11institutetext:  R. Horaud and G. Evangelidis 22institutetext: INRIA Grenoble
Rhône-Alpes
Montbonnot Saint-Martin, France
22email<EMAIL_ADDRESS><EMAIL_ADDRESS>33institutetext:
M. Hansard 44institutetext: School of Electronic Engineering and Computer
Science
Queen Mary University of London, United Kingdom
44email<EMAIL_ADDRESS>55institutetext: C. Ménier 66institutetext:
4D View Solutions
Grenoble, France
66email<EMAIL_ADDRESS>
# An Overview of Depth Cameras and Range Scanners Based on Time-of-Flight
Technologies††thanks: This work has received funding from the French Agence
Nationale de la Recherche (ANR) under the MIXCAM project ANR-13-BS02-0010-01,
and from the European Research Council (ERC) under the Advanced Grant VHIA
project 340113.

Radu Horaud  Miles Hansard  Georgios Evangelidis  Clément Ménier

(Received: date / Accepted: date)

###### Abstract

Time-of-flight (TOF) cameras are sensors that can measure the depths of scene-
points, by illuminating the scene with a controlled laser or LED source, and
then analyzing the reflected light. In this paper we will first describe the
underlying measurement principles of time-of-flight cameras, including: (i)
pulsed-light cameras, which measure directly the time taken for a light pulse
to travel from the device to the object and back again, and (ii) continuous-
wave modulated-light cameras, which measure the phase difference between the
emitted and received signals, and hence obtain the travel time indirectly. We
review the main existing designs, including prototypes as well as commercially
available devices. We also review the relevant camera calibration principles,
and how they are applied to TOF devices. Finally, we discuss the benefits and
challenges of combined TOF and color camera systems.

###### keywords:

LIDAR range scanners single photon avalanche diode time-of-flight cameras 3D
computer vision active-light sensors

##  1 Introduction

During the last decades, there has been a strong interest in the design and
development of range-sensing systems and devices. The ability to remotely
measure range is extremely useful and has been extensively used for mapping
and surveying, on board of ground vehicles, aircraft, spacecraft and
satellites, and for civil as well as military purposes. NASA has identified
range sensing as a key technology for enabling autonomous and precise planet
landing with both robotic and crewed space missions, e.g.,
amzajerdian2011lidar . More recently, range sensors of various kinds have been
used in computer graphics and computer vision for 3-D object modeling
blais2004review , Other applications include terrain measurement, simultaneous
localization and mapping (SLAM), autonomous and semi-autonomous vehicle
guidance (including obstacle detection), as well as object grasping and
manipulation. Moreover, in computer vision, range sensors are ubiquitous in a
number of applications, including object recognition, human motion capture,
human-computer interaction, and 3-D reconstruction Grzegorzek2013time .

There are several physical principles and associated technologies that enable
the fabrication of range sensors. One type of range sensor is known as LIDAR,
which stands either for “Light Imaging Detection And Ranging” or for “LIght
and raDAR”. LIDAR is a remote-sensing technology that estimates range (or
distance, or depth) by illuminating an object with a collimated laser beam,
followed by detecting the reflected light using a photodetector. This remote
measurement principle is also known as time of flight (TOF). Because LIDARs
use a fine laser-beam, they can estimate distance with high resolution. LIDARs
can use ultraviolet, visible or infrared light. They can target a wide range
of materials, including metallic and non-metallic objects, rocks, vegetation,
rain, clouds, and so on – but excluding highly specular materials.

The vast majority of range-sensing applications require an array of depth
measurements, not just a single depth value. Therefore, LIDAR technology must
be combined with some form of scanning, such as a rotating mirror, in order to
obtain a row of horizontally adjacent depth values. Vertical depth values can
be obtained by using two single-axis rotating mirrors, by employing several
laser beams with their dedicated light detectors, or by using mirrors at fixed
orientations. In all cases, both the vertical field of view and the vertical
resolution are inherently limited. Alternatively, it is possible to design a
scannerless device: the light coming from a single emitter is diverged such
that the entire scene of interest is illuminated, and the reflected light is
imaged onto a two-dimensional array of photodetectors, namely a TOF depth
camera. Rather than measuring the intensity of the ambient light, as with
standard cameras, TOFcameras measure the reflected light coming from the
camera’s own light-source emitter.

Therefore, both TOF range scanners and cameras belong to a more general
category of LIDARs that combine a single or multiple laser beams, possibly
mounted onto a rotating mechanism, with a 2D array of light detectors and
time-to-digital converters, to produce 1-D or 2-D arrays of depth values.
Broadly speaking, there are two ways of measuring the time of flight
remondino2013tof , and hence two types of sensors:

  * •

Pulsed-light sensors directly measure the round-trip time of a light pulse.
The width of the light pulse is of a few nanoseconds. Because the pulse
irradiance power is much higher than the background (ambient) irradiance
power, this type of TOF camera can perform outdoors, under adverse conditions,
and can take long-distance measurements (from a few meters up to several
kilometers). Light-pulse detectors are based on single photon avalanche diodes
(SPAD) for their ability to capture individual photons with high time-of-
arrival resolution cova1981towards , approximatively 10 picoseconds
($10^{-11}$ s).

  * •

Continuous-wave (CW) modulation sensors measure the phase differences between
an emitted continuous sinusoidal light-wave signal and the backscattered
signals received by each photodetector lange2001solid . The phase difference
between emitted and received signals is estimated via cross-correlation
(demodulation). The phase is directly related to distance, given the known
modulation frequency. These sensors usually operate indoors, and are capable
of short-distance measurements only (from a few centimeters to several
meters). One major shortcoming of this type of depth camera is the phase-
wrapping ambiguity hansard-2013 .

This paper overviews pulsed-light (section 2) and continuous wave (section 4)
range technologies, their underlying physical principles, design, scanning
mechanisms, advantages, and limitations. We review the principal technical
characteristics of some of the commercially available TOF scanners and cameras
as well as of some laboratory prototypes. Then we discuss the geometric and
optical models together with the associated camera calibration techniques that
allow to map raw TOF measurements onto Cartesian coordinates and hence to
build 3D images or point clouds (section 6). We also address the problem of
how to combine TOF and color cameras for depth-color fusion and depth-stereo
fusion (section 7).

##  2 Pulsed-Light Technology

As already mentioned, pulsed-light depth sensors are composed of both a light
emitter and light receivers. The sensor sends out pulses of light emitted by a
laser or by a laser-diode (LD). Once reflected onto an object, the light
pulses are detected by an array of photodiodes that are combined with time-to-
digital converters (TDCs) or with time-to-amplitude circuitry. There are two
possible setups which will be referred to as range scanner and 3D flash LIDAR
camera:

  * •

A TOF range scanner is composed of a single laser that fires onto a single-
axis rotating mirror. This enables a very wide field of view in one direction
(up to $360^{\circ}$) and a very narrow field of view in the other direction.
One example of such a range scanner is the Velodyne family of sensors
schwarz2010mapping  that feature a rotating head equipped with several (16, 32
or 64) LDs, each LD having its own dedicated photodetector, and each laser-
detector pair being precisely aligned at a predetermined vertical angle, thus
giving a wide vertical field of view. Another example of this type of TOF
scanning device was recently developed by the Toyota Central R&D Laboratories:
the sensor is based on a single laser combined with a multi-facet polygonal
(rotating) mirror. Each polygonal facet has a slightly different tilt angle,
as a result each facet of the mirror reflects the laser beam into a different
vertical direction, thus enhancing the vertical field-of-view resolution
niclass2013100 .

  * •

A 3D flash LIDAR camera uses the light beam from a single laser that is spread
using an optical diffuser, in order to illuminate the entire scene of
interest. A 1-D or 2-D array of photo-detectors is then used to obtain a depth
image. A number of sensor prototypes were developed using single photon
avalanche diodes (SPADs) integrated with conventional CMOS timing circuitry,
e.g., a 1-D array of 64 elements niclass2005design , 32$\times$32 arrays
albota2002three ; stoppa2007cmos , or a 128$\times$128 array niclass2008128 .
A 3-D Flash LIDAR camera, featuring a 128$\times$128 array of SPADs, described
in amzajerdian2011lidar , is commercially available.

###  2.1 Avalanche Photodiodes

One of the basic elements of any TOF camera is an array of photodetectors,
each detector has its own timing circuit to measure the range to the
corresponding point in the scene. Once a light pulse is emitted by a laser and
reflected onto an object, only a fraction of the optical energy is received by
the detector – the energy fall-off is inversely proportional to the square of
the distance. When an optical diffuser is present, this energy is further
divided among multiple detectors. If a depth precision of a few centimeters is
needed, the timing precision must be less than a nanosecond.111As the light
travels at $3\times 10^{10}$ cm/s, 1 ns (or $10^{-9}$ s) corresponds to 30cm.
Moreover, the bandwidth of the detection circuit must be high, which also
means that the noise is high, thus competing with the weak signal.

