typically used to describe non-LTE
plasmas, where the local population distribution is described by balancing
local collisional processes and non-local radiative processes. The CR model
uses multi-level atomic rate equations and radiation transport equations for
calculating atomic-level population [52, 271].

##  III Passive and active Imaging tools

Passive and active imaging tools are widely used for LPP characterization.
Fast gated photography employing ns/ps short gated cameras (ICCD, streak etc.)
is a valuable tool studying the hydrodynamic expansion features, plasma
morphology and excited species distribution in an LPP system. Similar features
can also be recorded using LIF and absorption imaging, however they are
recording the lower/ground state species. In this section, experimental
details and measurement examples of passive and active imaging tools are
given.

###  III.1 Fast photography

Time-gated or ungated cameras are widely used for two-dimensional (2D) imaging
and are perhaps one of the most direct characterization tools for LPPs. The
LPP community extensively uses ICCD cameras to capture plasma images in the
optical spectral region [284, 127]. For shorter wavelengths (X-ray, EUV, and
VUV), vacuum-compatible cameras or microchannel plates coupled to a CCD are
used in conjunction with a pinhole camera [14]. In this scenario, the position
of the pinhole with respect to the source and camera determines the
magnification. Because the dynamics of the LPP change significantly during the
earliest times of its expansion, higher magnification is favored for capturing
the internal structure and/or instabilities. Moreover, 2D snapshots of the 3D
plasma evolution, the plume morphology, and species distribution can be
gathered from imaging diagnostics [15].

Most of the reports in plasma imaging are focused in the visible spectral
range because of the availability of large aperture and ICCDs with high
quantum efficiencies operating in the VIS spectral region [7, 118, 157, 232].
The ICCD is usually positioned orthogonal to the plume expansion direction.
Appropriate notch filters in front of the camera reject scattered laser light
and avoid laser-borne damage to the ICCD. By selecting the gate width, delay,
and magnification, the spatiotemporal evolution of the supersonic plasma
expansion can be recorded with precision. Because of the electronic delay in
fast-gated devices, an advanced triggering approach must be adopted to record
the early stages of plasma evolution. The entire plume expansion dynamic can
be reconstructed by delaying the camera gate with respect to the arrival of
the laser pulse; however, ablation events from several consecutive laser
pulses are necessary to capture the complete temporal sequence.

Several authors used spectrally integrated, fast-gated imaging with ICCD for
analyzing plume morphology, velocity [191], species kinetics [75], shock
propagation and confinement in a background gas medium [127], plume splitting
[212], internal structures, and instabilities [90]. An example of the time-
resolved, spectrally integrated (350-800 nm) 2D expansion features of an
ultrafast LPP from a U target in air is given in Fig. 20 [172]. Here, plume
splitting and late time nanoparticle thermal emissions are observed. 2D gated
images of expanding LPPs are also used for matrix correction in LIBS [338] and
measurement of residual pressure in sealed containers [336].

Figure 20:  Time-resolved spectrally integrated 2D images of U plasma in 700
Torr air. Gate delay times are indicated above each plasma image. Each image
is from a single laser shot and was normalized to its maximum intensity. The
direction of the incident laser is indicated with a white arrow, and the
target position is shown with a grey rectangle in each image. From 171.

Monochromatic imaging is performed by positioning narrow bandpass filters
corresponding to various emission lines in front of the camera, and this
method is useful for recording the spatial distribution of species (atoms,
ions, molecules, etc.) in the plasma [9, 169]. It is appropriate to select an
isolated strong-line emission as well as a bandpass filter that transmits only
the selected line for avoiding spectral interference. Instead of a narrow band
line filter, the use of an acousto-optic tunable filter (ATOF) provides filter
transmission tunability [48]. Several groups use monochromatic imaging for the
optimization of the growth of films using PLD [22] to understand the plasma
oxidation [169] and nanoparticle generation [8]. Bai  _et al._ [15] studied
the emission morphology of various species in the plume as well as background
gas excitation using monochromatic imaging and reconstructed the plume
emission morphology by combining emission features from various species.
Studies showing such a spatiotemporal species’ emission distribution and its
dynamics play an essential role in optimizing LPP properties for various
applications.

For imaging the X-ray, soft X-ray, and EUV emission, metallic filters are
positioned in front of the pinhole with an appropriate thickness, which limits
the observed radiation to the spectral region of interest [14]. The
transmission details of high-energy radiation through various metallic filters
are tabulated [143].

