Adaptive Optics for Extremely Large Telescopes III
ANALYSIS OF “FRATRICIDE EFFECT’ OBSERVED WITH
GEMS AND ITS RELEVANCE FOR LARGE APERTURE
ASTRONOMICAL TELESCOPES
a
Angel Otárola1, , Benoit Neichel2, Lianqi Wang1, Corinne Boyer1, Brent Ellerbroek1, and François
Rigaut3
1
Thirty Meter Telescope Project, 1111 South Arroyo Parkway, Pasadena, California, USA
GEMINI Observatory, c/o AURA, Casilla 603, La Serena, Chile
3
Australian National University, Cotter road, Weston Creek, ACT 2611, Australia
2
Abstract. Large aperture ground-based telescopes require Adaptive Optics (AO) to correct for the distortions
induced by atmospheric turbulence and achieve diffraction limited imaging quality. These AO systems rely on
Natural and Laser Guide Stars (NGS and LGS) to provide the information required to measure the wavefront
from the astronomical sources under observation. In particular one such LGS method consists in creating an
artificial star by means of fluorescence of the sodium atoms at the altitude of the Earth's mesosphere. This is
achieved by propagating one or more lasers, at the wavelength of the Na D2a resonance, from the telescope up to
the mesosphere. Lasers can be launched from either behind the secondary mirror or from the perimeter of the
main aperture, the so-called central and side-launch systems, respectively. The central-launch system, while
helpful to reduce the LGS spot elongation, introduces the so-called “fratricide effect”. This consists of an increase
in the photon-noise in the AO Wave Front Sensors (WFS) sub-apertures, with photons that are the result of laser
photons back-scattering from atmospheric molecules (Rayleigh scattering) and atmospheric aerosols (dust and/or
cirrus clouds ice particles). This affects the performance of the algorithms intended to compute the LGS centroids
and subsequently compute and correct the turbulence-induced wavefront distortions. In the frame of the Thirty
Meter Telescope (TMT) project and using actual LGS WFS data obtained with the Gemini Multi-Conjugate
Adaptive Optics System (Gemini MCAO a.k.a. GeMS), we show results from an analysis of the temporal
variability of the observed fratricide effect, as well as comparison of the absolute magnitude of fratricide photon
flux level with simulations using models that account for molecular (Rayleigh) scattering and photons
backscattered from cirrus clouds.
1. Introduction
The so-called “fratricide effect” in the Laser Guide Star (LGS)/Adaptive Optics (AO) field, is when
photons from laser light propagating through the atmosphere are backscattered by air molecules, dust
particles, and cirrus cloud’s ice crystals and subsequently detected by a wavefront sensor (WFS) CCD
detector used to monitor a particular LGS in a artificial asterism. The term “fratricide” applies because
the photons detected in a particular WFS detector originate in the laser light used to create the other
LGSs in the asterism.
The backscattered photons contribute to increase the noise level in the WFS’s sub-apertures, making
difficult to compute the centroid of the corresponding LGS spots. Sometimes, the flux of back-scattered
a
e-mail : [email protected]
Adaptive Optics for Extremely Large Telescopes III
photons is significantly larger than the photon flux from the LGS spot, in which case –without proper
calibration procedures– render those sub-apertures unavailable for the determination of the wavefront
aberrations induced by fluctuations in the index of refraction along the path of the light through the
atmosphere. The consequence of missing sub-apertures affected by “fratricide effect”, typically in a
symmetric geometric pattern (see Fig. 1), is that of not being able to calibrate high-order phase
aberrations that share significant information in that pattern symmetry [1]. Additional figures that
illustrate well the “fratricide effect” patterns in LGS asterism and its impact is found in [2, 3].
The goal of this study is to compute the magnitude of the time variability of the Rayleigh
backscattering photon flux, along the “fratricide effect” pattern from wavefront sensor data stored in
circular buffers (CB) obtained during the first year of operation of the Gemini South Multi-Conjugate
Adaptive Optics System (Gemini MCAO a.k.a. GeMS). A good description of GeMS and its subsystems is found in [4].
