Design Report
TITLE
IMaX Final Optical Design
Code :
SUN-IMaX-RP-IX200-023
Issue/Rev. :
1A
Date :
11/05/2007
No. of pages :
52
Config. Doc. :
No
IMaX – A Magnetograph for SUNRISE
http://www.iac.es/proyect/IMaX
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Approval control
Prepared by
Revised by
Approved by
Authorized by
Carmen Pastor Santos
Tomás Belenguer Dávila
Alberto Alvarez Herrero
Raquel López Heredero
Alberto Alvarez Herrero
Lieselotte Jochum
Valentín Martínez
INTA
INTA
INTA
INTA
INTA
IAC
IAC
Date: 11/05/2007
IMaX is a joint development by a consortium of four institutions
Instituto de Astrofïsica de Canarias (IAC)
Instituto de Astrofísica de Andalucía (IAA)
Instituto Nacional de Técnica Aeroespacial (INTA)
Grupo de Astronomía y Ciencias del Espacio (GACE)
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Changes record
Issue
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11/05/07 All
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Change description
First Issue
Design Report
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Applicable documents
Nº
AD1
AD2
AD3
AD4
AD5
AD6
AD7
AD8
AD9
AD10
AD11
AD12
AD13
AD14
AD15
AD16
AD17
AD18
AD19
AD20
AD21
Document title
ISLiD-IMaX Optical Interface Control
Document
IMaX Requirements
Thermal analysis of the optical enclosure
ROCLI 1
ROCLI 2
Lens 1 Collimator
Lens 2 Collimator
Lens 1 Collimator Doublet
Lens 2 Collimator Doublet
Lens 1 Camera
Lens 2 Camera
Lens 1 Camera Doublet
Lens 2 Camera Doublet
Camera Doublet
Beamsplitter
Phase Diversity
Mirror 1
Mirror 2
Mirror 3
IMaX Optics Specification
TCE 116 Etalon Preliminary Optical Test
Report
Code
SUN-MPS-ID-LD000-001
Issue
1
SUN-IMaX-SP-GEN-001
SUN-IMaX-TN-IX300-005
SUN-IMaX-DR-IX200-001
SUN-IMaX-DR-IX200-001
SUN-IMaX-DR-IX200-003
SUN-IMaX-DR-IX200-004
SUN-IMaX-DR-IX200-005
SUN-IMaX-DR-IX200-006
SUN-IMaX-DR-IX200-008
SUN-IMaX-DR-IX200-009
SUN-IMaX-DR-IX200-010
SUN-IMaX-DR-IX200-011
SUN-IMaX-DR-IX200-012
SUN-IMaX-DR-IX200-013
SUN-IMaX-DR-IX200-014
SUN-IMaX-DR-IX200-015
SUN-IMaX-DR-IX200-015
SUN-IMaX-DR-IX200-017
SUN-IMaX-SP-IX200-004
SUN-IMaX-RP-IX200-020
3A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
1A
2A
1A
Code
SUN-IMaX-TN-IX200-022
Issue
2A
SUN-IMaX-TN-IX200-018
SUN-IMaX-RP-IX200-001
SUN-IMaX-TN-GEN-002
SUN-IMaX-TN-IX200-019
MIL STD 1246C
2A
1A
4B
1A
Reference documents
Nº
RD1
RD2
RD3
RD4
RD5
RD6
RD7
RD8
Document title
Characterization of a defocusing plate to
implement phase diversity in IMaX
IMaX ghost images, ASAP study
ROCLIs gamma radiation test report
Photon Flux Budget for IMaX
Particle contamination in IMaX
Product cleanliness levels and
contamination control program
Airborne particulate cleanliness classes in
cleanrooms and clean zones
M. Rimmer, “Analysis of Perturbed lens
Systems”
FED STD 209E
Appl. Opt.,Vol 9, 533 (1970)
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List of acronyms and abbreviations
AIV
Assembly, Integration and Verification
CCD
Coupled Charge Device
CL
Coherence length
FN
F-Number
IMaX
Imaging Magnetograph eXperiment
ISLiD
Image Stabilization and Light Distribution
LabC
Laboratory Conditions
MPS
Max-Planck-Institut für Sonnensystemforschung
MTF
Modulation Transfer Function
N/A
Not applicable
OPDP-V
Optical Path Difference (peak to valley)
OPDRMS
Optical Path Difference (root mean squared)
PDR
Preliminary Design Review
PSF
Point Spread Function
RMS
Root Mean Square
RMSWFE
Root Mean Square Wavefront Error
RSS
Root Sum Square
ROCLI
Retardador Óptico de Cristal Líquido
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CONTENTS
1.
INTRODUCTION ............................................................................................................ 8
2.
SCOPE............................................................................................................................... 8
3.
SOFTWARE TOOLS ...................................................................................................... 8
4.
MAIN CHANGES SINCE PRELIMINARY DESIGN REVIEW ............................... 8
5.
GENERAL DESCRIPTION OF THE FINAL DESIGN .............................................. 9
5.1
BLOCKS DIAGRAMS ............................................................................................................ 9
5.2
OPTICAL CONCEPT ........................................................................................................... 10
5.3
OPTIMIZATION .................................................................................................................. 11
5.4
OPTICAL MATERIALS. ...................................................................................................... 12
5.5
ATHERMALIZATION AND ACHROMATIZATION. ................................................................ 13
6.
IMAX OPTICS LAYOUT ............................................................................................. 15
7.
IMAGE QUALITY ........................................................................................................ 16
7.1
WAVEFRONT ANALYSIS. NOMINAL SYSTEM ................................................................... 16
7.2
ABERRATION CURVES ...................................................................................................... 17
7.3
NOMINAL MTF ................................................................................................................. 18
7.4
SPOTS DIAGRAM ............................................................................................................... 19
8.
GHOST AND STRAY LIGHT IMAGES .................................................................... 20
8.1
INTRODUCTION ................................................................................................................. 20
8.2
GHOST IMAGES ................................................................................................................. 21
8.2.1
Ghost images for one on-axis point source ............................................................... 21
8.2.2
Ghost images for a out-of-axis point source ............................................................. 23
8.3
ELIMINATION OF THE GHOST IMAGES. .............................................................................. 24
8.4
CONCLUSION OF THE GHOST PROCESS OF IMAX:............................................................. 24
9.
THERMAL BEHAVIOUR ............................................................................................ 25
9.1
IMAX OPERATIVE CONDITIONS ....................................................................................... 25
9.2
THERMAL SIMULATION APPROACH ................................................................................. 26
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9.3
IMAX THERMAL BEHAVIOUR .......................................................................................... 28
9.4
PHASE DIVERSITY THERMAL BEHAVIOUR ....................................................................... 29
10.
TOLERANCES, BORESIGHT AND SENSITIVITY ANALYSIS ........................... 30
10.1
INTRODUCTION ............................................................................................................. 30
10.2
TECHNICAL APPROACHES TO TOLERANCING ............................................................... 30
10.2.1
Summary of the Wavefront Differentials technical approach. .................................. 31
10.3
DESCRIPTION OF THE IMAX TOLERANCING STUDY ..................................................... 32
10.4
PERFORMANCE SUMMARY. WAVEFRONT ERROR DEGRADATION ................................ 34
10.5
BORESIGHT, IMAGE SCALE CHANGE AND IMAGE ROTATION ....................................... 34
10.6
COMPENSATORS RANGE OF MOVEMENT ....................................................................... 35
10.7
SUMMARY OF THE MOST CRITICAL TOLERANCES ......................................................... 35
10.8
TOLERANCES OF THE INTERFACE F4 ............................................................................ 36
11.
TEL-ISLID-IMAX IMAGE QUALITY EVALUATION. ERROR BUDGET......... 36
11.1
MTF .............................................................................................................................. 37
11.2
SPOTS DIAGRAM ........................................................................................................... 38
11.3
TOTAL WAVEFRONT ERROR ANALYSIS. ERROR BUDGET ....................................... 39
12.
PARTICLES CONTAMINATION IN IMAX OPTICS ............................................. 43
12.1
INTRODUCTION ............................................................................................................. 43
12.2
SUMMARY OF THE STUDY ............................................................................................. 43
12.3
CONCLUSIONS ............................................................................................................... 45
13.
RESULTS AND CONCLUSIONS ................................................................................ 46
ANNEX 1. SURFACE LISTING ............................................................................................. 47
ANNEX 2. CODEV MACRO FOR THERMAL BEHAVIOUR .......................................... 50
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1. INTRODUCTION
IMaX (Imaging Magnetograph eXperiment) is part of the payload of the SUNRISE balloon
project to study solar magnetic fields at high spatial resolution (100 km on the solar surface). It
makes images of the solar surface magnetic field by measuring the state of polarization of the
light within a selected spectral line. In this sense IMaX is a polarimeter. This spectral line is
sensitive to the solar magnetic fields though the Zeeman effect which induces various
polarization states of the emitted light. To meet this goal IMaX should work as a:
• High sensitivity polarimeter.
• High resolving spectral power.
• Near diffraction limited imager.
2. SCOPE
