Imax Final Optical Design

Design Report

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 2 of 52

Approval control

Carmen Pastor Santos INTA Prepared by Tomás Belenguer Dávila INTA Alberto Alvarez Herrero INTA Revised by Raquel López Heredero INTA Alberto Alvarez Herrero INTA Approved by Lieselotte Jochum IAC Valentín Martínez IAC Authorized by 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) Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 3 of 52

Changes record

Issue Date Section Page Change description 1A 11/05/07 All All First Issue Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 4 of 52

Applicable documents

Nº Document title Code Issue AD1 ISLiD-IMaX Optical Interface Control SUN-MPS-ID-LD000-001 1 Document AD2 IMaX Requirements SUN-IMaX-SP-GEN-001 3A AD3 Thermal analysis of the optical enclosure SUN-IMaX-TN-IX300-005 1A AD4 ROCLI 1 SUN-IMaX-DR-IX200-001 1A AD5 ROCLI 2 SUN-IMaX-DR-IX200-001 1A AD6 Lens 1 Collimator SUN-IMaX-DR-IX200-003 1A AD7 Lens 2 Collimator SUN-IMaX-DR-IX200-004 1A AD8 Lens 1 Collimator Doublet SUN-IMaX-DR-IX200-005 1A AD9 Lens 2 Collimator Doublet SUN-IMaX-DR-IX200-006 1A AD10 Lens 1 Camera SUN-IMaX-DR-IX200-008 1A AD11 Lens 2 Camera SUN-IMaX-DR-IX200-009 1A AD12 Lens 1 Camera Doublet SUN-IMaX-DR-IX200-010 1A AD13 Lens 2 Camera Doublet SUN-IMaX-DR-IX200-011 1A AD14 Camera Doublet SUN-IMaX-DR-IX200-012 1A AD15 Beamsplitter SUN-IMaX-DR-IX200-013 1A AD16 Phase Diversity SUN-IMaX-DR-IX200-014 1A AD17 Mirror 1 SUN-IMaX-DR-IX200-015 1A AD18 Mirror 2 SUN-IMaX-DR-IX200-015 1A AD19 Mirror 3 SUN-IMaX-DR-IX200-017 1A AD20 IMaX Optics Specification SUN-IMaX-SP-IX200-004 2A AD21 TCE 116 Etalon Preliminary Optical Test SUN-IMaX-RP-IX200-020 1A Report Reference documents

Nº Document title Code Issue RD1 Characterization of a defocusing plate to SUN-IMaX-TN-IX200-022 2A implement phase diversity in IMaX RD2 IMaX ghost images, ASAP study SUN-IMaX-TN-IX200-018 2A RD3 ROCLIs gamma radiation test report SUN-IMaX-RP-IX200-001 1A RD4 Photon Flux Budget for IMaX SUN-IMaX-TN-GEN-002 4B RD5 Particle contamination in IMaX SUN-IMaX-TN-IX200-019 1A RD6 Product cleanliness levels and MIL STD 1246C contamination control program RD7 Airborne particulate cleanliness classes in FED STD 209E cleanrooms and clean zones RD8 M. Rimmer, “Analysis of Perturbed lens Appl. Opt.,Vol 9, 533 (1970) Systems” Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 5 of 52

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)

OPDRMSOptical 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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 6 of 52

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 7 of 52

9.3 IMAX THERMAL BEHAVIOUR...... 28

9.4 PHASE DIVERSITY THERMAL BEHAVIOUR...... 29 10. TOLERANCES, BORESIGHT AND SENSITIVITY ANALYSIS...... 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

12.2 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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 8 of 52

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 Including current Including a lens module Image quality SUNRISE simulating the SUNRISE evaluation Telescope and Telescope and ISLiD ISLiD optical interface.

FN (F-Number) 53.63 45 Due to amendment to the IMaX photon flux analysis for the new CCDs. ( See AD2)

Reflectivity of the 30% 100% Due to the sensitivity of Folder Mirrors for the new CCD cameras Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 9 of 52

double pass (See AD2)

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 10 of 52

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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 11 of 52

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

F2 Absolute FOV Relative F5 F4 (arcseconds) FOV

Xangle Yangle X Y

F1 0 0 0 0

F2 0 +25 0 +1

F3 0 -25 0 -1 F9 F8 F1 F4 +25 +25 +1 +1 F5 -25 +25 -1 +1

F6 +25 -25 +1 -1

F7 -25 -25 -1 -1

F7 F6 F8 +25 0 +1 0 F3 F9 -25 0 -1 0

Figure 3. Points of the FOV used for optimization Table 1. FOV Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 12 of 52

5.4 Optical Materials. In the following chart we show the main characteristics of the glasses used for IMaX optical design.

