红外望远镜广角相机的光学设计Optical-System-Design-Description.doc

Document Number:
3.1-D-020-O
Issue:
1.3
Category:
Optics
Status:
Issued
Author:
David Henry
Date:
28-7-03

Document Title
Optical System Design Description
Document Number
3.1-D-020-O
Issue
1.3
Date
28th July 2003

Document Prepared By:
David Henry
Signature and Date

Document Approved By:
Eli Atad
Signature and Date

Document Released By:
David Lunney
Signature and Date

CHANGE RECORD
Issue
Date
Section affected
Change Description
0.1
2-11-00
All
First draft
0.2
2-11-01
2,3,4
Reformatted for PDR
Global coordinates added to section 4
0.3
11-3-02
All
Updated for Optical Design Review
0.4
23-4-02

Updated following Optical Design Review, and final specifications for manufacturers
1
24-4-02

First issue
1.1
28-6-02
4.3
4.6.3
Secondary mirror OD increased to 504mm
Room temperature global positions added
1.2
30-4-03
4.2, 4.5

4.6.3
Material for Y,J,H filters changed to BK7 due to coating problem on Infrasil. M2 and detector focus offsets updated to suit.
Room temperature global positions removed (superseded by mechanical design).
1.3
28-7-03
4.2
Field flattening lens moved away from detectors by 0.9mm due to changes to mechanical design of focal plane.
No other changes required to compensate

APPLICABLE DOCUMENTS
Reference
Document Title
Document Number
Issue & Date
AD1
UKIRT Optics ICD
1.1-D-050-O
1.0, 13/2/02
AD2
Optical system tolerance analysis
3.1-D-045-O

TABLE OF CONTENTS
1. INTRODUCTION 5
2. OPTICAL SYSTEM 6
2.1 General Introduction 6
2.2 Description of the optical system 7
2.3 Optical Materials 9
2.4 Obscurations in the Optical System 9
2.5 Filters 10
3. OPTICAL SYSTEM PERFORMANCE 11
3.1 Focal Length/Pixel Scale 11
3.2 MTF 11
3.3 Encircled Energy 13
3.4 Distortion 14
3.5 Wavefront Error 14
4. OPTICAL PRESCRIPTION 15
4.1 Optical Coordinate System 15
4.2 Baseline optical prescription 15
4.3 Clear apertures and component diameters 16
4.4 Corrector plate surface profile 16
4.5 Refocussing 17
4.6 Thermal effects 18
4.6.1 Refractive index thermal variation 18
4.6.2 Dimensional thermal variation 19

1. INTRODUCTION
This document describes the design of the optical system of the Wide Field Camera (WFCAM) for the UK Infrared Telescope (UKIRT).
This document contains the following:
· A detailed description of the optical system
· The performance of the optical system, in various formats
· The detailed prescription of the optical system
The optical design of WFCAM is carried out using the Zemax optical design programme. This document is based on design version WFCAM NEW 109.ZMX.
2. OPTICAL SYSTEM
2.1 GENERAL INTRODUCTION
WFCAM is a wide field imaging camera, primarily designed to carry out large scale semi-automatic surveys of the sky. It operates in the near IR (1-2.5mm).
It uses 4 2048x2048 pixel focal plane arrays. These are arranged in a 2x2 pattern, spaced by approximately 90% of a detector spacing. Four separate stepped exposures are taken and combined to produce a single image frame, covering approximately 0.9° x 0.9°.
Figure 1 shows the layout of the focal plane, together with the angular field coverage of the optical system.

Figure 1 – WFCAM Focal Plane Layout
In order to maximise survey speed a pixel scale of 0.4 arcsec/pixel (22.22 arcsec/mm, 18mm pixel) has been chosen. This gives a large field of view of 0.933° diameter. The optical system has been designed for a field of view of 0.94° diameter, giving a small margin over the required field of view.
The optical design has a re-imaged pupil where a cold stop is located. This stop minimises the thermal background to ensure maximum sensitivity in the K band, and helps to control stray light.
WFCAM has a number of interchangeable filters. The majority of the scientific goals for the instrument will be fulfilled using Y, J, H and K broadband filters. In addition, narrow band filters within this region may also be used.
The optical system has been optimised to give maximum performance in the four broadbands. The wavelengths used in the design for each of these wavebands are shown in Table 1.
Waveband
Lower l (mm)
Centre l (mm)
Upper l (mm)
Y
0.97
1.02
1.07
J
1.17
1.25
1.33
H
1.49
1.635
1.78
K
2.03
2.20
2.37
Table 1 - Wavebands
2.2 DESCRIPTION OF THE OPTICAL SYSTEM
Figure 2 shows an optical layout of the WFCAM optical system. Figure 3 and Figure 4 show close-ups of the cryostat optics and detector optics respectively.