The vast majority of pulse-light receivers are based on arrays of single
photon avalanche diodes which are also referred to as Geiger-mode avalanche
photodiodes (G-APD). A SPAD is a special way of operating an avalanche
photodiode (APD), namely it produces a fast electrical pulse of several volts
amplitude in response to the detection of a single photon. This electrical
pulse then generally trigers a digital CMOS circuit integrated into each
pixel. An integrated SPAD-CMOS array is a compact, low-power and all-solid-
state sensor niclass2008128 .

The elementary building block of semiconductor diodes and hence of photodiodes
is the $p-n$ junction, namely the boundary between two types of semiconductor
materials, $p$-type and $n$-type. This is created by doping which is a process
that consists of adding impurities into an extremely pure semiconductor for
the purpose of modifying its electrical (conductivity) properties. Materials
conduct electricity if they contain mobile charge carriers. There are two
types of charge carriers in a semiconductor: free electrons and electron
holes. When an electric field exists in the vicinity of the junction, it keeps
free electrons confined on the $n$-side and electron holes confined on the
$p$-side.

There are two types of $p-n$ diodes: forward-bias and reverse-bias. In
forward-bias, the $p$-side is connected with the positive terminal of an
electric power supply and the $n$-side is connected with the negative
terminal. Both electrons and holes are pushed towards the junction. In
reverse-bias, the $p$-side is connected with the negative terminal and the
$n$-side is connected with the positive terminal. Otherwise said, the voltage
on the $n$-side is higher than the voltage on the $p$-side. In this case both
electrons and holes are pushed away from the junction.

A photodiode is a semiconductor diode that converts light into current. The
current is generated when photons are absorbed in the photodiode. Photodiodes
are similar to regular semiconductor diodes. A photodiode is designed to
operate in reverse bias. An APD is a variation of a $p-n$ junction photodiode.
When an incident photon of sufficient energy is absorbed in the region where
the field exists, an electron-hole pair is generated. Under the influence of
the field, the electron drifts to the $n$-side and the hole drifts to the
$p$-side, resulting in the flow of photocurrent (i.e., the current induced by
the detection of photons) in the external circuit. When a photodiode is used
to detect light, the number of electron-hole pairs generated per incident
photon is at best unity.

An APD detects light by using the same principle aull2002geiger . The
difference between an APD and an ordinary $p-n$ junction photodiode is that an
APD is designed to support high electric fields. When an electron-hole pair is
generated by photon absorption, the electron (or the hole) can accelerate and
gain sufficient energy from the field to collide with the crystal lattice and
generate another electron-hole pair, losing some of its kinetic energy in the
process. This process is known as impact ionization. The electron can
accelerate again, as can the secondary electron or hole, and create more
electron-hole pairs, hence the term “avalanche”.

Figure 1:  The basic structure of an array of time of flight detectors
consists of Geiger-mode APDs (pink) bonded to complementary-metal-oxide-
semiconductor (CMOS) timing circuitry (blue). A photon of energy hv is
absorbed in the APD active area. The gain of the APD resulting from the
electron avalanche is great enough that the detector generates a pulse that
can directly trigger the 3.3 V CMOS circuitry. No analog-to-digital converter
is needed. A digital logic latch is used to stop a digital timing register for
each pixel. The time of flight is recorded in the digital value of the timing
register.

After a few transit times, a competition develops between the rate at which
electron-hole pairs are being generated by impact ionization (analogous to a
birth rate) and the rate at which they exit the high-field region and are
collected (analogous to a death rate). If the magnitude of the reverse-bias
voltage is below a value known as the breakdown voltage, collection wins the
competition, causing the population of electrons and holes to decline. If the
magnitude of the voltage is above the breakdown voltage, impact ionization
wins. This situation represents the most commonly known mode of operation of
APDs: measuring the intensity of an optical signal and taking advantage of the
internal gain provided by impact ionization. Each absorbed photon creates on
average a finite number $M$ of electron-hole pairs. The internal gain $M$ is
typically tens or hundreds. Because the average photocurrent is strictly
proportional to the incident optical flux, this mode of operation is known as
linear mode.

###  2.2 Single Photon Avalanche Diodes

The fundamental difference between SPADs (also referred to as Geiger-mode APD)
and conventional APDs is that SPADs are specifically designed to operate with
a reverse-bias voltage well above the breakdown voltage. A SPAD is able to
detect low intensity incoming light (down to the single photon) and to signal
the arrival times of the photons with a jitter of a few tens of picoseconds
cova1981towards . Moreover, SPADs behave almost like digital devices, hence
subsequent signal processing can be greatly simplified. The basic structure of
an array of time-of-flight detectors consists of SPADs bonded to CMOS timing
circuitry. A SPAD outputs an analog voltage pulse, that reflects the detection
of a single photon, and that can directly trigger the CMOS circuitry. The
latter implements time-to-digital converters to compute time-interval
measurements between a start signal, global to all the pixels, and photon
arrival times in individual pixels.

##  3 LIDAR Cameras

###  3.1 Velodyne Range Scanners

Whereas most LIDAR systems have a single laser that fires onto a rotating
mirror and hence are only able to view objects in a single plane, the high-
definition HDL-64E LIDAR range scanner from
Velodyne222http://velodynelidar.com/index.html uses a rotating head featuring
64 semiconductor lasers. Each laser operates at 905 nm wavelength, has a beam
divergence of 2 mrad, and fires 5 ns light pulses at up to $20,000$ Hz. The 64
lasers are spread over a vertical field of view, and coupled with 64 dedicated
photo detectors for precise ranging. The laser-detector pairs are precisely
aligned at vertical angles to give a $26.8^{\circ}$ vertical field of view. By
spinning the entire unit at speeds of up to 900 rpm (15 Hz) around its
vertical axis, a 360∘ field-of-view is generated.

Figure 2:  From left to right: VLP-16, HDL-32E, and HDL-64E high-definition
range scanners manufactured by Velodyne. These rotating scanners feature a
complete 360∘ horizontal field of view as well as 16, 32 and 64 laser-detector
pairs spread over a vertical field of view. The sensors range is from 1 m and
up to 120 m (depending on the material properties of the scanned object) with
a accuracy of 2 cm.

This allows the sensor to achieve data collection rates that are an order of
magnitude higher than most conventional designs. Over 1.3 million data points
are generated each second, independent of the spin rate. Velodyne also
commercializes 32 and 16 laser scanners with reduced vertical resolution. The
range scanners are shown on figure 2 and their main parameters and
specifications are summarized on Table 1.

A mathematical model of the Velodyne HDL-64E range scanner was developed in
glennie2007rigorous ; glennie2010static  together with a calibration model and
a practical method for estimating the model parameters. Extensive experiments
using this model show that the actual noise level of the range measurements is
3.0 to 3.5 cm, which is double the manufacturer specification. Subsequently,
the same authors analyzed the temporal stability (horizontal angle offset) of
the scanner glennie2011temporal .

###  3.2 Toyota’s Hybrid LIDAR Camera

Fig. 3 (left) shows a simplified diagram of the depth sensor system recently
developed at the Toyota Central R&D Labs, Japan niclass2013100 . A 870 nm
pulsed laser source with a repetition rate of 200 kHz emits an optical beam
with 1.5∘ and 0.05∘ of divergence in the vertical and horizontal directions,
respectively. While the optical pulse duration is 4 ns full-width at half-
maximum (FWHM), the mean optical power is 40 mW. The laser beam is coaxially
aimed at the three-facet polygonal mirror through an opening in the center of
an imaging concave mirror. Each facet of the polygonal mirror has a slightly
different tilt angle.

Model | Resolution (H$\times$V) | Range/Accuracy | FOV | Frame rate | Points/second | Laser | Pulse width
---|---|---|---|---|---|---|---
HDL-64E | $0.08^{\circ}\times 0.4^{\circ}$ | 2 – 120 m / 2 cm | $360^{\circ}\times 26.8^{\circ}$ | 5-15 Hz | 1,300,000 | 905 nm | 10 ns
HDL-32E | $0.08^{\circ}\times 1.33^{\circ}$ | 2 – 120 m / 2 cm | $360^{\circ}\times 31.4^{\circ}$ | 5-20 Hz | 700,000 | 905 nm | 10 ns
VLP-16 | $0.08^{\circ}\times 1.87^{\circ}$ | 2 – 100 m / 2 cm | $360^{\circ}\times 30^{\circ}$ | 5-20 Hz | 300,000 | 905 nm | 10 ns
Toyota | $0.05^{\circ}\times 1.5^{\circ}$ | not specified | $170^{\circ}\times 4.5^{\circ}$ | 10 Hz | 326,400 | 870 nm | 4 ns
Table 1:  The principal characteristics of the Velodyne LIDAR range scanners
and of Toyota’s LIDAR prototype that can operate outdoors. The maximum range
depends on the material properties of the targeted object and can vary from 50
m (for pavement) to 120 m (for cars and trees). All these range scanners use
class 1 (eye safe) semiconductor lasers.