This document contains an overview and description of the IMaX Final Optical Design. During
this phase we have completed a detailed analysis about IMaX nominal expected performance, as
well as a detailed analysis of the effect of tolerances and the operational environment on its
performance after the AIV phase and during flight. We also include a detailed analysis of the
Ghost images and Stray Light, and a Particles contamination analysis.
Surface Listing and Macros used for the analysis are included in Annexes 1 and 2.
3. SOFTWARE TOOLS
CODEV (Optical Research Associates) has been used for designing and analyzing the IMaX
optical configuration.
ZEMAX (ZEMAX Development Corp.) for analyzing the ISLiD optical configuration
ASAP -Advanced Systems Analysis Program. (Breault Research Organization) has been used
for analyzing the ghost and stray-light images.
RHINOCEROS (McNeel North America) has been used as a modeling tool.
4. MAIN CHANGES SINCE PRELIMINARY DESIGN REVIEW
In the following table we indicate the main changes in the system specification since PDR
Parameter
Value at PDR
Value at CDR
Remarks
Pixel Size
13µm
12µm
New CCD manufacturer
Dalsa
Optical Design and
Image quality
evaluation
Including current
SUNRISE
Telescope and
ISLiD
Including a lens module
simulating the SUNRISE
Telescope and ISLiD
optical interface.
FN (F-Number)
53.63
45
Due to amendment to
the IMaX photon flux
analysis for the new
CCDs. ( See AD2)
100%
Due to the sensitivity of
the new CCD cameras
(See AD2)
Reflectivity of the 30%
Folder Mirrors for
double pass
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5. GENERAL DESCRIPTION OF THE FINAL DESIGN
5.1 Blocks Diagrams
In order to clarify the description of the optical design we are including here 2 Blocks
Diagrams, corresponding to
1- The Optical Blocks of the Complete Optical System, from the scene to the final image.
2- The IMaX Blocks Diagram.
Figure 1. Optics Blocks Diagram from scene to final image
Figure 2. IMaX Blocks Diagram
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5.2 Optical Concept
IMaX is one of the modules of the SUNRISE Post Focus Instrumentation, being the
instrumentation in front of IMaX the SUNRISE Telescope and the ISLiD optical system.
The IMaX optical configuration consists of a set of prefilter and polarization modulation
elements (ROCLIs) followed by a collimation optical system, one single etalon filter in double
pass (etalon - retroprojector mirrors system - etalon), and an imaging optical system referred by
us as camera optical system. The final image splits into two CCD cameras and phase diversity
capability is included by means of the insertion of a plane parallel plate in the optical path.
The optical system is all refractive, being the only mirrors of the system the ones used for
folding and packaging. Three mirrors in total are needed for packaging reasons.
The optical interface with SUNRISE is the ISLiD Focus F4. Next to F4 we locate the prefilter
set and the liquid crystal optical retarders (ROCLIs). After suffering the selected polarization
the beam goes through a collimator system consisting of 2 lenses and a doublet. The focal
length of this collimator is 567.36 mm and its f-number is 25, matching the SUNRISE
Telescope and ISLiD f-number. The diameter of the resultant collimated beam is 25.6 mm.
(LabC)
In the collimated space we locate one solid Fabry-Perot Interferometer which cavity material
is LiNbO3 .The etalon works in double pass, i.e, the light goes through the etalon, retroreflects
back by a system of two mirrors and passes back through the etalon being the length of the
collimated beam larger than the coherence length of the light.
The beam is finally focused by a camera consisting of a doublet and two lenses, being the
camera focal length 1021 mm and producing an image IMaX f-number of 44.99 (LabC).
The magnification of IMaX is 1.799X in order to get to desired image f-number. This will
cover up 907 x 907 pixels, 12 m per pixel, which corresponds to a total IMaX FOV of
50arcseconds.
A polarizing beam splitter shall split the light into its two components of linear polarization
with an angle of 90º between the directions of propagation of the two exit beams in order to
achieve the requirement of mitigation of the intensity cross-talk effect into the polarization
images due to image jittering (see AD2).
Both subsystems, the collimator and the camera optical systems are telephoto lenses in order to
shorten the total length of the system, and they get reduction ratios of 0.53 for the collimator
and 0.57 for the camera.
In order to perform phase diversity correction on the image, a parallel plate can be inserted in
one of the channels in order to defocus the image on this channel with respect to the other
channel. The thickness of this plate will be 27mm and material Fused_Silica to produce the
specified defocusing range (see AD20 IMaX Optics Specification).
There will be no mechanisms for maintaining IMaX in focus during the flight.
The optical design has included a lens module simulating the SUNRISE telescope an ISLiD.
The lens module optical characteristics match the characteristics specified for the SUNRISE
telescope and ISLiD. In this way the incoming light goes through this lens module first and then
through IMaX. Nominal Image quality and optical performance are given at the image plane of
IMaX.
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In section 11 we will also evaluate the nominal final image characteristics for the whole optical
chain Telescope-ISLiD-IMaX, including the current Telescope-ISLiD optical system.
5.3 Optimization
The procedure we have followed to optimize the optical design will be summarized in this
section:
Firstly, we optimized the nominal optical design at the laboratory conditions (LabC), this is
20ºC and 1 atm. At the point where the design was nearly concluded, we evaluated the system
performance at the operational temperature and pressure conditions, which represents the
corresponding operational temperatures of every optical subset and an altitude of 40 Km. In this
way the last steps of the design consisted in alternative evaluation between the “best nominal
performance at laboratory conditions” and the “best performance at the operative conditions”.
We have chosen this way to proceed because the IMaX optics will be integrated and assembled
at laboratory conditions, but the specification is given at the operational conditions The link
between these two situations has been the determination of the Focus Positions for both
situations:
Nominal Design (LabC): (distance from F4 to IMaX prefilter): 31.53mm
Design at Operational Conditions: (distance from F4 to IMaX prefilter): 30.05mm
In this way, once the system has been assembled and integrated at the laboratory, we will
proceed to “defocus” the system to its operational focussing position in order to verify the
system performance at these conditions.
The points of the FOV used for the optimization are defined in the following figure and Table
Absolute FOV Relative
(arcseconds)
FOV
F2
F5
F4
Xangle Yangle X
F9
F8
F1
F6
F7
F3
Figure 3. Points of the FOV used for optimization
Y
F1
0
0
0
0
F2
0
+25
0
+1
F3
0
-25
0
-1
F4
+25
+25
+1
+1
F5
-25
+25
-1
+1
F6
+25
-25
+1
-1
F7
-25
-25
-1
-1
F8
+25
0
+1
0
F9
-25
0
-1
0
Table 1. FOV
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5.4 Optical Materials.
In the following chart we show the main characteristics of the glasses used for IMaX optical
design.
nd
Vd
dn/dT
(10-6/K)
 (10-6/K)
Ti (587nm)
(5mm)
Nr. of
elements
using it
B270_Schott
1.523
58.5
2.4
8.2
0.922
1
S-8612_Schott
1.542
No data
No data
9.6
0.720
1
GG495_Schott
1.540
No data
No data
9.6
0.990
2
Fused_Silica
1.458
67.8
8.6
0.5
0.999
12
SF1_Schott
1.717
29
6.4
8.1
0.999
2
SBSM22_Ohara
1.622
53
2.4
6.6
0.998
2
LiNbO2
2.305
No data
50
7.5
No data
1
N-BK7
1.5168
64.2
1.4
8.3
0.999
1
EFEL6_Hoya
1.5317
48.8
-1.1
9.8
0.998
2
MATERIAL
Table 2. IMaX Optical Materials
Where nd is the index of refraction for line d, Vd is the Abbe number, dn/dT is the temperature
coefficient of refractive index,  is thermal expansion coefficient, and Ti is the internal
transmission of the glass.
The preferred glass for IMaX optical system has been Fused_Silica. It has been used in 12 of
the 24 optical elements of the system. Some of its key properties are the following:
 Near zero thermal expansion
 Exceptionally good thermal shock resistance
 Very good chemical inertness
 Stress birefringence on the order of ordinary glasses
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The materials used for the prefilter set are B270_Schott, S-8612_Schott and GG-495_Schott.
These materials have been chosen and specified by the filter manufacturer.
Mirrors M1, M2 and M3 substrates: Fused_Silica
Beam Splitter: The material used for the beam splitter is NBK7_Schott.
Phase Diversity Plate: Fused_Silica. (See also RD1. Characterization of a defocusing plate to
implement phase diversity in IMaX)
5.5 Athermalization and Achromatization.
In order to be able to test and verify the optics of IMaX with our Zygo interferometer
(632.8nm), the system has been design for a wavelength range that includes that of the He-Ne.
In this sense IMaX has been achromatized for the range 524.87nm to 632.8nm.
The materials choice has a great impact on both the achromatization and the athermalization of
the instrument. So, for the doublets at IMaX we had to look for pairs of glasses that compensate
both the chromatic aberration and the sensitivity to changes in temperature. To have a first
approach to this choice of materials, we have calculated the change of the focal length of the
doublets with both the wavelength and the temperature, as follows:
The total power of a cemented doublet consisting of two lenses A and B can be expressed as
TOTAL   A   B , where   c(n  1) , (1) c is the lens curvature 1/r, and n the refractive
index
Then, the variation of the power with wavelength will be: (derivating (1) with respect to
wavelength)
 

