THE UNIVERSITY OF CHICAGO ENGINEERING CENTER

5640 S. Ellis Avenue, Chicago, IL 60637

Phone: (773) 834-3773

<wang@oddjob.uchicago.edu>

# MEMO

**To:** Al Harper

**From:** Shu-i Wang

**Date:** 4/4/01

**Re:** HAWC Optical Design

The HAWC Optical Design produces diffraction-limited images in 4
selectable bands between 50µm and 250µm (53µm, 88µm, 155µm, 215µm)

. Each passband has a different magnification to provide full spatial
sampling of the PSF with 1mm square detectors. The platescales are
listed in Table 1.

Table 1. HAWC passband platescales.

  ------ -------------------- -------------------- ------------------------
  Band   Center Wavelength    Platescale           FWHM Image Diameter (mm)
         (μm)                 (arcsec/mm)          

  1      53                   2.25                 6

  2      88                   3.5                  9

  3      155                  6                    16

  4      215                  8                    22
  ------ -------------------- -------------------- ------------------------

The optics uses a combination of reflective and refractive optics. A
warm, reflective fore-optics system images the telescope onto a common,
cold Lyot stop for all bands. This minimizes the size of the cryostat
pressure window and facilitates alignment with the telescope optics. A
Helium-cooled carousel mechanism located at the cold pupil plane allows
interchanging up to seven different Lyot masks and a cold shutter. Four
sets of selectable lenses and filters mounted on a helium-cooled
carousel mechanism re-image the telescope focal plane onto the detector
at the appropriate image scales for the four passbands. A schematic view
of HAWC (with light entering from the telescope on the right) is shown
in Figure 1. Figure 2 shows the layout of the Band 4 optics under the
normal convention of light travelling from left to right, where FFM is
the folding flat mirror, and FM is the field mirror. The four passbands,
defined by metal-mesh interference filters, coincide with atmospheric
windows. In addition to the 4 bands of imaging optics, a pupil reimaging
lens (PRL) can be flipped into the ray path between the detector fold
mirror and the detector array to view the pupil image/illumination. The
PRL is optimized for Band 3 and forms a 12mm diameter image of the pupil
at the detector. The PRL can also be used with the other 3 bands to view
an out-of-focus image of the pupil to check for uniformity of the pupil
illumination. In Band 1, the out-of-focus pupil image diameter is about
17mm. The pupil image diameter is about 16.5mm for both Bands 2 and 4.

![](media/image1.png){width="4.940277777777778in"
height="4.319444444444445in"}

Figure 1. Schematic View of HAWC Layout.

![](media/image2.wmf){width="5.659722222222222in"
height="1.7444444444444445in"}

Figure 2. Layout of HAWC Band 4 Optics.

Figures 3-6 shows the y-z plane layout of the cold optics inside the
cryostat for Bands 1-4, respectively. Figure 7 shows the raytrace of the
cold optics in the pupil reimaging mode for Band 3 with the telescope
secondary mirror as the object.

The window curvature is modeled with the curvature measured during the
2^nd^ pump down on 7/11/00 (last measurement, see Window3.doc). The
optics was optimized with the criteria of best performance with all
three of the last three sets of window profile measurements without
refocusing the telescope. The largest variation in rms spot diameter
between the three sets of measurements was about 15 microns.

![](media/image3.png){width="5.070138888888889in"
height="2.217361111111111in"}

![](media/image4.png){width="4.959722222222222in"
height="2.1152777777777776in"}Figure 3. HAWC Band 1 Cold Optical Layout.

Figure 4. HAWC Band 2 Cold Optical Layout.

![](media/image5.png){width="5.004861111111111in"
height="2.0131944444444443in"}

![](media/image6.png){width="5.004861111111111in"
height="2.1118055555555557in"}Figure 5. HAWC Band 3 Cold Optical Layout.

Figure 6. HAWC Band 4 Cold Optical Layout.

![](media/image7.png){width="5.004861111111111in"
height="2.0131944444444443in"}

Figure 7. HAWC Band 3 PRL Cold Optical Layout.

The re-imaging lenses in each band were optimized and evaluated in the
Zemax Optical Design Software[^1] using the center wavelength, the 10%
transmission short wavelength (λs~10%~), and the 10% transmission long
wavelength (λl~10%~) as defined in Table 2. (The bandwidth listed in
Table 2 is the full width half maximum (FWHM) bandwidth.) The three
wavelengths were equally weighted in Zemax. The optics is designed to
accommodate a 32x32 detector array with 1mm square pixels. All optics,
field stops, and baffles are oversized by at least 5 Airy rings (in
addition to the PSF central core) to minimize effects of diffraction on
the uniformity of illumination of the cold pupil. The observed
field-of-view (FOV) and the 5-Airy oversized FOV used to size the optics
are listed in Table 3. The 5-Airy field was calculated for the FWHM long
wavelength in each band. In optimizing the lens designs, the field was
defined by the center, 0.7(FOV), and the actual FOV for a 32x32 detector
array. (The 5-Airy FOV was given a weight of zero and did not contribute
to the optics optimization.) Simple spherical lenses sufficed to achieve
the required image quality.