The data available for this study, listed in Table 1, consists of 18 GeMS WFS data-cubes that were
obtained in the course of 2011. In each of these cases the lasers are propagated along the local zenith
direction. The data-cubes include the photon fluxes detected in a 32x32 pixels WFS detector array, as a
function of time, and for each of the 5 WFS in GeMS. The angular diameter of the 5 LGS spots
asterism created by GeMS in these runs is 60 arcsecs.
An example of the Rayleigh back-scattering pattern due to “fratricide effect”, including the photon flux
counts in two quad-cellsb, one affected by fratricide and another not-affected by fratricide effect, is
illustrated in Figure 1. This fratricide pattern corresponds to that detected in the wavefront sensor zero
(WFS0) of GeMS and is the pattern selected in this work for the analysis of time variability of the
“fratricide effect” photon flux.
As emphasized in Figure 1, the photon counts in a quad-cell affected by Rayleigh backscattering is
significantly larger than in those quad-cells only detecting the light from the corresponding LGS spot.
In this example the quad-cell that has detected back-scattered photons product of fratricide effect has
detected about 4 times more photons than the quad-cell detecting photons only from its corresponding
LGS. The problem is evident, without proper way to calibrate out the Rayleigh backscattering
emission, it would be impossible to estimate the centroid of the LGS spot imprinted in the
corresponding quad-cell, and subsequently not possible to compute the wavefront slopes around that
region of the WFS detector.
This work only intends to characterize the statistics of the temporal fluctuations of the photon fluxes
product of Rayleigh backscattering, and not the possible ways to calibrate out this unwanted effect.
Fig. 1 Example of an instantiation of the photon flux map in a 32x32 pixels frame (5ms integration time in this
case) detected in the GeMS’s WFS0’s detector. Two Quad-Cells are highlighted to show the calibrated photon
counts (photons/pixel/frame) in each of the 4 pixels of a corresponding Quad-Cell, one of which is affected by
b
A Quad-cell is composed of a 2x2 detector pixels array, and corresponds to a GeMS wavefront sensor subaperture. Each sub-aperture corresponds to a dimension of 50x50 cm on the Gemini telescope main aperture [4].
Adaptive Optics for Extremely Large Telescopes III
Raleigh backscattering due to fratricide effect, while the other fall in the fair region of the WFS detector. In the
case illustrated here the laser power is of 26.3W (5.26W used for each of the 5 LGS spots).
2. Statistics of the time variability of the photon flux due to “fratricide
effect” registered in the GeMS WFS0 detector
The data available for this study was supplied by the GeMS team and included 18 circular buffer (CB)
data files, those listed in Table 1. The information listed in Table 1, includes the name of the circular
buffer, the date and time of the observation, and importantly also includes the laser power during that
observation, as well as the frequency at which the Real Time Controller (RTC) was operating.
The sources of photon flux in the pixels of a WFS detector, can be represented by the sources shown in
Eq. 1.
Φ(t,P,CNa,τatm)= ΦLGS(t,P,CNa,τatm) + σe*N(0,1) + δi,j*{ΦRi,j(τ,P,τatm) + ΦAi,j(τ,P,τatm)+ ΦCi,j(τ,P,τatm)}
(1)
Where;
ΦLGS(t,P,CNa,τatm), is the total photon flux from a LGS, detected in pixel (i,j) of its corresponding WFS
detector, during an integration time (t). The magnitude of the flux depends on the laser power (P), the
sodium atoms column density in the mesosphere (CNa) and the total optical depth (τatm) of the
atmosphere at the wavelength of the laser light (in this case 589 nm). The sodium atoms column
density is a critical parameter for the LGS-AO system because relates directly to the magnitude of the
LGS and therefore the signal-to-noise ratio achieved at each of the WFS detector pixels in a given
integration time. This is why GeMS, depending on the Na atoms column density (that varies with
seasons and with time through an observation night), can adjust the RTC operation frequency between
100Hz and 800Hz [5], as possible to see in the last column of Table 1.