V
where V is the Abbe number
To achromatize the doublet we will have to minimize the change in the power of the doublet
with wavelength, this is
TOTAL   A   B  0 , this means that
A
VA

B
VB
(2)
Likewise, the variation of the power with temperature will be: (derivating (1) with respect to T)
dr
 dn 

r  (n  1)

d  dT 
dT n  1  1 dn



    
2
dT
r  n  1 dT
r

Where  
1 dn

n  1 dT
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1 dr
r dT
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(Coefficient of Thermal Expansion)
To athermalize the doublets we will have to minimize the change in the power of the doublet
with Temperature, this is
d
d
d
 A  B  0 , this means that      (3)
A A
B B
dT TOTAL
dT
dT
So, combining (2) and (3) we get:
 AVA   BVB
And we can then conclude that finding pairs of glasses whose V product are equal or similar is
needed for athermalizing achromatized doublets.
At the beginning of this phase, when we started the thermal behaviour analysis of IMaX, we
found a high sensitivity of the system to temperature changes, so we had to redesign the optics
due to the fact that the original doublets, consisting of the glasses F4_Schott and Fused Silica,
were not athermalized doublets. Finally we could find a better combination for the doublets with
the glasses SBSM22_Ohara and SF1_Schott.
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6. IMAX OPTICS LAYOUT
The following figure shows a layout of IMaX Optics. No mechanical parts are shown.
12:30:55
Light
goes from focus F4 to the CCD cameras.
ROCLIs
M3
M2
F4
M1
Etalon
Prefilter
Phase Diversity
Beamsplitter
CCDs
67.57
IMaX Final Optical Design
Positions: 1-2
CPS
Scale: 0.37
Figure 4. Optics layout of IMaX
MM
XZ
24-Nov-06
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7. IMAGE QUALITY
In the following sections we will evaluate the nominal image quality of IMaX in terms of the
Wavefront Aberration, Aberration Curves, MTF Plot and Spots Diagram. The evaluation
will be done for the nominal system without tolerances and at Laboratory Conditions.
Likewise, in section 13 we will also show the optics main parameters at both Laboratory and
Operative conditions.
The Image quality has been analyzed for the wavelength band: 525.02nm ±0.2nm.
Image quality evaluation for the Nominal system shows that IMaX does not exhibit big amounts
of aberration. IMaX has been well corrected and is nearly an aberration free optical system.
7.1 Wavefront Analysis. Nominal System
We have evaluated the RMS nominal wavefront aberration and the corresponding Strehl ratio at
the defined focal position of IMaX. (LabC)
The worst case corresponds to a RMS wavefront aberration of 0.075 waves, which corresponds
to a point of the FOV on axis, and Strehl ratio of 0.998, which is better than the specified value.
The following table shows the results obtained for each point of the FOV.
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
Y
FIELD
FRACTION
0
0
0
1
0
-1
1
1
-1
1
1
-1
-1
-1
1
0
-1
0
FOV
(deg)
0
0
0
0.007
0
-0.007
0.007
0.007
-0.007
0.007
0.007
-0.007
-0.007
-0.007
0.007
0
-0.007
0
BEST COMPOSITE FOCUS
FOCUS
RMS
STREHL
(mm)
(waves)
RATIO
-0.043892
0.0075
0.998
-0.043892
0.0038
0.999
-0.043892
0.0038
0.999
-0.043892
0.0069
0.998
-0.043892
0.0069
0.998
-0.043892
0.0069
0.998
-0.043892
0.0069
0.998
-0.043892
0.0031
1
-0.043892
0.0031
1
COMPOSITE RMS : 0.0057 waves. Units of RMS are waves at 525.1 nm
Table 3. Nominal RMS Wavefront for each point of the FOV
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7.2 Aberration Curves
The following figure shows the Transverse aberration (real-ray position measured from real
chief-ray position on image surface in mm.).The chosen scale 0.030mm corresponds to 0.14
arcseconds at the object space (100Km at the Sun surface). (LabC)
( X , Y )
-1.00
, 1.00
RELATIVE FIELD
Y-FAN
0.015
X-FAN
0.015
(-0.01 O , 0.01 O)
5
-0.015
-0.015
1.00, 1.00
RELATIVE FIELD
0.015
0.015
( 0.01 O , 0.01 O)
4
-0.015
-0.015
0.00, -1.00
RELATIVE FIELD
0.015
0.015
( 0.00 O , -0.01 O)
3
-0.015
-0.015
0.00, 1.00
RELATIVE FIELD
0.015
0.015
( 0.00 O , 0.01 O)
2
-0.015
-0.015
0.00, 0.00
RELATIVE FIELD
0.015
0.015
( 0.00 O , 0.00 O)
1
-0.015
-0.015
11:45:01
IMaX Final Design
RAY ABERRATIONS ( MILLIMETERS )
CPS
26-Jan-07
Figure 5. Transverse aberration curves
525.2700 NM
525.0700 NM
524.8700 NM
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7.3 Nominal MTF
There is no specification for the Modulation Transfer Function of IMaX. However, the goal is to
get near diffraction limited images for a perfect incoming wavefront in IMaX. The following
figure shows the polychromatic MTF plot for some points of the FOV. (LabC)
11:47:22
As we can appreciate IMaX is diffraction limited.
IMaX Final Design
Y
X
Y
X
Y
X
Y
X
Y
X
DIFFRACTION MTF
CPS
26-Jan-07
DIFFRACTION LIMIT
(0.000,0.000) DEG
(0.000,.0070) DEG
(0.000,-.007) DEG
(.0070,.0070) DEG
(-.007,.0070) DEG
WAVELENGTH
525.3 NM
525.1 NM
524.9 NM
WEIGHT
1
1
1
DEFOCUSING 0.00000
1.0
0.9
0.8
0.7
M
O 0.6
D
U
L 0.5
A
T
I
O 0.4
N
0.3
0.2
0.1
4.0
8.0
12.0
16.0
20.0
24.0
28.0
SPATIAL FREQUENCY (CYCLES/MM)
Figure 6. Polychromatic MTF.
32.0
36.0
40.0
X
Y
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7.4 Spots Diagram
The following figures show the geometrical structure of the polychromatic image at some points
of the field of view. (LabC)
Spots 2-Dimensional View
Figure 7. Geometrical structure of the polychromatic image at some points of the field
The black circle, on the figure on the left represents the size of the Airy disc (58m), and the
black square, represents the size of one pixel (12m). The figure on the right represents a 2Dimensional View of the Spots Diagram.
We can observe that the size of any spot across the FOV is smaller than the size of a pixel,
minimum resolving element, and well below the size of the Airy Disc.
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8. GHOST AND STRAY LIGHT IMAGES
8.1 Introduction
The influence on the PSF of the IMaX instrument produced by the retro reflection on
optical surfaces is considered and analyzed in detail for the actual configuration. The optical
elements have been updated with respect to the mechanical position required and with respect to
the coating performances obtained from suppliers, so it will be showed only the influence on the
ghost process of the IMaX Final Optical Design configuration selected in the CDR phase.
We have analyzed the final optical configuration of the IMaX instrument in order to
show what are the most critical components which produce the ghost images. If the optical
components are coated with a high antireflection coating (Transmission >0.988), the influence
in the ghost image is negligible, as it was showed in the PDR phase. But in order to known what
is the most critical surfaces in the actual design, in which a more emphasis in the coating
properties should be taken, a special study have been performed. In this study the optical lenses
have been considered with its real coating. The critical paths, despite of being energetically
lower than required, show the elements that a special care should be taken.
After this first study, the IMaX optical components have been analyzed considering the
real performances foreseen for each components. Some of them, like the etalon and prefilter,
have been considered in a simplified version to reduce the time elapsed in our simulation. The
global transmittance of the formers elements is only simulated using one of the faces as an
active surface. In this way the strength of signal through the double pass response is correctly
simulated, but not the real spectral response because, for example, the real ghost images process
could produce some extra widening of the spectral peaks that are not considered in our
simulation.
The coating and optical properties chosen are the worst cases for the transmittance for each
optical component and are as follows:

Prefilter with a transmittance of 65% (measured by IAC)

ROCLI´s with a transmittance of 97% (see RD3)

Etalon with a transmittance in single pass of 82% and absorption coefficient 0.04 mm-1

Flat Windows (Etalon and CCD windows) R=99%

Beam splitter

Input and output faces: R=99%

Internal Face: R=100% for S polarization
T=100% for P polarization
Extinction coefficient:1000:1

Folder mirrors (FM1, FM2) R=100%

The CCD area with a reflectivity of 10% (measured by IAC)
The values above showed are considered the worst cases for the transmittance for each optical
component.
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8.2 Ghost images
The methodology used in the quantification of the ghost effect is briefly summarized in
the current paragraph.
A normalized input flux of 1 Watt with S-polarization plane (Y-axis) has been
considered in all the cases. The flux obtained in the CCD for the total PSF (including ghost
image) has been compared with the flux obtained for the ghost image only. In order to do this,
we have saved the history (ray intersection and flux in each surface) of each most energetic path
selected by ASAP. This enable us to recover the different paths with the flux assigned in each
case.
In order to have a more realistic effect of the interaction of the ghost image with the
direct path we have considered the coherence length (CL) of the light produced by the spectral
selection produced by the etalon. The spectral resolution could be related with the longitudinal
coherence length by means of the next relationship:
2
CL 

Where Δλ is the spectral resolution (100 mÅ) and λ is the wavelength of interest
(525.02 nm) producing a value of CL=28 mm. This means that those images produced by the
reflections of different optical components with optical path lengths higher than the value of
CL, mentioned above, are summed incoherently. Values of optical path length lower than the
CL are summed coherently. This concept let us to have a more clear effect of the different ghost
images in the final PSF of the system, as it will be showed in the next paragraph, In some cases
the effect is like a veil spread over the PSF area of interest, and in another situations the effect is
like a real PSF with lower intensity.
With respect to criterion followed to quantify if a ghost flux is dangerous or not in each
case we have proceed with the comparison of the flux produced by the ghost image with respect
to the total flux calculated in two different areas; one of them with a diameter of 1 mm and
centered with the Airy disk, and another one considering the total detector area. In whatever
case we have considered negligible the effect of the ghost image if the total flux contained in the
ghost flux is lower than 1% of the corresponding to the PSF over a small area. In all the cases
we have take in to account too that the IMaX images require to have “a S/N ratio of 1000” (see
AD2 IMaX Requirements) which means that if the flux level is 3 orders of magnitude lower than
the maximum signal detectable, the influence of the ghost image is indistinguishable of the
noise inherent to the system.
8.2.1 Ghost images for one on-axis point source
In this study, we want to analyze the influence of the critical optical elements in the
ghost image generation process. These critical components are the Prefilter, ROCLIs, Etalon,
polarizing Beam-splitter cube and CCD-window. In this simulation we have considered the final
mechanical location of each component and, if possible, the commercial data of the coating for
each optical surface in order to have a more realistic behavior. As it was mentioned before, the
incident flux has been considered as 1W in the S-polarization plane. The simplified versions of
the active etalon and prefilter surfaces have been considered avoiding the multiple reflections
required to really simulate these components. The first study has been considered with the tilt of
the Etalon of 0.15º, value that was considered optimum in the previous phase (PDR). The
change of the cameras due to the problems with the first supplier forced to change the
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reflectivity of the folder mirrors for doing the double pass in the Etalon. The new reflectivity
(actually 100% versus the 30% before) has produced the apparition of new optical paths for the
ghost process. This new paths have been controlled with an extra tilt of the etalon to avoid that
the retro-reflection produced by this component were able to reach the CCD area. The lower
sensitivity of the new cameras has obliged too to the change of the focal length in the camera
optics block for getting much more flux. Consequently the #F number of this block has been
diminished to gather higher flux level. Both, the reduction of the corresponding focal length and
the increase in the reflectance of the mirror have been an enormous impact in the ghost process
in IMaX. This new situation has been studied first to understand the way in which these
problems could be solved.
In our first simulation, we have used a point source centered on axis and we have
considered 5 child rays for each parent ray. Those beams that after consecutive reflection or
refractions diminish its energy to values lower than 10-9 have been eliminated. This new
situation produces much more energetic paths that the situation before.
Figure 8: Optical Lay-out showing the behavior of the cube for the S-polarization.
The number of paths obtained is higher than 200 but we have analyzed only the 43 first
because are the most important. The ASAP structure let us to classify easily the most energetic
paths and to relate them with the object or their combination that produce the critical paths.
The most energetic paths are:

The PATH 1 that represents the direct beam that produces the PSF without ghost.

