1 ACTIVE OPTICS SYSTEM PERFORMANCE [10 pages, Bo]
In this section, we describe how we put together the various pieces we have discussed in previous
sections, to test the performance of the AOS by means of end-to-end full simulations.
1.1 PERTURBATION MODEL [4 pages, Bo]
As the starting point of the full simulations, we need to realistically simulate the initial state of the
system before the AOS corrections are applied. But note that in the simulations we present here, we do
not include look-up-table (LUT) and laser tracker as part of the closed loop. As the result, the initial
deviations of the rigid body degrees of freedom for both the M2 mirror and the camera from their
nominal positions are determined by the accuracy of the laser tracker. We assume that a certain
percentage of the mirror surface deformation due to gravity and bulk temperature change can be
removed by the LUT. More details on the accuracy of the laser tracker and assumptions on the LUT error
have been discussed in Secs. xxx and yyy, and numbers directly relevant to our simulations can be found
in Sec. 1.1.1.
Figure 1 shows the overall architecture of the simulations we present in this section. Yellow boxes show
the external input variables. Red arrows show the feedback loop. The green arrow shows that our
performance metric is the image quality at 40 field positions (RMS of the FWHM across the field). More
about the performance metric is discussed in Sec. 1.2.
Figure 1. The overall architecture of the simulations presented in this section.
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1.1.1 The telescope perturbation model
The telescope part of the perturbation model includes the following degrees of freedom: (1) 5 rigid body
degrees of freedom for M2: z motion, x-decenter, y-decenter, x-tilt, and y-tilt. These are controlled by
the M2 hexapod. (2) 5 rigid body degrees of freedom for camera: z motion, x-decenter, y-decenter, xtilt, and y-tilt. These are controlled by the camera hexapod. (3) Bending modes on M1/3. (4) Bending
modes on M2.
Based on the laser tracker uncertainty analysis, the z-position of the M2 relative to M1/3 can be known
with an accuracy of 10.8um. The lateral positions can be known within 23.0um and the tilts 43.6e-5
degree. For the camera, the corresponding numbers are 10.3um, 17.0um and 75.6e-5 degree. Gaussian
random numbers are generated for each of the 10 rigid body degrees of freedom, where the mean is
always zero, and the 2 standard deviation lower and upper bounds covering the corresponding ranges
specified above. These are taken as the initial rigid body displacements of the M2 and camera.
The mirror surface deformations for both the M1/3 and M2 are derived from their finite element
analyses (FEA), and are functions of telescope elevation, bulk temperature, and the temperature
gradients on the mirror surfaces. Figure 1 shows the gravity-induced deformations on M1/3 when the
telescope points at zenith (left) and horizon (right). The gravity-induced deformation at a random
elevation angle is determined using
Gravity-induced mirror deformation at elevation angle β =
(zenith deformation)*cos(β)+(horizon deformation)*sin(β)
(zenith deformation)*cos(β0)+(horizon deformation)*sin(β0)
where β0 = 0 is the pre-compensation angle for M1/3. The elevation angle for the simulations is drawn
randomly from the elevation distribution provided by the LSST Operation Simulation group, as shown in
Figure 2 (left). The gravity contribution to the mirror deformation is then combined with those due to
bulk temperature and temperature gradients. The 1C bulk temperature deformation and x-, y-, z-, and
radial thermal gradients deformations are given by the FEA data. The bulk temperature distribution, as
shown in Figure 2 (right) is assumed to be Gaussian, with -3C and 20C being the -2σ and 2σ bounds,
where σ is the standard deviation. Similar assumptions have been made on the temperature gradients,
with the x- and y-gradients (-2σ, 2σ) range covering a range of 0.4C, and z- and radial gradients covering
0.1C. We assume the LUT corrects 95% of the mirror deformation due to gravity and bulk temperature.
2
Figure 2. Gravity-induced mirror surface deformations on M1/3 for zenith (left) and horizon (right)
pointings.
Figure 3. Left: elevation angle randomly generated for 500 initial conditions (blue histogram). Red curve
shows the original elevation distribution provided by LSST Operation Simulation group. Right: bulk
temperature randomly generated for 500 initial conditions (blue histogram). Red curve shows the
Gaussian, from with the random numbers are drawn. See text for more details.