σe*N(0,1), this term is the detector’s photon-noise and for this case is represented to be of normal
distribution with zero mean value and photon-noise dispersion σe.
δi,j, is a delta function with value of 1 for those pixels affected by fratricide effect, and value of 0 for the
those pixels in the fair section of the WFS detector.
The fluxes within the curly bracket in Eq. 1 represent the contributions to the total backscattering flux
from atmospheric molecular Rayleigh backscattering ΦRi,j(τ,P,τatm), and Mie backscattering photons
with source in atmospheric aerosol particles, such as dust ΦAi,j(τ,P,τatm), and cirrus clouds ice crystals
ΦCi,j(τ,P,τatm). Each of these contributions has its own characteristic time scale.
Consequently, in order be able to study the fractional variability in the flux of the fratricide effect
pattern, it is necessary to isolate the photon flux due to backscattered photons, from the photons with
source in the LGS. Two methods were thought to accomplish the decoupling: one based on a time
domain analysis, and another one based on a spatial-domain approach. These methods are explained in
the following subsections including the results.
2.1. Method 1: WFS0 Frame-to-Frame time fractional-variability of the fratricide
effect
In this approach it is assumed that the LGS photon-flux in each pixel of the WFS detector changes
slowly. When looking at the magnitude of the fractional fratricide variability, we subtracted from each
instantaneous frame a running-average frame. Several time-scales for the running average where tried,
3s, 1s, 100ms and 50ms. The fractional time variability statistics, probability density function (PDF)
and cumulative function of the fratricide photon flux, computed for the WFS0 data, and for the total 18
CB analyzed in this study are shown in Fig. 2.
Three main conclusions can be obtained by inspection of the results shown in Fig. 2.
Adaptive Optics for Extremely Large Telescopes III
•
The first is the obvious one: the residuals, in the subtraction of a 3s average frame (and also the 1s
average frame), from an instantaneous WFS frame, show a probability density function with a clear
positive skewness. In other words there is a longer tail towards larger fractional residuals.
Obviously, as the average frame is computed more often, then there is a higher correlation between
the average frame being subtracted and a given subsequent instantaneous WFS frame reducing this
way the magnitude of the residuals. In this last case the probability density functions show a higher
kurtosis (narrower PDF) and shorter tail towards larger fractional residuals.
•
The second conclusion is that the residuals, after subtraction of an average updated every 3s
(1/3Hz), the worst case in this approach, are smaller than 15%.
•
And lastly, the third conclusion is that the PDF show a mean residual value, for the time
variability of fratricide photon flux, in the range of 5% to 7%.
The analysis of these results is included in the next section.
Fig. 2 Histogram of the fractional variability of photon flux with source in “fratricide effect” detected in the
GeMS WFS0 for all the CB files listed in Table 1. The fractional variability was obtained by subtracting a
running average WFS0-frame for time-scales of 3s, 1s, 100ms and 50ms (black, blue, green and red lines
respectively). The inset to the figure shows the cumulative function of the fractional variability.
2.2. Method 2: Fractional-variability of the backscattered photons, due to
fratricide effect, by subtraction of the LGS light detected in a neighbour quadcell
In this second method, the analysis was not done at detector pixel level, but rather the light was
integrated in each quad-cell. To learn the fractional variability in the flux of backscattered photons in a
given sub-aperture affected by fratricide, we assumed that the LGS integrated flux in that sub-aperture
is of the same magnitude that that detected in a WFS0 neighbor sub-aperture not affected by the
“fratricide effect”. In this way, the backscattered photons flux in those sub-apertures affected by the
“fratricide effect” was isolated by subtracting the LGS photon flux and detector noise measured in the
closest sub-aperture not affected by fratricide. The statistics of fractional variability was analyzed for
each sub-aperture in the WFS0 fratricide pattern individually and the results are shown in Fig. 3.
