# Spectroscopic Devices for Asteroseismology With Small Telescopes in NARIT

Somsawat Rattanasoon National Astronomical Research Institute of Thailand
(Public Organization)
260 Moo 4, T. Donkaew, A. Maerim, Chiangmai, 50180 Thailand  Eugene
Semenko111Corresponding author<EMAIL_ADDRESS>National Astronomical
Research Institute of Thailand (Public Organization)
260 Moo 4, T. Donkaew, A. Maerim, Chiangmai, 50180 Thailand  David Mkrtichian
National Astronomical Research Institute of Thailand (Public Organization)
260 Moo 4, T. Donkaew, A. Maerim, Chiangmai, 50180 Thailand  Saran
Poshyachinda National Astronomical Research Institute of Thailand (Public
Organization)
260 Moo 4, T. Donkaew, A. Maerim, Chiangmai, 50180 Thailand

###### Abstract

National Astronomical Research Institute of Thailand (NARIT) has a manifold
network of small telescopes installed worldwide. These telescopes serve
educational and research purposes and are equipped mainly with CCD detectors
for direct imaging and photometry. To extend the possible field of
applications, several telescopes were fitted with commercially available
medium-resolution spectrographs eShel from Shelyak. With these devices,
researchers in NARIT obtained a versatile tool for stellar spectroscopy. Here
we describe the current status of available equipment, possible ways of
upgrading, and briefly introduce the achieved results of the asteroseismologic
study of fast-rotating stars.

Keywords — spectroscopy, instrumentation, asteroseismology

##  1 Motivation

A fibre-fed medium-resolution echelle spectrograph eShel has been designed and
distributed for small telescopes by Shelyak Instruments (France) since 2008
(Thizy and Cochard, 2011). A typical device consists of a stationary
spectrograph block linked by a fibre with 50 $\mu$m core to the Fibre
Injection and Guiding Unit (FIGU) installed at the telescope side. FIGU is
also connected through a 200-$\mu$m fibre channel to the Calibration Unit
comprising halogen, LED, and ThAr lamps. Spectrograph and its components are
commercially available on the company’s website https://www.shelyak.com/.
Earlier models of eShel registered spectra within the wavelength range 430–700
nm with the resolution $R>10,000$. In 2018, after the upgrade, which affected
many components of eShel, the working range was significantly extended.

NARIT has a distributed network of small telescopes with apertures up to 1 m.
For the spectroscopy of relatively bright stars, these telescopes can
optionally be equipped with eShel. At the moment, NARIT has three devices with
serial numbers 6H-115 (2010), 6H-128 (2016), and 6H-171 (2018). All
spectrographs were acquired in their original complete set, thus having
limited capabilities. To enable observations of fainter objects and to
increase sensitivity in the blue part of the spectrum, we initiated a
substantial upgrade of a device with SN 6H-171.

##  2 Modification and Tests

The improved device received a new high-OH fibre with enhanced throughput in
the blue part of the spectrum, a new doublet collimator (Shelyak provided both
components), a new imaging lens, and a professional-grade CCD. All components,
except fibre, are shown in Fig. 1. As a detector, we use a water-cooled Andor
iKon-L system based on a $2048\times 2048$ pixels CCD array with 13.5 $\mu$m
pixel pitch. To match the plate scale to the increased pixel size, among
several lenses with comparable focus lengths available in the market, we
choose a commercial lens Sony FE 135 mm F1.8 GM, primarily due to its
outstanding optical quality. Subsequent testing of the whole assembly also
showed excellent transmission of the selected lens within the required range
of wavelengths. The imaging lens is attached to the CCD camera through a
specially designed adapter with an enclosed shutter.

Technical parameters of the original and upgraded versions of eShel are
summarized in Table 1.

Figure 1: Main elements of eShel upgraded in NARIT.

Table 1: Technical parameters of upgraded eShel. Asterisk indicates the new
elements with the same listed characteristics.

Parameter | Original Value | New value
---|---|---
FIGU $F\\#$ | F6 | original
Fibre core | 50 $\mu$m |  ∗50 $\mu$m
$f_{\mathrm{col}}$, $F\\#_{\mathrm{col}}$ | 125 mm, F5 |  ∗125 mm, F5
$d_{\mathrm{echelle}}$, $\theta_{\mathrm{b}}$ | 79 mm-1, 63∘ | original
Absolute orders $\\#$ | 32–52 | 24–57
Imaging lens | Canon EF 85 F1.8 | Sony FE 135 mm F1.8 GM
Detector (sensor) | ATIK 460 EX (Sony ICX694) | Andor iKon-L (E2V CCD42-40)
Sensor format |  $2749\times<EMAIL_ADDRESS>|  $2048\times<EMAIL_ADDRESS>

An upgraded variant of the spectrograph was installed for tests in a
spectrograph room of the Thai National Observatory (TNO) at Doi Inthanon
(Chiang Mai, Thailand) in a temperature-controlled environment. The FIGU was
mounted to the left Nasmyth port of the 1-m telescope of TNO. Tests were
performed in December 2022 and January 2023 under affordable weather
conditions and were aimed at the verification of the optical performance of
the assembly. Observational data include a standard set of calibrations (bias,
flat, ThAr) and spectra of the selected stars and daytime sky. Two-dimensional
raw FITS images were reduced using the pipeline PyYAP (http://github.com/ich-
heisse-eugene/PyYAP), specially adapted to a new device.