-6 MATERIAL nd Vd dn/dT  (10 /K) Ti (587nm) Nr. of (10-6/K) (5mm) 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 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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 13 of 52

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)    where V is the Abbe number V To achromatize the doublet we will have to minimize the change in the power of the doublet with wavelength, this is

 A B TOTAL   A  B  0 , this means that   (2) VA VB

Likewise, the variation of the power with temperature will be: (derivating (1) with respect to T)

 dn  dr  r  (n 1) d dT dT n 1 1 dn           2   dT r r  n 1 dT  1 dn Where    n 1 dT Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 14 of 52

1 dr And   (Coefficient of Thermal Expansion) r dT To athermalize the doublets we will have to minimize the change in the power of the doublet with Temperature, this is

d d A dB    0 , this means that      (3) dT TOTAL dT dT A A B B

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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 15 of 52

6. IMAX OPTICS LAYOUT The following figure shows a layout of IMaX Optics. No mechanical parts are shown.

Light12:30:55 goes from focus F4 to the CCD cameras.

ROCLIs M3 M2

F4 M1 Etalon Prefilter

Phase Diversity

Beamsplitter

67.57 MM XZ Positions: 1-2 IMaX Final Optical Design Scale: 0.37 CPS 24-Nov-06 Figure 4. Optics layout of IMaX Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 16 of 52

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.

BEST COMPOSITE FOCUS FIELD FOV FOCUS RMS STREHL FRACTION (deg) (mm) (waves) RATIO X 0 0 -0.043892 0.0075 0.998 Y 0 0 X 0 0 -0.043892 0.0038 0.999 Y 1 0.007 X 0 0 -0.043892 0.0038 0.999 Y -1 -0.007 X 1 0.007 -0.043892 0.0069 0.998 Y 1 0.007 X -1 -0.007 -0.043892 0.0069 0.998 Y 1 0.007 X 1 0.007 -0.043892 0.0069 0.998 Y -1 -0.007 X -1 -0.007 -0.043892 0.0069 0.998 Y -1 -0.007 X 1 0.007 -0.043892 0.0031 1 Y 0 0 X -1 -0.007 -0.043892 0.0031 1 Y 0 0

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 17 of 52

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 ) Y-FAN -1.00 , 1.00 X-FAN 0.015 RELATIVE FIELD 0.015 ( -0.01 O, 0.01 O)

-0.015 -0.015

1.00 , 1.00 RELATIVE FIELD 0.015 ( 0.01 O, 0.01 O) 0.015

-0.015 -0.015

0.00 , -1.00 RELATIVE FIELD 0.015 ( 0.00 O, -0.01 O) 0.015

-0.015 -0.015

0.00 , 1.00 RELATIVE FIELD 0.015 ( 0.00 O, 0.01 O) 0.015

-0.015 -0.015

0.00 , 0.00

RELATIVE FIELD

O O 0.015 ( 0.00 , 0.00 ) 0.015

-0.015 -0.015

IMaX Final Design 525.2700 NM

1 525.0700 NM 0 :

5 524.8700 NM

4 RAY ABERRATIONS ( MILLIMETERS ) : 1 1 CPS 26-Jan-07

Figure 5. Transverse aberration curves Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 18 of 52

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.

DIFFRACTION LIMIT IMaX Final Design Y (0.000,0.000) DEG X WAVELENGTH WEIGHT Y (0.000,.0070) DEG X 525.3 NM 1 Y (0.000,-.007) DEG DIFFRACTION MTF X 525.1 NM 1 Y X (.0070,.0070) DEG 524.9 NM 1 Y CPS 26-Jan-07 X (-.007,.0070) DEG DEFOCUSING 0.00000 1.0

0.7 M O 0.6 D U L A 0.5 T I O 0.4 N 0.3

X 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0 Y SPATIAL FREQUENCY (CYCLES/MM) Figure 6. Polychromatic MTF. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 19 of 52

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 2- Dimensional 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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 20 of 52

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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 21 of 52

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:

l 2 CL = Dl 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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 22 of 52 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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 23 of 52

 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鬃a d = F ' e - 2 鬃 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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 24 of 52

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.

Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 25 of 52

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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 26 of 52

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). Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 27 of 52

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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 28 of 52

9.3 IMaX Thermal Behaviour The graphics below shows the defocus at the image plane (CCD) in mm for every thermal case.

IMaX Thermal Behaviour

0,75 cold d

e 0,5 f o c u s

m 0,25 m

0 operative

-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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 29 of 52

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.

1,12 cold 1,1

s 1,08 a d

b 1,06 m a l 1,04 n i operative s

u 1,02 c o f

e 1 d 0,98 0,96 0,94 hot 0,92 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%. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 30 of 52

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 31 of 52

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 dp, where dp is the variation in a parameter • The associated change in the wave aberration is dw = (dw/dp)dp, 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): 2 2   a1p1  b1p1  a2p2  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) Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 32 of 52

• 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). Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 33 of 52

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 34 of 52

 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 WFE Nominal DESIGN WFE DESIGN + TOL 0.00, 0.00 0.0062 0.0431 0.00, 1.00 0.0034 0.0438 0.00,-1.00 0.0034 0.0438 1.00, 1.00 0.0077 0.0451 -1.00, 1.00 0.0077 0.0451 1.00,-1.00 0.0077 0.0451 -1.00,-1.00 0.0077 0.0451 1.00, 0.00 0.0026 0.0435 -1.00, 0.00 0.0026 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 0.008546 (0.8%) Image Rotation 0.000123 rad (25.4arcseconds) Boresight: X-shift 0.050053 mm Y-shift 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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 35 of 52

10.6 Compensators range of movement

The range of movement needed for each compensator and their accuracy are as follows:

COMPENSATOR RANGE OF MOVEMENT ACCURACY Collimator doublet 1.8mm along the optical axis 0.01mm Camera doublet 2.6mm along the optical axis 0.01mm Mirrors 1 and 2 1arcmin 10arcseconds Mirror 3 1arcmin 10arcseconds CCD cameras 0.8mm in both directions Better than 0.05mm perpendicular to the optical axis 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 and for each doublet) setup for centering while 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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 36 of 52

Elements: Lenses in collimator and camera doublets

procedure for the mounting of 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

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 37 of 52

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 38 of 52

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 39 of 52

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: defocus(in _ units _ of _ ) OPD  PV 8* FN 2

And to convert this value into rms

OPD OPD  PV RMS 4 where OPD is the Optical Path Difference and FN is the F-Number at the image plane (where the defocus is produced). Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 40 of 52

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 41 of 52

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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 42 of 52

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:

2 Strhel_ Ratio= e-(2p wfe ) where wfe is rms wfe in  Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 43 of 52

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).

2 2 轾log C C轾log C part -轾 log( 5) ( part ) {臌 ( ) 臌 } 0.773 犏 10= 0.02·cc · p · t · C _ SL log 5 臌犏 ( )

This equation permit to calculate the surface cleaning level as a function of the air quality cleaning room (classroom level) Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 44 of 52

So, considering the most dangerous situation (up-horizontal surface orientation), the resolution of the equation takes the following graphical aspect Figure 17):

3 1 10 1000 500 7 30

SurfClLevH(10 i)

SurfClLevH(100 i)

SurfClLevH(1000 i) 100 SurfClLevH(10000 i)

SurfClLevH(100000 i)

47.441 10 3 1 10 100 1 10 3 1 i 110 t (days)

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), SurfClLevH( C _ SL , t ) SurfClLevV( C _ SL , t ) = 10

3 1 10 1000 500 7 30

SurfClLevV(10 i) 1 100 SurfClLevV(100 i)

SurfClLevV(1000 i)

SurfClLevV(10000 i) 10 SurfClLevV(100000 i)

4.744 1 3 1 10 100 1 10 3 1 i 110 t (days) Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 45 of 52

Figure 18. Surface cleanliness level versus exposed time for different air quality classroom levels Vertical surface-normal air. 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), SurfClLevH( C _ SL , t ) SurfClLevA( C _ SL , t ) = 100

3 1 10 1000 500 7 30

SurfClLevA(10 i) 1 100

SurfClLevA(100 i)

SurfClLevA(1000 i) 10 SurfClLevA(10000 i)

SurfClLevA(100000 i) 1

0.1 0.1 3 1 10 100 1 10 3 1 i 110 t (days)

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. Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 46 of 52

 Independently of the classroom level in which a sensitive optical surface is, after some time of exposure the surface will be dirty.