In this analysis care was taken to scale the photon flux in each CB files to a common nominal laser
power level. As possible to see in Table 1, the nominal laser power varies from observation-toobservation. Therefore, in order to get the fractional variability of backscattered photon flux in each of
the sub-apertures affected by “fratricide effect”, and using all CB files for the common statistics, the
Adaptive Optics for Extremely Large Telescopes III
fluxes were linearly scaled such as if the nominal laser power in each test was the same and equal to
40W.
The results in Fig 3 show that the fractional variability increases from the center sub-apertures to the
outside ones. The flux detected in the inner sub-apertures originates at relatively lower levels in the
atmosphere, while the flux detected in the outer sub-apertures comes from the higher levels. The
normalized backscattering photon fluxes profiles shown in Fig. 3 (right side) help illustrate the altitude
ranges (for a 1-arcmin angular diameter asterism) contributing to the fratricide pattern along the 4 LGSc
fratricide patterns detected in the WFS0 detector.
Fig. 3 (left) Mean fractional variability of the back-scattered photon flux, due to fratricide effect, in each of the
WFS0 sub-apertures in the fratricide pattern. The statistics in each sub-aperture were computed including the data
from all the CB files listed in Table 1. (right) fractional variability of photon flux due to backscattered photons
(along each of the arms in the WFS0 fratricide pattern) as a function of altitude. In this case the fluxes were
normalized to their values in the inner most sub-aperture. The red line shows an exponential decay with scale
height of 7 km along the fratricide profile.
In the results shown in Fig. 3, the most reliable numbers are those in the central section of each arm in
the “fratricide effect” pattern, this because the fratricide spatial-pattern for GeMS changes with time.
This happens because the fast tip/tilt mirrors (FSM) or Fast Steering Arrays (FSA) are not in a pupil
plane of the Laser Launch Telescope (LLT). Consequently, as reported in [4], the laser beam footprints
continuously changes on the LLT primary mirror, making also the “fratricide pattern” to change with
time.
3. Analysis of results
An important question is: What should be the order of fractional fluctuations to be expected in the
residuals of backscattered photons produce of “fratricide effect”? To answer this question we have to
recall what are the sources that contribute to the backscattering of photons in the LGS system. One
important contributing factor is molecular Rayleigh backscattered photons, and this is modeled by the
volume backscattering coefficient (β) [6, and references therein], which is proportional to the air
molecules number density (or equivalently the ratio of atmospheric pressure and temperature). Eq. 2, is
an accurate relation of β at any given altitude (h) and at a given wavelength (λ) of interest, as a
function of its value at the surface level (βs) and the temperature (T) and pressure (P) of the atmosphere
along the vertical profile of the atmosphere.
β(λ,h)= βs(λ,h=0)∗T(h=0)/P(h=0)*P(h)/T(h)
(2)
Taking partial derivative of Eq. 2, it can be show that the fractional variability of the air volume
backscattering coefficient is proportional to the fractional variability of atmospheric pressure and that
of atmospheric temperature (Eq. 3).
c
The upper-left fratricide pattern has source in the LGS-1, upper-right (LGS-2), bottom-right (LGS-3), bottomleft (LGS-4) in the asterism created by GeMS.