The surface deformation on M2 is dealt with in a way similar to M1/3. Since M2 will be fabricated from
ion figuring facing down, the pre-compensation for gravity still happens at zenith pointing. The M2 ULE
has a coefficient of thermal expansion that is 1% of the M1/3 borosilicate. Consequently, unlike M1/3,
the M2 mirror does not have a thermal control system. The z- and radial gradients on M2 are assumed
to be 1C, covering (-2σ, 2σ) of a Gaussian. The x- and y-gradient contributions to M2 surface
deformation are neglected, because they have been found to be much smaller than those due to z- and
radial gradients (Ref. M2 SPIE).
Figure 4 shows the weighted RMS of the FWHM across the field for 500 randomly perturbed initial
telescope states (left), and its distribution histogram(right). Note that these are with telescope
3
perturbations model only. The camera internal distortions and atmosphere, which will be described in
following sections, are not included.
Figure 4. Weighted RMS of the FWHM for 500 randomly perturbed initial telescope states (left), and its
distribution histogram (right).
1.1.2 Camera internal distortions
The camera internal optics distortions are modeled according to FEA data from the LSST camera team.
These include 6 rigid body degrees of freedom (z motion, x-decenter, y-decenter, and rotations about
the x-, y- and z-axes) for each of the 5 optical components of the LSST camera (L1, L2, filter, L3, and focal
plane), and surface deformations on the 6 surfaces of the 3 lenses. Each of these degrees of freedom is
modeled as a function of gravity, camera rotation angle, and soak temperature. The camera rotation
angle plays a role because of the asymmetry of the camera around the optical axis. The gravitational
deformations are calculated by combining those at zenith and horizon pointings and with camera
rotation at zero and 90 degrees, using the sinine and cosine of the elevation angle and the camera
rotation angle. The thermal contribution to each of the camera internal degrees of freedom is calculated
by the FEA at -10C to 25C, with 5C step size, and interpolated to random soak temperatures in the
simulations. The camera is pre-compensated at zenith pointing and 0C soak temperature. Figure 5
shows the camera internal distortions in one of the simulation runs.
4
Figure 5. Camera internal distortions in one of the simulation runs. Upper panel shows the rigid body
motions of the L1, L2, filter, L3 and focal plane (FP). The lower panel shows the lens surface
deformations expressed as stardard Zernike polynomials Z4-Z22. Note that although some of the surface
sag Zernikes are relatively large, the two surfaces of a lens are often deformed in a similar way so that
largely cancel.
1.1.3 Atmosphere
Our atmosphere is simulated using the Arroyo library (Ref. to Arroyo). The atmosphere is modeled using
6 layers of Komolgorov phase screens at various heights. Based on historic DIMM data at Cerro Pachon,
and the current understanding on its outer scale, for our simulations, we use r0=17cm, and assume an
infinite outer scale. This is a conservative assumption, because the outer scale preferentially reduces
atmospheric contribution to the low order modes that are typically difficult to distinguish from
misalignment errors. More details on the justification of this atmosphere parameterization can be found
in Sec. xxx.
Ideally, to simulate the effect of the atmosphere on the wavefront images, one needs to divide each 15s
exposure into infinitesimal time intervals. This means we need to create a series of instantaneous phase
screens and raytrace through them in turn, to accumulate photons on the wavefront sensors and form
wavefront images. However, this requires a large amount of computation, and becomes impractical with
large-scale simulations. We have therefore come up with an approximation technique, to save on
computation, and without much sacrifice of the fidelity of the simulations.
In our approximation of the effect of the atmosphere, instead of integrating on the wavefront images,
we integrate on the optical path difference (OPD). Raytracing through the time-integrated OPD phase
5
screen captures the intensity and shape variations in the intra and extra focal images caused by the
atmosphere. The atmospheric blurring effects are then added by convolving the intra and extra focal
images with the time-integrated atmospheric PSF.
The convolution approximation of the atmosphere is validated by running our wavefront estimation
algorithm on images created using two methods. The first is the brute-force method, where we divide
each 15s exposure into 300 time intervals, each 50ms long. In ZEMAX, using our unperturbed LSST
model, we put on the integrated OPD phase screen for the first 50ms, accumulate the photons, then
replace the phase screen with the time-integrated OPD for the 2nd 50ms, and so on. The second is the
convolution approximation of the atmosphere as described above. The total numbers of photons traced
are the same for the two approaches. After doing this for 86 statistical independent exposures, where
each exposure consists of forming 4 pairs of defocused images at the four corners, we compare the
mean and variance of the wavefrnot measurements. The results are shown in Figure 6. The difference
between the two methods are found to be negligible.