##  3 Results

Test images taken with the upgraded device showed remarkable aberrations
arising from the misaligned optical elements of the spectrograph. As this
problem appeared in the direction perpendicular to dispersion, it influenced
the overall throughput and the level of scattered light. Still, it didn’t
affect the spectral resolution and transmission of the device. Thus we leave
the evaluation of the total throughput and stability for future works and
concentrate here primarily on studying these unaffected characteristics.

###  3.1 Transmission

Analysis of observational data revealed significantly improved spectrum
quality due to better control of aberrations and enhanced transmission in the
Sony lens. In the images, the point spread function remains nearly stable
across the field of view in the 380-850 nm wavelength range. As a result, the
shortwave limit of the working spectral range has been extended by 70 nm, from
450 nm to 380 nm. In the infrared, the working range of the current setup is
limited by 900 nm. In Fig. 2, we show four samples of the observed spectrum of
the daytime sky.

Figure 2: Four samples of the solar spectrum taken at TNO during day time.

###  3.2 Resolving power

The resolving power of the modified eShel was evaluated by fitting the
Gaussian function to the emission lines of the ThAr spectrum. This procedure
is implemented as a standard step of processing in PyYAP.

Inspection of the ThAr spectra showed that the focus of the imaging camera
remained stable during all observational nights. Within the spectrograph’s
working wavelength range, the resolving power $R=\lambda/\Delta\lambda$ varied
from $10,000$ to $12,500$, with the median $R=11,700$ evaluated from 355 lines
in a single image. The resolving power does not variate significantly between
nights: the full width at half maximum (FHWM) of the mean ThAr line equals 3.7
pixels, close to the optimal sampling.

##  4 Scientific Application

A medium-resolution fibre-fed spectrograph, in combination with a 1-meter
class telescope, can be a powerful instrument for the spectroscopy of
relatively bright sources. Literature has many examples of using eShel in
stellar physics and the physics of the Solar system objects. Due to its
compact design and high positional stability, this spectrograph appears even
in the observations of the extrasolar planets. The thing is that the accuracy
of the radial velocity measurements reported in Kovács et al. (2014), Pribulla
et al. (2015), and Engel et al. (2017) was better than 100 m s-1 for the stars
brighter than 11 magnitudes and exposure time under one hour. Such
characteristics enable the detection and observation of hot Jupiters around
the brightest stars. Kovács et al. (2014) also gave the example of how to use
eShel for observation of pulsating stars (cepheids).

The proposed upgrade opens new perspectives for the family of small telescopes
in NARIT, as we have several spectrographs which, after the improvement, can
be installed at any of our telescopes. In this way, it becomes possible to
move part of scientific proposals aimed at studying exoplanets, active solar-
like stars, binary and multiple stars from the main 2.4-m Thai National
Telescope to smaller instruments without losing the efficiency and observing
time. However, the main stimulus which led us to this technical work was the
capability of using this device for asteroseismology of the brightest fast-
rotating pulsating stars.

To demonstrate the efficiency of eShel in asteroseismological observations, in
Fig. 3, we show an example of non-radial pulsations discovered in a
4-magnitude fast-rotating star. A typical pattern of waves propagating across
the averaged spectral profile is in the left panel of 3. The right panel shows
the 2D periodogram used for the identification of frequencies of pulsation. In
this example, the star has been observed continuously with short exposures for
more than five hours with the original version of eShel and the 1-m telescope
of NARIT. The upgraded version of the spectrograph will allow us to increase
the signal-to-noise ratio (SNR) of observational data and, thus, expand the
number of potential targets or increase the temporal resolution of data with
shorter exposure time preserving the same level of SNR.

Figure 3: Dynamic spectrum and a 2D periodogram used for the discovery of non-
radial pulsation in a bright fast-rotating A-type star.

#### ORCID identifiers of the authors

0000-0002-1912-1342 — Eugene Semenko
0000-0001-5094-3910 — David Mkrtichian

#### Author contributions

SR, ES, and DM are responsible for formulating the project, its technical
implementation, and carrying out the observations. ES and DM are responsible
for data reduction and analysis. SP contributed to the project administration.
All authors equally contributed to the text of the article.

#### Conflicts of interest

The authors declare no conflict of interest.

## References

  * Engel et al. (2017) Engel, M., Shahaf, S. and Mazeh, T. (2017) The eShel Spectrograph: A Radial-velocity Tool at the Wise Observatory.  Publications of the ASP, 129(976), 065002.  https://doi.org/10.1088/1538-3873/aa65c6.
  * Kovács et al. (2014) Kovács, J., Csák, B., Cseh, B., Szabados, L., Szabó, G. M., Dózsa, Á., Kiss, L. L. and Jankovics, I. (2014) Medium-resolution echelle spectroscopy of pulsating variables and exoplanet host stars with sub-meter telescopes.  Contributions of the Astronomical Observatory Skalnate Pleso, 43(3), 451–453.  https://doi.org/10.48550/arXiv.1401.6818.
  * Pribulla et al. (2015) Pribulla, T., Garai, Z., Hambálek, L., Kollár, V., Komžík, R., Kundra, E., Nedoroščík, J., Sekeráš, M. and Vaňko, M. (2015) Affordable échelle spectroscopy with a 60 cm telescope.  Astronomische Nachrichten, 336(7), 682.  https://doi.org/10.1002/asna.201512202.
  * Thizy and Cochard (2011) Thizy, O. and Cochard, F. (2011) Spectrographs for small telescopes.  In Active OB Stars: Structure, Evolution, Mass Loss, and Critical Limits, edited by Neiner, C., Wade, G., Meynet, G. and Peters, G., vol. 272, pp. 282–283.  https://doi.org/10.1017/S174392131101057X.