Adaptive Optics for Extremely Large Telescopes III
dβ/β=dP/P - dT/T ≈ -dT/T
(3)
Importantly, the fractional variability of atmospheric pressure can be neglected on the grounds that
pressure fluctuations in short intervals of time in the atmosphere are significantly small. Consequently,
without loss of generality it can be said that the magnitude of fractional fluctuations in the photon flux
due to Rayleigh backscattering is well represented by the magnitude of fractional fluctuations of air
temperature along the laser light propagation path. The fractional change of temperature in the
atmosphere in short timescales is well below 1% [7]. Therefore, the mean residual values of fratricide
photon flux, in the range of 5% to 7% –as shown by the results in Fig. 2 and Fig. 3– might be affected
by some other type of variability. To bring light into this question, the data contained in one of the CB
files (of 20-seconds length) was analyzed to look for the fractional flux fluctuation in the fratricide
affected pixels, as well as, in those pixels not affected by fratricide. The results are shown in Fig. 4.
Fig. 4 Mean photon-flux fractional variability in WFS0 after subtraction of a 3s running-average frame from the
next instantanous frame: (black dots) only for the pixels affected by fratricide effect, (red dots) for those pixels
not-affected by the WFS0 “fratricide effect” pattern. One example of the flux fractional variability in the nonfratricide-pattern pixels is shown in the right hand side section of the figure.
The results plotted in Fig. 4 show a degree of positive correlation between the time series of mean
photon flux fractional fluctuations of the fratricide affected pixels and the non-fratricide affected pixels
(the fair section of the WFS detector). The higher bias in the fluctuations in the fair pixels is due to the
relatively lower absolute flux in those cells, as shown in Fig. 1.
The common element between the fratricide affected pixels and those non-affected by fratricide (that
only contain the flux from the corresponding LGS) is in fact the laser light. Consequently, it is likely
that most of the photon flux variability possible to see in the fratricide affected pixels is due to laser
power variability at time scales of second(s). This point was discussed during one of the poster sessions
in the AO4ELT3 conference with C. D’Orgeville, whom confirmed that the current generation laser at
GeMS has been characterized to shows power fluctuations of order 6% [8].
4. Discussion and Conclusions
GeMS WFS data and telemetry data is most valuable for the community to study various important
phenomena, for characterization of the technical performance of AO technology (deformable mirrors,
LGS performance, turbulence related phenomena, etc.). Importantly because of its multi LGS asterism,
it is most helpful to study the magnitude and variability of the “fratricide effect”.
The analysis of the fractional variability in the WFS0 pattern using 18CB files available for this study
shows a mean fractional variability in the range 5% to 7% in frame-to-frame fluctuations at scales of
about 3s. The maximum fractional variability from the statistics is up to 15%. However, and as shown
in section 3, it is likely the variability of backscattered photons, due to fratricide, is convoluted with the
time fluctuations of the GeMS’s laser power.
Adaptive Optics for Extremely Large Telescopes III
Regarding possible ways that can be explored for calibration and removal of the fratricide effects are:
A) Regular detuning of the laser light from the optimum to interact with the sodium atoms in the
mesosphere, and registration of the photon flux due to Rayleigh/Mie backscattering only. The major
source of variability between laser detuned-calibrations would be the photons backscattered from cirrus
clouds, which have a faster fluctuation than molecular Rayleigh backscattering, and of other aerosols
sources. Unfortunately laser detuning, as a way of calibration, is not possible for GeMS due to the fact
its “fratricide” pattern is not fixed on the corresponding WFS detectors [4].
B) Determination of the Rayleigh backscattering photon flux along the fratricide pattern by means of
physical/mathematical modeling. For an effective determination of the photon flux magnitude in each
pixel requires of an accurate knowledge of the thermodynamic state of the atmosphere along the line of
sight, as well as the location of sources of backscattering, for instance cirrus clouds, the ice particle
concentration and it size and shape distributions. Assumptions can be made for that effect but at the
cost of leaving a residual level of photon emission not properly calibrated. A modeling approach, fed
with information about the actual position of the LGS spots (as possible to infer from FSM/FSA data)
is an option being explored for GeMS [1,3]. Models for quantification of the photon flux due to
fratricide have been developed in the context to understand it and estimating its effect during the
planning and design of new large aperture telescopes such as the TMT [6]. An example of model
output and comparison to actual observations is shown in Fig. 5.