24 other paths are produced by the reflection on the active face of the Etalon,
showing the critical behavior of this component.

The second energetic group of paths is produced by the surface of the etalon’s
windows and the reflection produced by the detector surface. These paths are more
energetic than those produced by the combination of the etalon and another surface
wit antireflective coating
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Another energetic PATH is originated by the Prefilter pack which is produced by
the tilt angle required for tunning this component. The high reflectance of the
prefilter (0.35%) and the tilt in Y-axis (2.1º) in combination with the diverging
singlet (Lens 2 collimator) of this arm, produce a very high path trough the system
that should be eliminated by the stray-light concept as shown below. Fortunately,
the high deviation of this beam does not influence in the final ghost images obtained
because this path is not collected by the rest of the optics, but a special care should
be taken to avoid its influence in the stray-light analysis.
The peak value obtained for the ghost lobes are 2.0 orders of magnitude lower than the PSF
peak, what means that this intense ghost image should be attenuated.
In order to verify the simulation performed in ASAPTM, we need to evaluate that the flux
collected in a small area is big enough to collect the spreading of the PSF of the system but
small enough to avoid the flux collected by other paths superposed to the PSF. So a 2 mm
square area has been considered to analyze the flux received. The total flux obtained using
ASAPTM is 0.3 W which could be correlated with the coating properties selected in each surface.
we obtain the flux in the detector, F’ after considering the surfaces involved as:
F’=0.65x0.974x0.992x0.822x1.02x0.992x0.97x0.999x0.97x0.992x0.9=0.308W
If we consider the absorption coefficient in the etalon we get the final flux F as:
F  F ' e2 d  F ' e20.040.282  0.302
that corresponds exactly with the value provided by ASAPTM
8.2.2 Ghost images for a out-of-axis point source
To analyze better the influence of the ghost images produced in IMaX we performed a
new simulation in which the object point is shifted to the lower position of the Field of view
(Y=-3.2 mm).
The PATH 1 corresponding to the PSF collects the 84% of the energy collected in the
detector. The most energetic path found is related with the interaction of the reflected beam in
the active surface of the etalon and the CCD surface. This interaction produces a pattern that
extends across the detector area.
If the path corresponding to the PSF is eliminated the strength of the ghost peak is
clearly showed. The final value obtained is higher than required. This peak is produced mainly
by the back reflection in the etalon surfaces which produces a very sharp image on the CCD
area.
If we move the point source to the upper position of the Field of View, Y=3.2 mm the
situation is more or less similar. In the transversal section of the flux on the detector area we can
see that there is again a relatively intense peak in the middle of the graph. This ghost is
produced in a similar way that in the above case: by the reflection on the active surface of the
etalon. The combination of all paths involved has a peak value of 2.4 orders lower than the peak
of the PSF. This value suggests that the tilt of the Etalon should be increased in order to avoid
the influence of the retro reflection.
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8.3 Elimination of the ghost images.
The tilt of the Etalon around the X axis an angle of 0.36 assures that the reflection
produced by this component is outside the CCD area. We have analyzed both extreme of the
FOVs, i.e. at Y=3.3 mm. and Y=-3.3 mm and the results obtained are similar; the ghost images
have diminished considerably. The ghost peak obtained is 3 orders of magnitude lower than the
peak of the PSF. We have noted that the ghost PATHS more energetic found are related with the
back reflection of etalon’s windows that produce a PSF ghost image well focused on the CCD
area. To avoid this influence we tilt too the etalon subassembly an angle of 0.36º around the X
axis. The peak value obtained for this situation is lower than 4 orders of magnitude with respect
the PSF peak, showing the way in which the ghost process could be totally controlled in IMaX.
8.4 Conclusion of the ghost process of IMaX:




To avoid the influence of the ghost images the total etalon subassembly an angle of
0.36º around X axis.
The most critical components are those located in the parallel beam and special care
will be taken to assure that these components do not produce any back reflection
towards the CCD area.
The ROCLIs and polarizing Beam Splitter produce a ghost image that spread over the
image plane without influence in ghost process.
During AIV phase, a specific test should be performed to assure that during the
accumulate acquisition image process is not going to show any ghost image.
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9. THERMAL BEHAVIOUR
IMaX optics consists of different subsystems which will work at different nominal temperatures
and that will be subjected to temperature changes during its operation in flight. The operative
temperatures and variation ranges for every subsystem are described below.
In this section we will simulate the operational conditions of IMaX optics and we will evaluate
the performance degradation of IMaX due to the environment. We will simplify the problem
considering the total degradation as a defocus. Then we will calculate the corresponding WFE
due to the estimated defocus.
We will also evaluate the thermal behaviour of the system when the phase diversity parallel
plate is in the path.
9.1 IMaX Operative Conditions
The operative pressures and temperature variation ranges roughly estimated during operation for
every subsystem in IMaX are described in the Table 4 (unpublished update of AD3). In the
current state of the thermal control design, the foreseen operative temperatures have a high
degree of uncertainty. Nevertheless, in this analysis we are interested in the acceptable
temperature variation range which will be an input for the thermal control designers, because
during the AIV phase the actual subsystem temperatures will be determined and the focus will
be adjusted.
SUBSYSTEM
TEMPERATURE
PRESSURE
ROCLIS
352.5ºC
2.87 mbar
ETALON
35 0.01ºC
1 atm. filled with air
DOUBLETS
29 4ºC
2.87 mbar
Etalon MIRRORS
29 4ºC
2.87 mbar
BS
15 8ºC
2.87 mbar
PHASE DIVERSITY
15 8ºC
2.87 mbar
UPPER OPTICAL BENCH
18 8ºC
2.87 mbar
MID OPTICAL BENCH
15 8ºC
2.87 mbar
LOWER OPTICAL BENCH
14 8ºC
2.87 mbar
CCDs
20 2.5ºC
2.87 mbar
Table 4. IMaX operative conditions
Note: The Pressure of 2.87 mbar corresponds to 40Km height.
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9.2 Thermal Simulation Approach
IMaX Thermal behaviour has been simulated with CODEV. CODEV capability to simulate
environmental changes is somehow limited. The most important CODEV limitations for this
type of analysis are:



The mechanical lens supports are highly simplified, assuming basic spacers represented
by its thickness and thermal expansion coefficient. We have assumed aluminium
spacers between the optical elements.
Tilted and decentered systems may not be properly modified, due to lack of modeling
capacity on how decentered/tilted elements are mounted. Then we had to evaluate our
system as being in line, without tilts, folding mirrors or bends. Optical components and
their spacers are assumed to remain in contact. No induced effects such as strain or
stress birefringence are modeled.
It is not possible to directly simulate a system in which different subsystems operate at
different temperatures. We have needed to write specific Macro sequence files to
simulate each thermal situation individually. See Annex 2
However, the simulation in CODEV takes into account the following:
Modifications with pressure:

It modifies the refraction indexes and the air spacers thicknesses according to the type
of glass and pressure contained in the spacer.
Modifications with temperature:

It modifies the refraction indexes at each wavelength according to the dn/dT values.

It scales the elements thicknesses according to the expansion coefficient ()