# Optical turbulence profiling at the Table Mountain Facility with the Laser
Communication Relay Demonstration GEO downlink

Marcus Birch  1,2,* Sabino Piazzolla  2 Preston Hooser  2 Francis Bennet  1
Tony Travouillon  1 William Buehlman  2  1Advanced Instrumentation Technology
Centre, Research School of Astronomy and Astrophysics, Australian National
University, Canberra, ACT 2611, Australia
2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA,
USA 91109<EMAIL_ADDRESS>
††journal: opticajournal††articletype: Research Article

We present the first time the profile of atmospheric optical turbulence has
been measured using the transmitted beam from a satellite laser communication
terminal. A Ring Image Next Generation Scintillation Sensor (RINGSS)
instrument for turbulence profiling, as described in Tokovinin (MNRAS, 502.1,
2021), was deployed at the NASA/Jet Propulsion Laboratory’s Table Mountain
Facility (TMF) in California [1]. The optical turbulence profile was measured
with the downlink optical beam from the Laser Communication Relay
Demonstration (LCRD) Geostationary satellite. LCRD conducts links with the
Optical Communication Telescope Laboratory ground station and the RINGSS
instrument was co-located at TMF to conduct measurements. Turbulence profiles
were measured at day and night and atmospheric coherence lengths were compared
with other turbulence monitors such as a solar scintillometer and Polaris
monitor. RINGSS sensitivity to boundary layer turbulence, a feature not
provided by many profilers, is also shown to agree well with a boundary layer
scintillometer at TMF. Diurnal evolution of optical turbulence and measured
profiles are presented. The robust correlation of RINGSS with other turbulence
monitors demonstrates the concept of free-space optical communications
turbulence profiling, which could be adopted as a way to support optical
ground stations in a future Geostationary feeder link network. These results
also provide further evidence that RINGSS, a relatively new instrument
concept, is effective even in strong daytime turbulence and with reasonable
ground layer sensitivity.

##  1 Introduction

Turbulence degrades free-space optical communication (FSOC) links,
particularly for high data rates and coherent links where technologies like
adaptive optics (AO) are often employed to compensate [2, 3]. Monitoring
atmospheric turbulence, particularly with the detailed measurements of a
turbulence profiler, can support the operation and design of AO systems or the
forecasting of turbulence conditions, both important capabilities for future
FSOC networks [4, 5]. Geostationary orbit (GEO) feeder links have been
proposed as way to implement global FSOC networks and numerous countries are
progressing this capability [6, 7, 8].

The Laser Communications Relay Demonstration (LCRD) is a payload that was
launched to GEO in 2021 onboard the STPSat-6 satellite to demonstrate a FSOC
relay, conducting simultaneous bi-directional links with the Optical
Communications Telescope Laboratory (OCTL) at Table Mountain Facility (TMF)
and another optical ground station at Haleakala, Hawaii [9].

We demonstrate the concept of FSOC turbulence profiling by using the downlink
signal from LCRD near $1550$ nm as opposed to celestial objects typically used
for turbulence monitors. The narrow linewidth from the satellite downlink
allows narrowband filtering for 24 hr measurements and high signal-to-noise
down to very shallow solar-separation angles while the stability of GEO allows
for long observation periods with minimal pointing and tracking. Furthermore,
FSOC turbulence profiling inherently observes through a slant path parallel to
the OGS conducting the link, which is beneficial when interpreting these
results for OGS operation.

We have deployed a Ring Image Next Generation Scintillation Sensor (RINGSS) at
TMF to conduct the turbulence profiling with the LCRD downlink beam. RINGSS
was first outlined in [1] as an evolution of the well-established MASS
profiler [10]. RINGSS is simple and low-cost in comparison with most previous
profiling instruments and its applicability to FSOC is highlighted in [11].
RINGSS can be implemented with a telescope as small as 5" using commercial
off-the-shelf components, unlike the more well-known MASS or SCIDAR [12].
RINGSS produces thin ring images when defocused which can be used to estimate
the vertical profile of turbulence if images are captured at high enough
speeds to resolve turbulent motion as azimuthal variation around the ring,
explained in subsection 2.1.

##  2 RINGSS at Table Mountain Facility

Figure 1: RINGSS instrument with sliding-roof enclosure at Table Mountain
Facility, California. Inset map shows proximity to Optical Communications
Telescope Laboratory (OCTL).

The RINGSS instrument implemented for this experiment uses a 25 cm Schmidt-
Cassegrain telescope and a 320x256 InGaAs array with reimaging optics to
induce the required image specifications. The system produces a ring image at
the InGaAs array obtained by using a high secondary obstruction (50% by
diameter) which is achieved with a 3D printed aperture mask.

A narrow linewidth filter at $1550$ nm is placed in the lens barrel before the
reimaging optics, ensuring high signal strength at all times of day and even
with shallow solar separation. The bright downlink beam from LCRD allows 200
µs exposure times, though the frame rate is limited to 700 Hz. This very short
exposure time reduces the blurring of turbulent motion to improve accuracy,
particularly in the presence strong turbulence. We house the instrument in a
sliding-roof enclosure at TMF close to OCTL, shown in Figure 1. This proximity
ensures both systems are observing through a similar atmospheric channel. As
LCRD is in a equatorial geostationary orbit, both RINGSS and OCTL statically
point at approximately 50∘ in elevation during links with minimal tracking and
pointing required. However, the optics of this system induces strong coma that
requires tight centering within $\pm 10$ arcseconds of the optical axis.