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 )

VALUE at VALUE at PARAMETER SPECIFICATION LabC Operation Wavelenght range 525,020,2nm As specified As specified FOV (XxY) >50x50 arc seconds As specified As specified Distortion ------0.06% 0.012% F/N at image plane 45 44.99 45.01 Image scale (arcsec/pixel) 0.055 0.055 0.055 Angel of incidence on <0.58º 0.44º 0.44º Collimated beam WFE Phase Diversity 0.25 rms (12%) 0.25 rms 0.28 rms 0.998 nominal Strehl Ratio 0.998 nominal 0.95 / 0.8 0.85 with (nominal / with tol.) 0.83 in operation tolerances Telecentricity at image Telecentric 22 arseconds 35 arseconds plane 60 arcsec As specified. Stray Light and ghost By means of images <1% PSF Not evaluated tilting the etalon 0.36º 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 Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 47 of 52

ANNEX 1. SURFACE LISTING RDY THI RMD GLA OBJ: INFINITY INFINITY STO: INFINITY 0.000000 2: INFINITY 25000.000000 3: INFINITY 0.000000 MOD: MFL:25000.000000 MRD: 1.00E-10 MFF: -2.50E+04 MBF:25000.000000 MEN: 0.000000 MED: -1.000000 MFD: 0.000000 4: INFINITY 25000.000000 5: INFINITY 0.000000 6: INFINITY 31.530000 XDE: -0.256962 YDE: 0.000000 ZDE: 0.000000 ADE: 0.000000 BDE: 0.000000 CDE: 0.000000 7: INFINITY 4.000000 B270_SCHOTT SLB: "Prefilter" XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 ADE: 0.000000 BDE: -2.100000 CDE: 0.000000 8: INFINITY 0.500000 9: INFINITY 2.000000 'GG495' 10: INFINITY 2.000000 'S8612' 11: INFINITY 2.000000 'GG495' 12: INFINITY 0.000000 13: INFINITY 2.000000 XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 ADE: 0.000000 BDE: 2.100000 CDE: 0.000000 14: INFINITY 6.000015 SILICA_SPECIAL SLB: "rocli 1" 15: INFINITY 5.000000 16: INFINITY 6.000015 SILICA_SPECIAL SLB: "rocli 2" 17: INFINITY 10.400000 18: 27.25420 4.170000 SILICA_SPECIAL SLB: "coll_lens 1" 19: 613.06000 34.250000 20: -16.07900 3.560000 SILICA_SPECIAL SLB: "coll_lens 2" 21: 41.20000 171.750000 22: -778.89000 2.500000 SF1_SCHOTT SLB: "coll_doublet" 23: 105.09800 7.780000 XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 ADE: 0.000000 BDE: 0.000000 CDE: 0.000000 24: 131.45000 6.500000 SBSM22_OHARA 25: -93.33000 15.000000 26: INFINITY 0.000000 27: INFINITY 0.000000 XDE: 17.500000 YDE: 0.000000 ZDE: 0.000000 ADE: 0.000000 BDE: 0.000000 CDE: 0.000000 28: INFINITY 14.000000 SILICA_SPECIAL SLB: "Etalon Window 1 Pass_1" XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 ADE: 0.360000 BDE: 0.000000 CDE: 0.000000 29: INFINITY 0.000000 30: INFINITY 15.359000 31: INFINITY 0.282000 'LiNbO3' Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 48 of 52

SLB: "Etalon Pass_1" 32: INFINITY 0.000000 33: INFINITY 15.359000 34: INFINITY 14.000000 SILICA_SPECIAL SLB: "Etalon Window 2 Pass_1" 35: INFINITY 0.000000 36: INFINITY 0.000000 XDE: -17.500000 YDE: 0.000000 ZDE: 0.000000 ADE: -0.360000 BDE: 0.000000 CDE: 0.000000 37: INFINITY 85.000000 38: INFINITY -17.500000 REFL SLB: "Folding Mirror 1" XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 BEN ADE: 0.000000 BDE: 45.000000 CDE: 0.000000 39: INFINITY -17.500000 SLB: "dummy" 40: INFINITY 85.000000 REFL SLB: "Folding Mirror 2" XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 BEN ADE: 0.000000 BDE: 45.000000 CDE: 0.000000 41: INFINITY 0.000000 42: INFINITY 0.000000 43: INFINITY 0.000000 44: INFINITY 0.000000 45: INFINITY 0.000000 XDE: 17.500000 YDE: 0.000000 ZDE: 0.000000 ADE: 0.000000 BDE: 0.000000 CDE: 0.000000 46: INFINITY 14.000000 SILICA_SPECIAL XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 ADE: -0.360000 BDE: 0.000000 CDE: 0.000000 47: INFINITY 0.000000 48: INFINITY 0.000000 49: INFINITY 15.359000 50: INFINITY 0.282000 'LiNbO3' SLB: "Etalon Pass_2" 51: INFINITY 0.000000 52: INFINITY 15.359000 53: INFINITY 14.000000 SILICA_SPECIAL SLB: "Etalon Window 1 Pass_2" 54: INFINITY 0.000000 55: INFINITY 0.000000 XDE: -17.500000 YDE: 0.000000 ZDE: 0.000000 ADE: 0.360000 BDE: 0.000000 CDE: 0.000000 56: INFINITY 15.000000 57: INFINITY 0.000000 58: INFINITY 0.000000 59: 285.92000 8.000000 SBSM22_OHARA SLB: "camera_doublet" 60: -230.41000 2.500000 SF1_SCHOTT 61: -1678.80000 196.350000 62: INFINITY 0.000000 REFL XDE: 0.000000 YDE: 0.000000 ZDE: 0.000000 BEN ADE: 0.000000 BDE: 45.000000 CDE: 0.000000 63: INFINITY -204.710000 64: 202.42000 -3.600000 SILICA_SPECIAL SLB: "camera_lens 1" 65: -28.18400 -60.610000 66: 298.54000 -10.000025 SILICA_SPECIAL Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 49 of 52