Note that the atmosphere at the four wavefront sensors are highly correlated within each simulation,
due to the common ground layer in the simulation of the atmosphere.
Figure 6. Comparion of wavefront mean and variance between the brute-force atmosphere
implementation (red) and the convolution approximation (blue) using 86 uncorrelated sets of
atmosphere realizations. The telescope model is a ZEMAX unperturbed telescope model. Black lines
show the telescope intrinsic aberrations.
6
1.1.4 Implementation of the perturbations in ZEMAX
We use the optical design software ZEMAX as our raytracing engine. For current simulations, the LSST
optical design version 3.3 is used. Figure 7 shows 3D layout of the LSST model in ZEMAX, for both the onaxis and off-axis configurations.
Figure. 7. ZEMAX modeling of the LSST optical system showing rays converging onto the center of the
focal plane (left) and those onto the center of a wavefront sensor at 1.767◦ off the optical axis (right)
The rigid body degrees of freedom are implemented in ZEMAX by means of coordinate breaks and
surface pickups. The atmosphere is represented by an annular Zernike phase screen, whose coefficients
are obtained by expanding the time-integrated atmospheric OPDs onto annular Zernike basis functions.
The mirror and lens surface deformations are realized using standard Zernike sags.
Most of the telescope perturbation variables belong to the category of controlled variables, x, as shown
in Figure 1. In reality, there will be high order deformations on the M1/3 and M2 surfaces that will not
be controlled by the actuators. To simulate this effect, we keep Zernike coefficients up to Z28 on the
standard Zernike sags that represent the surface deformations. In our optical reconstructor, we control
Zernikes up to Z21 on the mirror surfaces. The control strategies are discussed in more detail in Sec. 7
and Sec. 1.3. All the camera internal degrees of freedom are part of x2, the uncontrolled variables.
1.2 PERFORMANCE METRIC [3 pages, Bo]
The LSST error budget on the image quality (IQ) is specified in terms of the Gaussian Quadrature of the
FWHM at a set of field positions. These positions form a 5-ring, 8-arm structure, as shown in Figure 8.
Points on the same ring have same weights. The weights for the rings are (going from center to outside):
0.2369, 0.4786, 0.5689, 0.4786, and 0.2369. The definition of IQ uses the FWHM, which is difficult
to define and compute for elliptical non-Gaussian Point Spread Functions (PSF). In practice, we compute
RMS spot sizes and scale by a constant factor of 1.665 to convert to FWHM (assuming circular Gaussian
PSF).
7
Figure 8. The distribution of field points in LSST focal plane. The blue squares show positions of the
science rafts.
Our task at hand is then to relate the FWHM at these field positions to the perturbation variables. We
know that our perturbation variables are not independent in terms of affecting the FWHM or IQ. One
motion could cancel another. For example, pistoninng the camera largely has the same effect as
pistoning M2. The modeling of the performance metric is therefore a two-step process:
1. We know that our optical system is linear – that is, the signed Zernikes are linear functions of
the perturbation variables, when the control variables do not deviate too much from their
nominal positions. We will verify the linearity to the extend that the perturbation variables
reflect their actual on-telescope values. We will calculate sensitivity matrices.
2. In the second step, we relate the FWHM at a field position to the wavefront Zernikes at the
same field position. If each Zernike affects the FWHM in independent ways, their relation should
be largely quadratic. Considering that the shift in the ray hit position on the image plane is
proportional to the slope of the wavefront at the pupil, the empirical form we’ve come up with
is
FWHM 2f = å (a f ,i Zi2 + b f ,i Zi ) + c f + å (corf ,i, j Zi Z j )
i
i, j
where f is the field number, Zi is the RMS of the ith order annular Zernike, which does not
include the LSST as-designed aberration, a, b, and c are constants to be determined, and cor is a
matrix with the cross-Zernike correlation coefficients.
8
1.2.1 Linearity and sensitivity matrices
To verify the linearity of the system, we perturb the telescope control variables one at a time, while
fixing other variables at zero, and look at how the perturbed variable affects the wavefront Zernikes. For
both the Zernikes on the mirror surfaces and the wavefront Zernikes, we include up to Z22 (in terms of
radial and azimuthal frequencies: (6,0). Our Zernike ordering follow those of Noll 1976 and Mahajan
1981, which are the same as ZEMAX). In this study, we’ve looked 45 field positions, including the center
of the focal plane, the 5-ring, 8-arm structure shown in Figure 7, and the 4 wavefront chip centers:
(±1.185o, ±1.185o). For each perturbation variable, we vary the magnitude of the motion within the
range that reflects the actual on-telescope values. One example is shown in Figure 9, where the
wavefront focus term (z4) at one of the wavefront chip centers is shown as a function of M2 x-decenter.