It scales the spacers diameters and thicknesses according to the expansion coefficient.
The simulation consisted of the analysis of the performance (in terms of defocus at the focal
plane) for three thermal cases (operative, hot and cold case). The rest of the aberrations were
not significantly affected by the thermal changes.
The simulation only studies the defocus produced by the temperature variation during
IMaX operation, and on a pretended IMaX in line (The folder mirrors are not
considered).
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The cases under study are shown in the following table:
SUBSYSTEM
OPERATIVE HOT CASE
COLD CASE
ROCLIS
35C
37.5C
32.5C
ETALON
35C
35C
35C
DOUBLETS
29 C
33C
24.5C
Etalon MIRRORS
29C
33C
24.5C
BS
15C
22.5C
7.5C
Phase Diversity
15C
22.5C
7.5C
Upper Opt. Bench
18C
25.5C
11C
Mid Opt. Bench
15C
22.5C
7.5C
Lower Opt. Bench
14C
22.1C
6.5C
CCDs
20C
20C
15C
Table 5. Thermal Cases
Pressure Conditions for all of the thermal cases:
 Etalon: pressurized at 1 atm, filled with air
 Rest of the system: Pressure 2.15 mbar (40Km height).
For each case the specific macro was run in order to assign the temperatures and pressures to
every surface and for each subsystem. The macro calculates and makes the primary changes in
the constructional parameters due to changes in temperature and pressure.
For every glass or optical material in the system we needed to know the Temperature
Coefficients of Refractive Index (dn/dT) and the Thermal expansion Coefficient (). As shown
in Table 2. IMaX Optical Materials in section 5.4, the manufactures of the filters GG495 and
S8612 cannot guarantee nor give any data about the Temperature Coefficients of Refractive
Index, so for our study we have replaced both materials by the glass BaK2, which index of
refraction is very similar to both of the coloured filters.
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9.3 IMaX Thermal Behaviour
IMaX shows
Thermal
Behaviour
The graphics below
the defocus
at the image plane (CCD) in mm for every thermal case.
1
0,75 cold
defocus in mm
0,5
0,25
0
operative
-0,25
-0,5
-0,75
hot
-1
Figure 9. IMaX Thermal Behaviour
The total range of defocus observed at the image plane and during flight goes from –0.87mm to
+0.760 (1.63mm). This value corresponds to an OPD or wavefront error of 0.026,o (/39) (See
Section 11.3), considering the total degradation as a defocus, which is the only thermal error
effect studied herein.
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9.4 Phase Diversity Thermal Behaviour
Phase Diversity attempts to produce a wavefront error of 1 (p-v) in the optical channel where it
is inserted. This value of 1 (p-v) or approximately /4 rms, is equivalent to a defocus at the
image plane of 8.51mm.
In this section we will evaluate the change in the wavefront error of this channel during
operation.
We will consider the thermal cases indicated in Table 5. Thermal Cases, section 9.2.
In the following figure we show the RMS WFE in waves (peak to valley) for every thermal
case. Phase Diversity Thermal Behaviour
1,14
1,12
cold
defocus in lambdas
1,1
1,08
1,06
1,04
1,02
operative
1
0,98
0,96
0,94
0,92
hot
0,9
Figure 10. Phase Diversity Thermal Behaviour
As a conclusion, the Phase Diversity channel will exhibit a RMS Wavefront error during IMaX
operation as shown in the Figure. The worst case represents a change in the wavefront error
during operation about 12%.
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10. TOLERANCES, BORESIGHT AND SENSITIVITY ANALYSIS
10.1 Introduction
Tolerancing provides information about the sensitivity of an optical system to typical fabrication
and mounting errors. Tolerancing can also help to determine which design to make if you have a
selection of lens designs to choose from, as well as determine the manufacturing tolerances you
need to maintain to achieve a particular level of performance.
The optical designer should choose a figure of merit for the Sensitivity Analysis. The figure of
merit measures the performance, and indicates how good the system is.
Compensators are parameters that can be adjusted in the actual system to improve performance
during the AIV phase. Any lens parameter in the optical system can be made into a
compensator.
10.2 Technical Approaches to Tolerancing
Tolerancing is a critical step in the design of an optical system. The objective is to define a
fabrication and assembly tolerance budget and to accurately predict the resulting as-built
performance, including the effects of compensation. Also part of the study is determining the
best set of compensators.
We have used CODEV software for the study of IMaX tolerancing. The algorithmic approach
in CODE V is called Wavefront Differential Tolerancing (TOR option). This is the approach
we have used for our study, however there exist some other approaches that can be used. The
two traditional approaches to tolerancing are the Finite Differences and the Monte Carlo
Analysis.
The Finite Differences approach individually varies each parameter within its tolerance range
and predicts the system performance degradation on a tolerance-by-tolerance basis. These
individual results are statistically combined to yield a total system performance prediction. This
method accurately predicts performance sensitivity to individual tolerances, which allows
determination of the parameters that are “performance drivers”. However since the Finite
Differences method does not consider how cross-terms (these are the simultaneous parameter
changes by multiple tolerances) interact, its prediction of overall performance is typically
optimistic.
The Monte Carlo approach is to vary all of the parameters that have an associated tolerance by
random amounts within each tolerance range. Then the resulting system performance is
analysed. This process is repeated many times with different random perturbations (each
analysis is referred as a trial). If many trials are run (100 to 1000 is typical), an accurate
statistical prediction of the probability of achieving a particular performance level can be
generated. Since all the parameters are being varied at the same time, The Monte Carlo method
accounts for cross-terms. However, we will get no information about individual tolerance
sensitivities (which allows determination of the “performance drivers”), and thus cannot select
the best set of tolerances to minimize cost.
Both the Finite Differences and Monte Carlo tolerancing methods are very computationally
intensive and can be very slow. CODEV supports both tolerancing methods, but the primary
tolerance analysis feature of CODEV uses a Wavefront Differential algorithm that is very fast,
and provides information about both individual tolerance sensitivities (like the Finite
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Differences method) and an accurate performance prediction, including the effect of cross-terms
(like the Monte Carlo method).
The reason that the Wavefront Differential approach is so fast compared to either the Finite
Differences or Monte Carlo methodologies is that the nominal system is ray traced once, and all
the required information for further analysis is extracted by CODE V algorithms from this ray
trace of the nominal system. The algorithmic foundation for the Wavefront Differentials
analysis method is based originally on the work of Hopkins & Tiziani, and the detailed
algorithms developed by Mathew Rimmer (See RD8) are used in CODE V’s tolerancing feature
(TOR)
The accuracy of the Wavefront Differential method is subject to a few assumptions. The
primary assumption is that ray optical path differences (OPDs) due to tolerance
perturbations vary linearly with tolerance change. This assumption is typically valid if the
tolerance perturbation results in a small degradation of the nominal performance. This is in fact
what the designer typically tries to achieve when tolerancing a system. Another assumption of
Wavefront Differential tolerancing method is that the overall performance probability has a
Gaussian form, defined by a mean and sigma. This assumption is typically valid if each
tolerance is contributing about the same to the overall performance degradation. When this is
not the case, the Gaussian probability assumption tends to be conservative. It is important to
understand that CODE V’s TOR option does include cross-terms. Wavefront differentials are
computed for each individual tolerance and for every pair of tolerances, so these important
factors are included in the overall predicted performance for the system.
10.2.1 Summary of the Wavefront Differentials technical approach.
In this section we summarize the technical approach, based on the Wavefront Differentials,
followed for the calculation of tolerances, compensating elements and sensitivity
coefficients.(see RD8 for further details)
•
•
•
•
•
Integral expressions can be developed to describe RMS wavefront error (or MTF if
desired) in terms of the complex field (amplitude and phase) across the exit pupil
The integrals are expanded in a Taylor series to second order in p, where p is the
variation in a parameter
The associated change in the wave aberration is w = (dw/dp)p, where we assume that
d2w/dp2 = 0
The wavefront derivatives, dw/dp, are determined during ray tracing
The wavefront differentials allow CODE V to compute the merit function (RMSWFE in
our case) as a general quadratic function of a parameter change for each of the
tolerances:
  ap 2  bp  c
•
The coefficients a, b, c are functions of the wavefront aberrations and the derivatives of
the wavefront aberrations in the exit pupil.
The quadratic function can be extended to a function of multiple variables by taking
combinations of wavefront differentials for two parameters at a time (i.e., the tolerance
cross-terms):
  a1p12  b1p1  a2p22  b2p2  d12p1p2  c
•
For each tolerance, TOR computes the mean and sigma of the performance criterion
from the coefficients of the quadratic equation
This computation assumes that the tolerance distributions are symmetric (CODE V
only supports tolerance distributions symmetric about the nominal value)
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Presently, TOR assumes (via the Central Limit Theorem) that the final performance
probability distribution is a Gaussian, defined by a mean and a variance obtained by
summing the means & variances from all the tolerances
The Gaussian assumption provides a very good approximation for predicted as-built
performance
– Generally conservative
– The actual performance probability distribution may be different, especially if
there is a small number of “drivers”
For each field, a summary is generated of the probabilities of achieving given levels of
performance
– This includes cross terms (effects of one tolerance on another)
The performance probabilities are dependent on the probability distributions of the
individual tolerances
– Most tolerances use a uniform distribution
– 2-D tilts and decenters use a truncated Gaussian distribution
The performance distribution calculation is based on statistical summing which results
in a Gaussian performance distribution
– The 2 point (97.7%) is labeled "Probable change"
– It means that 97.7% of the fabricated systems will have this performance
loss or less
10.3 Description of the IMaX Tolerancing Study
The tolerancing stage of the optical design requires close interaction between optical and
mechanical designers, as well as it must comply with the assembly and integration procedure
chosen for our optical system.
At the time we are writing this document, the detailed mechanical design and integration plan
have not been finished. In this sense, we will have to update the set of tolerances obtained in our
study, when these documents give us some more detail. However, in order to find a first but
good enough approach to the IMaX tolerancing study, we have defined a set of compensating
parameters that best simulate the preliminary assembly and alignment process. The approach
then consists of the choice of some quality compensators that correct the quality degradation
and force boresighting at the same time. In CODEV compensators may be labeled so that they
work with a similarly labeled subset of the tolerances, and/or the BOR command (for
boresighting).
CODEV also permits what is called “Interactive tolerancing”, which allows quick
recalculation when a tolerance value is changed or updated. It also provides a spreadsheet style
for rapid “what if” tolerancing. This is possible because the Sensitivity Coefficients are saved
after initial run.
We have used the Wavefront Differentials technical approach defined in the previous
section, controlling boresight at the same time. In this way we will get information about how
tolerances are affecting the wavefront error, on the one hand, and on the other hand how they
are affecting what CODEV calls tolerance-induced distortion (lateral shift of the chief ray at
the image plane (boresight), image scale change and image rotation).
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The way CODEV computes this tolerance-induced distortion is shown in the following figure.
‘
Figure 11. Schematic of tolerance-induced distortion
The solid grid shows the original chief ray positions (before applying the tolerance). For
illustration’s sake, this is shown as a distortion free rectilinear grid. The circles correspond to
the chief ray positions after a tolerance is applied. In general, the tolerance will induce shifts and
distortions. The position deviations of the circles from the solid grid are computed and listed.
The dashed grid is a shifted, scaled, and rotated grid which best fits the positions of the
tolerance-shifted chief rays.
For our tolerancing study, we have defined the following 3 subsets of labelled tolerances:
 Tolerances for the collimator elements (label col)
 Tolerances for the camera elements (label cam)
 Uncompensated tolerances such as compensator residuals or interface tolerances (label
mir, des)
Likewise, we have defined labelled compensators, which match the labelled subsets of
tolerances:
 Collimator doublet (focus) compensates the collimator centered tolerances
 Camera doublet (focus)  compensates the camera centered tolerances and the
residuals of the collimator doublet
 Mirrors 1 and 2 (tilt)  helps finding the optical axis in the first steps of the integration,
and fine adjusts the spectral response of the etalon
 Mirror 3 (tilt)  helps finding the optical axis in the first steps of the integration.
 CCD cameras (centering, in both directions perpendicular to the optical axis) 
compensates the collimator and camera decentered tolerances, compensates the mirrors
residuals and corrects boresight.
The advantages we have found in using this procedure for our tolerancing analysis can be
summarized as follows:
 By using labelled tolerances and compensators, we can faithfully simulate the assembly
and alignment process
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 Some of the compensators, such as the centering of the CCDs, are used both to
compensate the optical quality and to compensate boresight
 With this scheme we get three blocks of information:
o RMS Wavefront error degradation,
o Boresight
o Image Scale Change and Image rotation
The results of this evaluation will be shown in the following sections.
10.4 Performance Summary. Wavefront Error degradation
In the following Table we show the tolerances effect on the RMS wavefront aberration. Within
the column WFE Nominal DESIGN are the values of the RMS wavefront aberration, for the
Nominal Design and within the column WFE DESIGN + TOL are the values for the Design
with Tolerances after compensation. See compensators range of movement in section 10.6 of
this document.
RELATIVE FOV
0.00, 0.00
0.00, 1.00
0.00,-1.00
1.00, 1.00
-1.00, 1.00
1.00,-1.00
-1.00,-1.00
1.00, 0.00
-1.00, 0.00
WFE Nominal DESIGN
0.0062
0.0034
0.0034
0.0077
0.0077
0.0077
0.0077
0.0026
0.0026
WFE DESIGN + TOL
0.0431
0.0438
0.0438
0.0451
0.0451
0.0451
0.0451
0.0435
0.0435
Table 6: Performance Summary. Polychromatic RMS Wavefront Aberration.
The worst case corresponds to a RMS wavefront aberration of 0.0451 or /22. This value has
been entered in Table 8 . Total Error Budget, section 11 of this document, in order to compute
the total IMaX Wavefront Error.
10.5 Boresight, Image Scale Change and Image Rotation
The analysis of the tolerance-induced distortion gives us the following information:
Image Scale change
Image Rotation
Boresight:
X-shift
Y-shift
0.008546 (0.8%)
0.000123 rad (25.4arcseconds)
0.050053 mm
0.050053 mm
Due to the fact that IMaX splits the final image in two, therefore working at two different image
planes, we have evaluated the Boresight between CCDs: relative boresight between both image
planes. This is due to the deviation angle error in the Beamsplitter and the CCD positioning
error. The deviation angle error can be corrected with the CCD alignment capability, therefore
the only remaining error will be the CCD positioning error, or 0.05mm
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10.6 Compensators range of movement
The range of movement needed for each compensator and their accuracy are as follows:
COMPENSATOR
Collimator doublet
Camera doublet
Mirrors 1 and 2
Mirror 3
CCD cameras
RANGE OF MOVEMENT
1.8mm along the optical axis
2.6mm along the optical axis
1arcmin
1arcmin
0.8mm in both directions
perpendicular to the optical axis
ACCURACY
0.01mm
0.01mm
10arcseconds
10arcseconds
Better than 0.05mm
Table 7. Compensators range of movement
10.7 Summary of the most critical tolerances
In this section we summarize IMaX optics most critical tolerances. The most contributing lenses
to a degradation of the WFE are the lenses that use a great part of their aperture to produce the
image. In this way, the lenses near a pupil will contribute the most to the WFE. In addition to
this, the lenses far-off from the image plane and with a long focal length, will contribute the
most to the boresight error.
At IMaX the lenses of the collimator doublet and the camera doublet fulfil both conditions.
They are located very near a pupil and they are far-off the image plane. In this sense we found
that surface quality, wedge, centering and tilt for those lenses were the most demanding
tolerances. For this reason we have built a prototype of this piece in order to previously test the
achievement of the required tolerances.
Elements: Lenses in collimator and camera doublets
TOLERANCE
VALUE
COMMENTS
Centering
30 to 50m (for each element Development of a special
setup for centering while
and for each doublet)
cementing the lens on
mounting.
Development of a specific
alignment and centering
procedure for the mounting of
the doublet.
Barrel Tilt
30 arcseconds to 1arcmin (for Development of a special
each element and for each setup for centering while
doublet)
cementing the lens on
mounting
Development of a specific
alignment and centering
procedure for the mounting of
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Elements: Lenses in collimator and camera doublets
TOLERANCE
VALUE
COMMENTS
the doublet.
Surface quality
/20
Achievable. Cost Increase
Surface Irregurarity
/40
Achievable. Cost Increase
Wedge
0.7 - 1 arcmin. or 6 -10 m
Achievable. Cost Increase
Elements: Mirrors M1 , M2 and M3
TOLERANCE
VALUE
COMMENTS
Surface quality
/20
Achievable. Cost Increase
Tilt Adjustment Accuracy
10 arcseconds
By means of precision mechanism
The optical manufacturing tolerances and the positioning tolerances of every element at IMaX
are included in documents AD4 to AD19 and AD20.
10.8 Tolerances of the Interface F4
In this section we summarise the tolerances at F4, referred to the integration ISLiD - IMaX,
agreed with MPS. (See also AD1 ISLiD-IMaX Optical Interface Control Document)