Streak cameras, on the other hand, provide simultaneous spatial and temporal
features of LPPs and capture the entire spatiotemporal dynamics of LPPs in a
single laser shot [266]. In this device, a streak tube is positioned in front
of the image intensifier to sweep the electrons generated on a photocathode
radially. Streak cameras provide a high dynamic range, excellent time
resolution ranging from several femtoseconds to picoseconds, and ultrahigh
sensitivity across wavelengths from X-rays to NIR. By combining the streak
camera with a spectrograph, time-resolved, single-shot spectroscopic analysis
of the LPP is carried out [267].

###  III.2 LIF and absorption imaging

Fast-gated imaging employing ICCD records the emission from the excited atoms,
ions, and molecules. However, a plasma plume contains both excited- and
ground-state species. The hydrodynamics of species in the lower state can be
monitored using LIF or absorption imaging. Planar LIF imaging is a well-
established method in combustion measurements and analysis of engine gases and
steady-state plumes, especially for monitoring various molecular species of
gas such as acetone, OH, CH, and NO and their instantaneous distribution and
number density [260]. However, the number of studies on the application of LIF
imaging to LPPs to monitor atomic and molecular species in the ground state is
limited.

For performing LIF imaging, a tunable second laser is used to preferentially
excite selected ground-state atomic or molecular transitions. Because LIF
emission depends on a selected transition, it inherently provides the
distribution of individual species in the plasma, similar to monochromatic
self-emission imaging described earlier. Several groups have used LIF for
investigating the dynamical behaviour of LPP expansion [244, 279, 236]. Miyabe
_et al._ [236] studied the dynamics of an LPP in the presence of ambient gas
and noticed that a significant portion of ground-state atoms and ions
accumulate in the contact region between the plasma and ambient gas. Examples
of LIF images obtained from LPPs generated on various metal and metal oxide
targets are given in Fig. 21 [235].

Figure 21:  (a) LIF images for Gd, Hf, Zr, and Ti species observed with a
metal and (b) mixed oxide samples at 1.5 µs delay at an ablation energy of 0.5
mJ. The plasmas were produced using 532 nm pulses from a frequency-doubled
Nd:YAG laser, and 6 Torr He gas was used as a background medium. From 235.

Resonant absorption properties of the LPP can also be utilized for species-
specific imaging similar to monochromatic self-emission imaging and LIF
imaging. Several authors performed absorption imaging of laser ablation plumes
using CW probe laser when it is in resonance with a selected atomic or
molecular transition [33, 289]. Gilgenbach _et al._ used a pulsed dye laser
for resonance absorption photography (DLRAP) to study the hydrodynamics of
excimer laser ablation processing of polymers and metals both in vacuum and
background gas environments [101, 317]. For this, they used a collimated dye
laser beam, which was absorbed by atomic or molecular species in the plume and
cast a shadow on a photographic film. This method combines the features of
absorption spectroscopy and shadowgraphy.

##  IV Optical Probing

Optical probing methods involve the use of an external electromagnetic
source,typically a laser or an arc lamp, for measuring the properties of the
plasma, and they are routinely used by the LPP community for accessing the
density changes in the plasma by measuring the probe beam’s phase
(interferometry), displacement (shadowgraphy [282]), refraction angle
(Schlieren imaging [282], Moiré deflectometry, angular refractive
refractometer [91]), or measuring the scattered signal from the plasma species
[93]. Among these, shadowgraphy and Schlieren imaging are the oldest and
remain a traditional method for imaging shock waves in large-scale experiments
and are widely used for understanding LPP shock wave generation and
propagation into an ambient gas medium, as well as for monitoring internal
structures and material ejection. Although both shadowgraphy and Schlieren
imaging provide qualitative pictures of plasma density variation and shocks,
these techniques are not precise enough to extract plasma density. The
interferometry diagnostic tool is one of the most common methods for measuring
plasma density [280, 152, 42]. However, at higher densities typically seen in
HEDP plasmas, the interference fringe become closer and are eventually
unresolvable. The angular refractive refractometer is a useful tool for
obtaining the complete density profile in long scale-length LPPs where
interferometry does not work [91].

There are three methods involved in the light-scattering techniques, viz.
Rayleigh, Raman, and Thomson. Rayleigh scattering is elastic scattering from
the particles and molecules and is regularly used by the combustion community
[105]. Raman scattering corresponds to inelastic scattering from molecules.
Thomson scattering corresponds to the elastic scattering of optical photons
from the free electrons in the plasma. Thomson scattering is one of the most
accurate methods for measuring the temperature and density of an LPP with no
presumptions about the thermodynamic equilibrium or symmetry. With the first
experiments done soon after the invention of the laser [185], Thomson
scattering (TS) has now developed into an established temporal and spatially
resolved measurement technique for electron density, electron temperature, ion
temperature, and electron and ion distribution functions of plasmas generated
by both low-and high-intensity lasers [104, 276, 246, 256].