Although the LCRD downlink is bright enough to easily observe the ring with a
smaller aperture, constraints of sizing the ring image with small format and
large pixel size (12.5 µm) InGaAs arrays makes a 25cm telescope worthwhile.
The RINGSS reimaging optics resize the pixel scale to achieve an optimal
conjugation height as described in [1]. The optics are also designed to
achieve the $1:10$ ratio of spherical aberration to defocus necessary for a
conic wavefront, i.e. producing a close to “diffraction-limited” ring width of
2 pixels (Figure 2). Ring width ($R_{\text{width}}$) and radius
($R_{\text{radius}}$) are critical parameters for the instrument, the latter
is kept to $10\pm 1$ pixels while $R_{\text{width}}$ is generally maintained
as $<3$ pixels.

Figure 2 shows an idealised ring image from our specifications compared with a
sample of data from LCRD. In stronger turbulence conditions $R_{\text{width}}$
increases from the desired width, partially due to the blurring of radial
motion. Image quality parameters, e.g. $R_{\text{width}}$,
$R_{\text{radius}}$, and coma, are used in the software as inputs for auto-
focusing, tracking, or rejecting erroneous data.

Figure 2: Comparison between the theoretical and measured ring image produced
from the defocused LCRD signal using RINGSS instrument. Measured data here is
in pixel units and only a small time-averaged sample.

###  2.1 RINGSS background

RINGSS captures defocused ring images of the LCRD downlink at high speed
($700$ Hz), measuring scintillation as azimuthal variations of intensity
around the ring over time. Scintillation around the ring image is decomposed
into angular frequencies which when combined with theoretical relations for
how different frequencies propagate, allows for the optical turbulence profile
to be estimated. The frequency spectrum of scintillation relates to the
perturbed wavefront having travelled through the atmospheric column because a
defocused image approximates the pupil. A brief explanation of the operational
principle is provided below but see [1] for a comprehensive explanation. The
angular power spectrum (APS), as measured from scintillation around the ring,
is retrieved with annular masks corresponding to discrete angular frequencies.
For a given angular frequency, $m$, masks applied to the high speed series of
images produce a term, $\langle|a_{m}|^{2}\rangle$, to recover the power of
that frequency [1]. The value $\langle|a_{m}|^{2}\rangle$ can be thought of as
the azimuthal temporal variance through a frequency filter, hence the set of
$\langle|a_{m}|^{2}\rangle$ over a range of $m$ represents the APS. The APS is
measured in real-time every few seconds from sets of 2000 images.

With the APS measured, RINGSS then relies on a principle similar to MASS and
other scintillation-based turbulence profilers, weighting functions can be
formulated to describe how spatial frequencies propagate and instrument
response to those optical aberrations. Optical turbulence at any altitude is
assumed to have a Kolmogorov spectrum with a strength given by the coefficient
of the refractive index structure function, $C_{n}^{2}$, in units $m^{-2/3}$.
The general principle for weighting functions is that higher frequencies
dissipate faster than lower frequencies, such that the shape of the APS can
indicate the height of turbulence [10, 13, 14, 15, 1]. The process of
computing weighting functions is best explained by Tokovinin in [1], however
an important consideration here is that the LCRD downlink is monochromatic,
simplifying the process by ignoring polychromatic corrections implemented for
prior instruments [16, 14]. Weighting functions are also dependent on
conjugation height, itself a function of defocus or the ring radius, e.g.
$R_{\text{radius}}=10\pm 1$ pixels corresponds to conjugation heights of
$\approx 780\pm 100$, so drifts in defocus can lead to substantial error
particularly for turbulence near the surface. We minimise this by building a
look-up table of $W_{m}(z)$ for different conjugation heights, which is
matched to $R_{\text{radius}}$ measured in real-time. Figure 3 shows a number
of weighting functions for $m=2,4$ and $8$ at the nominal defocus
($R_{\text{radius}}=10$ pixels) with inset masks to highlight the amplitude
and phase components of filters propagated in the process of computing
$W_{m}(z)$.

We use these weighting functions known a priori and the APS measured in real-
time, to then consider the atmospheric turbulence profile as $N$ discrete
columns of turbulence with strength
$J_{i}=\int_{z_{i}}^{z_{i+1}}C_{n}^{2}(h)dh$ that can be solved as a linear
system. A set of altitudes $\\{z_{0},...,z_{i},...,z_{N-1}\\}$ with $N=8$ from
0 to 16 km is used in keeping with the vertical resolution of the instrument
put forth in [1] optimised for instrument response. Equation 1 shows the
linear system which is solved using non-negative least squares to recover the
vector of $J_{i}\forall z_{i}$, i.e. the optical turbulence profile. This
discrete layered approach is also used in practice for numerical propagation
methods for simulating links through the atmosphere [17, 18]. For a given $m$,
Equation 1 can be written as Equation 2 with rows of the two-dimensional
$W_{m}(z_{i})$ matrix becoming functions as shown in Figure 3. The maximum
angular frequency, $M$, is constrained by the Nyquist sampling criteria of two
pixel resolution in azimuth, which is $\approx 30$ for $R_{\text{radius}}=10$
pixels, though we set $M=20$ due to noise near this upper limit [1].