Table 2. HAWC Filter Passbands[^2].

  --------------- ------------------- ---------------- -------------------
  Bandwidth       λs~10%~ (μm)        λc (μm)          λl~10%~ (μm)
  (dλ/λ)                                               

  0.10            48.1                53               58.8

  0.10            81.3                88               95.2

  0.14            140.8               155              172.4

  0.20            190.5               215              246.9
  --------------- ------------------- ---------------- -------------------

Table 3. HAWC Field-of-view.

  ------- ------------ ------------------- ------------ -------------------
          32x32                            12x32        
          Detector                         Detector     
          Array                            Array        

  Band    FOV (arcmin) FOV + 5 Airy        FOV (arcmin) FOV + 5 Airy
                       (arcmin)                         (arcmin)

  1       1.2x1.2      2.14x2.14           0.45x1.2     1.39x2.14

  2       1.87x1.87    3.42x3.42           0.7x1.87     2.25x3.42

  3       3.2x3.2      5.99x5.99           1.2x3.2      3.99x5.99

  4       4.27.4.27    8.25x8.25           1.6x4.27     5.59x8.25
  ------- ------------ ------------------- ------------ -------------------

Other factors in the design merit function included the positioning of
the optics to correspond with the carousel mechanisms and the rms spot
diameter for each field point. A full ghost analysis was performed
iteratively with the lens design to minimize and eliminate where
feasible all ghosts in the system. Lenses were shaped to reduce the
ghost intensity to below noise levels. The lenses will also be
anti-reflection (AR) coated with a coating optimized for each filter
band. (The lenses will be AR coated with either thin layers of PE/PP by
QMCError: Reference source not found, or with Parylene C by Spectral
Systems[^3].) The filters were spaced apart and tilted at 10 degrees
successively in the opposite direction to eliminate ghosting. The
filters were modeled by a constant index of 2 with a thickness of 9λ/5
for hot-press filtersError: Reference source not found and 50 μm for
air-gap filters. The filter thicknesses entered in the raytraces are
listed in Table 4. Blocking filters CD1 & CB4 were not included in the
optics models. The only significant source of ghosting is the window
ghost due to the front-back window surface reflections where the maximum
total ghost energy, as defined in the ghost document, is 0.2% in Band 1.

Table 4. HAWC Filter Size Model.

  ---------- ----------- -------- ------------- ---------- ---------- ---------
  Filter     Type        λ~50%~   Thickness     Mount Size O.D. (mm)  C.A. (mm)
                         (µm)     (µm)                                

  (CB1)      Hot-press   37       66.6                                

  CB2        Hot-press   40.8     73.44         7          76.987     64.999

  CB3        Hot-press   45.5     81.9          6          65.608     55.804

  (CB4)      Hot-press   50.5     90.9                                

  ED_B1      Air-gap     55.9     50            6          65.608     55.804

  ED_B2 (1)  Air-gap     92.6     50            6          65.608     55.804

  ED_B2 (2)  Air-gap     84       50            6          65.608     55.804

  B_B2       Hot-press   71.4     128.52        6          65.608     55.804

  ED_B3 (1)  Air-gap     166.7    50            6          65.608     55.804

  ED_B3 (2)  Air-gap     144.9    50            6          65.608     55.804

  B_B3       Hot-press   111.1    199.98        Custom     89.916\*   76.2

  ED_B4 (1)  Air-gap     238.1    50            7          76.987     64.999

  ED_B4 (2)  Air-gap     196.1    50            Custom     89.916\*   76.2

  B_B4       Hot-press   166.7    300.06        Custom     97.409\*   82.55
  ---------- ----------- -------- ------------- ---------- ---------- ---------

\*Actual O.D. TBD. Used O.D.=1.18(C.A.) as a placeholder for now, where
1.18=(O.D.)/(C.A.) of the two standard size filters.

The optics for each band was modeled in Zemax with three configurations.
The first configuration models the flight configuration, with a
temperature of --50C for the foreoptics and --267C for the cold optics
inside the dewar. The second configuration models cold testing in a lab,
with a temperature of 20C for the foreoptics and --267C for the cold
optics. The third configuration models a warm dewar in the lab, with a
temperature of 20C for both the foreoptics and the dewar optics. The
optics was optimized for the cold flight configuration. The differences
in rms spot diameters between the cold flight configuration and the cold
lab configuration are less than 10 μm.