More plots showing the linearity between Z4-Z22 and any controlled degrees of freedom are available
upon request.
The elements of the sensitivity matrices are obtained by calculating the slopes of the linearity plots. Due
to the good linearity we have observed, for a degree of freedom x, the slope is simply calculated using
x=0 and x=x1, where x1 is the smallest positive x on the plots. The criteria in choosing x1 is that it should
be close to its on-telescope values and be outside of the non-linear trough around x=0.
Figure 9. The linearity between the wavefront focus term (Z4) and M2 x-decenter. Blue crosses are
Zernike coefficients directly from ZEMAX. Red circles are results of the wavefront estimation using the
defocused images.
1.2.2 FWHM as a function of wavefront Zernikes
The empirical form of the FWHM model is given at the beginning of Sec. 1.2. Here we describe how we
determine the a, b, c coefficients, and the correlations terms, and how we validated the model, so that it
can be used in our optimal control strategy.
To determine the a, b, and c coefficients for Zernike Zi, we set all other Zernikes to zero, and vary Zi,
then plot FWHM2 as a function of Zi. Figure 10 (left) shows one example, where we observe that the
relation between FWHM2 and Z4 is indeed quadratic. We fit the data to y=ax2+bx+c, to get the a,b, and c
9
coefficients for a specific field position and Zi. Similarly, to determine the correlation between z4 and
z11, we set all other Zernikes to zero, vary them within their realistic ranges, and look at the changes in
FWHM2. Figure 10 (right) shows the correlation between z4 (focus) and z11 (spherical aberration). The
correlations are found to have their largest values between Zernikes with the same angular frequencies.
The cross-angular-frequency correlations are mostly small and negligible.
Figure 10. Examples of determinations of the parameters in the FWHM model. Red circles are data from
ZEMAX. The least-square fits to the data are shown in red.
Note that the c terms in the FWHM2 equation is field-dependent, but is not a function of Zernikes. Using
the technique above, we get a c value from every quadratic fit, the difference between which is
consistent with statistical fluctuations in the FWHM calculations in ZEMAX due to the number of rays
traced. In our final model we take the value of c to be the average from the individual quadratic fits.
Because here the wavefront Zernikes do not include the LSST as-designed aberrations, the fielddependent constant c represents the image quality of the unperturbed LSST in terms of FWHM. Figure
11 shows the LSST intrinsic FWHM as a function of field number.
Figure 11. LSST intrinsic FWHM as a function of field number. Field No. 0 is at the center of the focal
plane, which is not used in the performance metric. The ordering of the field is from center to outside.
For each ring, we start from positive x-axis, and go counter-clockwise.
The linear term b is generally small. It doesn’t contribute much to the FWHM at individual field points. In
10
averaging over the field, it becomes even less significant. Typically the value of a Zernike that reduces
the linear term at one field point will increase it at another, so the effect averages out.
The FWHM model has been validated using random combinations of Zernike coefficients, as shown in
Table 1. For three randomly picked field points, we compare the predicted FWHM at several field
positions with values determined by means of raytracing in ZEMAX. In all cases, the difference is
observed to be within 1%, including computation errors. 100,000 rays are launched in ZEMAX for each
FWHM value determined. The average of the numbers in the difference columns is 0.07%
Table 1. Validation of the FWHM model using random combinations of Zernikes.
1.3 SIMULATION RESULTS [3 pages, Bo]
Detailed discussions on the control – how to make use of our wavefront measurements to best optimize
the IQ, has been presented in detail in Sec. 7. Here we present simulation results.
1.3.1 Problems with the pseudo-inverse of the A-matrix
The simplest reconstructor is the pseudo-inverse of the sensitivity matrix, a.k.a., A-matrix. However, this
pseudo-inverse has several problems, which have been discussed in detail in Sec. 7. The one that is most
problematic for our simulations is the near-degeneracy in the A-matrix. The A-matrix for one of the
wavefront chip centers is shown in figure 7-3. For example, a piston motion in M2 has a nearly identical
effect as a piston motion in the camera.