For all optical probing tools, one of the important considerations is the
critical density ($n_{c}$) of the plasma corresponding to the probe laser beam
wavelength, which is given by $n_{c}\approx 1.1\times 10^{21}\lambda^{-2}$
where $\lambda$ is the probe beam wavelength in µm and $n_{c}$ is in cm-3.
When the electron density of the plasma $n_{e}<n_{c}$, the plasma is
underdense and the probe will propagate through the plasma. However, when
$n_{e}>n_{c}$, the plasma is overdense and opaque for the probe beam. For
example, the critical density of the plasmas for the Nd:YAG laser wavelength
and its harmonics (1064 nm, 532 nm, and 266 nm) are $\approx 9.7\times
10^{20}$ cm-3, $\approx 3.9\times 10^{21}$cm-3, and $\approx 1.6\times
10^{22}$cm-3, respectively and therefore represent the upper limits of
measurable density if one of these wavelengths are used for optical probing.
Shorter probing wavelengths can penetrate higher-density regions of the plasma
compared to longer wavelengths.

In this section, the details of shadowgraphy, Schlieren, interferometry, and
Thomson scattering are discussed.

###  IV.1 Shadowgraphy

In the most general terms and in the present context, a shadowgram is the
shadow of a plasma on a photographic screen or on a CCD/CMOS camera. This
shadowgram represents the second spatial derivative of the refractive index
($\partial^{2}\mu/\partial x^{2}$), which will reveal the inhomogeneities in
the medium of interest in the optical path [282]. Because
$\partial^{2}\mu/\partial x^{2}$ is much larger than $\partial\mu/\partial x$
in scenarios such as shock waves, turbulence, etc., the shadowgram imaging
tool is ideally suited for recording sharp refractive index gradients in the
expanding plume boundary. For example, shock waves produce a strong, higher
derivative of the refractive index and appear as sharp lines in a shadowgram.

Light with planar and spherical wavefronts can be a source for generating the
shadow. Laser beams traditionally provide extremely high-quality collimated
beams and are therefore a suitable light source for recording a shadowgram.
They are also useful for avoiding chromatic aberration effects and provide
large photon flux to overcome thermal emission from LPPs. Considering the
transient nature of laser ablation plumes, pulsed lasers with shorter pulse
widths are preferred illumination sources, especially for capturing the early
dynamics of the plume.

Two types of shadowgraphy are routinely used for studying LPP shock expansion:
_viz._ direct shadowgraphy and focused shadowgraphy. In direct shadowgraphy
(Fig. 22a), a laser light source is used for casting a shadow of the LPP
directly onto the detector. In focused shadowgraphy (Fig. 22b), a relay lens
is used to cast the shadow of the plume onto the detector. The advantage of
focused shadowgraphy is that one can vary the magnification of the image at
the detector plane; however, the aperture size of the lens or mirror used for
focusing may limit the field of view. Considering small sizes of LPPs in the
air at atmospheric pressure ($\sim$ 1-3 mm), the focused shadowgraphy is
superior for visualizing the shock waves, the internal structures of the
plume, and for capturing turbulent mixing.

Both continuous wave (CW) or pulsed laser beams can be used for performing
shadowgraphy of laser ablation plumes. In the former case, the time resolution
is provided by the detector (e.g., ICCD), while in the latter, the pulse width
of the laser determine the time resolution with the use of a regular CCD or
CMOS camera. The dynamics of shock expansion during LPP evolution are
typically captured using shadowgraphy by delaying the probe laser with respect
to the plasma production laser. An example of a shadowgram image recorded
during LPP expansion from a metal target at 1-atmosphere pressure using
focused shadowgraphy is given in Fig. 22c, which shows primary and secondary
shock waves along with material ejection [139]. Fig. 22d gives the time
sequence of laser-detonated air breakdown, highlighting features such as shock
expansion, shock decoupling from the plasma, and turbulent mixing [131]. The
high repeatability of the LPPs, which enable consistent comparison of
shadowgrams from different ablation events, allows movies to be created that
show dynamics. The quality of the shadowgram depends strongly on the
illumination beam transverse profile, camera specifications (pixel density,
dynamic range), and optics. The presence of dust particles on the camera or
optics may generate interference fringes in the shadowgram, and the shadowgram
image quality can be improved by background subtraction.