The glasses were modeled with custom glass files in Zemax for the warm
and cold indices. Index and absorption data from Loewenstein (1.5K &
300K data)[^4] were used for the silicon lenses in Band 1 and the pupil
reimaging lens (PRL); data from Brehat & Wyncke (10K & 300K data)[^5]
were used for the crystal quartz lenses in the other bands. Lens
transmissions, shown in Table 5, were modeled with the TFCalc Thin Film
Design Software for Windows[^6]. In Table 5, t~c~ is the lens center
thickness, t~e~ is the lens edge thickness, t~AR~ is the AR coating
thickness, T~abs~ is the transmission due to material absorption, and
T~total~ is the total lens transmission. The actual transmissions could
be a couple of percent less than the theoretical values shown in Table
5. The silicon lenses were modeled with a single layer Parylene AR
coating. Parylene was modeled with a constant refractive index of 1.6
without absorption due to a lack of absorption data[^7]. The AR coatings
are quite thin and the Parylene absorption is thus expected to be less
than a couple of percent. The crystal quartz lenses were modeled with a
single layer polyethylene[^8] AR coating. The transmission data are
listed in ASCII text files L1-1.txt and L2-1.txt for the Band 1 lenses,
L1-2.txt and L2-2.txt for the Band 2 lenses, L1-3.txt for the Band 3
lens, L1-4.txt for the Band 4 lens, and PRL.txt for the pupil reimaging
lens. These files are available at the irma.yerkes.uchicago.edu ftp
site, directory /pub/wang. The files contain extrapolated transmission
values from 0.3 -- 400 μm in increments of 0.1 μm. However, the actual
silicon data only covers from about 28.57 -- 33.33 μm, and extrapolation
beyond this range should be cautioned. The crystal quartz data covers
from about 16.67 -- 500 μm.

Table 5. Lens AR Coating Models.

  --------- ----------- ------- ------- --------------- --------- -------- ----------
  Element   Material    t~c~    t~e~    Coating         t~AR~     T~abs~   T~total~
                        (mm)    (mm)    Material        (um)               

  L1-1      Silicon     2.3     1.681   Parylene C      8.8 ± 1   0.86     0.79
                                                        µm                 

  L1-2      Crystal     3.2     1.943   PE/PP           14.4 ± 1  0.98     0.96
            Quartz                                      µm                 

  L1-3      Crystal     3.0     2.025   PE/PP           25.4 ± 1  0.99     0.98
            Quartz                                      µm                 

  L1-4      Crystal     4.5     1.999   PE/PP           35.4 ± 1  0.99     0.98
            Quartz                                      µm                 

  L2-1      Silicon     2.0     3.270   Parylene C      8.8 ± 1   0.98     0.97
                                                        µm                 

  L2-2      Crystal     2.0     3.539   PE/PP           14.4 ± 1  0.98     0.98
            Quartz                                      µm                 

  PRL-1     Silicon     5.3     1.979   Parylene C      25.8 ± 1  0.72     0.55
                                                        µm                 

  PRL-2                                                           0.82     0.47

  PRL-3                                                           0.90     0.82

  PRL-4                                                           0.92     0.75
  --------- ----------- ------- ------- --------------- --------- -------- ----------

The geometric spot diameters, diffraction encircled energy, mtf and
distortion plots are listed below for documenting the design image
quality of the HAWC optics. The geometric spot diameters for the imaging
optics are shown in Figures 8-11 for Bands 1-4, respectively. Boxes in
the spot diagrams are 1mm x 1mm square (single pixel). The field
positions are the corner edges of the field of view, the center of the
field, and the corner edges of the 5-Airy oversized fields. This is the
geometric spot pattern only and does not take diffraction into account.
Figures 12-15 show the diffraction encircled energy vs. radius from
centroid for the 4 bands. One tick on the x-axis equals 1mm (1 pixel).
The curves are for the same 9 points sampled in the geometric spot
diagrams. The 80% encircled energy occurs at a radius of 2.5 pixels or
less. Figures 16-19 show the diffraction modulation transfer function
(MTF) for all field points. Distortion is characterized in Figures
20-23. The square grid is a 32x32 image at the HAWC detector of a square
grid of the telescope focal plane that would just fill the HAWC field of
view. The size of each square in the grid represents one pixel. The
distortion is a small fraction of a pixel.

![](media/image8.png){width="5.333333333333333in" height="4.0in"}

Figure 8. Geometric Spot Diameter for HAWC Band 1 Optics.

![](media/image9.png){width="5.333333333333333in" height="4.0in"}

Figure 9. Geometric Spot Diameter for HAWC Band 2 Optics.

![](media/image10.png){width="5.333333333333333in" height="4.0in"}

Figure 10. Geometric Spot Diameter for HAWC Band 3 Optics.

![](media/image11.png){width="5.333333333333333in" height="4.0in"}

Figure 11. Geometric Spot Diameter for HAWC Band 4 Optics.