Defocus (optical axis direction) adjustable with accuracy 0.25mm

Optical Bench Tilt: adjustable with accuracy 3 arcmin

Boresight or Lateral Displacement in both directions perpendicular to the optical axis:
adjustable with accuracy 0.2mm
11. TEL-ISLID-IMAX IMAGE QUALITY EVALUATION. ERROR BUDGET
In this section we will evaluate the nominal image quality at the IMaX focal plane when
working with the actual SUNRISE Telescope and ISLiD optical system. The evaluation will be
done for the nominal system without tolerances and at Laboratory Conditions and in terms of
the MTF and Spots Diagram.
In section 11.3 we will evaluate the Error Budget for the whole optical chain (Telescope –
ISLiD – IMaX) as in operation, this is, taking into account all type of errors that can be present
during the operation
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11.1 MTF
In this section we show the comparison between the Polichromatic MTF at F4 (Telescope
+ISLiD) and the MTF at the IMaX CCDs (Final image of IMaX). As we can see IMaX
contribution to the MTF degradation is hardly noticeable
Figure 12. MTF at F4
Figure 13. MTF at IMaX CCD
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11.2 Spots Diagram
In this section we show the comparison between the Spots Diagram at F4 (Telescope +ISLiD)
and at the CCDs (Final image of IMaX). The black circle represents the size of the Airy Disc.
As we can see the shape of the diagrams at F4 is the same than the shape at the final image,
meaning that IMaX is hardly contributing to the main aberrations of the whole chain.
Figure 14. Spots Diagram at F4
Figure 15. Spots Diagram at IMaX CCD
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11.3 Total Wavefront Error Analysis. ERROR BUDGET
In this section we will statistically analyze the Total Wavefront Error at the image plane of
IMaX. In this way we are also considering the contribution of the instrumentation in front of
IMaX, (Telescope and ISLiD) as being part of the final image formation.
We will take into account all type of errors that can be present during the operation of IMaX,
such as:
 Manufacturing errors
 Assembly and integration errors
 Thermal errors
The units we will be using for the WFE are waves at the reference wavelength (525.02nm).
In order to convert defocus errors into wavefront errors and vice versa, we will use the
following expression which calculates the WFE due to a defocus at the image plane:
OPD P V 
defocus(in _ units _ of _  )
8 * FN 2
And to convert this value into rms
OPDRMS 
OPDP V
4
where OPD is the Optical Path Difference and FN is the F-Number at the image plane (where
the defocus is produced).
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The sources of error that contribute to a degradation of the wavefront error at the IMaX image
plane have been distributed in the following groups:
Figure 16 IMaX WFE Budget
The calculation of the Total Wavefront Error, will be done attending to this error distribution
and to the following expression:
IMaX WFE
TOTAL WFE (Tel. + ISLiD + IMaX) = RSS
Interface ISLiD – IMaX WFE
Telescope + ISLiD WFE
where
IMaX WFE = RSS
IMaX Optomechanical WFE
IMaX Thermal WFE
and
IMaX Optics WFE,(without etalon)
IMaX Optomechanical WFE = RSS
IMaX Etalon WFE
Where equal colours are summed following the RSS rule
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Telescope & ISLiD WFE
The contribution of the Telescope and ISLiD to the final image WFE has been evaluated by
MPS and is shown at AD1 ISLiD-IMaX Optical Interface Control Document
/8.25
Interface ISLiD – IMaX WFE
The contribution of the interface at F4 to the final image WFE will be the estimated residual
defocus error between ISLiD and IMaX, due both to the integration between them and the
defocus during flight. This value has been has been also taken from AD1 and has been
converted into WFE as explained above
±0.25mm  /42
IMaX WFE
We have split the IMaX contribution to the total WFE in the following subgroups:
 IMaX Optomechanical WFE (Optomechanical and manufacturing errors)
o
IMaX Optics WFE,(without etalon) All optical elements contribution, but the
etalon (computed by CODEV, /22, See section 10.4)
o
IMaX Etalon WFE Etalon contribution (measured at the interferometer, /23)
(see AD21-TCE 116 Etalon Preliminary Optical Test Report).
 IMaX Thermal WFE (Thermal errors)
o
(computed by CODEV, 0.27mm at F4, 0.9mm at the image plane /38)
(See section 9.3)
These contributions give a WFE for IMaX of 0.069 or /15, which is slightly better than the
specified value.
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In the following table we show the Total Error Budget, where all the sources of error are
statistically added to get the Total WFE of the chain Telescope & ISLiD & IMaX. The
evaluation method or the origin of the error sources are also indicated in the table. The
corresponding Strehl Ratio is also indicated at the bottom of the table. The values corresponding
to IMaX are highlighted in red.
WFE rms
Total Tel-ISliD-IMaX WFE
0,141 ( / 7,08)
Tel-ISLiD WFE…………………………………
0,121 ( / 8,25) Interface doc
Interface ISLiD-IMaX…………………………
0,024 Interface doc
IMaX WFE………………………………………
0,069 ( / 14,56)
Optomechanical IMaX WFE……………………………………
0,063
Optics WFE (without etalon)…………………………………..
0,046 code V
Etalon Measured WFE…………………………………………
0,043 measured (3 May 06)
Thermal WFE……………………………………………………. 0,026 code V
Strehl Ratio
Tel & ISLiD & IMaX…
0,45
Tel & ISLiD…………..
0,56
IMaX only……………
0,83
Table 8 . Total Error Budget
Cells with the same colour are RSS-summed. Partial and total RSS sums are shown at the
corresponding column on the left.
Strehl Ratio has been calculated by the following expression:
Strhel _ Ratio  e(2 wfe)
where wfe is rms wfe in 
2
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12. PARTICLES CONTAMINATION IN IMAX OPTICS
12.1 Introduction
The contamination study and conclusions are the same as in the PDR phase.
The presence of particles on optical surfaces will reduce the strength of the signal reflected to
the next optical element. In general, the particles will have a high absorptivity to the incident
wavelength and consequently the transmittance of the optical component will be diminished. In
this section the influence on the IMaX performances produced by particles contamination in
optical surfaces is considered and analyzed. A separate technical note (see RD5) describes in
more detail the results obtained.
In general not only the transmittance of the optical system will be affected by the presence of
particles. The scattering of light produced by this small size diffracting elements produces a
disastrous distribution of light over the detecting area that could reduce yet more the ability of
the optical system to collect energy.
The buildup of particles over an optical surface is directly related to the amount of particles in
the surrounding air. The gravity, the viscous drag and other complicated effects produce the
degradation of the optical quality of the non protected optical surfaces during time because more
particles will fall out of the atmosphere onto exposed surfaces. In this sense, despite of an
optical surface could be consider clean at the beginning of a integration plan and in a
determinate classroom level after some exposure elapsed time the surface will be dirty
independently the classroom level selected.(the better the air class level , the longer the elapsed
time before cleaning the surface ). Our study tries to understand what is the maximum time that
the IMaX optical system could survive without lost of performances before cleaning when the
instrument is submitted to a specific classroom level. The MIL STD 1246C (RD6) and FED
STD 209E (RD7) have been followed.
12.2 Summary of the Study
We have evaluated the relationship between the cleaning class and the surface cleaning level as
a function of the exposure time to the mentioned ambient conditions. It is started from an
empirical observation that indicates that the average fallout rate of 5-m particles onto
horizontal is given by (RD5):
dN 5m, t 
 cc. p * C _ SL0.773
dt
where cc= 1, dN/dt is the fall out ratio measured per ft 3 and day, p = 2851 for a standard
cleaning room (between 15 to 20 air changes per hour).
After some rearrangement of the equations it is found the last mathematical expression which
has to resolved numerically (RD5).
 log  C part   ClogC part 2 log52 
 0.02·cc·p·t·C _ SL0.773

