Download appendix 4.8.b gsmt image quality degradation due to wind load

APPENDIX 4.8.B
GSMT IMAGE QUALITY DEGRADATION DUE TO
WIND LOAD
Report prepared for the New Initiatives Office, December 2001.
GSMT Image Quality Degradation
due to Wind Load
NIO-TNT-003 Issue 1.B
05-Dec-2001
George Angeli
1
GSMT Image Quality Degradation due to Wind Load : NIO-TNT-003 Issue 1
rev B
by George Angeli
This report summarizes the effects of the wind on the image quality. The wind load was
calculated as follows:
-
wind velocity at secondary from Gemini South measurement c00030oo;
-
wind forces on secondary acting on tripod vertex;
-
wind forces on secondary due to secondary cylinder only;
-
wind pressures on primary simply patched from Gemini South measurement c00030oo.
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Table of Contents
1. Model description ............................................................................................................. 4
Simulink model for wind load .......................................................................................... 5
2. Simulation results............................................................................................................. 6
3. Control considerations................................................................................................... 12
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Chapter 1. Model description
The structural model used in this simulation was extracted from the IDEAS FEA model of the
point design and described in NIO-TNT-002 issue 1.B (GSMT Primary Mirror Deformation due to
Wind Load).
However, the output of the model was modified to generate an estimate of the optical quality of
the telescope. Consequently, the role of the Output Block is to link the image quality of the
telescope to the structural modes through the optical sensitivity matrix K. By multiplying this
matrix with the modal coefficients, the model is able to estimate the image aberration expressed
in Zernike terms.
z = ∑ T k Wk F qm = K primary q m + K sec ondary q m = Kq m
k
Here z is the Zernike coefficient vector characterizing the wavefront aberrations (optical path
differences); qm is the modal coefficient vector; F is the matrix of the eigenvalues; Wk is a
weighting factor matrix for each surface representing the nodal participation of the given optical
surface; while T k denotes the Zernike fit. The summation goes through all optical surfaces, in our
case it’s for the primary and the secondary mirrors.
Like for the mechanical displacements, the columns of Kprimary and Ksecondary as well as of K are
the “optical mode shapes” of the system, respectively, meaning the optical responses to unit
modal vectors. Actually, that’s the way these columns are calculated in the calc_Zernike.m script,
using the results of the NIO internal report “Image Motion and Image Quality of the GSMT Optical
System” (by Myung Cho, July 2001). To calculate the aberrations - expressed in Zernike
coefficients - corresponding to the mirror rigid body motions, first we should determine the vector
Xp and Xs containing the x, y and z translations as well as the x and y rotations of the primary
and secondary mirrors.
The x and y translations are the averages of the x and y displacements of the mirror support
nodes. The z translation and the x, y rotations are determined as the first three Zernike
coefficients of mirror deformation. For the secondary mirror, the fit is somewhat unusual, since it’s
evaluated only on the circumference of the surface – that’s where the secondary support nodes
are. Since the radius of the secondary mirror is 1 meter, no normalization is necessary. The fit is
done by custom function zernike3.m
The Zernike coefficients are expressed in OPD and measured in meter.
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Simulink model for wind load
[time,sec_forcex]
-C-
-C-
From Workspace
X Force
Bvertex
[time,sec_forcey]
Y Force
From Workspace1
Z Force
Out
Matrix
Multiply
x' = Ax+Bu
y = Cx+Du
kprimary
Product
GSMT Structure
-C-
Secondary Vertex
ksecondary
[time,sec_forcez]
From Workspace2
Product2
Matrix
Multiply
Product1
-C-
primary_OPD
To Workspace3
zernike_OPD
To Workspace1
secondary_OPD
To Workspace2
[time,primaryforce_patched]
Matrix
Multiply
From Workspace3
Product3
Bprimary
Matrix
Multiply
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Chapter 2. Simulation results
PSD calculation for Zernike expansion of OPD. The PSDs of the Zernike terms provide insight
into the behavior of the telescope structure under significant wind load. The PSD is estimated
with Welch's method using 50% overlapped Hamming windows of 256 samples. The function
used is welch256.m listed in the Appendix. The following figures demonstrate the PSDs for the
individual Zernike terms. Each figure has three curves showing separately the effects of
secondary structure deformation, primary mirror deformation, and the total OPD due to wind load.
The figures were created in Zernikegraph_OPD.m.
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7
8
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RMS calculations. As a sanity check we calculate the square root of the integral of Zernike
PSDs and compare it to the RMS values determined from the time functions of the Zernikes
terms. The calculation is done in zer_sanity_OPD.m. The values are in meter.
Table 2-1. RMS values for Zernike terms
Zernike
RMS OPD
RMS OPD
RMS OPD
RMS OPD
RMS OPD
RMS OPD
terms
primary
from PSD
secondary
from PSD
total
from PSD
#1
5.86
6.02
30.8
31.4
36.0
36.8
#2
29.0
28.9
26.7
26.5
11.1
11.0
#3
0.13
0.13
0.13
0.12
0.02
0.02
#4
0.01
0.01
0.01
0.01
0.01
0.01
#5
0.002
0.002
0.01
0.01
0.01
0.01
#6
0.15
0.15
0.58
0.59
0.47
0.48
#7
0.14
0.14
0.83
0.83
0.96
0.96
#8
0.003
0.003
0.003
0.003
0.005
0.005
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Zernike Expansion (RMS) of the Image Aberration due to Wind Load
-5
4
x 10
total
due to secondary motion
due to primary motion
3.5
RMS Zernike coefficient [m]
3
2.5
2
1.5
1
0.5
0
1
2
3
4
5
Zernike number
11
6
7
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Chapter 3. Control considerations
Control model description.Our objective with this highly simplified control model is to give a
zero order estimate for the major parameters of the secondary rigid body motion control. Instead
of a feedback loop, the required secondary position is determined by minimizing the aberration at
each sampling point. In other words, the structure is bending on its own way, without actuator
interaction, and the calculation gives a secondary mirror position relative to the bent position,
which would be the "optimal" to minimize the RMS of the first 8 Zernike terms. The considered
secondary motions are Tz, Rx and Ry.
This approach obviously avoids two important aspects: (i) there is no interaction between the
"correction" and the structural dynamics of the telescope, and (ii) there are no realization
constrains on the "correction" meaning it has virtually infinite bandwidth and range.
The temporal RMS of the "optimal" secondary mirror motions Tz, Rx and Ry are 0.39 µm, 1.41
arcsecond and 4.74 arcsecond, consecutively.
The script doing the optimization is opt_secondary_tt.m.
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Table 3-1. Temporal RMS values of Zernike terms (in µm)
Zernike terms
Before correction
After correction
#1
36.0
0.01
#2
11.1
0.01
#3
0.02
0.0003
#4
0.01
0.01
#5
0.01
0.01
#6
0.47
0.9
#7
0.96
0.98
#8
0.05
0.05
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