As a result, in one revolution of 100 ms, the polygonal mirror reflects the
laser beam into three vertical directions at $+1.5^{\circ}$, 0∘, and
$-1.5^{\circ}$, thus covering, together with the laser vertical divergence, a
contiguous vertical FOV of 4.5∘. During the 170∘ horizontal scanning, at one
particular facet, back-reflected photons from the targets in the scene are
collected by the same facet and imaged onto the CMOS sensor chip at the focal
plane of the concave mirror. The chip has a vertical line sensor with 32
macro-pixels. These pixels resolve different vertical portions of the scene at
different facet times, thus generating an actual vertical resolution of 96
pixels. Since each macro-pixel circuit operates in full parallelism, at the
end of a complete revolution, 1020$\times$32 distance points are computed.
This image frame is then repartitioned into 340$\times$96 actual pixels at 10
FPS. An optical near-infrared interference filter (not shown in the figure) is
also placed in front of the sensor for background light rejection.

The system electronics consists of a rigid-flex head-sensor PCB, a laser
driver board, a board for signal interface and power supply, and a digital
board comprising a low-cost FPGA and USB transceiver. Distance, intensity, and
reliability data are generated on the FPGA and transferred to a PC at a
moderate data rate of 10 Mbit/s. The system requires only a compact external
AC adapter from which several other power supplies are derived internally.

Figure 3:  A simplified diagram of a depth sensor system developed by Toyota
(left) and a view of the complete system (right).

###  3.3 3D Flash LIDAR Cameras

A 3D Flash LIDAR is another name used to designate a sensor that creates a 3D
image (a depth value at each pixel) from a single laser pulse that is used to
flood-illuminate the targeted scene or objects. The main difference between a
LIDAR camera and a standard LIDAR device is that there is no need of a
mechanical scanning mechanism, e.g., rotating mirror. Hence, a Flash LIDAR may
well be viewed as a 3D video camera that delivers 3D images at up to 30 FPS.
The general principle and basic components are shown of Fig. 4. Flash LIDARs
use a light-pulse emitted by a single laser, that is reflected onto a scene
object. Because the reflected light is further divided among multiple
detectors, the energy fall-off is considerable. Nevertheless, the fact that
there is no need for scanning represents a considerable advantage. Indeed,
each individual SPAD is exposed to the optical signal for a long period of
time, typically of the order of ten milliseconds. This allows for a large
number of illumination cycles that can be averaged to reduce the various
effects of noise.

Figure 4:  This figure illustrates the basic principle of a Flash LIDAR
camera. An eye-safe laser flood-illuminates an object of interest.

The MIT Lincoln Laboratory reported the development of 3D Flash LIDAR long-
range (up to 500 m) camera prototypes based on a short-pulse (1 ns) microchip
laser, transmitting at a wavelength of 532 nm, and SPAD/CMOS imagers
albota2002three ; aull2002geiger . Two LIDAR camera prototypes were developed
at MIT Lincoln Laboratory, one based on a 4$\times$4 pixels SPAD/CMOS sensor
combined with a two-axis rotating mirror, and one based on a 32$\times$32
pixels SPAD/CMOS sensor.

|
---|---
Tiger Eye (new) | Tiger Eye (old)
|
Dragon Eye | Portable 3D
Figure 5:  3D Flash LIDAR depth cameras manufactured and commercialized by
Advanced Scientific Concepts, Santa Barbara, CA. These cameras use a single
pulsed-light diffused laser beam and can operate outdoors in adverse
conditions at up to 30FPS.

Advanced Scientific Concepts
Inc.333http://www.advancedscientificconcepts.com/index.html developed a 3D
Flash LIDAR prototype stettner2008three  as well as a number of commercially
available LIDAR cameras, e.g., Fig. 5. The
TigerEye/TigerCup444http://www.advancedscientificconcepts.com/products/tigercub.html
is truly a 3D video camera. It is equipped with an eye-safe 1570 nm laser,
with a CMOS 128$\times$128 pixels sensor, and it delivers images at 10-30 FPS.
It has an interchangeable lens such that its range and field of view (FOV) can
vary: 3${}^{\circ}\times 3^{\circ}$ FOV and range up to 1100 meters,
8.6${}^{\circ}\times 8.6^{\circ}$ FOV and range up to 450 meters,
45${}^{\circ}\times 22^{\circ}$ FOV and range up to 150 meters, and
45${}^{\circ}\times 45^{\circ}$ FOV and range up to 60 meters.

The
DragonEye/GoldenEye555http://www.advancedscientificconcepts.com/products/portable.html
3D Flash LIDAR space camera delivers both intensity and depth videos at 10
FPS. It has a 128$\times$128 SPAD based sensor and its FOV is of
45${}^{\circ}\times 45^{\circ}$ which is equivalent of a 17 mm focal length
and it can range up to 1500 m. The DragonEye was tested and used by NASA for
precision navigation and safe landing amzajerdian2011lidar . The
specifications of these cameras are summarized in Table 2.

Camera | Resolution | Range | Mult. cameras | FOV | FPS | Laser | Indoor/out
---|---|---|---|---|---|---|---
TigerEye-1 | 128$\times$128 | 1100 m | not specified | $3^{\circ}\times 3^{\circ}$ | 10-30 | 1570 nm | no/yes
TigerEye-2 | 128$\times$128 | 450 m | not specified | $8.6^{\circ}\times 8.6^{\circ}$ | 10-30 | 1570 nm | no/yes
TigerEye-3 | 128$\times$128 | 150 m | not specified | $45^{\circ}\times 22^{\circ}$ | 10-30 | 1570 nm | no/yes
TigerEye-4 | 128$\times$128 | 60 m | not specified | $45^{\circ}\times 45^{\circ}$ | 10-30 | 1570 nm | no/yes
DragonEye | 128$\times$128 | 1500 m | not specified | $45^{\circ}\times 45^{\circ}$ | 10-30 | 1570 nm | no/yes
Real.iZ VS-1000 | 1280$\times$1024 | 10 m | possible | $45^{\circ}\times 45^{\circ}$ | 30-450 | 905 nm | yes/yes
Basler | 640$\times$480 | 6.6 m | not specified | $57^{\circ}\times 43^{\circ}$ | 15 | not specified | yes/yes
Table 2:  This table summarizes the main features of commercially available 3D
Flash LIDAR cameras. The accuracy of the depth measurements announced by the
manufacturers are not reported in this table as the precision of the
measurements depend on a lot of factors, such as the surface properties of the
scene objects, illumination conditions, frame rate, etc.

###  3.4 Other LIDAR camera

Recently, Odos Imaging666http://www.odos-imaging.com/ announced the
commercialization of a high-resolution pulsed-light time-of-flight camera,
Fig. 6. The camera has a resolution of 1280$\times$1024 pixels, a range up to
10 m, a frame rate of 30 FPS and up to 450 FPS, depending on the required
precision (Table 2. It can be used both indoor and outdoor (for outdoor
applications it may require additional filters). One advantage of this camera
is that it delivers both depth and standard monochrome images. Another LIDAR
camera is Basler’s pulsed-light camera based on a Panasonic TOF CCD sensor.
The main characteristics of these cameras are summarized in Table 2.

Figure 6:  The high-resolution real.iZ pulsed-light LIDAR camera manufactured
by Odos Imaging.

##  4 Continuous-Wave Technology

All these depth sensors share some common characteristics, as follows
lange2001solid ; remondino2013tof :

  * •

The transmitter, a light emitter (generally a LED, or light-emitting diode)
sends light onto an object and the time the light needs to travel from the
illumination source to the object and back to the sensor is measured.

  * •

In the case of continuous-wave (CW), the emitted signal is a sinusoidally
modulated light signal.

  * •

The received signal is phase-shifted due to the round trip of the light
signal. Moreover, the received signal is affected by the object’s
reflectivity, attenuation along the optical path and background illumination.

  * •

Each pixel independently performs demodulation of the received signal and
therefore is capable of measuring both its phase delay as well as amplitude
and offset (background illumination).

The imaging principle of a CW-TOF camera is shown on Fig. 7.

Figure 7:  This figure shows the image formation principle of 3D Flash LIDARs
and continuous-wave TOF cameras.