![](media/image12.png){width="5.333333333333333in" height="4.0in"}

Figure 12. Diffraction Encircled Energy for HAWC Band 1 Optics.

![](media/image13.png){width="5.333333333333333in" height="4.0in"}

Figure 13. Diffraction Encircled Energy for HAWC Band 2 Optics.

![](media/image14.png){width="5.333333333333333in" height="4.0in"}

Figure 14. Diffraction Encircled Energy for HAWC Band 3 Optics.

![](media/image15.png){width="5.333333333333333in"
height="4.010416666666667in"}

Figure 15. Diffraction Encircled Energy for HAWC Band 4 Optics.

![](media/image16.png){width="5.333333333333333in" height="4.0in"}

Figure 16. MTF for HAWC Band 1 Optics.

![](media/image17.png){width="5.333333333333333in" height="4.0in"}

Figure 17. MTF for HAWC Band 2 Optics.

![](media/image18.png){width="5.333333333333333in" height="4.0in"}

Figure 18. MTF for HAWC Band 3 Optics.

![](media/image19.png){width="5.333333333333333in" height="4.0in"}

Figure 19. MTF for HAWC Band 4 Optics.

![](media/image20.png){width="5.333333333333333in" height="4.0in"}

Figure 20. Distortion Grid at Detector Array for HAWC Band 1 Optics.

![](media/image21.png){width="5.333333333333333in" height="4.0in"}

Figure 21. Distortion Grid at Detector Array for HAWC Band 2 Optics.

![](media/image22.png){width="5.333333333333333in" height="4.0in"}

Figure 22. Distortion Grid at Detector Array for HAWC Band 3 Optics.

![](media/image23.png){width="5.333333333333333in" height="4.0in"}

Figure 23. Distortion Grid at Detector Array for HAWC Band 4 Optics.

A simulated image of the pupil in Band 3 is shown in Figure 24. The box
in Figure 24 represents a 12x32 detector array. (The cross in the center
is an artifact.) The pupil reimager was initially designed with the Lyot
stop at the cold paraxial pupil image formed by the FM, and the PRL 60mm
after the DFM. The PRL was optimized for best rms spot size of the pupil
image at the detector array with the telescope secondary as the object,
taking into account ghosting considerations. Although the PRL was
optimized for Band 3, we intend to use the PRL with all bands.
Therefore, silicon was chosen as the PRL glass material for its small
chromatic aberration. After a tolerance analysis and truncation of some
dimensions during the request for lens quotes, the pupil reimager design
was reoptimized. The Lyot stop was placed at the smallest geometric
pupil image location, keeping the rest of the optics fixed. Then,
placement of the PRL was optimized for the best rms spot size of the
pupil image with the telescope secondary as the object.

![](media/image24.png){width="6.039583333333334in"
height="2.5416666666666665in"}

Figure 24. Simulated Geometric Pupil Image.

The image quality for the pupil reimaging mode can be characterized by
the rms spot diameter of the pupil image of various points on the
telescope secondary mirror/pupil object. Figure 25 shows the geometric
spot diameter for the center, edge, and 0.7(edge radius) image points of
the pupil. Boxes in the spot diagrams are 1mm x 1mm square (single
pixel). Another figure of merit for the pupil reimager is the separation
of the star images within the field of view, which can lead to a
blurring of the effective pupil image. The separations between the pupil
image centers from various field points are listed below each pupil
image in Figure 26.

A design decision I made for both the imaging optics and the pupil
reimager is to keep the cold filters and lenses centered on the
mechanical axis defined as the normal center to the cryostat window.
This differs slightly from the optical axis due to the tilts of the
filters. Normally in an optical design the optics are decentered to take
into account the lateral shift in the optical axis due to tilted
elements. However, the tilts here are very small (very thin filters) and
have minimal effect on the image quality. It would not be worth the
mechanical complexity to put the slight filter decenters into the
design.

![](media/image25.png){width="5.333333333333333in" height="4.0in"}

Figure 25. Geometric Spot Diameter of the Pupil Reimager for Band 3.

![](media/image26.png){width="5.333333333333333in" height="4.0in"}

Figure 26. Geometric Pupil Images of Various Star Object Fields.

A thermal analysis was performed on the optical design using Zemax to
calculate warm-cold changes in the optics. Before we discuss the thermal
analysis, it\'s important to understand the coordinate system
conventions.

HAWC has several coordinate systems. Below are the transformations
between the SOFIA Aircraft Coordinates, (Xa, Ya, Za), the Cryostat
Coordinates, (Xc, Yc, Zc), and the Optics Coordinates, (Xo, Yo, Zo).
Figure 24 shows the sign convention of the Aircraft Coordinate System.
Figure 25 shows the sign convention of the Cryostat and the Optics
Coordinate Systems. The Optics Coordinate System follows the Zemax sign
convention. It is the coordinate system used for documenting the optics.
In addition, Figure 26 shows the transformation between the Lens Wheel
Coordinates and the Optics Coordinates for relating the carousel wheel
to the optics.

