Sloan Digital Sky Survey Telescope Technical Note 19980416
The Sloan Digital Sky Survey 2.5-meter telescope:
optics
Patrick Waddell, Edward J. Mannery
ASTRONOMY BOX 351580, University of Washington Seattle, Washington
98195
James E. Gunn
Princeton University, Astronomy Department, Peyton Hall Princeton,
New Jersey 08544
Stephen M. Kent
Fermi National Accelerator Laboratory, MS 127, Box 500 Batavia,
Illinois 60510
CONTENTS
ABSTRACT
The Sloan Digital Sky Survey (SDSS) 2.5-meter telescope optical
design is optimized for wide field (3°), broadband (300 nm to
1060 nm) CCD imaging and multi-fiber spectroscopy. The system has
very low distortion, required for time-delay-and-integrate imaging,
and chromatic aberration control, demanded for both imaging and
spectroscopy. The Cassegrain telescope optics include a transmissive
corrector consisting of two aspheric fused quartz optical elements in
each configuration. The details of the fabrication of these elements
are discussed. Included is the design, development and performance of
custom optical coatings applied to these optics.
Keywords: Large Optics, optics fabrication, optical
coatings
1. INTRODUCTION
To accomplish the SDSS primary missions of acquiring wide field
time-delay-and-integrate (TDI) imaging of the North Galactic Cap, and
subsequent fiber optic fed multi-object spectroscopy of approximately
one million objects within this region of interest, a dedicated
special purpose telescope of moderate aperture has been designed and
is nearly assembled at Apache Point Observatory. The optical design
and tolerances and derived fabrication specifications target a system
that performs at sub-arcsecond levels across the full 3° field
of view.
Table 1 summarizes the 2.5-m telescope image quality budget and
includes the contribution from each element. These are expressed in
arcseconds rms image diameter and corresponding surface quality units
expressed as r0, for two zenith angles, 0° and
60°. The parameter r0 is used with an atmospheric
turbulence model to generate a structure function that in turn serves
as the figure specification for the corresponding optical surface.
Seeing and r0 for each optical surface in the telescope
are related by
where d is the on-axis diameter of the part being specified
and D is the telescope aperture diameter and seeing,
q, is in arcseconds. Note that for each
optical element, and not detailed here, the error allocations may be
further subdivided into the categories of polishing, figure testing,
supports and actuators, coatings, temperature nonuniformity, and wind
forces. The values listed here include these effects. Additionally,
these figures of merit must be combined with the errors in the
optical design, local and site seeing and the effects of TDI scanning
to derive final focal plane images.
Table 1. The 2.5-m telescope image error budget.
Source Image size (arcsec dia. rms) Actual surface r0 (cm)
zenith distance--> 0° 60° 0° 60°
Primary
|
0.312
|
0.349
|
39
|
35
|
Secondary
|
0.266
|
0.274
|
46
|
35
|
Common corrector
|
0.074
|
0.076
|
166
|
16
|
Lower corrector
|
0.055
|
0.056
|
222
|
360
|
Collimation, focus, tracking
|
0.179
|
0.179
|
68
|
180
|
Total
|
0.457
|
0.487
|
27
|
120
|
2. THE 2.5-M TELESCOPE OPTICAL
DESIGN
The design produces image sizes which match the pixel size (24
mm) of available large format scientific
imagers, provides precise control of distortion to allow TDI imaging
over a very large field (wherein all chips in the mosaic array are
clocked synchronously), and includes the lateral color control
demanded for fiber fed spectroscopy. The solution for the 2.5-m
telescope takes advantage of the fact that, for a given strength, a
Gascoigne plate corrects astigmatism in a Ritchey-Chrétien
telescope at a rate of the square of the distance from the focal
plane, while the lateral color and distortion increase linearly with
the distance. The solution is to use a pair of corrector elements,
the first of which is of the Gascoigne form and of weak power,
located some distance away from the focal plane. In our case, this
optic is at approximately the vertex of the primary. The second
corrector element figure is in the negative of the usual form and
placed closer to the focal plane. In this manner astigmatism is
corrected while no lateral color or distortion is introduced. In
practice, imaging and spectroscopy modes will implement separate
final corrector elements. That associated with imaging actually
serves as the front window and mechanical support for the camera
detectors and cryostat walls, while the final element for
spectroscopy will be clamped into place with the plug-plate
cartridges. A paper on the details of the 2.5-m telescope optical
design is planned.