We demonstrate the near-degeneracy problem with an example, as shown in Figure 12. In this test, we
perturb the telescope by giving a -50um motion to the camera hexapod. We then take the true
wavefront from ZEMAX, and multiple it with the pseudo-inverse of a truncated A-matrix. Note that there
is no wavefront sensing or images involved here. This is a pure test of the control strategy. In Figure 11,
the red triangles show the degrees of freedom that are turned off. Blue triangles show those that are
turned on. The only difference between the upper and lower plots is the Z11 (spherical aberration) on
the two mirror surfaces. The correlations between Z11 (spherical aberration) on the mirror surfaces and
the pistons motions of M2 and camera are seen, which is also obvious from the state correlation matrix
shown in Figure 7-6.
11
Figure 12. A test of the near-degeneracy in the A-matrix using simulations.
We need to note here that a lot of the degeneracy we see in these simulations may be due to the fact
that we are using standard Zernikes on the mirror surfaces, instead of the actual bending modes. The
correlations between deformations in the M1/3 and M2 are large when both are described as Zernikes.
In reality the bending modes are M1/3 and M2 are very different. This is also true for the correlation
between the M2 and camera pistons and the axi-symmetric Zernikes on the mirror surfaces, and for
coma and misalignment. The coma bending mode is different from the Zernike coma. However, Zernike
coma applied to the optical surface should be very close to Zernike coma from optical misalignment. It
should be easier to differentiate between the actual bending mode coma and misalignment coma than
what we are now modeling. So our simulations here have their limitations. Nevertheless, since it will
likely be easier to converge with the bending mode surfaces, if we can get the Zernike surface
deformation correction to work, correcting the actual telescope should be easier.
1.3.2 Two control strategies
We have exercised two control strategies to eliminate the degeneracy.
In the first strategy, we freeze a subset of the control degrees of freedom at their nominal positions. In
the simulations of this control strategy, we decided to remove all rigid body motions of M2 from the
AOS control loop. The idea is that the laser track is used to set the position of M2 at the beginning of the
night with respect to the current operating conditions of the telescope. Thereafter the LUT and
temperature metrology on the structure is used to offset the M2 z-position. The remaining optical
focus/spherical affects are then corrected using the wavefront feedback and the remaining degrees of
freedom. If we find the system is drifting into the non-linear regime we can reset the M2 position using
the laser track at a modest cost in time (~10 min).
Because of the degeneracy between the Zernike modes on the two mirror surfaces, we freeze all M2
12
surface deformations. (more on justification?) The focus term on M1/3 is also frozen, since it is highly
correlated with the piston of the camera.
From the control algorithm point of view, we need to remove the columns of the A-matrix
corresponding to the frozen degrees of freedom, then apply the pseudo-inverse of the truncated Amatrix on the wavefront measurement vector.
The other control strategy that has been implemented in our simulations is the weighted control
strategy that has been discussed in detail in Sec. 7. This optimizes both the IQ across the field and the
motions of the control variable, so that we avoid using differentials of motions to correct small
aberrations, which often leads to large swings in the control variables. Note that the optimization of
parameters in this control strategy has not been done. The current F matrix is obtained by assuming R=I,
a unit weight. By doing that we are simply assuming that a command of 1um on any mirror (rigid body
or deformation) is equivalent, and equivalent in cost to 1 um of FWHM. So are 1 arcsec of x-tilt and y-tilt
on M2 and the camera.
The truncated A-matrix strategy, nevertheless, is more intuitive. It demonstrates that our understanding
of the system behavior is correct. In the rest of this section, we show results from both control
strategies.
1.3.3 Tests of truncated A-matrix strategy without atmosphere
For a better understanding of the system and the control, we have exercised the truncated A-matrix
control strategy using the telescope and camera perturbation models as described in Secs. 1.1.1 and
1.1.2, without turning on the atmosphere. The wavefront sensor measurements are assumed to be
perfect in these tests, that is, we get the wavefront from ZEMAX raytracing directly, without creating the
defocused images.
Using our telescope and camera perturbation models, we generated 500 initial states of LSST. We then
apply the pseudo-inverse of the truncated A-matrix to the wavefront vector. The controlled degrees of
freedom are the 5 rigid body motions of the camera, and Z5-Z13, or Z5-Z19 on M1/3. Figure 13 shows
the RMS of FWHM across the field before and after the AOS corrections for the first 48 simulations.
Green line shows the RMS of FWHM for an unperturbed telescope. Since we only make a one-time
correction here, we have used gain=1 for both correction schemes. Including Z14-Z19 is seen be to help
with the reduction of the wavefront, therefore the IQ, due to the existence of high order terms
introduced in both the telescope perturbation and camera distortion models.