Figure 2 – WFCAM Optical Layout

Figure 3 – Cryostat Optical Layout

Figure 4 – Detector Optical Layout
WFCAM uses the existing UKIRT primary mirror. This forms the aperture stop for the optical system. The following parameters for the primary mirror are assumed (see AD1).
· Diameter 3802.5mm
· Focal length 9516mm
· Conic constant -1
To achieve the large required field of view, the WFCAM system uses a new secondary mirror, giving an f/9 intermediate focus at around 5.7 metres in front of the primary mirror. The secondary mirror is mounted on a fast 2-axis precision tip/tilt stage. This is in turn mounted on a HEXAPOD stage, allowing precise movement of the secondary mirror in 6 axes.
At the intermediate focus, a large field lens is placed. This forms an image of the entrance pupil (the primary mirror) inside the cryostat. The lens is equi-convex.
The next element in the beam is the cryostat window. This is a plane parallel window.
The next optical element is a corrector plate. One side of the plate is flat, and the other side has an aspheric profile. It is similar in shape to a Schmidt plate, but is not placed at a pupil image. It therefore helps to correct off axis image quality (particularly coma) as well as spherical aberration.
Inside the cryostat an image of the primary mirror is produced by the field lens. The cold stop is located here. The size and position of the cold stop aperture are optimised for stray light rejection in the K-band.
The tertiary mirror is located at the rear of the cryostat. This converts the f/9 beam from the secondary mirror into the f/2.44 beam required to give the correct pixel scale. The tertiary mirror is a concave ellipsoid.
The beam then passes through the filters. Four separate filters are used, one for each detector array. These are mounted in a mechanism which allows them to be placed in the beam. Each filter is plane parallel. A filter exchange mechanism selects the appropriate filter for use, with the unused filters being stored out of the beam at the side of the cryostat. The filters are discussed in more detail below.
Directly in front of the focal plane is a plano-concave fused silica field flattening lens.
The full optical prescription of the system is given in section 4.
2.3 OPTICAL MATERIALS
Most refractive elements in the system are fabricated from Heraeus INFRASIL 302, an infrared grade fused silica. Figure 5 shows the typical transmission of this material.
IR grade fused silica gives excellent transmission at the wavelengths of interest, together with extremely high refractive index uniformity. This is an important consideration bearing in mind the large size of some of the components.

Figure 5 – Transmission of Heraeus Infrasil
The filters for Y,J and H bands are on Schott N-BK7 substrates (K band filters are on Infrasil).
2.4 OBSCURATIONS IN THE OPTICAL SYSTEM
The optical design chosen for WFCAM mounts the detector arrays in the incoming beam. These therefore cause an obstruction in the beam, leading to loss of image quality and throughput.
For the purposes of calculating the baseline performance of the optical system, the following obscurations are included in the optical system.
· A circular hole (1m diameter) in the primary mirror
· A square obscuration (142mm x 142mm) located at the position of the filters, between the cold stop and the tertiary mirror. This models the effect on the beam of the obstruction caused by the filters and focal plane unit.

2.5 FILTERS
The plot below shows the beam footprint on the front surface of the filters (in J band). A beam is shown coming from the corner of each detector, giving 16 beams in all.

Figure 6 – Filter footprints
From this we can see that there is no overlap between the beams from each separate detector. This allows the use of separate smaller filters for each detector. The required beam size for each filter is 52mm.
3. OPTICAL SYSTEM PERFORMANCE
3.1 FOCAL LENGTH/PIXEL SCALE
Table 2 gives the focal length and pixel scale of the optical system at the centre wavelength of each waveband. Pixel scale is calculated assuming an 18mm square pixel.
Waveband
Centre l (mm)
Focal Length (mm)
Pixel scale (arcsec/pixel)
Y
1.035
9265.971
0.40069
J
1.25
9271.198
0.40046
H
1.635
9278.419
0.40015
K
2.2
9281.900
0.40000
Table 2 – Focal length and pixel scale
3.2 MTF
Figure 7 shows the diffraction MTF of the system up to a spatial frequency of 27 cycles/mm, in each of the wavebands. The specification frequency for the MTF is at 1.2 cycles/arcsec (26.67 cycles/mm).
MTF - Y Band MTF - J Band

MTF - H Band MTF - K Band

Figure 7 – MTF in Y,J, H and K bands
Figure 8 shows the variation of MTF (at 27 cycles/mm) with field angle in each of the four wavebands. For each waveband, the plot shows the sagittal (diamond), tangential (square) and average (solid) MTF. The dashed line indicates the (on axis) diffraction limit for each waveband.

Figure 8 – Variation of MTF with field angle
3.3 ENCIRCLED ENERGY
Figure 9 shows encircled energy radius plots for each of the four main wavebands.
Encircled Energy - Y Band Encircled Energy - J Band

Encircled Energy - H Band Encircled Energy - K Band

Figure 9 – Encircled energy in Y,J,H and K bands
Figure 10 shows the 50% and 80% encircled energy diameter (in arcsec) as a function of field angle for each of the four main wavebands.