$\begin{bmatrix}\langle|a_{0}|^{2}\rangle\\\ \langle|a_{1}|^{2}\rangle\\\
\vdots\\\ \langle|a_{m}|^{2}\rangle\\\ \vdots\\\
\langle|a_{M}|^{2}\rangle\end{bmatrix}=\begin{bmatrix}W_{0}(z_{0})&W_{0}(z_{1})&\cdots&W_{0}(z_{i})&\cdots&W_{0}(z_{N-1})\\\
W_{1}(z_{0})&W_{1}(z_{1})&\cdots&W_{1}(z_{i})&\cdots&W_{1}(z_{N-1})\\\
\vdots&\vdots&\ddots&\vdots&\ddots&\vdots\\\
W_{m}(z_{0})&W_{m}(z_{1})&\cdots&W_{m}(z_{i})&\cdots&W_{m}(z_{N-1})\\\
\vdots&\vdots&\ddots&\vdots&\ddots&\vdots\\\
W_{M}(z_{0})&W_{M}(z_{1})&\cdots&W_{M}(z_{i})&\cdots&W_{M}(z_{N-1})\end{bmatrix}\begin{bmatrix}J_{z_{0}}\\\
J_{z_{1}}\\\ \vdots\\\ J_{z_{i}}\\\ \vdots\\\ J_{z_{N-1}}\end{bmatrix}$ (1)

Figure 3: Weighting functions, $W_{m}(z)$ from $0$ to $16$ km for $m=2,4,8$
with displays of the phase ($F_{\varphi}$) and amplitude ($F_{\chi}$)
frequency filters that are used for building the instrument response function
and computing weighting functions. The y-axis is representative of a
contribution normalised over all frequencies, e.g. increasing values of $m=2$
with distance

$\langle|a_{m}|^{2}\rangle=\sum_{i=0}^{N-1}J_{i}W_{m}(z_{i})$ (2)

Once we derive the set of $J_{i}$, we compute a number of integrated
parameters from the turbulence profile. The atmospheric coherence length or
Fried parameter ($r_{0}$) describes the general turbulence conditions and is
used for comparison with other turbulence monitors. The method of computing
$r_{0}$ from $J_{i}$ is given in Equation 3 and referred to as
$r_{0,\text{scint}}$ to differentiate from the separate method of estimating
$r_{0}$ described in subsection 2.2. The value
$\cos{\left(\zeta\right)}\sum_{i=0}^{N-1}J_{i}$ in Equation 3 represents the
airmass-corrected integral of the turbulence profile with zenith angle,
$\zeta$, which is simply the site latitude when observing an equatorial orbit.
The $\cos{(\zeta)}$ term takes the turbulence measured through the slant path
and scales it to represent turbulence at zenith. All $r_{0}$ values throughout
this paper are reported for $\lambda=500$ nm and airmass-corrected to zenith
in keeping with the convention for generalising turbulence conditions. Other
parameters such as the atmospheric coherence time and isoplanatic angle can
also be recovered from the turbulence profile and used for additional purposes
such as informing system design, e.g. AO speed requirements or point-ahead
compensation as discussed in section 6.

$r_{0,\text{scint}}=\left(16.7\lambda^{-2}\cos{\left(\zeta\right)}\sum_{i=0}^{N-1}J_{i}\right)^{-3/5}$
(3)

###  2.2 Radial motion turbulence measurement

Radial motion around the ring can be used to measure the integrated turbulence
strength in a manner similar to a Differential Image Motion Monitor (DIMM), in
addition to the primary method discussed previously [19]. This technique
involves splitting the ring into eight radial sectors of equal azimuth and
observing the variance of the ring radii from sets of opposing sectors, i.e. 4
directions of motion. Radial motion is differential in the sense it is
relative to the ring’s center, making it independent of wind shake and other
phenomena but sensitive to ring width calibration to prevent motion blurring.
Variance of these four opposing sector sets is analogous to the two
perpendicular directions used for measuring differential motion in a DIMM.
Masks corresponding to each sector are used to compute the temporal variance,
$\sigma_{2r}^{2}$, similar to how the APS is computed from azimuthal motion.
The four sets of opposite sectors are averaged to estimate $\sigma_{2r}^{2}$.
A normalisation constant for sector weights, $C_{r}$, is then used as in
Equation 4 to compute $r_{0,\text{sector}}$, where $D$ is the telescope
diameter. See [1] for further information on $\sigma_{2r}^{2}$ and $C_{r}$,
where the latter is similar to the normalised weighting coefficient used for
DIMMs. $r_{0,\text{sector}}$ is reported for $\lambda=500$ nm and air-mass
corrected to zenith in the same way as $r_{0,\text{scint}}$, although
$\sigma_{2r}^{2}$ and $C_{r}$ are computed with the $1550$ nm wavelength of
operation.

$r_{0,\text{sector}}=0.98\lambda^{4/5}\left(\frac{\sigma_{2r}^{2}}{4C_{r}}\right)^{3/5}D^{1/5}$
(4)

##  3 Calibration

A preliminary dataset with RINGSS at TMF of approximately 5 days is used in
this paper over a number of LCRD links that were conducted sporadically at
daytime and nighttime. In this section we explain how a number of parameters
such as $R_{\text{width}}$, $R_{\text{radius}}$, and coma can be used to
assess data reliability or tune operation. While inputs for focus and pointing
control loops are important, maintaining data integrity throughout the
processing pipeline is also critical as sudden drops in quality can be common,
e.g. from very high winds near the telescope.