Aircraft Coordinates: (Xa, Ya, Za) = (-Zc, Yc, Xc)

Cryostat Coordinates: (Xc, Yc, Zc) = (Za, Ya, -Xa)

Optics Coordinates: (Xo, Yo, Zo)

(0, 0, 0) is defined to be the front surface center of the cryostat
window.

To transform from (Xc, Yc, Zc) to (Xo, Yo, Zo):

Xo = -Xc\*COS(-50) - Yc\*SIN(-50)

Yo = -Xc\*SIN(-50) + Yc\*COS(-50)

Zo = -Zc

To transform from (Xo, Yo, Zo) to (Xc, Yc, Zc):

Xc = -Xo\*COS(-50) - Yo\*SIN(-50)

Yc = -Xo\*SIN(-50) + Yo\*COS(-50)

Zc = -Zo

![](media/image27.png)

Figure 24. Aircraft Coordinate System.

![](media/image2.wmf)Figure 25. Cryostat and Optics Coordinate Systems.

![](media/image3.png){width="3.6597222222222223in"
height="3.709722222222222in"}

Figure 26. Lens Wheel Coordinates.

The 4 bands of HAWC optics and the pupil reimager were designed with a
(temperature, pressure) setting of (-50C, 1 atm.) for the foreoptics,
and (-267C, 0 atm.) for the cold optics inside the dewar. To model the
optics thermal behavior, two additional configurations were added to
model the warm and cold configurations in a laboratory setting. Table 6
shows the optics configurations in Zemax.

Table 6. Optics (Temperature, Pressure) Configurations in Zemax.

  ----------------- -------------------------- --------------------------
  Configuration     Foreoptics                 Cold Cryostat Optics

  1                 (-50C, 1 atmosphere)       (-267C, 0 atmosphere)

  2                 (20C, 1 atmosphere)        (-267C, 0 atmosphere)

  3                 (20C, 1 atmosphere)        (20C, 1 atmosphere)
  ----------------- -------------------------- --------------------------

Using the Zemax thermal pickup function, changes in the optics
curvature, thickness, index (manually entered in cold and warm glass
files for HAWC), diameters, and positions can be calculated for each
(temperature, pressure) setting. This is how the lens cold
specifications were converted into warm manufacturing specifications.
The dividing line between the foreoptics and the cold cryostat optics is
the cryostat window. The window is modeled with the foreoptics
temperature. A global shift is applied to all the elements after the
window with a dummy surface in the Zemax lens files to model the thermal
positional change in the cryostat suspension system. Tim Rennick
calculated the global (∆Xo, ∆Yo, ∆Zo) cold to warm shift between the
warm foreoptics and the cold cryostat optics as (-0.6mm, -1.032mm,
-0.029mm), in spreadsheet cte001011.xls. (This global shift will change
with the new suspension design and should be updated after the new
design is completed.) Tables 7 & 8 show the thermal coefficient of
expansion (CTE) values entered into Zemax to model the camera. The
optics mounts in both the foreoptics and the cryostat were modeled with
Aluminum alloy 6061. The lenses were also manually decentered in the
warm configuration to model the lens mount design. The amount of lens
decentering is shown in Figure 9. Note, unlike lens specifications in
Zemax where the center-to-center distances are used, the thermal
expansion is computed along a length of material which extends from the
edge of the surface to the edge of the next surface. This means tilted
surface (i.e. filters) positions may not be calculated correctly.
Because of the complexity of modeling the cryostat thermally, all optics
positions should be checked separately in the Pro-E model and/or
manually.

Table 7. HAWC Material Thermal Coefficient of Expansion.

  ---------------------------- ------------------ ----------------------------------------------- -------------
  Element                      Material           TCE (m/m-K)                                     Temperature

  Optics mounts, support       Aluminum alloy     1.45E-05[^9]                                    -267C
  structures                   6061                                                               

  FFM, FM                      Fused Silica       5.50E-07[^10]                                   -50C

  Window                       HDPE               1.30E-04[^11]                                   -50C

  Filters                      HPFILTER (HDPE)    1.30E-04Error: Reference source not             -267C
                                                  found^,Error:\ Reference\ source\ not\ found^   
  ---------------------------- ------------------ ----------------------------------------------- -------------

Table 8. Lens Thermal Coefficient of Expansion and Change in Diameter.