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Figure 13. RMS of FWHM across the field before and after the AOS corrections for 48 initial states. The
atmosphere has been turned off and perfect wavefront sensors are assumed.
1.3.4 Full simulations: truncated A-matrix & control weighting
To perform the final end-to-end full simulations consists of the following steps
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Generate 500 instances of the LSST using the telescope and camera perturbation models;
Take one of the 500 initial conditions, and perturb the ZEMAX LSST model accordingly;
Randomly pick one set of time-integrated OPD, and implement in ZEMAX as phase screens;
Raytrace high S/N and high resolution intra and extra focal images at four wavefront chip
centers (average S/N=25 on each LSST 10um pixel; high resolution images have pixel size of
1um);
Convolve the intra and extra focal images with the time-integrated atmospheric PSF, and
decrease the image resolution;
Run wavefront estimation algorithm on the intra and extra focal images;
Repeat steps 3-6, to get second set of wavefront measurements at the four corners for the 2nd
exposure. Note that the atmosphere for the two exposures are uncorrelated;
Average the wavefront measurements from the two exposures;
Apply one of the two optical reconstructors to the wavefront measurement vector, multiply by
the gain factor to get the corrections to be applied to the next visit;
Apply corrections to the control variables;
Evaluate the FWHM at 40 field positions. Gravitational and thermal changes between visits are
ignored. Camera internal distortions remain unchanged at all times for each simulation run;
Repeat steps 3-11 for subsequent visits. Observe the improvements in IQ after each visit.
Figure 14 shows an example of the wavefront measurement from the first exposure where the
telescope is still in its initial state.
14
Figure 14. An example of the wavefront measurement from the first exposure where the telescope is
still in its initial state. Black line shows the ZEMAX truth with the time-integrated OPD phase screen. Blue
triangles are results obtained by running the wavefront curvature sensing (WCS) algorithm on the high
resolution images before convolution with the atmospheric PSF. Red circles are from running the WCS
algorithm on the final images after convolution and with 10um pixel size.
For the same simulation run, Figure 15 shows control motions dictated by the truncated A-matrix
strategy with gain=1, and the predicted performance in terms of wavefronts at the four corners,
assuming the atmosphere does not change between visits and no drifts in gravitational and thermal
conditions.
Figure 15. Control motions dictated by the truncated A-matrix strategy with gain=1. The first two rows
show the motions required on the various degrees of freedom. Red triangles mark the degrees of
freedom that have been frozen at their nominal positions. Blue triangles show the controlled motions.
15
The lower two rows show the predicted performance on wavefront at the four corners, assuming the
atmosphere does not change between visits and no drifts in gravitational and thermal conditions. This is
the same simulation run as shown in Figure 14.
For the same simulation run, Figure 16 shows the change in RMS of FWHM across the field after a few
visits, for the two control strategies, and gain=1 and gain=0.3. In the case of the 100% gain, the FWHM
quickly drops close to that of an unperturbed telescope, then fluctuates above it, primarily due to the
changing atmosphere. For the 30% gain test, it is seen that the FWHM drops more slowly, but eventually
converges without much fluctuation.
Figure 16. Change in RMS of FWHM across the field for one of the simulation runs after a few visits.
Figure 17 shows the control motions and predicted wavefront performance after the first visit for
another simulation run, assuming gain=1. This example is for the control weighting strategy. This is one
of the more extreme cases, where the initial wavefront has a large defocus term. This large defocus
term comes from the camera internal optics, caused by the relatively high soak temperature (18.03C, in
this example). Figure 18 shows the performance of both control strategies. In the case of the control
weighting strategy, in order to quickly bring the FWHM close to the desired range, we have applied a
100% gain for the first iteration (after the initial 39 seconds). After that, we use the 30% gain to avoid
fluctuation due to atmosphere. Note that the y-axis in Figure 18 is in logarithmic scale.
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Figure 17. Control motions dictated by the control weighting strategy for a simulation run with large
defocus in initial wavefront. The control uses gain=1. The upper two rows show the motions required on
the various degrees of freedom. The lower two rows show the predicted performance on wavefront at
the four corners, assuming the atmosphere does not change between visits and no drifts in gravitational
and thermal conditions.
Figure 18. Change in RMS of FWHM across the field for one of the simulation runs after a few visits. The
initial state has has a large defocus in the wavefront, due to the camera internal optics.
17