Once data cubes are captured with RINGSS and the APS is measured, images
outside the specification of $9<R_{\text{radius}}<11$ and
$R_{\text{width}}<3.5$, are flagged as low quality and ignored when computing
profiles for real-time display of the turbulent conditions (but are saved
nonetheless for analysis of instrument performance such as presented here).
Once profiles are computed we can estimate both $r_{0,\text{scint}}$ and
$r_{0,\text{sector}}$, and use the ratio
$r_{0,\text{scint}}/r_{0,\text{sector}}$ for a prima facie indication of
accuracy. The radial motion method, $r_{0,\text{sector}}$, is partially
independent from the measured optical turbulence profile used for estimating
$r_{0,\text{scint}}$. This comparison is similar to the benefit offered from
the common implementation of a combined MASS-DIMM instrument [13]. This ratio
and the norm of the residuals from solving Equation 2, $\sigma_{NNLS}$, can
then be used to indicate low quality data. We also compute profiles from
approximately 2 minute rolling averages of the APS, which helps to constrain
the solution and ensure all layers return a non-zero estimate of $J_{i}$ [14].

Figure 4: Corner plot displaying the correlation between a number of important
parameters for data and image quality, measured from preliminary observations
at TMF. Diagonal entries show the histogram of values corresponding to each
columns parameter. Dashed red line is the line of best fit from a linear
regression between parameters and the $R$ values are the Pearson correlation
coefficients between parameters. $r_{0}$ is in centimetres, scaled to $500$
nm, as is done throughout this study.

Detecting low-quality data can be difficult if image quality typically
degrades in strong turbulence, requiring careful calibration for any relations
that might exist. We produce a corner plot, Figure 4, to show correlations
between parameters of interest. Figure 4 shows that
$r_{0,\text{scint}}/r_{0,\text{sector}}$ is largely independent of turbulence
strength but a loose correlation exists for other parameters with increasing
turbulence (decreasing $r_{0}$). $\sigma_{NNLS}$ is correlated with image
specification parameters in Figure 4, and outliers of $\sigma_{NNLS}$ from the
weak relation with $r_{0}$ were often found to correspond with poor image
quality, e.g. weak signal from thin cloud or wind shake causing the spot to
temporarily leave the region-of-interest. We aim to find more robust
correlations between all parameters shown in Figure 4 to optimise performance
and maintain data integrity.

###  3.1 Dual $r_{0}$ comparison

Figure 5: Comparison of alternate Fried parameter, $r_{0}$, measurement
techniques with preliminary RINGSS measurements at TMF. Scintillation $r_{0}$
is the integral of turbulence profile. Sector $r_{0}$ derives from the radial
motion method of $r_{0}$ estimation. Linear regression fit is shown in solid
red line and compared with a slope ($\alpha$) of $1$ in dashed green. Pearson
correlation coefficient, $R$, between measures is shown as $0.95$. Systematic
offset, $\beta$, from linear regression is in units of metres.

Figure 5 highlights the relation between $r_{0,\text{scint}}$ and
$r_{0,\text{sector}}$ over a range of turbulence strengths with measurements
conducted in daytime and nighttime at TMF. Although Figure 5 displays a robust
relation between these measurement techniques, there is a significant trend of
$r_{0,\text{sector}}$ overestimating turbulence with respect to
$r_{0,\text{scint}}$. $r_{0,\text{sector}}$ is typically expected to be larger
than $r_{0,\text{scint}}$, as described in [1], and the opposite result here
could be caused by numerous issues such as strong upper layer turbulence,
astigmatism, or error in the expected pixel scale. Pixel scale for this system
cannot be easily measured due to the narrow linewidth filter blocking all
stars, i.e. plate-solving or binaries cannot be observed to measure pixel
scale. If the system is not at the ideal focal length, this could also cause
the larger than expected ring widths we observe. Further observations are
required to constrain these relations and propose explanations. No correlation
was observed between upper atmosphere $C_{n}^{2}$ and this ratio over the
preliminary dataset, so we choose not to reproduce that plot here. Another
possible cause of this is how each method differs in response to deviations
from the weak-scintillation regime, so more data in weaker turbulence could be
used to assess this theory [1, 14]. Nonetheless we consider the strong
correlation between $r_{0}$ methods a good first indicator the instrument is
producing reliable results.

##  4 Accuracy analysis

We compare against three turbulence monitors at TMF to further assess RINGSS.
Comparing turbulence monitors is often difficult due to different measurement
techniques, positions on the mountain, and from the stochastic nature of
turbulence, nonetheless this remains the best tool available [20]. TMF hosts a
solar scintillometer, Polaris monitor, and boundary-layer scintillometer, the
latter being covered separately in section 5 [21, 22]. The solar
scintillometer was previously calibrated against a solar DIMM and is mounted
alongside the Polaris monitor on the roof of OCTL, approximately 50 m from
RINGSS (see Figure 1) [22]. All instruments, including RINGSS, are airmass-
corrected to represent values at zenith for appropriate comparison.

A nearly continuous observing block from the 24th of May 2023 is plotted in
Figure 6 to highlight the comparison with the solar scintillometer and Polaris
monitor, in addition to showing the diurnal evolution of turbulence. Residuals
are computed by time-averaging all methods into two-minute bins. Gaps of
RINGSS data in Figure 6 are due to technical issues and pauses in LCRD
operations. There is also a break between when the solar scintillometer
operates and the Polaris monitor is able to begin measurements. Figure 6 shows
that two different $r_{0}$ estimates from RINGSS agree with two separate
instruments over the presented time range, and that the technique is reliable
in strong daytime turbulence. Provided the scintillation spectrum saturates in
strong turbulence, presenting a major challenge for profilers which rely on
weak-scintillation assumptions, the performance we see in daytime conditions
is encouraging. Turbulence is significantly weaker at $1550$ nm than typical
observations in the visible, which is undoubtedly a major factor for RINGSS
measurements remaining reliable, in addition to the saturation-correction we
apply as described in [1] and developed in [14].