###  4.1 Demodulation Principle

Let $s(t)$ and $r(t)$ be the optical powers of the emitted and received
signals respectively:

$\displaystyle s(t)$ $\displaystyle=a_{1}+a_{2}\cos(2\pi ft),$ (1)
$\displaystyle r(t)$ $\displaystyle=A\cos(2\pi ft-2\pi f\tau)+B,$ (2)

where $f$ is the modulation frequency, $\tau$ is the time delay between the
emitted and received signals, $\phi=2\pi f\tau$ is the corresponding phase
shift, $a_{1}$ and $a_{2}$ are the offset and amplitude of the modulated
emitted signal, $A$ is the amplitude of the received signal, and $B$ is the
offset of the received signal due to background illumination (illumination
other than the emitter itself). The cross-correlation between the powers of
the emitted and received signals can be written as:

$\mathcal{C}(x)=\lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{+T/2}s(t)r(t-x)\mathrm{d}t.$
(3)

By substituting $s(t)$ and $r(t)$ with their expressions (1) and (2) and by
developing the terms, we obtain:

$\displaystyle\mathcal{C}(x,\tau)=$
$\displaystyle\lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{+T/2}\Big{(}a_{2}B\cos(2\pi
ft)$ $\displaystyle+a_{2}A\cos(2\pi ft)\cos(2\pi ft-2\pi f(\tau+x))$
$\displaystyle+a_{1}A\cos(2\pi ft-2\pi f(\tau+x))\Big{)}\mathrm{d}t$
$\displaystyle+a_{1}B.$ (4)

Using the identities

$\displaystyle\lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{+T/2}\cos
t\;\mathrm{d}t$ $\displaystyle=0$
$\displaystyle\lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{+T/2}\cos
t\cos(t-u)\;\mathrm{d}t$ $\displaystyle=\frac{1}{2}\cos u,$

we obtain:

$\displaystyle\mathcal{C}(x,\tau)$ $\displaystyle=\frac{a_{2}A}{2}\cos(2\pi
f(x+\tau))+a_{1}B.$ (5)

Using the notations $\psi=2\pi fx$ and $\phi=2\pi f\tau$, we can write:

$\mathcal{C}(\psi,\phi)=\frac{a_{2}A}{2}\cos(\psi+\phi)+a_{1}B.$ (6)

Let’s consider the values of the correlation function at four equally spaced
samples within one modulation period,
$\psi_{0}=0,\psi_{1}=\pi/2,\psi_{2}=\pi$, and $\psi_{3}=3\pi/2$, namely
$C_{0}=\mathcal{C}(0,\phi),C_{1}=\mathcal{C}(\pi/2,\phi),C_{2}=\mathcal{C}(\pi,\phi)$,
and $C_{3}=\mathcal{C}(3\pi/2,\phi)$, e.g., Fig. 8. These four sample values
are sufficient for the unambiguous computation of the offset $B$, amplitude
$A$, and phase $\phi$ lange2001solid :

$\displaystyle\phi$
$\displaystyle=\arctan\left(\frac{C_{3}-C_{1}}{C_{0}-C_{2}}\right)$ (7)
$\displaystyle A$
$\displaystyle=\frac{1}{a_{2}}\sqrt{(C_{3}-C_{1})^{2}+(C_{0}-C_{2})^{2}}$ (8)
$\displaystyle B$
$\displaystyle=\frac{1}{4a_{1}}\left(C_{0}+C_{1}+C_{2}+C_{3}\right)$ (9)

###  4.2 Pixel Structure

An electro-optical demodulation pixel performs the following operations,
buttgen2008robust :

  * •

light detection, the incoming photons are converted into electron charges;

  * •

demodulation (based on correlation),

  * •

clocking, and

  * •

charge storage.

The output voltage of the storage capacitor, after integration over a short
period of time $T_{i}$, is proportional to the correlation ($R$ is the optical
responsivity of the detector):

$V(x)=\frac{RT_{i}}{C_{S}}C(x)$ (10)

Hence, the received optical signal is converted into a photocurrent.

The samples are the result of the integration of the photocurrent of a
duration $\Delta t<1/f$. In order to increase the signal-to-noise ratio of one
sampling process, the samples $C_{0}$ to $C_{3}$ are the result of the
summation over many modulation periods (up to hundreds of thousands). A pixel
with four shutters feeding four charge storage nodes allows the simultaneous
acquisition of the four samples needed for these computations. The four
shutters are activated one at a time for a time equal to $T/4$ (where $T$ is
the modulation period), and the shutter activation sequence is repeated for
the whole integration time $T_{i}$ which usually includes hundreds of
thousands of modulation periods.

Figure 8:  This figure shows the general principle of the four-bucket method
that estimates the demodulated optical signal at four equally-spaced samples
in one modulation period. A CCD/CMOS circuit achieves light detection,
demodulation, and charge storage. The demodulated signal is stored at four
equally spaced samples in one modulation period. From these four values, it is
then possible to estimate the phase and amplitude of the received signal as
well as the amount of background light (offset).

###  4.3 Depth Estimation from Phase

A depth value $d$ at each pixel is computed with the following formula:

$d=\frac{1}{2}c\tau$ (11)

where $c$ is the light speed and $\tau$ is the time of flight. Since we
measure the phase $\phi=2\pi f\tau$, we obtain:

$d=\frac{c}{4\pi f}\phi=\frac{c}{4\pi
f}\arctan\left(\frac{C_{3}-C_{1}}{C_{0}-C_{1}}\right)$ (12)

Nevertheless, because the phase is defined up to $2\pi$, there is an inherent
phase wrapping ambiguity in measuring the depth:

  * •

Minimum depth: $d_{\min}=0\;\;(\phi=0)$

  * •

Maximum depth: $d_{\max}=\frac{c}{2f}\;\;(\phi=2\pi)$.

The depth at each pixel location $(i,j)$ can be written as a function of this
wrapping ambiguity:

$d(i,j)=\left(\frac{\phi(i,j)}{2\pi}+n(i,j)\right)d_{\max}$ (13)

where $n=0,1,2,\ldots$ is the number of wrappings. This can also be written
as:

$d(i,j)=d_{TOF}(i,j)+n(i,j)d_{\max}$ (14)

where $d$ is the real depth value and $d_{TOF}$ is the measured depth value.
It is important to stress that the number of wrappings is not the same at each
pixel. Let’s consider a modulation frequency $f=30$ MHz, the unambiguous range
of the camera is in this case from $d_{\min}=0$ to $d_{\max}=5$ meters. The
ambiguity decreases as the modulation frequency decreases, but in the same
time the accuracy decreases as well. Several methods were proposed in the
literature to solve for the phase wrapping ambiguity Ghiglia94 ; Opri07 ;
Bioucas-Dias07 ; Payne09 ; McClure10 ; Droeschel10b ; Droeschel10a ; Choi10 ;
Choi12a

To summarize, the following remarks can be made concerning these depth-camera
technologies:

  * •

A CW-TOF camera works at a very precise modulation frequency. Consequently, it
is possible to simultaneously and synchronously use several CW-TOF cameras,
either by using a different modulation frequency for each one of the cameras,
e.g., six cameras in the case of the SR4000 (Swiss Ranger), or by encoding the
modulation frequency, e.g., an arbitrary number of SR4500 cameras.

  * •

In order to increase the signal-to-noise ratio, and hence the depth accuracy,
CW-TOF cameras need a relatively long integration time (IT), over several time
periods. In turn, this introduces motion blur hansard-2013  (chapter 1) in the
presence of moving objects. Because of the need of long IT, fast shutter
speeds (as done with standard cameras) cannot be envisaged.

To summarize, the sources of errors of these cameras are: demodulation,
integration, temperature, motion blur, distance to the target, background
illumination, phase wrapping ambiguity, light scattering, and multiple path
effects. A quantitative analysis of these sources of errors is available in
foix-2011 . In the case of several cameras operating simultaneously,
interferences between the different units is an important issue.

##  5 TOF Cameras

In this section we review the characteristics of some of the commercially
available cameras. We selected those camera models for which technical and
scientific documentation is readily available. The main specifications of the
overviewed camera models are summarized in Table 3.

###  5.1 The SR4000/SR4500 Cameras

The SR4000/4500 cameras, figure 9, are manufactured by Mesa Imaging, Zurich,
Switzerland.777http://www.mesa-imaging.ch/ They are continuous-wave TOF
cameras that provide depth, amplitude, and confidence images with a resolution
of 176$\times$144 pixels. In principle, the cameras can work at up to 30 FPS
but in practice more accurate depth measurements are obtained at 10-15 FPS.

The modulation frequency of the SR4000 camera can be selected by the user. The
camera can be operated at:

  * •

$29$ MHz, 30 MHz, or $31$ MHz corresponding to a maximum depth of $5.17$ m,
$5$ m and $4.84$ m respectively.

  * •

$14.5$ MHz, 15.0 MHz, or $15.5$ MHz corresponding to a maximum depth of
$10.34$ m, $10$ m and $9.67$ m respectively.

This allows the simultaneous and synchronous use of up to six SR4000 cameras
to be used together with any number of color cameras.