Fig. 5 (left) Magnitude of the photon flux due to “fratricide effect” in GeMS WFS0 (frame extracted from CB
12351020110, laser power = 26.3W). (right) Modeled photon flux due to “fratricide effect” using the model
explained in [6]. The model was run for the GeMS asterism geometry, with laser power = 26.3W, using the LGSF
parameters (BTO throughput = 0.53, Downlink throughput=0.483, Temperature & Pressure profiles extracted
from the ECMWF for the closest time 00UT, assuming a total optical depth of 0.16 and a cirrus cloud (at 13km
above surface) of optical depth = 0.0451.
The model results (right section in Fig. 5) produce azimuthally symmetric results. However, for this
example two simulations were combined, one with only molecular Rayleigh backscattering which
represents fairly well the observed fratricide photon flux along the LGS-2, LGS-3 and LGS-4 patterns,
and one other simulation where besides the molecular Rayleigh backscattering, a cirrus cloud located at
an altitude of 13 km above ground level with a optical depth of 0.0451 was added, this represents better
represents the results along the LGS-1 fratricide pattern.
Based on the conclusion above, it would be advisable to conduct an on-sky test with GeMS to study the
fratricide effect taking care of gathering telemetry laser power data at a convenient high rate. In this
way, the variability of the laser light during the observations can be calibrated out.
Adaptive Optics for Extremely Large Telescopes III
Table 1. Circular Buffer data files used for the determination of the time variability of photon flux due
to “fratricide effect”. The LGS asterisms where generated at a zenith angle of 0 degrees (local zenith).
Data File
Local Date & Time
Laser Power
[W]
RTC Frequency
[Hz]
CB 11109092002
CB 11109095142
CB 11111010136
CB 12351015401
CB 12351015720
CB 12351020110
CB 12351020736
CB 11360204434
CB 11361005349
CB 12023221308
CB 12025214151
CB 12025215013
CB 12025222444
CB 12025222732
CB 12025223017
CB 12025234647
CB 12026000251
CB 12026002213
19-Apr-2011 06:09:33
19-Apr-2011 06:41:04
20-Apr-2011 21:51:03
04-Nov-2011 03:53:19
04-Nov-2011 03:56:36
04-Nov-2011 04:00:25
04-Nov-2011 04:06:55
14-Nov-2011 23:02:49
15-Nov-2011 03:12:04
13-Dec-2011 00:30:21
14-Dec-2011 23:59:02
15-Dec-2011 00:11:49
15-Dec-2011 00:41:26
15-Dec-2011 00:44:12
15-Dec-2011 00:46:57
15-Dec-2011 02:03:28
15-Dec-2011 02:19:32
15-Dec-2011 02:38:54
40.0
39.2
29.8
27.3
26.1
26.3
26.6
40.3
39.6
39.2
42.8
42.8
42.2
42.2
42.8
42.4
43.2
40.8
400
402
400
200
200
200
200
401
401
200
200
200
401
400
399
400
401
399
Acknowledgments
The TMT Project gratefully acknowledges the support of the TMT collaborating institutions. They
are the Association of Canadian Universities for Research in Astronomy (ACURA), the California
Institute of Technology, the University of California, the National Astronomical Observatory of Japan,
the National Astronomical Observatories of China and their consortium partners, and the Department
of Science and Technology of India and their supported institutes. This work was supported as well by
the Gordon and Betty Moore Foundation, the Canada Foundation for Innovation, the Ontario Ministry
of Research and Innovation, the National Research Council of Canada, the Natural Sciences and
Engineering Research Council of Canada, the British Columbia Knowledge Development Fund, the
Association of Universities for Research in Astronomy (AURA) and the U.S. National Science
Foundation.
Thanks to the Gemini Observatory (GeMS team) for providing the data for this study.
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