 10
 log  5 
This equation permit to calculate the surface cleaning level as a function of the air quality
cleaning room (classroom level)
So, considering the most dangerous situation (up-horizontal surface orientation), the resolution
of the equation takes the following graphical aspect Figure 17):
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3
7
500
30
SurfClLevH ( 10  i)
SurfClLevH ( 100  i)
SurfClLevH ( 1000  i)
100
SurfClLevH ( 10000  i)
SurfClLevH ( 100000  i)
47.441
10
1
10
1
1 10
3
100
i
t (days)
110
3
Figure 17. Surface cleanliness level versus exposed time for different air quality classroom
levels (Horizontal up-ward facing surface-normal).
If it is considered a vertical orientation for the surface, its particle density levels are reduced to
10 times lower than that obtained for the ‘horizontal up-ward facing’ case.
Thus (see also Figure 19),
SurfClLevV (C _ SL, t ) 
1000
1 10
SurfClLevH (C _ SL, t )
10
3
500
7
30
SurfClLevV( 10  i) 1
SurfClLevV( 100  i)
100
SurfClLevV( 1000  i)
SurfClLevV( 10000  i)
SurfClLevV( 100000  i)
10
4.744
1
1
1
10
100
i
t (days)
1 10
3
3
110
Figure 18. Surface cleanliness level versus exposed time for different air quality classroom
levels Vertical surface-normal air.
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If it is considered the surface down-facing oriented, its particle density levels are reduced to 100
times lower than that obtained for the ‘horizontal up-ward facing’ case. Thus (see also RD 9),
SurfClLevA(C _ SL, t ) 
SurfClLevH (C _ SL, t )
100
1 10
3
1000
500
7
SurfClLevA ( 10  i) 1
30
100
SurfClLevA ( 100  i)
SurfClLevA ( 1000  i)
10
SurfClLevA ( 10000  i)
SurfClLevA ( 100000  i)
1
0.1
0.1
1
1
10
100
i
t (days)
1 10
3
110
3
Figure 19: Surface cleanliness level versus exposed time for different air quality classroom
levels Horizontal down-ward facing surface-normal air.
The information deduced from Figure 17 to Figure 19 let us to understand what is the maximum
exposure time that IMaX could withstand for maintaining a surface level of interest. For
example, if it is required to assure a surface cleanliness level better than 200 for each optical
surface the maximum exposure time for a 100 level Classroom is 40 days but for a 10,000
classroom level the maximum exposure time is 4 days. These curves will be used to prepare the
particulate quality control during the AIV plan.
We have estimated the lost in performances of IMaX with respect to the cleanliness level
required using ASAP. A specific scattering model on each optical surface have been created and
related with the particulate contamination on each surface. The ratio of the foreseen PSF of the
system with respect to energy scattered by the surfaces let us to clarify the cleanliness level
required. The most relevant results are summarized in the next paragraph.
12.3 Conclusions

The recommended surface level class for IMaX optical instrument should be 200 or
better. To achieve this, a specific control plan during integration phases should be
considered.

The external surfaces should be cleaned to maintain the surface class level required. If
one process during integration phase is going to be performed in a non-controlled
classroom the maximum exposure time should be decided from Figure 17 to Figure 19.