Figure 6: Sample of Fried parameter RINGSS measurements from the
24${}^{\text{th}}$ of May 2023 demonstrating a strong correlation with two
separate instruments over daytime and nighttime. Gaps in data are caused by a
combination of technical issues and pauses in LCRD transmission. Lower inset
shows the residuals between the solar scintillation and the Polaris monitor to
RINGSS normalised against measured RINGSS $r_{0}$ values. The three phases of
twilight and nighttime are shown in shaded regions toward the right.

We then compare between all instruments over the entire dataset, time-
averaging to 10 minute bins for comparison as shown in Figure 7. Although any
degree of time-averaging is necessary for comparison, 10 minute bins are
chosen partly because these instruments are not in the same position on the
mountain, and not observing through the same channel, hence we don’t expect
short term agreement ($\lesssim 1$ minute). Further, we choose 10 minutes as
an intuitive yet arbitrary scale to characterise current conditions by given
the stochastic nature of turbulence. Figure 7 shows the Pearson correlation
coefficients ($R$) and linear regression fits between RINGSS, the Polaris
monitor, and solar scintillometer over this preliminary dataset. We observe
reasonable correlation coefficients, i.e $R>0.7$ for all cases, promising in
the context of turbulence monitors, but large systematic offsets ($\beta$) and
slopes all significantly less than $1$. Nighttime RINGSS observations tends to
agree more with the Polaris monitor than daytime RINGSS with the solar
scintillometer. This could be either due to RINGSS being more accurate in
weaker turbulence, e.g. due to insensitivity or increased error towards a
strong boundary layer, or that the Polaris monitor is more accurate than the
solar scintillometer. In all cases we observe RINGSS estimating stronger
turbulence than alternate instruments, though more data is required to assess
whether this is systematic. Long term operation of RINGSS at TMF is required
to see if these early promising correlations improve and hold over a broader
range of conditions. Inherently different measurement techniques, instrument
error, and different positions on TMF are all reasons to not expect a robust
agreement between instruments in the long-term that might be expected of other
meteorological parameters.

Figure 7: Correlation plots between both the RINGSS $r_{0,\text{scint}}$ and
$r_{0,\text{sector}}$ with the Polaris monitor and solar scintillometer.
Linear regression fits shown in solid black line. Annotated $R$ values
represent the Pearson correlation coefficient. $\alpha$ is the fitted slope
and $\beta$ (shown in units of cm) are the systematic offsets from the fit,
i.e. the intercept.

##  5 Boundary layer measurements

Turbulence will typically be worst in the daytime, where a convective boundary
layer can form and dominate turbulence, so sensitivity to this layer is
critical [23]. We are therefore interested in determining the accuracy of
RINGSS near the surface in daytime, i.e. limiting turbulence conditions in
daytime operation. To assess RINGSS accuracy in this regime we compare with a
boundary layer scintillometer (BLS) which is installed at OCTL to sample
$C_{n}^{2}$ at high frequency in a horizontal channel at all times of day
[21]. The BLS measures turbulence over a valley to a nearby mountain from TMF
in the same direction that RINGSS observes LCRD, though its location at OCTL
is raised off the ground unlike RINGSS. We compare BLS measurements with
RINGSS turbulence boundary layer estimates by dividing the lowest $J_{i}$
integral by layer height, i.e. from $0$ m to $250$ m, to estimate $C_{n}^{2}$.
This method assumes a uniform distribution of $C_{n}^{2}$ through the layer
but given RINGSS is observing over a steep valley and at a slant path we
cannot justify a more sophisticated solution.

Figure 8 shows the distribution of $C_{n}^{2}$ from the BLS compared with the
ground layer $C_{n}^{2}$ estimate from RINGSS. We observe agreement within
expectations for differing instruments measuring $C_{n}^{2}$, though with
heteroscedasticity towards small $C_{n}^{2}$ likely due to a lack of data and
different paths through the boundary layer. Nonetheless, Figure 8 demonstrates
that RINGSS is capable of approximately estimating the boundary layer
turbulence even in daytime. However, it should be noted that this preliminary
dataset represents fairly weak boundary layer turbulence, even at daytime,
likely due to the steep valley, altitude of TMF, and cool weather.
Significantly more data is required over a substantial dynamic range to
established a robust correlation with RINGSS and the BLS, particularly for
$C_{n}^{2}>10^{-15}$. Correlation of boundary layer turbulence with wind-speed
and direction from meteorological instruments will also be considered in
future work.

Figure 8: Comparison of simultaneous measurements of boundary layer turbulence
from a boundary layer scintillometer and RINGSS at TMF during daytime and
nighttime. Pearson correlation coefficient, $R$, is displayed on lower right.
Linear regression is shown with green dashed line with slope, $\alpha$, and
intercept, $\beta$. RINGSS boundary layer estimate is the average $C_{n}^{2}$
from $0$ m to $250$ m obtained by dividing the first profile layer by layer
thickness.

