Sloan Digital Sky Survey Telescope Technical Note 19980416

The Sloan Digital Sky Survey 2.5-meter telescope: optics

CONTENTS

• Abstract
• Introduction
• The 2.5-M telescope optical design
• The primary mirror
• The secondary mirror
• The common corrector
• The imaging corrector
• The spectrograph corrector
• Summary
• Acknowledgments
• References

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 t_c 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.

Table 3. The Optical Design for the SDSS Telescope, Spectroscopic Mode.

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 specification for the common corrector. Two regions of the optic, and inner 150 mm section and an outer annulus were stitched together to complete the test.

Figure 6. The common corrector surface errors, as compared with the fabrication specification are plotted as a function of spatial scale.

As seen in the upper right section of the wavefront error diagram⁷ in Figure 7, the optic has a turned edge. It is possible to avoid use of this region, for imaging, by installing the lens in the telescope with a preferential orientation relative to the array of camera detectors (see also Figure 10). This optic is mounted to the instrument rotator in such a way that it co-rotates with the instrument, and thus preserves this alignment.

Figure 7. Wavefront error fringe map for the outer annulus region of the common corrector. Contours are l/4, where l = 632 nm. For this figure, the "TOP" fiducial mark on the edge of the lens is at the top of the drawing; the aspheric side of the lens faces toward the viewer, out of the page.

Subsequent to polishing the optic was anti-reflection (AR) coated by QSP Optical, Santa Ana, California. The requirements for the common corrector coatings (per side) call for average reflectance across the 320 nm to 1100 nm optical bandpass to be less than 1.5%, with peak reflectance to be less than 2.0%. Absorption at 320 nm is required to be less than 0.4%. This level of performance is achieved with a 12 layer coating (Figure 8). The coatings, applied at a temperature of about 200°C, are durable but easily removed if required.

 

Figure 8. Reflectance of each surface of the common corrector is plotted as a function of wavelength. The entrance and exit sides of the optic are the aspheric and flat sides, respectively. The noise seen redward of 850 nm is described by QSP to be a problem internal to the reflectometer.

The common corrector was mounted using an elastomer bonding ring8 at the University of Washington and delivered to APO in November 1997.

6. THE IMAGING CORRECTOR

The imaging corrector, made of Corning 7940 fused silica, is 45 mm thick by about 813 mm in diameter. The optic was figured and polished by D. A. Loomis of Custom Optics, Incorporated, Tucson, AZ The specification on the figure slope error requirement is less than 50 µrad rms on spatial scales less than the size of a CCD, or 50 mm, and a peak sagitta error of 25 µm in surface height. The piece was tested using a calibrated traveling micrometer and the results, as shown in Figure 9, indicate that the sagitta specification is well met across the optic. To inspect slope errors at higher spatial frequencies, a check plate was positioned on the corrector to reveal the smoothness over small areas.

Once the figuring effort was completed, approximately 100 holes were drilled into the exit or flat side of the optic to adapt to the camera detector mounts and cryostats. Some of these mount holes can be seen in Figure 12.

Figure 9. Surface height errors, as measured across the imaging corrector surface.

QSP Optical developed a custom AR coating for the first surface of the imaging corrector. The coating reduces the nominal 3% losses at this interface, and more importantly, reduces the intensity of ghost images. Although the optic is used across the widest optical band of the survey, 300 to 1060 nm, the layout of the detectors is such that the optic can be divided up into a series of strips, each of which must pass only a smaller subset of this optical band (Figure 10). Consequently, a series of coatings was applied to the glass using a special mask set (Figure 11) which conformed to the aspheric optic. Figure 12 shows the coated optic. The plot in Figure 13 shows the performance of each of the individual coating bands relative to the survey filter bandpasses. The piecewise performance is nearly an order of magnitude better than that possible for a single broadband coating.

Figure 10. The layout of the camera filter bands is shown. Note also the locations of the approximately 100 holes which were drilled into the optic to support the detector mounts and cryostats.

 

Figure 11. Tooling and a number of the masks used to fabricate the imaging corrector AR coating. The masks were designed and precisely machined to conform to the surface along chords of the aspheric optic at the deposition temperature of 200°C.

 

Figure 12. A single straight fluorescent lamp reflects from the highly aspheric surface of the imaging corrector and coating.

 

Figure 13. The AR coating performance for the imaging corrector is plotted with wavelength. The labeled bars, above the measured reflectance plots, indicate the half-power bandpasses of the filters. The noise seen redward of 850 nm is described by QSP to be a problem internal to the reflectometer.

Subsequent to coating, the optic was delivered to Princeton in May 1996, for integration with the imaging camera. The second surface was not coated. Filters with AR coatings were bonded directly to the corrector second surface at Princeton.