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Figure 10 – Variation of encircled energy diameter with field angle
3.4 DISTORTION
Figure 11 shows the percentage optical distortion as a function of field angle at the central wavelength of each of the four main wavebands.

Figure 11 – Variation of distortion with field angle
3.5 WAVEFRONT ERROR
Figure 12 shows the OPD performance of the system in the four main wavebands.
OPD - Y Band OPD - J Band

OPD - H Band OPD - K Band

Figure 12 – Wavefront error in Y,J,H and K bands
4. OPTICAL PRESCRIPTION
4.1 OPTICAL COORDINATE SYSTEM
The coordinate system used is shown in Figure 13.

Figure 13 – WFCAM Coordinate System
The origin of the coordinate system is at the pole of the primary mirror, and the optical axis of the system lies along the Z-axis. Light travelling from the sky towards the primary mirror is travelling along the positive Z-axis. All dimensions are in mm.
4.2 BASELINE OPTICAL PRESCRIPTION
The baseline optical prescription is given in Table 3.
Surface
Radius
Conic Constant
Glass
Thickness
Global Position
Primary Mirror
-19032
-1

-8655
0
Secondary Mirror
-2413.8
-3.61

2891
-8655
Field Lens (front)
1656

Infrasil
80
-5764
Field Lens (back)
-1656

2168
-5684
Window (front)
Flat

Infrasil
35
-3516
Window (back)
Flat

230
-3481
Corrector Plate (front)
6611.297953

Infrasil
35
-3251
Corrector Plate (back)
Flat

1016.1
-3216
Filter Obstruction
Flat

5.5
-2199.9
Cold Stop
Flat

1299
-2194.4
Tertiary Mirror
-2097.4
-0.069

-1304.5
-895.4
Filter (front)
Flat

(3)
-5
-2199.9
Filter (back)
Flat

-7.9
-2204.9
Field Flattener (front)
Flat

Infrasil
-10
-2212.8
Field Flattener (back)
-2093.5

-16.9
-2222.8
Detector
Flat

-2239.7
Table 3 – WFCAM Optical Prescription
Notes:
1) All dimensions and parameters are at the nominal operating temperature.
2) Global positions indicate the location of the pole of the surface along the Z axis.
3) Filter material - Y,J,H bands - Schott N-BK7; K band - Infrasil
4.3 CLEAR APERTURES AND COMPONENT DIAMETERS
The beam diameter, clear aperture diameter and outside diameter for each element is shown in Table 4
Surface
Beam
Diameter (1)
Clear
Aperture (2)
Outside
Diameter (3)
Notes
Primary
3800
3800
3800

Secondary
487.119
496
504

Field Lens (front)
534.560
539
560

Field Lens (back)
531.239

Window (front)
456.505
460
480

Window (back)
455.695

Corrector Plate (front)
448.053
450
490

Corrector Plate (back)
447.282

Tertiary Mirror
797.907
802
814

Filter (front)
50.9
53
55
(4)
Filter (back)
49.5

(4)
Field Flattener (front)
113.831
120
128
(5)
Field Flattener (back)
111.056

(5)
Table 4 – Optical element diameters
Notes:
1) The beam diameter is the size of the nominal optical beam on the surface
2) The clear aperture is the minimum optical aperture required, allowing for tolerance buildup, flexure, etc.
3) The outside diameter is the physical size of the component, allowing for mounting.
4) Size of an individual square filter element – dimensions are edge lengths
5) Field flattener lens is square – dimensions are edge lengths
4.4 CORRECTOR PLATE SURFACE PROFILE
The front surface of the corrector plate is a high order aspheric surface. The surface sag is described by the following equation:

z(r) surface sag at radial coordinate r
c surface curvature, c=1/radius of curvature
a2,a4,a6 aspheric coefficients

Table 5 gives the coefficients of this surface at the nominal operating temperature of 250K.
Parameter
Value
Radius of curvature
6611.297953
R2 term
-5.3091568x10-5
R4 term
-2.3896351x10-10
R6 term
-1.9966489x10-16
Table 5 – Corrector plate aspheric coefficients (250K)
Figure 14 shows the profile of the surface sag, together with the deviation of the aspheric profile from the best fit sphere.

Figure 14 – Corrector plate aspheric profile
Table 6 shows a table of the sag values against radius (at 250K).
Radius
Sag
Radius
Sag
Radius
Sag
0
0.0000
80
0.1344
160
0.4173
10
0.0023
90
0.1668
170
0.4473
20
0.0090
100
0.2013
180
0.4730
30
0.0201
110
0.2374
190
0.4933
40
0.0354
120
0.2745
200
0.5070
50
0.0548
130
0.3118
210
0.5128
60
0.0780
140
0.3486
220
0.5094
70
0.1047
150
0.3840
225
0.5037
Table 6 – Aspheric Profile Sag
4.5 REFOCUSSING
To achieve optimum performance, the optical system requires refocussing of the secondary mirror and detector for each o