Figure 22:  Experimental schematic for (a) direct shadowgraphy and (b) focused
shadowgraphy set up. The pump laser is used to generate plasma, and a
transverse probe laser is used for generating shadowgram images. (c) A typical
LPP shadowgram image recorded using focused shadowgraphy (ns LPP, Al plasma in
air, 150 ns after onset). Both primary and secondary shock waves are clearly
visible along with material ejection From 139. (d) Shadowgrams taken at
different times during the evolution of laser-detonated air plasma. From 131.

There are numerous reports on using shadowgrams for studying the propagation
of shock waves during laser-plasma generation in gases, liquids, and solids in
a background medium [30, 295, 281, 307, 114, 231]. The shadowgram technique is
capable of monitoring laser-supported detonation (LSD) waves, primary and
secondary shock waves, mass ejecta, and turbulent mixing as shown in Figs. 22c
and 22d. Shadowgraphy is also used for elucidating the role of the cavitation
bubble during nanoparticle formation [47]. Previous studies employing
$\approx$10 ns duration laser pulses as a probe showed the presence of
darkened regions in the shadowgrams without any structures at the earliest
times of plasma evolution and described due to high densities of the plasma
and/or the expansion of the plasma during the probe laser pulse duration
[131]. It indicates the necessity of shorter pulse (fs or ps) lasers for
tracking early time information of the plasma, which reduces the effects of
large-density gradients seen during the early times of LPP evolution [264].
Shorter wavelength lasers will be useful for negating the deflection effects
at the critical density surface. Key  _et al._ [174] unveiled early time
dynamics of high-density LPP using X-ray shadowgraphy.

The shadowgraphy imaging technique is not typically used for quantification of
fundamental plume properties because of the challenges associated with beam
diffraction, small angle deflection, and solving the Poisson equation on large
data arrays. However, Gopal  _et al._ [106] demonstrated that the
shadowgraphic technique could be used for measuring 2D density profiles of
laser breakdown of air by relating the transverse variation of the optical
path of the sample to the shadowgram. They compared the measured density
values to simultaneously measured density by employing Nomarski interferometry
and found that the shadowgraphic technique provided better sensitivity. Kasim
_et al._ [164] retrieved quantitative information from shadowgrams, based on
computational geometry with measurement uncertainties less than 10%.

Traditionally, the second harmonic radiation from a Nd:YAG laser ($\lambda$ =
532 nm) is used for probing laser plasmas, and recording is performed using a
conventional CCD or CMOS detector. The drawbacks of using such a system are
the inability to penetrate at high densities due to plasma critical density at
532 nm and inflexibility of capturing the time sequence of events on a single
plasma. Due to critical density effects, the visible lasers are capable of
probing only densities much less than the solid density hence limiting
penetration and the phenomena that can be measured. So the development of
compact and tabletop sources emitting in EUV or soft X-ray spectral region
such as high order harmonic radiation, discharge-driven x-ray lasers etc.
could be very impactful for studying high density plasma regime [122, 174].

Several groups recently used high-speed cameras and time-stretch imaging
techniques for capturing time sequence of shadowgram images during a single
plasma event. For example, laser diode illumination in conjunction with a
high-speed camera was used to demonstrate a sequence of shock wave propagation
and their interplay with cavitation structures in transparent media [2]. In
another study, time-stretch imaging was used to record the time lapse of shock
wave propagation during a single-shot LPP, enabling its full dynamics to be
monitored [124]. Multiple shadowgram/Schlieren images were captured by
splitting the beams into four and probing the plasma at various delays by
using a regular CMOS digital single-lens reflex (DSLR) camera as the detector
[57]. In high-speed laser stroboscopic videography, a high-repetition-rate
probe laser in conjunction with a high-speed camera is used for capturing the
time sequence of images during a single-shot laser ablation [302].

###  IV.2 Schlieren imaging

The Schlieren method is very closely related to shadowgraphy, with subtle
differences. Shadowgram provides a shadow of an object and not a focused
image, while Schlieren gives an optical image that bears an optical conjugate
relationship with an object. Secondly, the Schlieren image requires spatial
filtering of refracted light, which is typically done with the use of a knife-
edge or a pinhole at the Fourier plane. Thirdly, the Schlieren image displays
the deflection angle, while the shadowgram gives the ray displacement
resulting from the deflection. Finally, Schlieren images provide the first
spatial derivative of the refractive index ($\partial\mu/\partial x$), while
the shadowgram corresponds to the second derivative. Therefore, the Schlieren
tool is better suited for recording weaker disturbances because of higher