The modulation frequency of SR4500 is of $13.5$ MHz which allows a maximum
depth of 9 m. Moreover, an arbitrary number of SR4500 cameras can be combined
together because the modulation frequency is encoded differently for each
unit.

|
---|---
Figure 9:  The SR4000 (left) and SR4500 (right) CW-TOF cameras manufactured by Mesa Imaging. |
---|---
Figure 10:  The DS311 (left) and DS325 (rigtht) CW-TOF cameras manufactured by
SoftKinetic.

###  5.2 The Kinect v2 RGB-D Camera

The Kinect color and depth (RGB-D) camera, manufactured by Microsoft, was
recently upgraded to Kinect v2. Unlike the former version that was based on
structured-light technology, the latter uses a time-of-flight sensor payne2014
; bamji20150  and was mainly designed for gaming sell2014xbox . Kinect-v2
achieves one of the best image resolution among TOF cameras commercially
available. Moreover, it uses multiple modulation frequencies (10-130 MHz) thus
achieving an excellent compromise between depth accuracy and phase unwrapping,
i.e. Section 4.3 above. In bamji20150  it is reported that the Kinect v2 can
measure depth in the range 0.8-4.2 m with an accuracy of 0.5% of the measured
range. Several recent articles evaluate the Kinect v2 sensor for mobile
robotics fankhauser2015kinect  and in comparison with the structured-light
version sarbolandi-2015 .

It is interesting to note that Kinect v2 is heavier than its predecessor (970
g instead of 170 g) requires higher voltage (12 V instead of 5 V) and power
usage (15 W instead of 2.5 W).

###  5.3 Other CW TOF cameras

The following depth cameras are based on the same continuous wave demodulation
principles (see Table 3 for a summary of the characteristics of these
cameras):

  * •

DS311 and DS325 cameras, figure 10, manufactured by
SoftKinetic,888http://www.softkinetic.com/

  * •

E70 and E40 manufactured by Fotonic,999http://www.fotonic.com/

  * •

TOF sensor chip manufactured by PMD.101010http://www.pmdtec.com/,

  * •

The D-imager manufactured by Panasonic has a range up to 15 cm. It was
discontinued in March
2015.111111http://www2.panasonic.biz/es/densetsu/device/3DImageSensor/en/

Camera | Resolution | Range | Mult. cameras | FOV | Max FPS | Illumination | Indoor/out
---|---|---|---|---|---|---|---
SR4000 | 176$\times$144 | 0$-$5 or 0$-$10 m | 6 cameras | $43^{\circ}\times 34^{\circ}$ | 30 | LED | yes/no
SR4500 | 176$\times$144 | 0$-$9 m | many cameras | $43^{\circ}\times 34^{\circ}$ | 30 | LED | yes/no
DS311 | 160$\times$120 | 0.15$-$1 or 1.5$-$4.5 m | not specified | $57^{\circ}\times 42^{\circ}$ | 60 | LED | yes/no
DS325 | 320$\times$240 | 0.15$-$1 m | not specified | $74^{\circ}\times 58^{\circ}$ | 60 | diffused laser | yes/no
E70 | 160$\times$120 | 0.1$-$10 m | 4 cameras | $70^{\circ}\times 53^{\circ}$ | 52 | LED | yes/yes
E40 | 160$\times$120 | 0.1$-$10 m | 4 cameras | $45^{\circ}\times 34^{\circ}$ | 52 | LED | yes/yes
Kinect v2 | 512$\times$424 | 0.8$-$4.2 m | not specified | $70^{\circ}\times 60^{\circ}$ | 30 | LED | yes/no
Table 3:  This table summarizes the main features of commercially available CW
TOF cameras. The accuracy of the depth measurements announced by the
manufacturers are not reported in this table as the precision of the
measurements depend on a lot of factors, such as the surface properties of the
scene objects, illumination conditions, frame rate, etc.

##  6 Calibration of Time-of-Flight Cameras

Both pulsed-light and continuous-wave TOF cameras can be modeled as pinhole
cameras, using the principles of projective geometry. The basic projection
equation is

$\left(\begin{array}[]{c}x\\\
y\end{array}\right)=\frac{1}{Z}\left(\begin{array}[]{c}X\\\
Y\end{array}\right).$ (15)

This implies that the homogeneous coordinates of an image-point
$\mbox{\boldmath$p$}=(x,y,1)^{\top}$ are projectively equal to the scene-
coordinates $\mbox{\boldmath$P$}=(X,Y,Z)^{\top}$, specifically:

$Z\mbox{\boldmath$p$}=\mbox{\boldmath$P$}.$ (16)

In practice, a realistic model of the projection process involves the
intrinsic, extrinsic, and distortion parameters, as described below zhang-2000
; Hartley03 ; bradski-2008 .

###  6.1 Intrinsic Parameters

A digital camera records the image in pixel-units, which are related to the
coordinates $(x,y)^{\top}$ in (15) by

$\displaystyle u$ $\displaystyle=\alpha_{u}x+u_{0}$ (17) $\displaystyle v$
$\displaystyle=\alpha_{v}y+v_{0}.$

In these equations we have the following _intrinsic parameters_ :

  * •

Horizontal and vertical factors, $\alpha_{u}$ and $\alpha_{v}$, which encode
the change of scale, multiplied by the focal length.

  * •

The image center, or _principal point_ , expressed in pixel units:
$(u_{0},v_{0})$.

Alternatively, the intrinsic transformation (17) can be expressed in matrix
form, $\mbox{\boldmath$q$}=\mbox{\bf A}\mbox{\boldmath$p$}$ where
$\mbox{\boldmath$q$}=(u,v,1)$ are pixel coordinates, and the $3\times 3$
matrix A is defined as

$\mbox{\bf A}=\left(\begin{array}[]{ccc}\alpha_{u}&0&u_{0}\\\
0&\alpha_{v}&v_{0}\\\ 0&0&1\end{array}\right).$ (18)

Hence it is possible to express the _direction_ of a visual ray, in camera
coordinates, as

$\mbox{\boldmath$p$}=\mbox{\bf A}^{-1}\mbox{\boldmath$q$}.$ (19)

A TOF camera further allows the 3D _position_ of point $P$ to be estimated, as
follows. Observe from equation (16) that the Euclidean norms of $P$ and $p$
are proportional:

$\|\mbox{\boldmath$P$}\|=Z\|\mbox{\boldmath$p$}\|.$ (20)

The TOF camera measures the distance $d$ from the 3D point $P$ to the optical
center,121212In practice it measures the distance to the image sensor and we
assume that the offset between the optical center and the sensor is small so
$d=\|\mbox{\boldmath$P$}\|$. Hence the $Z$ coordinate of the observed point is

$Z=\frac{\|\mbox{\boldmath$P$}\|}{\|\mbox{\boldmath$p$}\|}=\frac{d}{\|\mbox{\bf
A}^{-1}\mbox{\boldmath$q$}\|}.$ (21)

We can therefore obtain the 3D coordinates of the observed point, by combining
(16) and (19), to give

$\mbox{\boldmath$P$}=\frac{d}{\|\mbox{\bf
A}^{-1}\mbox{\boldmath$q$}\|}\mbox{\bf A}^{-1}\mbox{\boldmath$q$}.$ (22)

Note that the point is recovered in the camera coordinate system; the
transformation to a common ‘world’ coordinate system is explained in the
following section.

###  6.2 Extrinsic Parameters

A rigid transformation from the arbitrary world coordinate frame
$\mbox{\boldmath$P$}_{\\!w}=(X_{w},Y_{w},Z_{w})^{\top}$ to the camera frame
can be modelled by a rotation and translation. This can be expressed in
homogeneous coordinates as:

$\left(\begin{array}[]{c}\mbox{\boldmath$P$}\\\
1\end{array}\right)=\left(\begin{array}[]{cc}\mbox{\bf R}&\
\mbox{\boldmath$T$}\\\
\mathbf{0}&1\end{array}\right)\left(\begin{array}[]{c}\mbox{\boldmath$P$}_{\\!w}\\\
1\end{array}\right).$ (23)

The $3\times 3$ matrix R has three degrees of freedom, which can be identified
with the angle and normalized axis of rotation. Meanwhile, the $3\times 1$
translation vector is defined by $\mbox{\boldmath$T$}=-\mbox{\bf
R}\mbox{\boldmath$C$}$, where $C$ contains the world coordinates of the
camera-centre. Hence there are six _extrinsic parameters_ in the
transformation (23). The equation can readily be inverted, in order to obtain
world coordinates from the estimated point $P$ in equation (22).

Figure 11:  This figure shows a setup for TOF calibration. The calibration
board is the same one used for color camera calibration and it can be used to
estimate the lens parameters as well.