##  6 Profile results

We show average turbulence profiles measured by RINGSS over the preliminary
dataset in Figure 9, split into daytime and nighttime. Turbulence profiles are
the series of $J_{i}$ integrals representing
$J_{i}=\int_{z_{i}}^{z_{i+1}}C_{n}^{2}(h)dh$ with units $m^{1/3}$. Figure 9
shows the characteristic dissipation of boundary layer turbulence at night
time, and a moderate increase in the free atmosphere. Note that we do not
sample the full range of daytime and nighttime due to the constraints of LCRD
operations, daytime is typically morning and nighttime typically early
evening. As RINGSS continues to operate and develop into an automated system
at TMF, we aim to build robust statistical estimates of the profile. Profiling
also provides the ideal input for any turbulence forecasting systems, to be
explored in future work, as it can be paired with meteorological forecasts of
wind speed and temperature profiles [4]. Although we have presented
comparisons of RINGSS against integrated turbulence monitors, a critical part
of future work will be to compare profiles such as in Figure 9 against other
daytime turbulence profilers, e.g. the 24hSHIMM [24].

Turbulence profiling also allows us to estimate a number of important
integrated parameters, particularly important for AO operation at OCTL during
LCRD links. Table 1 shows the average atmospheric coherence time ($\tau_{0}$),
Greenwood frequency ($f_{G}$) and isoplanatic angle ($\theta_{0}$) from all
measured profiles in the preliminary dataset, split into daytime and
nighttime. Estimating $\tau_{0}$ and $f_{G}$ requires knowledge of the wind
speed profile, though the turbulence-weighted wind velocity, $\bar{V}$, can be
substituted for some loss of accuracy [25]. Equation 5 shows how $\tau_{0}$
and $f_{G}$ are computed for $\bar{V}$ if wind speed profiling, e.g. measured
by a Stereo-SCIDAR, is not available [26].

$\tau_{0}=0.314\frac{r_{0,\text{scint}}}{\bar{V}}\>\>\>\>\>f_{G}=0.43\frac{\bar{V}}{r_{0,\text{scint}}}$
(5)

Figure 9: Turbulence profiles measured by RINGSS at the Table Mountain
Facility, California. Day and night time profiles are split to highlight the
diurnal evolution of turbulence, particularly in the boundary layer. $J_{i}$
values refer to discrete layers of turbulence representing integrals of
$C_{n}^{2}dh$.

To estimate $\bar{V}$ with RINGSS we instead use the atmospheric second moment
of the wind, $V_{2}$, described by Kornilov in [27] with implementation for
RINGSS described in [1]. $V_{2}$ is principally measured with RINGSS from the
defocus velocity, a concept with origins in the FADE instrument, and has been
shown to follow $V_{5/3}$ closely, which defines $\tau_{0}$ [15]. We do not
reproduce this methodology here, as it is involved and best explained by
Kornilov [25, 15, 27]. Measuring $V_{2}$ and the defocus velocity is sensitive
to blurring so the short exposure time, $200$ µs, afforded by the strong LCRD
downlink is significant in improving accuracy here.

Table 1: Integrated parameters from RINGSS turbulence profile measurements at TMF. Data from short preliminary dataset is split into daytime and nighttime LCRD links. Uncertainties are the standard deviation from all parameter calculations over the dataset |  $r_{0,\text{scint}}$ [cm] |  $r_{0,\text{sector}}$ [cm] |  $f_{G}$ [Hz] |  $\theta_{0}$ [arcsec] |  $\tau_{0}$ [ms]
---|---|---|---|---|---
Night | $7.2\pm 1.8$ | $6.0\pm 1.6$ | $55\pm 19$ |  $1.7\pm 0.5$" | $2.7\pm 0.8$
Day | $5.0\pm 1.4$ | $4.3\pm 1.2$ | $68\pm 33$ | $2.1\pm 0.4$ | $2.2\pm 0.4$

In Table 1 we see almost all parameters degrade in daytime compared with
nighttime, however $\theta_{0}$ worsens slightly at nighttime due to the
increased turbulence above 2 km visible in Figure 9. This highlights one of
the benefits of profiling over integrated turbulence measurements, i.e.
$\theta_{0}$ is an important parameter to consider for uplink pre-compensation
with AO which is driven by high altitude turbulence [28].

##  7 Conclusion

We have successfully demonstrated the deployment of a RINGSS turbulence
profiler, an instrument initially demonstrated in 2021, and conducted the
first turbulence profiling with a laser communications satellite using the
LCRD GEO optical downlink signal [1]. This is also the first time that a
RINGSS instrument has been used in daytime and strong turbulence conditions,
highlighting the measurement technique is robust over a broad range of
conditions. Preliminary results have been compared with a suite of other
turbulence monitors at TMF, showing the reasonable correlations despite the
small dataset and difficulties of finding agreement among turbulence
instruments. Efforts are also ongoing to automate this instrument with closed-
loop tracking, auto-focusing, and an observatory control system. While we
currently lack the data to make broad and robust statements on the instrument
performance and site characteristics we have demonstrated the unique concept
of FSOC turbulence profiling which could improve the performance of GEO feeder
networks. Future operations of RINGSS at TMF alongside LCRD operations will
aim to constrain the correlations we have presented here and develop this
instrument into a capability for improving reliability with short-term
turbulence prediction and inform the AO control system on OCTL.

Funding Funding for MB to undertake this research was provided by the
Australian Commonwealth Scientific and Industrial Research Organisation
(CSIRO) under the postgraduate supplemental scholarship scheme. MB is also
supported by the Australian Research Training Program.

Acknowledgments The research was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration.
The authors would like to thank the LCRD and OCTL operational teams. We also
thank Andrei Tokovinin at the National Optical-Infrared Astronomy Research
Laboratory for providing advice and input toward implementing the RINGSS
instrument.

Disclosures The authors declare no conflicts of interest.

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