7. THE SPECTROGRAPH CORRECTOR

The final optical element used in spectrograph mode, the spectrograph corrector, is also made of Corning 7940 fused silica, grade 5F. The optic is 727 mm in diameter and is 10 mm thick, and was figured and polished, using proprietary computer control techniques, by Tinsley Laboratories, Incorporated, Richmond, CA, in July, 1996.

The lens figuring specifications for the spectrograph corrector call for peak to valley (p-v) slope errors, over 95% of the clear aperture, to be less than 150 µrad p-v for spatial frequencies below 160 mm, with a straight line increase in slope errors allowed for larger spatial scales. At 700 mm, slope errors of 600 µrad p-v are permitted. Over 100% of the part, the small spatial scale errors must be less than 250 µrad p-v. The spherical side of the finished part from Tinsley has slope errors of less than 50 µrad p-v over spatial frequencies below 160 mm and below 10 µrad p-v for larger spatial scales. Slope errors for the aspheric side appear to be on the order of 10 times better than this.

As with the imaging corrector, a check plate (250 mm diameter) was positioned on the corrector to reveal the smoothness over small areas. At very small spatial scales (1 and then 5 mm), using a Chapman MP-2000 microscope with a Nomarski objective, micro-roughness was measured to be less than 11 Å rms.

Subsequent to polishing, the optic was AR coated by QSP Optical. The requirements for the spectrograph corrector coatings (per side) call for average reflectance across the 390 nm to 910 nm optical bandpass to be less than 0.8%, with peak reflectance less than 1.4%. This level of performance is achieved, as shown in Figure 16, with a 12 layer coating. The coatings, applied at a temperature of about 200°C, are durable but easily removed if required.

 

Figure 16. Reflectance of each surface of the spectrographic corrector is plotted as a function of wavelength. The entrance and exit sides of the optic are the concave and convex sides, respectively. The noise seen redward of 850 nm is described by QSP to be a problem internal to the reflectometer.

8. SUMMARY

As of February, 1998, the optics for imaging mode for the SDSS 2.5-m telescope are at the Apache Point Observatory site. In addition, tooling is in hand to assemble and mechanically collimate each subassembly.

The optics are of excellent quality, with each element meeting or exceeding fabrication requirements. During the test of each optic care has been taken to measure optical surfaces and axes with respect to mechanical references to sufficient accuracies such that, in principle, mechanical collimation of the telescope should be sufficient to meet the required image quality budget.

9. ACKNOWLEDGMENTS

It is a pleasure to thank Ian MacMillan and Geza Keller of QSP Optical for their efforts and accomplishments with the difficult task of developing the unique AR coatings for the transmissive optics and for providing us with the coating reflectance measurements presented herein. We also thank Shu-I Wang of the University of Chicago for additional help with the coating effort. In that regard, we are also thankful to Dan Skow and the Instrument Makers in the University of Washington Physics Shop who worked tirelessly to develop an excellent mask set in preparations for the imaging corrector coatings.

We are also grateful to Jon Davis, Mark Klaene and Dan Long of the Apache Point Observatory for their secure handling of large optics and commensurate skill in applying reflective coatings.

10. REFERENCES

1. L. R. Dettmann and D. L. Modisett, "Interferogram acquisition using a high-frame-rate CCD camera", in Optical Manufacturing and Testing II, H. P. Stahl, ed., Proceedings of SPIE 3134, p. 429 (1997).

2. J. H. Burge, D. S. Andersen, D. A. Ketelsen and C. S. West, "Null test optics for the MMT and Magellan 6.5-m f/1.25 primary mirrors", in Advanced Technology Optical Telescopes V, Proc. SPIE 2199, pp. 658-669 (1994).

3. Optical Sciences Center, University of Arizona, "Fabrication of the 2.5-m primary mirror for the Sloan Digital Sky Survey Telescope - Final Report", (1997).

4. D. Andersen, H. Martin, J. Burge and D. Ketelsen, "Rapid fabrication strategies for primary and secondary mirrors at Steward Observatory Mirror Laboratory", in Advanced Technology Optical Telescopes V, Proc. SPIE 2199, pp. 199-210 (1994)

5. J. H. Burge, "Measurement of large convex aspheres, in Optical Telescopes of Today and Tomorrow, Proc. SPIE 2871, pp. 362-373 (1997).

6. Steward Observatory Mirror Lab, University of Arizona, "Fabrication and testing of the 1.15-m secondary mirror for the Sloan Digital Sky Survey Telescope - Final Report", (1996).

7. Contraves, Inc., "Grind and figure flat silica corrector for the Sloan Digital Sky Survey Telescope - Corrector Final Report", (1997).

8. P. R. Yodel, Jr., Mounting Lenses in Optical Instruments, SPIE Optical Engineering Press, pp. 43-45 (1995).

9. Tinsley Laboratories, Inc., "Certificate of compliance - Spectrograph corrector final report", (1996).

10. D. Andersen, J. Burge, "Swing-arm profilometry of aspherics, in Optical Manufacturing and Testing, Proc. SPIE 2536, pp. 169-179 (1995).