  --------- ------------- ---------------- ------- --------------- ----------- ----------
  Element   Material      avg TCE          ∆T      Warm Diameter   ∆Diameter   Decenter

                          (C^-1^)          \(C\)   (in)            (in)        (in)

  L1-1      Silicon       7.53E-07Error:   -287    2.0472          -0.0004     -0.0002
                          Reference source                                     
                          not found                                            

  L1-2      Crystal       4.07E-06Error:   -287    2.0472          -0.0024     -0.0012
            Quartz        Reference source                                     
                          not found                                            

  L1-3      Crystal       4.07E-06         -287    2.1260          -0.0025     -0.0012
            Quartz                                                             

  L1-4      Crystal       4.07E-06         -287    3.1890          -0.0037     -0.0019
            Quartz                                                             

  L2-1      Silicon       7.53E-07         -287    1.5748          -0.0003     -0.0002

  L2-2      Crystal       4.07E-06         -287    1.7717          -0.0021     -0.0010
            Quartz                                                             

  PRL       Silicon       7.53E-07         -287    3.0000          -0.0006     -0.0003
  --------- ------------- ---------------- ------- --------------- ----------- ----------

Table 9. Lens Warm-Cold Decenters.

  --------- ---------------- ---------------- ------------- ---------------
  Element   Optics                            Zemax         
            Coordinate                        Cold-Warm     
            System                            Decenters     

            Xo Decenter (in) Yo Decenter (in) DCXo (mm)     DCYo (mm)

  L1-1      0.0001           -0.0002          -0.0032       0.0046

  L1-2      0.0007           -0.0010          -0.0174       0.0249

  L1-3      0.0007           -0.0010          -0.0181       0.0258

  L1-4      0.0011           -0.0015          -0.0271       0.0388

  L2-1      0.0001           -0.0001          -0.0025       0.0035

  L2-2      0.0006           -0.0008          -0.0151       0.0215

  PRL       0.0002           -0.0003          -0.0047       0.0067
  --------- ---------------- ---------------- ------------- ---------------

Table 10 lists the warm and cold optics specifications from the thermal
analysis. The warm specifications were sent in request for quotes to
various manufacturers. Tables 11-14 lists the warm and cold global
coordinates for each optical element in the optics coordinate system.
The warm coordinates are for a warm cryostat in the lab, and the cold
coordinates are for the cooled cryostat in-flight.

Table 10. Optics Warm and Cold Specs.

![](media/image4.wmf){width="6.059722222222222in"
height="3.767361111111111in"}

Table 11. Warm and Cold Band 1 Optics Coordinates.

  --------------- ----------- ----------- ----------- ----------- -----------
  **Warm                      ** **       ** **       ** **       ** **
  Dimensions**                                                    

  Surf            Xow (mm)    Yow (mm)    Zow (mm)    XoTILT      YoTILT
                                                      (deg.)      (deg.)

  Primary         0           -1129.131   5058.120    0           -90

  Secondary       0           1624.679    5058.120    0           -90

  Tertiary        0           -139.131    5058.120    0           -45

  FFM             0           -139.131    154.292     0           9

  TFP             0           -69.599     368.288     0           18

  FM              0           0.000       582.493     0           9

  Window S1       0           0.000       0.000       0           0

  Window S2       0           0.000       -0.840      0           0

  CB2, Center     -0.6        -1.038      -40.649     0           10

  CB3, Center     -0.6        -1.025      -112.582    0           -10

  Lyot Stop       -0.6        -1.032      -150.840    0           0

  L1-1 S1         -0.6032     -1.027      -165.901    0           0

  ED_B1, Center   -0.6        -1.036      -186.090    0           10

  L2-1 S1         -0.6025     -1.029      -399.579    0           0

  DFM             -0.6        -1.032      -490.134    0           -45

  Detector        -0.6        -181.380    -490.134    0           -90

  Cold Dimensions                                                  

  Surf            Xoc (mm)    Yoc (mm)    Zoc (mm)    XoTILT      YoTILT
                                                      (deg.)      (deg.)

  Primary         0           -1129.058   5057.714    0           -90

  Secondary       0           1624.753    5057.714    0           -90

  Tertiary        0           -139.058    5057.714    0           -45

  FFM             0           -139.058    154.495     0           9

  TFP             0           -69.529     368.483     0           18

  FM              0           0.000       582.470     0           9

  Window S1       0           0.000       0.000       0           0

  Window S2       0           0.000       -0.832      0           0

  CB2, Center     0           -0.006      -40.611     0           10

  CB3, Center     0           0.007       -112.244    0           -10

  Lyot Stop       0           0.000       -150.342    0           0

  L1-1 S1         0           0.000       -165.342    0           0

  ED_B1, Center   0           -0.004      -185.456    0           10

  L2-1 S1         0           0.000       -398.043    0           0

  DFM             0           0.000       -488.242    0           -45

  Detector        0           -179.600    -488.242    0           -90
  --------------- ----------- ----------- ----------- ----------- -----------

Table 12. Warm and Cold Band 2 Optics Coordinates.