Figure 1. The optics cross section for the imaging
configuration of the 2.5-m telescope. The rays shown are from the
edge of the field, 1.5° off axis. The first transmissive
corrector is nearly coincident with the vertex of the primary
mirror. The second transmissive corrector is just before the focal
surface.
Below, in Tables 2 and 3, are summarized the basic prescriptions
for imaging and spectrometric modes. In these tables, c are
the curvatures, positive if concave right. k are the conic
constants ( k = 0 is a sphere, k = -1 a paraboloid, k < -1 a
hyperboloid, -1 <k < 0 a prolate ellipsoid, and k > 0 an
oblate ellipsoid; generally, k = -e2). s are the spacings in
millimeters from the previous surface, positive if to the right.
Glass is the material following the surface. The sign of `glass'
changes for reflections and is positive for rightward-moving rays,
negative for left. a2, a4, a6 and a8 are
the aspheric coefficients for polynomial aspherics, where the general
form of the surface is
where tc is the solution to the conic surface
equation
.
The index of refraction for fused quartz, fq, is 1.46415 at
470 nm.
Table 2. The Optical Design for the SDSS
Telescope, Camera Mode.
surface
|
e
|
s
|
glass
|
a2
|
a4
|
a6
|
a8
|
k
|
cleardiam
|
1
|
-8.889e-5
|
0.0
|
-air
|
0.0
|
0.0
|
3.81e-22
|
.1.52e-29
|
-1.285
|
2500
|
2
|
-1.390e-4
|
-3646.14
|
air
|
0.0
|
0.0
|
1.79e-19
|
0.0
|
-11.97
|
1080
|
3
|
0.0
|
3621.59
|
fq
|
2.321e-5
|
-1.173e-10
|
-7.87e-17
|
1.59e-22
|
0.0
|
722
|
4
|
0.0
|
12.0
|
air
|
0.0
|
0.0
|
0.0
|
0.0
|
0.0
|
721
|
5
|
0.0
|
714.0
|
fq
|
0.0
|
0.0
|
0.0
|
0.0
|
0.0
|
657
|
6
|
0.0
|
45.0
|
bk7
|
-2.732e-4
|
2.056e-9
|
-6.53e-15
|
5.23e-20
|
0.0
|
652
|
7
|
0.0
|
5.0
|
air
|
0.0
|
0.0
|
0.0
|
0.0
|
0.0
|
651
|
8
|
0.0
|
8.0
|
air
|
0.0
|
0.0
|
0.0
|
0.0
|
0.0
|
651
|
Table 3. The Optical Design for the SDSS
Telescope, Spectroscopic Mode.
surface
|
e
|
s
|
glass
|
a2
|
a4
|
a6
|
a8
|
k
|
cleardiam
|
1
|
-8.889e-5
|
0.0
|
-air
|
0.0
|
0.0
|
3.81e-22
|
.1.52e-29
|
-1.285
|
2500
|
2
|
-1.390e-4
|
-3646.14
|
air
|
0.0
|
0.0
|
1.79e-19
|
0.0
|
-11.97
|
1080
|
3
|
0.0
|
3621.59
|
fq
|
2.321e-5
|
-1.173
|
-7.87e-17
|
1.59e-22
|
0.0
|
722
|
4
|
0.0
|
12.0
|
air
|
0.0
|
0.0
|
0.0
|
0.0
|
0.0
|
721
|
5
|
-4.307e-4
|
672.64
|
fq
|
0.0
|
0.0
|
0.0
|
0.0
|
0.0
|
657
|
6
|
0.0
|
10.0
|
air
|
-7.747e-5
|
-4.123e-10
|
-6.53e-15
|
5.23e-20
|
0.0
|
656
|
7
|
0.0
|
86.61
|
air
|
0.0
|
0.0
|
0.0
|
0.0
|
0.0
|
653
|
3. THE PRIMARY MIRROR
The primary mirror is a borosilicate honeycomb blank and was cast
by Hextek Corporation, Tucson, AZ in July 1992. The casting technique
is similar to that developed at the University of Arizona Mirror Lab,
except that the furnace is not rotated. The first casting attempt
failed during annealing and cracks were found when in the blank when
the oven was opened. The causes of the failure were identified and
corrected and the mirror was reheated in January, 1993 to fuse the
cracks. After a successful anneal, the blank was cleaned and
inspected and found to be of excellent quality with low residual
stresses.
The Optical Sciences Center (OSC) at the University of Arizona
took on the project to generate, figure and polish the mirror. While
under subcontract to Arizona Technologies, Incorporated, in Tucson
AZ, for optical generation, the blank experienced a significant
accidental fracture. During the generation of the front plate, power
to the grinding wheel failed while the feed screw for the wheel
continued to advance and the turntable continued to rotate the blank.