###  6.3 Lens Distortion Model

A commonly used lens distortion model widely used for color cameras,
bradski-2008 ; gonzalez-2011 , can be adopted for TOF cameras as well: the
observed distorted point $(x_{l},y_{l})$ results from the displacement of
$(x,y)$ according to:

$\left(\begin{array}[]{c}x_{l}\\\
y_{l}\end{array}\right)=l_{\rho}(r)\left(\begin{array}[]{c}x\\\
y\end{array}\right)+\mbox{\boldmath$l$}_{\tau}(x,y)$ (24)

where $l_{\rho}(r)$ is a scalar radial function of $r=\sqrt{x^{2}+y^{2}}$, and
$\mbox{\boldmath$l$}_{\tau}(x,y)$ is a vector tangential component. These are
commonly defined by polynomial functions

$\displaystyle l_{\rho}(r)$
$\displaystyle=1+\rho_{1}r^{2}+\rho_{2}r^{4}\quad\text{and}$ (25)
$\displaystyle\mbox{\boldmath$l$}_{\tau}(x,y)$
$\displaystyle=\left[\begin{array}[]{cc}2xy&r^{2}+2x^{2}\\\
r^{2}+2y^{2}&2xy\end{array}\right]\left(\begin{array}[]{c}\tau_{1}\\\
\tau_{2}\end{array}\right)$ (30)

such that the complete parameter-vector is
$[\rho_{1}\;\rho_{2}\;\tau_{1}\;\tau_{2}]$. The images can be undistorted, by
numerically inverting (30), given the lens and intrinsic parameters. The
projective linear model, described in sections (6.1–6.2), can then be used to
describe the complete imaging process, with respect to the undistorted images.

It should also be noted, in the case of TOF cameras, that the outgoing
infrared signal is subject to optical effects. In particular, there is a
radial attenuation, which results in strong vignetting of the intensity image.
This can be modeled by a bivariate polynomial, if a full photometric
calibration is required lindner-2010 ; hertzberg2014tof .

###  6.4 Depth Distortion Models

TOF depth estimates are also subject to systematic nonlinear distortions,
particulalry due to deviation of the emitted signal from the ideal model
described in Section 4.1. This results in ‘wiggling’ error of the average
distance estimates, with respect to the true distance foix-2011 ;
fursattel2015comparative . Because this error is systematic, it can be removed
by reference to a precomputed look-up table kahlmann2006tof . Another
possibility is to learn a mapping between raw depth values, estimated by the
sensor, and corrected values. This mapping can be performed using regression
techniques applied to carefully calibrated data. A random regression forest is
used in ferstllearning  to optimize the depth measurements supplied by the
camera. A kernel regression method based on a Gaussian kernel is used in
kuznetsova2014calibration  to estimate the depth bias at each pixel. Below we
describe an efficient approach, which exploits the smoothness of the error,
and which uses a $B$-spline regression lindner-2010  of the form:

$d^{\prime}(x,y)=d(x,y)-\sum_{i}^{n}\beta_{i}B_{i,3}\bigl{(}d(x,y)\bigr{)}$
(31)

where $d^{\prime}(x,y)$ is the corrected depth. The spline basis-functions
$B_{i,3}(d)$ are located at $n$ evenly-spaced depth control-points $d_{i}$.
The coefficients $\beta_{i}$, $i=1,\ldots,n$ can be estimated by least-squares
optimization, given the known target-depths. The total number of coefficients
$n$ depends on the number of known depth-planes in the calibration procedure.

###  6.5 Practical Considerations

To summarize, the TOF camera parameters are composed of the pinhole camera
model, namely the parameters $\alpha_{u},\alpha_{v},u_{0},v_{0}$ and the lens
distortion parameters, namely $\rho_{1},\rho_{2},\tau_{1},\tau_{2}$. Standard
camera calibration methods can be used with TOF cameras, in particular with
CW-TOF cameras because they provide an amplitude+offset image, i.e. Section 4,
together with the depth image: Standard color-camera calibration methods, e.g.
OpenCV packages, can be applied to the amplitude+offset image. However, the
low-resolution of the TOF images implies specific image processing techniques,
such as Hansard-2014 ; kuznetsova2014calibration . As en example, Fig. 12
shows the depth and amplitude images of a calibration pattern gathered with
the SR4000 camera. Here the standard corner detection method was replaced with
the detection of two pencils of lines that are optimally fitted to the OpenCV
calibration pattern.

TOF-specific calibration procedures can also be performed, such as the depth-
wiggling correction lindner-2010 ; kuznetsova2014calibration ; ferstllearning
. A variety of TOF calibration methods can be found in a recent book
Grzegorzek2013time . A comparative study of several TOF cameras based on an
error analysis was also proposed fursattel2015comparative .

One should however be aware of the fact that depth measurement errors may be
quite difficult to predict due to the unknown material properties of the
sensed objects and to the complexity of the scene. In the case of a scene
composed of complex objects, multiple-path distortion may occur, due to the
interaction between the emitted light and the scene objects, e.g. the emitted
light is backscattered more than once. Techniques for removing multiple-path
distortions were recently proposed freedman2014sra ; son2016automatic .

Figure 12:  The depth (left) and amplitude (middle) images of an OpenCV
calibration pattern grabbed with an SR4000 camera. The actual image resolution
is of $176\times 144$ pixels. The amplitude image (middle) has undergone lens
undistortion using the model briefly described in section 6.3. The calibration
pattern detected in the amplitude image (right) using the method of
Hansard-2014 .

##  7 Combining Multiple TOF and Color Cameras

In addition to the image and depth-calibration procedures described in section
6, it is often desirable to combine data from multiple devices. There are
several reasons for this, depending on the application. Firstly, current depth
cameras are pinhole devices, with a single optical centre (16). This means
that the resulting point-cloud data is viewpoint dependent; in particular,
depth discontinuities will give rise to holes, when the point cloud is viewed
from a different direction. Secondly, it is often desirable to combine
multiple point clouds, in order to reduce the amount and the anisotropy of
sensor noise. Thirdly, typical TOF devices do not capture colour data; hence
it may be necessary to cross-calibrate one or more RGB cameras with the depth
sensors.

Both pulsed-light and continuous-wave TOF cameras work at a precise wavelength
in the (near-)infrared domain. They are equipped with an optical band-pass
filter properly tuned onto the wavelength of the light emitter. This allows,
in principle, simultaneous capture from multiple TOF cameras with each
signaling at its own modulation frequency, so that interference is unlikely.
As mentioned above, not all of the TOF manufacturers allow a user-defined
modulation frequency (see Table 3). Because of different spectra, TOF cameras
do not interfere with typical color cameras, and can be easily combined. In
either combination, however, the cameras must be synchronized properly, that
is, a common clock signal should trigger all of the cameras.

The simplest possible combination is one TOF and one color camera. Some of the
available TOF cameras, e.g., Microsoft Kinect v2 and SoftKinetic DS311/DS325
have a built-in color camera with its own sensor and lens, which is mounted a
few centimeters away from the TOF camera. Note that only real.iZ by Odos
Imaging uses the same pixel to acquire both color and depth measurements, thus
eliminating the additional calibration and registration. 131313There has been
an attempt at a similar architecture in kim2012cmos ; this 3D and color camera
is not commercially available.

Another possible setup is to use one TOF camera and two color cameras
Gudmundsson2008 ; zhu-2008 ; gandhi-2012 ; evangelidis-2015 ; mutto-2015,
e.g., Fig. 14. The advantage of using two color cameras is that they can be
used as a stereoscopic camera pair. Such a camera pair, once calibrated,
provides dense depth measurements (via a stereo matching algorithm) when the
scene is of sufficient texture and lacks repetitive patterns. However,
untextured areas are very common in man-made environments, e.g. walls, and the
matching algorithm typically fails to reconstruct such scenes. While TOF
cameras have their own limitations (noise, low resolution, etc.) that were
discussed above, they provide good estimates regardless of the scene texture.
This gives rise to mixed systems that combine active-range and the passive-
parallax approaches and overcome the limitations of each approach alone. In
particular, when a high-resolution 3D map is required, such a mixed system is
highly recommended. Roughly speaking, sparse TOF measurements are used as a
regularizer of a stereo matching algorithm towards a dense high-resolution
depth map evangelidis-2015 .

Given that TOF cameras can be modeled as pin-hole cameras, one can use
multiple-camera geometric models to cross-calibrate several TOF cameras or any
combination of TOF and color cameras. Recently, an earlier TOF-stereo
calibration technique hansard-2011  was extended to deal with an arbitrary
number of cameras Hansard2015 . It is assumed that a set of calibration
vertices can be detected in the TOF images, and back-projected into 3D. The
same vertices are reconstructed via stereo-matching, using the high resolution
RGB cameras. Ideally, the two 3D reconstructions could be aligned by a rigid
3D transformation; however, this is not true in practice, owing to calibration
uncertainty in both the TOF and RGB cameras. Hence a more general alignment,
via a 3D projective transformation, was derived. This approach has several
advantages, including a straightforward SVD calibration procedure, which can
be refined by photogrammetric bundle-adjustment routines. An alternative
approach, initialized by the factory calibration of the TOF camera, is
described by Jung2014 .