  ---------------- ---------- ----------- ----------- ----------- -----------
  **Warm                      ** **       ** **       ** **       ** **
  Dimensions**                                                    

  Surf             Xow (mm)   Yow (mm)    Zow (mm)    XoTILT      YoTILT
                                                      (deg.)      (deg.)

  Primary          0          -1129.131   5058.120    0           -90

  Secondary        0          1624.679    5058.120    0           -90

  Tertiary         0          -139.131    5058.120    0           -45

  FFM              0          -139.131    154.292     0           9

  TFP              0          -69.599     368.288     0           18

  FM               0          0.000       582.493     0           9

  Window S1        0          0.000       0.000       0           0

  Window S2        0          0.000       -0.840      0           0

  CB2, Center      -0.6       -1.038      -40.649     0           10

  CB3, Center      -0.6       -1.025      -112.582    0           -10

  Lyot Stop        -0.6       -1.032      -150.840    0           0

  ED_B2.1, Center  -0.6       -1.036      -169.091    0           10

  L1-2 S1          -0.6174    -1.007      -185.789    0           0

  ED_B2.2, Center  -0.6       -1.028      -224.158    0           -10

  B_B2, Center     -0.6       -1.043      -266.703    0           10

  L2-2 S1          -0.6151    -1.011      -402.303    0           0

  DFM              -0.6       -1.033      -490.139    0           -45

  Detector         -0.6       -181.380    -490.139    0           -90

  **Cold                                                           
  Dimensions**                                                    

  Surf             Xoc (mm)   Yoc (mm)    Zoc (mm)    XoTILT      YoTILT
                                                      (deg.)      (deg.)

  Primary          0          -1129.058   5057.714    0           -90

  Secondary        0          1624.753    5057.714    0           -90

  Tertiary         0          -139.058    5057.714    0           -45

  FFM              0          -139.058    154.495     0           9

  TFP              0          -69.529     368.483     0           18

  FM               0          0.000       582.470     0           9

  Window S1        0          0.000       0.000       0           0

  Window S2        0          0.000       -0.832      0           0

  CB2, Center      0          -0.006      -40.611     0           10

  CB3, Center      0          0.007       -112.244    0           -10

  Lyot Stop        0          0.000       -150.342    0           0

  ED_B2.1, Center  0          -0.004      -168.516    0           10

  L1-2 S1          0          0.000       -185.148    0           0

  ED_B2.2, Center  0          0.004       -223.367    0           -10

  B_B2, Center     0          -0.011      -265.732    0           10

  L2-2 S1          0          0.000       -400.765    0           0

  DFM              0          0.000       -488.242    0           -45

  Detector         0          -179.600    -488.242    0           -90
  ---------------- ---------- ----------- ----------- ----------- -----------

Table 13. Warm and Cold Band 3 Optics Coordinates.

  ---------------- ---------- ----------- ----------- ----------- -----------
  **Warm                      ** **       ** **       ** **       ** **
  Dimensions**                                                    

  Surf             Xow (mm)   Yow (mm)    Zow (mm)    XoTILT      YoTILT
                                                      (deg.)      (deg.)

  Primary          0          -1129.131   5058.120    0           -90

  Secondary        0          1624.679    5058.120    0           -90

  Tertiary         0          -139.131    5058.120    0           -45

  FFM              0          -139.131    154.292     0           9

  TFP              0          -69.599     368.288     0           18

  FM               0          0.000       582.493     0           9

  Window S1        0          0.000       0.000       0           0

  Window S2        0          0.000       -0.840      0           0

  CB2, Center      -0.6       -1.038      -40.649     0           10

  CB3, Center      -0.6       -1.025      -112.582    0           -10

  Lyot Stop        -0.6       -1.032      -150.840    0           0

  L1-3 S1          -0.6181    -1.006      -165.901    0           0

  ED_B3.1, Center  -0.6       -1.032      -186.066    0           10

  ED_B3.2, Center  -0.6       -1.032      -241.066    0           -10

  B_B3, Center     -0.6       -1.032      -403.991    0           10

  DFM              -0.6       -1.033      -490.144    0           -45

  PRL              -0.6047    -61.079     -490.137    0           -90

  Detector         -0.6       -181.380    -490.144    0           -90

  **Cold                                                           
  Dimensions**                                                    

  Surf             Xoc (mm)   Yoc (mm)    Zoc (mm)    XoTILT      YoTILT
                                                      (deg.)      (deg.)