SLB: "camera_lens 2" 67: 46.63900 -2.000000 68: INFINITY -25.400000 NBK7_SCHOTT SLB: "Beam Splitter Cube" 69: INFINITY -69.970000 70: INFINITY -1.000000 EFEL6_HOYA SLB: "Detector Window" 71: INFINITY -1.050000 IMG: INFINITY 0.000000 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 BEN ADE: 0.000000 BDE: 45.000000 CDE: 0.000000

70: INFINITY 12.690000 AIR 71: INFINITY 27.000000 SILICA_SPECIAL 72: INFINITY 30.280000 AIR 73: INFINITY 1.000000 EFEL6_HOYA SLB: "Detector Window" 74: INFINITY 1.050000 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 50 of 52

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 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 51 of 52

!SUPERFICIES DEL MODULO SIMULADOR DEL TELESCOPIO + ISLID exp s0..5 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 s27 ^fet*8.66 ^fet*8.66 ^fet*8.66 dn s30 ^fet*50 ^fet*50 ^fet*50 dn s33 ^fet*8.66 ^fet*8.66 ^fet*8.66 dn s45 ^fet*8.66 ^fet*8.66 ^fet*8.66 dn s49 ^fet*50 ^fet*50 ^fet*50 dn s52 ^fet*8.66 ^fet*8.66 ^fet*8.66 exp s27 ^fet*5 exp s29 ^fet*236 exp s30 ^fet*75 exp s32 ^fet*236 exp s33 ^fet*5 exp s37..38 ^fesp*236 exp s45 ^fet*5 exp s48 ^fet*236 exp s49 ^fet*75 exp s51 ^fet*236 exp 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 s21 ^fd*6.85 ^fd*6.86 ^fd*6.86 dn s23 ^fd*2.50 ^fd*2.50 ^fd*2.50 exp s21 ^fd*81.375 exp s22 ^fd*236 exp s23 ^fd*66.536 exp s24 ^fd*236 dn s58 ^fd*2.50 ^fd*2.50 ^fd*2.50 Design Report Code: SUN-IMaX-RP-IX200-023 Iss/Rv: 1A Date: 11/05/07 IMaX Final Optical Design Page: 52 of 52 dn s59 ^fd*6.85 ^fd*6.86 ^fd*6.86 exp s55 ^fd*236 exp s58 ^fd*66.536 exp s59 ^fd*81.375

!SUPERFICIES DEL CONJUNTO BEAMSPLITTER. CAMBIAN A LA TEMPERATURA DADA POR ^tbs !CALCULADO MEDIANTE EL FACTOR ^fbs dn s63 ^fbs*8.66 ^fbs*8.66 ^fbs*8.66 dn s65 ^fbs*8.66 ^fbs*8.66 ^fbs*8.66 dn s67 ^fbs*1.6 ^fbs*1.6 ^fbs*1.6 exp s63 ^fbs*5 exp s64 ^fbs*236 exp s65 ^fbs*5 exp s66 ^fbs*236 exp s67 ^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 s20 ^fbsup*236 exp s60 ^fbsup*236 exp s62 ^fbmed*236 exp s68 ^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 s69 ^fccd*86 exp s70 ^fccd*236 exp s71 ^fccd*236 go