A different cross-calibration method can be developed from the constraint that
depth points lie on calibration planes, where the latter are also observed by
the colour camera zhang-2011 . This method, however, does not provide a
framework for calibrating the intrinsic (section 6.1) or lens (section 6.3)
parameters of the depth camera. A related method, which does include
distortion correction, has been demonstrated for Kinect v1 herrera-2012 .

Finally, a more object-based approach can be adopted, in which dense
overlapping depth-scans are merged together in 3D. This approach, which is
ideally suited to handheld (or robotic) scanning, has been applied to both
Kinect v1 Newcombe11  and TOF cameras cui-2013 .

Figure 13:  A single system (left), comprising a time-of-flight camera in the
centre, plus a pair of ordinary color cameras. Several (four) such systems can
be combined together and calibrated in order to be used for 3D scene
reconstruction (right).

Figure 14:  Calibration images from synchronized captures. The greyscale
images provided by the color camera pair are shown onto the left and onto the
right. The middle smaller images correspond to enlarged depth and amplitude
images provided by the TOF camera.

##  8 Conclusions

Time of flight is a remote-sensing technology that estimates range (depth) by
illuminating an object with a laser or with a photodiode and by measuring the
travel time from the emitter to the object and back to the detector. Two
technologies are available today, one based on pulsed-light and the second
based on continuous-wave modulation. Pulsed-light sensors measure directly the
pulse’s total trip time and use either rotating mirrors (LIDAR) or a light
diffuser (Flash LIDAR) to produce a two-dimensional array of range values.
Continuous-wave (CW) sensors measure the phase difference between the emitted
and received signals and the phase is estimated via demodulation. LIDAR
cameras usually operate outdoor and their range can be up to a few kilometers.
CW cameras usually operate indoor and they allow for short-distance
measurements only, namely up to 10 meters. Depth estimation based on phase
measurement suffer from an intrinsic phase-wrapping ambiguity. Higher the
modulation frequency, more accurate the measurement and shorter the range.

Generally speaking, the spatial resolution of these sensors is a few orders of
magnitude (10 to 100) less than video cameras. This is mainly due to the need
to capture sufficient backscattered light. The depth accuracy depends on
multiple factors and can vary from a few centimeters up to several meters. TOF
cameras can be modeled as pinhole cameras and therefore one can use standard
camera calibration techniques (distortion, intrinsic and extrinsic
parameters). One advantage of TOF cameras over depth sensors based on
structured light and triangulation, is that the former provides an
amplitude+offset image. The amplitude+offset and depth images are gathered by
the same and unique sensor, hence one can use camera calibration techniques
routinely used with color sensors to calibrate TOF cameras. This is not the
case with triangulation-based range sensors for which special-purpose
calibration techniques must be used. Moreover, the relative orientation
between the infrared camera and the color camera must be estimated as well.

TOF cameras and TOF range scanners are used for a wide range of applications,
from multimedia user interfaces to autonomous vehicle navigation and
planetary/space exploration. More precisely:

  * •

Pulsed-light devices, such as the Velodyne, Toyota, and Advanced Scientific
Concepts LIDARs can be used under adverse outdoor lighting conditions, which
is not the case with continuous-wave systems. These LIDARs are the systems of
choice for autonomous vehicle driving and for robot navigation (obstacle, car,
and pedestrian detection, road following, etc.). The Toyota LIDAR scanner is a
laboratory prototype, at the time of writing.

  * •

The 3D Flash LIDAR cameras manufactured by Advanced Scientific Concepts have
been developed in collaboration with NASA for the purpose of planet landing
amzajerdian2011lidar . They are commercially available.

  * •

The SR4000/45000 cameras are used for industrial and for multimedia
applications. Although they have limited image resolution, these cameras can
be easily combined together into multiple TOF and camera systems. They are
commercially available.

  * •

The Kinect v2, SoftKinetic, Basler and Fotonic cameras are used for multimedia
and robotic applications. They are commercially available, some of them at a
very affordable price. Additionally, some of these sensors integrate an
additional color camera which is internally synchronized with the TOF camera,
thus yielding RGB-D data. Nevertheless, one shortcoming is that they cannot be
easily externally synchronized in order to build multiple-camera TOF-TOF or
TOF-color systems.

  * •

The real.iZ is a prototype developed by Odos Imaging. It is a very promising
camera but its commercial availability is not clear and the time of the
writing of this paper.

In conclusion, time-of-flight technologies are used in many different
configurations, for a wide range of applications. The refinement,
commoditization, and miniaturization of these devices is likely to have an
increasing impact on everyday life, in the near future.

## References

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# Identification of autoionizing states of atomic chromium for resonance
photo-ionization at the ISOLDE-RILIS

T. Day Goodacre  K. Chrysalidis  D. Fedorov  V. N. Fedosseev  B. A. Marsh  P.
Molkanov  R. E. Rossel  S. Rothe  C. Seiffert  CERN, CH-1211 Geneva 23,
Switzerland School of Physics and Astronomy, The University of Manchester,
Manchester, M13 9PL, United Kingdom Petersburg Nuclear Physics Institute,
188350 Gatchina, Russia Institut für Physik, Johannes Gutenberg Universität,
D-55099 Mainz, Germany Faculty of Design, Computer Science and Media,
Hochschule RheinMain, Wiesbaden, Germany

###### Abstract

The resonance ionization laser ion source (RILIS) is the principal ion source
of the ISOLDE radioactive beam facility based at CERN. Using the method of in-
source resonance ionization spectroscopy, an optimal three-step, three-
resonance photo-ionization scheme has been developed for chromium. The scheme
uses an ionizing transition to one of the 14 newly observed autoionizing
states. This work increases the range of ISOLDE-RILIS ionized beams to 32
chemical elements. Details of the spectroscopic studies are described and the
new ionization scheme is summarized. A link to the complete version of this
document will be added here following publication:

###### keywords:

RILIS , ISOLDE , chromium , autoionizing , laser ionization

††journal: arxiv

##  1 Introduction

###  1.1 The ISOLDE-RILIS

ISOLDE is an isotope separator on-line (ISOL) type, radioactive ion beam
facility connected to the CERN accelerator complex [1]. Radionuclides are
produced with a pulsed 1.4 GeV proton beam of up to 2 µA average current that
is impacted upon a ”thick target”. Reaction products, created via
fragmentation, spallation and fission, are stopped and thermalized within the
target material. The target is heated to enable sufficiently volatile elements
to diffuse through the target material and then effuse, via a transfer line,
to an ion source typically for 1+ ionization.

The resonance ionization laser ion source (RILIS) is the principal ion source
of the ISOLDE facility, used for 75$\%$ of the ISOLDE physics experiments in
2015. The hot cavity RILIS operation at ISOLDE is based on the following three
principles:

  1. 1.

The distribution of the atomic energy levels is unique to a particular
element.

  2. 2.

Electric dipole transitions between electronic states of the atom can be
driven by an external photon field, when the photon energy corresponds to the
transition energy.

  3. 3.

Ions in the hot cavity environment (typically a 3 mm internal diameter metal
tube heated up to 2400 K) are transversally confined by the cavity walls,
which are positively charged as a result of thermally induced electron
emission, enhancing ion survival rates.

The RILIS targets a progressive series of resonant atomic excitations, using
multiple tunable lasers, before a final ionizing step: either a resonant
transition to an autoionizing state or non-resonant ionization to the
continuum [2]. Ionization via an autoionizing resonance is preferred as the
photo-absorption cross-section for resonant transitions can be orders of
magnitude higher than for non-resonant ionization, often making saturation of
the transition feasible with the typically available laser power [3].

The development of a RILIS scheme for chromium was initiated following
interest from the ISOLDE solid state physics group and the ISOLTRAP
collaboration for experiments involving neutron deficient and neutron rich
isotopes respectively [4, 5]. Previous chromium production at ISOLDE used arc
discharge ion sources, most recently a VD5 ”hot plasma” variant of the ISOLDE
Versatile Arc Discharge Ion Source (VADIS), coupled to a ZrO2 or a Y2O3 target
[6]. The ”universal” ionization efficiency of the VD5 VADIS limits the
achievable beam purity for some isotopes due to isobaric contamination,
particularly if a UCX target is used [7]. A viable RILIS scheme therefore
enhances the purity of chromium ion beams. In addition to offering the other
advantages of element selective ionization with the RILIS, such as the ability
to remove the laser ionized chromium component of the ion beam by blocking one
of the resonant transitions, enabling measurements to be made both with the
lasers blocked and unblocked for signal identification.