  Primary          0          -1129.058   5057.714    0           -90

  Secondary        0          1624.753    5057.714    0           -90

  Tertiary         0          -139.058    5057.714    0           -45

  FFM              0          -139.058    154.495     0           9

  TFP              0          -69.529     368.483     0           18

  FM               0          0.000       582.470     0           9

  Window S1        0          0.000       0.000       0           0

  Window S2        0          0.000       -0.832      0           0

  CB2, Center      0          -0.006      -40.611     0           10

  CB3, Center      0          0.007       -112.244    0           -10

  Lyot Stop        0          0.000       -150.342    0           0

  L1-3 S1          0          0.000       -165.342    0           0

  ED_B3.1, Center  0          0.000       -185.434    0           10

  ED_B3.2, Center  0          0.000       -240.204    0           -10

  B_B3, Center     0          0.000       -402.453    0           10

  DFM              0          0.000       -488.242    0           -45

  PRL              0          -59.819     -488.242    0           -90

  Detector         0          -179.600    -488.242    0           -90
  ---------------- ---------- ----------- ----------- ----------- -----------

Table 14. Warm and Cold Band 4 Optics Coordinates.

  ------------------ ----------- ----------- ---------- ---------- ----------
  **Warm Dimensions              ** **       ** **      ** **      ** **
  (mm)**                                                           

  Surf               Xow (mm)    Yow (mm)    Zow (mm)   XoTILT     YoTILT
                                                        (deg.)     (deg.)

  Primary            0           -1129.131   5058.120   0          -90

  Secondary          0           1624.679    5058.120   0          -90

  Tertiary           0           -139.131    5058.120   0          -45

  FFM                0           -139.131    154.292    0          9

  TFP                0           -69.599     368.288    0          18

  FM                 0           0.000       582.493    0          9

  Window S1          0           0.000       0.000      0          0

  Window S2          0           0.000       -0.840     0          0

  CB2, Center        -0.6        -1.038      -40.649    0          10

  CB3, Center        -0.6        -1.025      -112.582   0          -10

  Lyot Stop          -0.6        -1.032      -150.840   0          0

  ED_B4.1, Center    -0.6        -1.036      -186.091   0          10

  ED_B4.2, Center    -0.6        -1.028      -241.091   0          -10

  L1-4 S1            -0.6271     -0.993      -259.922   0          0

  B_B4, Center       -0.6        -1.058      -404.085   0          10

  DFM                -0.6        -1.034      -490.144   0          -45

  Detector           -0.6        -181.381    -490.138   0          -90

  **Cold                                                            
  Dimensions**                                                     

  Surf               Xoc (mm)    Yoc (mm)    Zoc (mm)   XoTILT     YoTILT
                                                        (deg.)     (deg.)

  Primary            0           -1129.058   5057.714   0          -90

  Secondary          0           1624.753    5057.714   0          -90

  Tertiary           0           -139.058    5057.714   0          -45

  FFM                0           -139.058    154.495    0          9

  TFP                0           -69.529     368.483    0          18

  FM                 0           0.000       582.470    0          9

  Window S1          0           0.000       0.000      0          0

  Window S2          0           0.000       -0.832     0          0

  CB2, Center        0           -0.006      -40.611    0          10

  CB3, Center        0           0.007       -112.244   0          -10

  Lyot Stop          0           0.000       -150.342   0          0

  ED_B4.1, Center    0           -0.004      -185.446   0          10

  ED_B4.2, Center    0           0.004       -240.216   0          -10

  L1-4 S1            0           0.000       -258.969   0          0

  B_B4, Center       0           -0.025      -402.550   0          10

  DFM                0           0.000       -488.242   0          -45

  Detector           0           -179.600    -488.242   0          -90
  ------------------ ----------- ----------- ---------- ---------- ----------

[^1]: Focus Software, Inc. Web Site:
    [http://www.focus-software.com](http://www.focus-software.com/).

[^2]: Private Conversation with Ken Wood of QMC Instruments, Ltd (9/00).

[^3]: Specialty Coating Systems. Web Site: http://www.scscookson.com
    (9/99).

[^4]: \"Optical constants of far infrared materials. 2: crystalline
    solids\", E. Loewenstein, D. Smith & R. Morgan, Applied Optics, Vol.
    12, No. 2, pp. 398-406 (2/73).

[^5]: \"Measurement of the optical constants of crystal quartz at 10K
    and 300K in the far infrared spectral range: 10-600 cm^-1^\", F.
    Brehat & B. Wyncke, Int. J. of IR & Millimeter Waves, Vol. 18, No.
    9, pp. 1663-1679 (\'97).

[^6]: Software Spectra, 14025 N.W. Harvest Lane, Portland, OR 97229.
    Phone: (503)690-2099 (2/98).

[^7]: Private conversation with Jim Heaney.

[^8]: \"Optical constants of far infrared materials. 3: plastics\", D.
    Smith & E. Loewenstein, Applied Optics, V14 #6, pp. 1335-1341
    (6/75).

[^9]: \"Helium Cryogenics\", Steven S. Van Sciver, Kluwer
    Academic/Plenum Publishers (11/86).

[^10]: \"Fabrication Methods for Precision Optics\", Hank H. Karow, John
    Wiley & Sons, Inc. (1993).

[^11]: Goodfellow Web Site: <http://www.goodfellow.com/> (7/00).