Independently of the classroom level in which a sensitive optical surface is, after some
time of exposure the surface will be dirty.
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13. RESULTS AND CONCLUSIONS
The following Table shows the optics main parameters at both Laboratory conditions and during
operation, and compares them with the specified values. The values under column VALUE at
operation are the mean of all the values considered. (See Table 5. Thermal Cases )
PARAMETER
SPECIFICATION
Wavelenght range
525,020,2nm
>50x50 arc seconds
FOV (XxY)
-------------------Distortion
45
F/N at image plane
0.055
Image scale (arcsec/pixel)
Angel of incidence on
<0.58º
Collimated beam
WFE Phase Diversity
0.25 rms (12%)
Strehl Ratio
(nominal / with tol.)
Telecentricity at image
plane
Stray Light and ghost
images
0.95 / 0.8
VALUE at
LabC
As specified
As specified
-0.06%
44.99
0.055
VALUE at
Operation
As specified
As specified
0.012%
45.01
0.055
0.44º
0.44º
0.25 rms
0.998 nominal
0.85 with
tolerances
0.28 rms
0.998 nominal
0.83 in operation
Telecentric
60 arcsec
22 arseconds
35 arseconds
<1% PSF
As specified.
By means of
tilting the
etalon 0.36º
Not evaluated
Table 9: Optics main parameters
The nominal optical design meets desired performance criteria, and contains margin to be
applied to fabrication and alignment tolerances.
This document contains a simplified analysis of the Thermal behaviour of IMaX.
Stray light for the nominal design can be well controlled with the conventional inclusion of
paints and baffles.
The recommended surface level class for IMaX optical instrument should be 200 or better.
To achieve this, a specific control plan during integration phases should be considered.
Design Report
IMaX Final Optical Design
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ANNEX 1. SURFACE LISTING
OBJ:
STO:
2:
3:
RDY
INFINITY
INFINITY
INFINITY
INFINITY
THI
INFINITY
0.000000
25000.000000
0.000000
MOD:
MFL:25000.000000
MRD:
1.00E-10
MFF:
-2.50E+04
MBF:25000.000000
MED:
-1.000000
MFD:
0.000000
4:
INFINITY
25000.000000
5:
INFINITY
0.000000
6:
INFINITY
31.530000
XDE:
-0.256962
YDE:
0.000000
ADE:
0.000000
BDE:
0.000000
7:
INFINITY
4.000000
SLB: "Prefilter"
XDE:
0.000000
YDE:
0.000000
ADE:
0.000000
BDE:
-2.100000
8:
INFINITY
0.500000
9:
INFINITY
2.000000
10:
INFINITY
2.000000
11:
INFINITY
2.000000
12:
INFINITY
0.000000
13:
INFINITY
2.000000
XDE:
0.000000
YDE:
0.000000
ADE:
0.000000
BDE:
2.100000
14:
INFINITY
6.000015
SLB: "rocli 1"
15:
INFINITY
5.000000
16:
INFINITY
6.000015
SLB: "rocli 2"
17:
INFINITY
10.400000
18:
27.25420
4.170000
SLB: "coll_lens 1"
19:
613.06000
34.250000
20:
-16.07900
3.560000
SLB: "coll_lens 2"
21:
41.20000
171.750000
22:
-778.89000
2.500000
SLB: "coll_doublet"
23:
105.09800
7.780000
XDE:
0.000000
YDE:
0.000000
ADE:
0.000000
BDE:
0.000000
24:
131.45000
6.500000
25:
-93.33000
15.000000
26:
INFINITY
0.000000
27:
INFINITY
0.000000
XDE:
17.500000
YDE:
0.000000
ADE:
0.000000
BDE:
0.000000
28:
INFINITY
14.000000
SLB: "Etalon Window 1 Pass_1"
XDE:
0.000000
YDE:
0.000000
ADE:
0.360000
BDE:
0.000000
29:
INFINITY
0.000000
30:
INFINITY
15.359000
31:
INFINITY
0.282000
SLB: "Etalon Pass_1"
RMD
MEN:
ZDE:
CDE:
ZDE:
CDE:
GLA
0.000000
0.000000
0.000000
B270_SCHOTT
0.000000
0.000000
'GG495'
'S8612'
'GG495'
ZDE:
CDE:
0.000000
0.000000
SILICA_SPECIAL
SILICA_SPECIAL
SILICA_SPECIAL
SILICA_SPECIAL
SF1_SCHOTT
ZDE:
CDE:
0.000000
0.000000
SBSM22_OHARA
ZDE:
CDE:
0.000000
0.000000
SILICA_SPECIAL
ZDE:
CDE:
0.000000
0.000000
'LiNbO3'
Design Report
IMaX Final Optical Design
32:
33:
34:
SLB:
35:
36:
XDE:
ADE:
37:
38:
SLB:
XDE:
ADE:
39:
SLB:
40:
SLB:
XDE:
ADE:
41:
42:
43:
44:
45:
XDE:
ADE:
46:
XDE:
ADE:
47:
48:
49:
50:
SLB:
51:
52:
53:
SLB:
54:
55:
XDE:
ADE:
56:
57:
58:
59:
SLB:
60:
61:
62:
XDE:
ADE:
63:
64:
SLB:
65:
66:
SLB:
Code:
Iss/Rv:
Date:
Page:
INFINITY
0.000000
INFINITY
15.359000
INFINITY
14.000000
"Etalon Window 2 Pass_1"
INFINITY
0.000000
INFINITY
0.000000
-17.500000
YDE:
0.000000
ZDE:
-0.360000
BDE:
0.000000
CDE:
INFINITY
85.000000
INFINITY
-17.500000
REFL
"Folding Mirror 1"
0.000000
YDE:
0.000000
ZDE:
0.000000
BDE:
45.000000
CDE:
INFINITY
-17.500000
"dummy"
INFINITY
85.000000
REFL
"Folding Mirror 2"
0.000000
YDE:
0.000000
ZDE:
0.000000
BDE:
45.000000
CDE:
INFINITY
0.000000
INFINITY
0.000000
INFINITY
0.000000
INFINITY
0.000000
INFINITY
0.000000
17.500000
YDE:
0.000000
ZDE:
0.000000
BDE:
0.000000
CDE:
INFINITY
14.000000
0.000000
YDE:
0.000000
ZDE:
-0.360000
BDE:
0.000000
CDE:
INFINITY
0.000000
INFINITY
0.000000
INFINITY
15.359000
INFINITY
0.282000
"Etalon Pass_2"
INFINITY
0.000000
INFINITY
15.359000
INFINITY
14.000000
"Etalon Window 1 Pass_2"
INFINITY
0.000000
INFINITY
0.000000
-17.500000
YDE:
0.000000
ZDE:
0.360000
BDE:
0.000000
CDE:
INFINITY
15.000000
INFINITY
0.000000
INFINITY
0.000000
285.92000
8.000000
"camera_doublet"
-230.41000
2.500000
-1678.80000
196.350000
INFINITY
0.000000
REFL
0.000000
YDE:
0.000000
ZDE:
0.000000
BDE:
45.000000
CDE:
INFINITY
-204.710000
202.42000
-3.600000
"camera_lens 1"
-28.18400
-60.610000
298.54000
-10.000025
"camera_lens 2"
SUN-IMaX-RP-IX200-023
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SILICA_SPECIAL
0.000000
0.000000
0.000000
0.000000
BEN
0.000000
0.000000
BEN
0.000000
0.000000
SILICA_SPECIAL
0.000000
0.000000
'LiNbO3'
SILICA_SPECIAL
0.000000
0.000000
SBSM22_OHARA
SF1_SCHOTT
0.000000
0.000000
BEN
SILICA_SPECIAL
SILICA_SPECIAL
Design Report
IMaX Final Optical Design
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67:
68:
46.63900
-2.000000
INFINITY
-25.400000
SLB: "Beam Splitter Cube"
69:
INFINITY
-69.970000
70:
INFINITY
-1.000000
SLB: "Detector Window"
71:
INFINITY
-1.050000
IMG:
INFINITY
0.000000
SUN-IMaX-RP-IX200-023
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NBK7_SCHOTT
EFEL6_HOYA
SURFACE LISTING FOR PHASE DIVERSITY BRANCH:
68:
INFINITY
-12.700000
NBK7_SCHOTT
SLB: "Beam Splitter Cube"
69:
INFINITY
12.700000
REFL
NBK7_SCHOTT
XDE:
0.000000
YDE:
0.000000
ZDE:
0.000000
ADE:
0.000000
BDE:
45.000000
CDE:
0.000000
70:
71:
72:
73:
INFINITY
12.690000
INFINITY
27.000000
INFINITY
30.280000
INFINITY
1.000000
SLB: "Detector Window"
74:
INFINITY
1.050000
BEN
AIR
SILICA_SPECIAL
AIR
EFEL6_HOYA
Design Report
IMaX Final Optical Design
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ANNEX 2. CODEV MACRO FOR THERMAL BEHAVIOUR
res imax45_enlinea
thi s6 30.05
!el anterior thi se obtiene de optimizar a 40km de altura y
temperatura nominal de cada subconjunto
!FICHERO QUE DEJA EL CONJUNTO ROCLIS A LA TEMPERATURA DADA POR ^tem
!Y CAMBIA LOS CONJUNTOS ETALONES, DOBLETES, BS Y BANCO A ^te ^tbs y
^tb
!EL FICHERO DE PARTIDA ESTA A 20ºC
!EL TELESCOPIO NO CAMBIA
!DN ES *10-6
!EXP ES *10-7
!METER TEMPERATURAS DE CADA SUBCONJUNTO
!temperatura de los Roclis
^tem == 35
!temperatura de los etalones
^tet == 35
!temperatura de los dobletes
^td == 29
!temperatura de los espejos del etalon
^tesp == 29
!temperatura de BS
^tbs == 15
!temperatura de la bancada parte superior
^tbsup == 18
!temperatura de la bancada parte media
^tbmed == 15
!temperatura de la bancada parte inferior
^tbinf == 14
!temperatura de la CCD
^tccd == 19.9
!FACTORES DE CAMBIO EN LOS DN Y EXP DE CADA SUBCONJUNTO
^fet == (^tet - 20)/(^tem - 20)
^fd == (^td - 20)/(^tem - 20)
^fesp == (^tesp - 20)/(^tem - 20)
^fbs == (^tbs - 20)/(^tem - 20)
^fbsup == (^tbsup - 20)/(^tem - 20)
^fbmed == (^tbmed - 20)/(^tem - 20)
^fbinf == (^tbinf - 20)/(^tem - 20)
^fccd == (^tccd - 20)/(^tem - 20)
env
tem ^tem
tok y
alt 40000
!presurizacion de las CCD
!pre s70 argon 760
!presurizacion del etalon
pre s29 air 760
pre s32 air 760
pre s48 air 760
pre s51 air 760
!SUPERFICIES DEL MODULO SIMULADOR DEL TELESCOPIO + ISLID
Design Report
IMaX Final Optical Design
exp s0..5
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51 of 52
0.00000001
!SUPERFICIES DEL CONJUNTO ROCLIS. CAMBIAN A LA TEMPERATURA DADA POR
^tem
!POR ESTA RAZON NO SE METE SUPERFICIE A SUPERFICIE, YA QUE LAS COGE
ENV
!ESTO ES ASI SOLO PARA ESTE CONJUNTO
!METO dn/dT DE B270 POR NO ESTAR EN EL CATALOGO DE CODEV
dn
s7
2.4 2.4 2.4
!SUPERFICIES DEL CONJUNTO ETALONES Y ESPEJOS ETALONES.
!CAMBIAN A LA TEMPERATURA DADA POR ^tet y ^tesp
!CALCULADO MEDIANTE EL FACTOR ^fet Y ^fesp
dn
dn
dn
dn
dn
dn
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
exp
s27
^fet*8.66 ^fet*8.66 ^fet*8.66
s30
^fet*50 ^fet*50 ^fet*50
s33
^fet*8.66 ^fet*8.66 ^fet*8.66
s45
^fet*8.66 ^fet*8.66 ^fet*8.66
s49
^fet*50 ^fet*50 ^fet*50
s52
^fet*8.66 ^fet*8.66 ^fet*8.66
s27
^fet*5
s29
^fet*236
s30
^fet*75
s32
^fet*236
s33
^fet*5
s37..38 ^fesp*236
s45
^fet*5
s48
^fet*236
s49
^fet*75
s51
^fet*236
s52
^fet*5
!SUPERFICIES DEL CONJUNTO BANCADA. CAMBIAN A LA TEMPERATURA DADA POR
^tbsup ^tbmed y ^tbinf
!CALCULADO MEDIANTE EL FACTOR ^fbsup, ^fbmed y ^fbinf
exp
s20
^fbsup*236
exp
s36
^fbsup*236
exp
s39
^fbsup*236
exp
s60
^fbsup*236
exp
s62
^fbmed*236
exp
s68
^fbinf*236
!SUPERFICIES DEL CONJUNTO DOBLETES. CAMBIAN A LA TEMPERATURA DADA POR
^td
!CALCULADO MEDIANTE EL FACTOR ^fd,
dn
dn
exp
exp
exp
exp
s21
s23
s21
s22
s23
s24
^fd*6.85 ^fd*6.86 ^fd*6.86
^fd*2.50 ^fd*2.50 ^fd*2.50
^fd*81.375
^fd*236
^fd*66.536
^fd*236
dn
dn
s58
s59
^fd*2.50 ^fd*2.50 ^fd*2.50
^fd*6.85 ^fd*6.86 ^fd*6.86
Design Report
IMaX Final Optical Design
exp
exp
exp
s55
s58
s59
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52 of 52
^fd*236
^fd*66.536
^fd*81.375
!SUPERFICIES DEL CONJUNTO BEAMSPLITTER. CAMBIAN A LA TEMPERATURA DADA
POR ^tbs
!CALCULADO MEDIANTE EL FACTOR ^fbs
dn
dn
dn
s63
s65
s67
^fbs*8.66 ^fbs*8.66 ^fbs*8.66
^fbs*8.66 ^fbs*8.66 ^fbs*8.66
^fbs*1.6 ^fbs*1.6 ^fbs*1.6
exp
exp
exp
exp
exp
s63
s64
s65
s66
s67
^fbs*5
^fbs*236
^fbs*5
^fbs*236
^fbs*71
!SUPERFICIES DEL CONJUNTO BANCO. CAMBIAN A LA TEMPERATURA DADA POR
^tbsup,^tbmed y ^tbinf
!CALCULADO MEDIANTE EL FACTOR ^fbsup,fbmed y fbinf
exp
exp
exp
exp
s20
s60
s62
s68
^fbsup*236
^fbsup*236
^fbmed*236
^fbinf*236
!SUPERFICIES DEL CONJUNTO CCD. CAMBIAN A LA TEMPERATURA DADA POR ^tccd
!CALCULADO MEDIANTE EL FACTOR ^fccd
dn
s69
^fccd*(-1.1) ^fccd*(-1.1) ^fccd*(-1.1)
exp
exp
exp
s69
s70
s71
^fccd*86
^fccd*236
^fccd*236
go