##  2 Ionization of chromium atoms in a hot cavity

Chromium has a first ionization potential of 6.77 eV [8]. Consequently, with
sufficient heating of the sample of stable chromium, a surface ion signal
measurable on an ISOLDE Faraday cup ($>$100 fA) is expected from a tungsten
hot cavity ion source heated to 2400 K.

##  3 Experimental set-up

The RILIS scheme development for chromium took place at ISOLDE using the RILIS
laser system and a tungsten hot cavity ion source mounted on the general
purpose separator (GPS) frontend. The ISOLDE-RILIS is primarily made up of
broadly tunable lasers to maximize the spectral range and flexibility of the
of the system, with a combination of three dye lasers and three
Titanium:Sapphire (Ti:Sa) lasers. An independent 40 W average power, TEM00,
frequency doubled Nd:YVO4 (532 nm) Lumera Blaze laser, is available for
ionization schemes using a non-resonant final ionizing step [9]. The lasers
are pulsed at a repetition rate of 10 kHz, approximately the frequency
required to ensure atoms effusing through the ion source are illuminated by a
minimum of one set of laser pulses. The tunable lasers are typically pumped by
frequency doubled Nd:YAG (532 nm) lasers; however, the dye lasers can also be
pumped with the third harmonic of the Nd:Yag (355 nm) to extend their possible
tuning range. Through the use of non-linear optics for 2nd, 3rd and 4th
harmonic generation, an unbroken spectral coverage between 210 nm and 950 nm
is achieved. The wavelengths of the RILIS lasers are measured using a
HighFinesse/Ångstrom WS7 wavelength meter. Two dye lasers, one frequency
doubled Ti:Sa laser and the 532 nm Blaze laser, highlighted in the schematic
of the RILIS laser system presented in Figure 1, were used during the scheme
development of chromium.

Figure 1: Schematic of the RILIS layout and the experimental set-up for the
development of a RILIS scheme for chromium

For RILIS scheme development, capillary mass markers loaded with stable
isotopes of the element of interest are connected to the rear of a hot cavity,
providing a continuous supply of atoms within the ion source as they are
heated and evaporated. As depicted in Figure 1, the RILIS laser beams were
directed through the GPS dipole magnet, to converge within the hot cavity ion
source. The ion source assembly was maintained at a voltage of 30 kV and a
grounded extraction electrode was positioned $\sim$ 60 mm from the exit of the
ion source. Ions created in the ion source drifted towards the cavity exit
under the influence of a longitudinal voltage drop resulting from the
resistive heating of the hot cavity. At the exit of the hot cavity, the ions
were extracted by the penetrating field of the extraction electrode and
accelerated to form a 30 keV ion beam. The ions passed through the ISOLDE GPS
dipole magnet for mass selection before being directed to a Faraday cup for
measurement of the ion current.

The 357.9 nm light for the first step transition was produced by frequency
doubling the output of a Ti:Sa laser and the 697.8 nm light for the second
step transition was produced by a dye laser containing Pyridine 1 dye
dissolved in ethanol. A second dye laser, containing Rhodamine 6G dye
dissolved in ethanol, was used applied as a third excitation step to above the
first ionization potential and scanned to search for autoionizing states. The
52Cr (stable) ion current was measured whilst recording the scanning laser
wavelength using the RILIS data acquisition system [10]. Since the purpose of
the spectroscopic study was the identification of an optimal RILIS scheme for
chromium beam production at ISOLDE, typical RILIS operating conditions were
maintained (laser linewidths and power levels were not optimized for spectral
resolution). The RILIS laser parameters are described in detail by Fedosseev
et al. and Rothe et al. [11, 12].

##  4 Results and discussion

The procedure used for laser resonance ionization scheme development for the
ISOLDE-RILIS was reviewed by Fedosseev et al. [13]. According to Boltzmann’s
equation, the 3d5(6S)4s a7S3 atomic ground state of chromium is 97 $\%$
populated at 2400 K. Thus, all of the RILIS schemes considered here originate
from the atomic ground state. Extensive atomic line data is available for
chromium, including numerous autoionizing states [14, 8, 15]. Following a
review of these atomic lines and energy levels, suitable first and second
steps for a RILIS scheme were identified, details of the transitions are
presented in Table 1.

Table 1: The first and second resonant transitions used in the chromium scheme development. Spectroscopic information is taken from NIST database [8] Transition | Upper state config., term, J | Wavenumber | Air wavelength |
---|---|---|---|---
(cm-1) |  | (cm-1) | (nm) |
0 - 27935 | 3d4(5D)4s4p3P∘, y7P∘, 4 | 27935 | 357.9 |
27935 - 42261 | 3d5(6S)4d, e7D, 5 | 14325 | 697.8 |

The upper level of the second transition lies at an energy of 42261 cm-1,
$\sim$12314 cm-1 ($\sim$812 nm) below the ionization threshold [8]. When
considering the suitability of a transition, information concerning the
photoabsorption cross-section of the candidate transition was compared to
similar data for transitions used in existing RILIS schemes, for which a
saturation measurement has been performed. This provides a reliable estimate
of the feasibility of saturating a proposed transition with the laser power
that is typically available from the RILIS lasers. Where available, an
excitation scheme consisting of states with progressively increasing
statistical weights is preferred, as this increases the maximum achievable
ionization efficiency in the RILIS ionization geometry.

Initially a three step, two resonance scheme, with a non-resonant final step
at 532 nm was demonstrated
($\\{\lambda_{1}\left|\lambda_{2}\right|\lambda_{3}\\}=\\{357.9~{}$nm$|697.8~{}$nm$|532~{}$nm${}^{NR}\\}$),
verifying the suitability of the transitions found in literature. The non-
resonant final step was then replaced with the tunable dye laser containing
Rhodamine 6G dye dissolved in ethanol to excite from the 3d5(6S)4d e7D5 level
at 42261 cm-1 and scan above the ionization potential. 14 new autoionizing
states were observed in the scan between 17204 cm-1 and 17854 cm-1.

Table 2: An autoionizing states of chromium, accessed by a single photon transition from the 3d5(6S)4d e7D5 level at 42261 cm-1. Energy | Transition | Air wavelength
---|---|---
(cm-1) | (cm-1) | (nm)
59523 | 17262 | 579.1

The optimal scheme, corresponding to the highest observed 52Cr ion current, is
presented in Figure 2, along with laser scans of the three resonances.

Figure 2: The optimal RILIS ionization scheme for chromium and scans of the
three resonant transitions.

Time constraints limited the investigation of saturation levels to only the
$\\{357.9~{}$nm$|697.8~{}$nm$|579.1~{}$nm${}^{AI}\\}$ scheme. The saturation
of the first two resonant transitions was verified and a saturation
measurement of the third resonant transition was made by measuring the 52Cr
ion current while varying the third step laser power, the transition was not
saturated with an estimated 1.3 W of laser light transmitted to the ion
source. A redistribution of the pump laser power for the dye lasers could
enable up to 7 W of laser power at 579 nm to be delivered to the ion source,
increasing the total efficiency of the scheme.

Using the scheme depicted in Figure 2, a laser to surface ionization ratio of
2200:1 was recorded with the hot cavity heated to 2400 K. The ion signal when
applying the $\\{357.9~{}$nm$|697.8~{}$nm$|579.1~{}$nm${}^{AI}\\}$ scheme, was
a factor of two greater than the ion signal observed when using the
$\\{357.9~{}$nm$|697.8~{}$nm$|532~{}$nm${}^{NR}\\}$ scheme with non-resonant
ionization despite an estimated 24 W of 532 nm laser light transmitted to the
ion source.

Chromium extraction from ISOLDE UCx targets has been verified, using surface
ionization, as far in to the neutron rich region as 59Cr [16]. This
demonstrates the possibility of extracting chromium isotopes with half lives
of the order of 100 ms. The validity of the new RILIS scheme has been
demonstrated on-line at ISOLDE with the measurement of RILIS ionized,
radiogenically produced 52Cr. A factor of 800 enhancement of the ion signal
was observed, from an ion beam composed of multiple elements with the line
heated to 2400 K.

##  5 Conclusion

14 new autoionizing states of chromium have been observed, during off-line
testing at the ISOLDE-RILIS. From this work, an optimal
$\\{357.9~{}$nm$|697.8~{}$nm$|579.1~{}$nm${}^{AI}\\}$ RILIS scheme was
identified. The scheme was verified on-line at ISOLDE, using radiogenically
produced chromium from a UCX target. As a result, RILIS ionized chromium beams
are now available for experiments at ISOLDE.

##  6 Acknowledgements

This project has received funding through the European Union s Seventh
Framework Programme for Research and Technological Development under Grant
Agreements 262010 (ENSAR), 267194 (COFUND), and 289191 (LA3NET).

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