The resulting fracture was remarkably cylindrical, cut through the
front surface, about 85 mm outside the edge of the center hole and
into the 24 ribs below. In some cases the fracture continued down to
the back plate, but not through it. Arizona Technologies successfully
completed the repair efforts, which included the removal of the inner
fractured section in a complete annulus. Subsequent to this accident,
optical generation was completed at OSC.
Testing during the final figuring and polishing phases was
accomplished using high speed phase retrieval testing
techniques1 and null lenses fabricated also by OSC.
Although precise metering techniques were employed to accurately
construct the null optics, the assembled null lens was independently
verified2 with the use of a computer generated hologram
(CGH).
The fabrication tolerance specification for the primary mirror
surface figure3 is the wavefront structure function of the
standard model of atmospheric seeing with image full-width at
half-maximum equal to 0.20 arcseconds. At very small spatial scales
this specification is relaxed such that scattering of light outside
of the seeing disk is less than 13%. This target structure function
and that of the final mirror figure3 are plotted in
Figure2.
Figure 2. Square root of the wavefront
distribution function for the primary (crosses) and specification
(curve).
Much of the error, on large spatial scales of Figure 2 are due to
about 230 nm of astigmatism in the mirror figure. A series of tests
were accomplished which indicated that the astigmatism could be
corrected with forces applied to the mirror. These forces are in the
range of 20 to 40 N, if applied at 2 points. Corrected, the structure
function of the surface errors improves as seen in Figure
33.
Figure 3. Square root of the wavefront
distribution function for the primary, with astigmatism and
spherical aberration removed (crosses) and specification (curve).
Subsequent to the efforts at OSC, the primary was aluminized at
NOAO's Kitt Peak 4 m telescope aluminizing facility, and then
delivered to APO in July 1996.
4. THE SECONDARY
MIRROR
The secondary mirror is a borosilicate hot gas fusion blank
manufactured by Hextek. Optical generation, edging and hole drilling,
were done at Hextek. Astronomically Xenogenic Enterprises (AXE),
Tucson, AZ, generated the blank to a sphere. The blank was delivered
to SOML ground to a radius of 7331 ± 6 mm, well within the 7334
± 25 mm specification.
The SDSS 1.1 m secondary was the first optic to be figured,
polished and tested with a new facility developed by SOML for
fabricating large secondary optics4. The figuring was
accomplished using SOML's stressed lap tooling and then tested, first
with a swing arm profilometer10 (SAP) and later using a newly
developed technique which references the figured optic to a test
plate upon which has been written a CGH pattern5. For very
large secondaries, such as the SDSS 1.1 m optic, this CGH technique
is the only method available for full aperture testing. The system
worked extremely well.
The polishing cell for the secondary was designed such that during
testing the entire unit is oriented so that the mirror faces down
toward the test optics. The mirror support in this orientation
consists of a series of pads bonded to a whiffle arrangement and is
similar to the support method used in the telescope. Another
important feature of the cell is that during polishing, when the
mirror is face up (Figure 4) a mass, analogous to the mirror, pulls
down on the mirror mount attach pads. In this manner, the
deformations which would be induced by the support forces when the
mirror is installed in the telescope are polished out.
Figure 4. The secondary is seen on the SOML
polishing turntable. The swing arm profilometer (SAP) is seen at
the lower right. The stressed lap polisher is seen at the upper
left.
As for the primary, the fabrication tolerance specification for
the secondary mirror surface figure is the wavefront structure
function derived from a standard model of atmospheric seeing with
image full-width at half-maximum equal to 0.20 arcseconds. At small
spatial scales this specification is relaxed such that scattering of
light outside of the seeing disk is less than 25% at 350 nm. This
target structure function and that of the final mirror figure are
plotted in Figure 56.
Figure 5. Square root of the wavefront
distribution function for the secondary (crosses) and
specification (curve).
The secondary was delivered to APO in August 1996 and aluminized
at the NSO facilities in Sunspot, New Mexico.
5. THE COMMON CORRECTOR
The first Gascoigne lens is the last optic that is common to both
the imaging and spectroscopic modes and is therefore dubbed the
common corrector. The lens is 802 mm in diameter, by about 12 mm
thick and is made of Corning 7940 fused silica, grade 5F. The optic
was figured and polished by Contraves, Incorporated, Pittsburgh, PA.
The effort was completed in December 1996.
Figure 6 shows the final surface structure function7 for the
optical clear aperture, as compared with the specific