Fabricating segments for the GSMT primary mirror requires addressing three significant challenges: (1) to produce segments in quantities approximately 10 times the number produced for the two Keck telescopes combined; (2) to develop techniques for precise polishing and testing to a range of aspheric figures; and (3) to accomplish 1 and 2 quickly and economically.
This section summarizes the results of an initial investigation of each of the above, and spells out a technology development plan that the New Initiatives Office (NIO) believes will serve the interests of several extant efforts to explore design concepts for extremely large telescopes (ELTs).
Our technical summary draws on: (1) discussions held at an AURA-sponsored workshop aimed at exploring key GSMT technology issues; (2) studies and plans developed by the California Extremely Large Telescope (CELT); and (3) visits to selected optics firms that are well-qualified to carry out forefront commercial efforts in segment fabrication and polishing. The latter visits involved key personnel from both CELT and NIO, consultations among whom also inform the following discussion.
Both the GSMT and CELT approaches-and presumably those of other ELT programs-will require fabrication and polishing of off-axis aspheres.
The difficulty of figuring aspheric optics by traditional means is approximately in proportion to the slope of the aspheric departure. As surfaces depart more and more from a spherical shape, increasingly smaller tools are required to obtain a reasonably good fit between the tool and the optical surface.
Some advanced polishing machines have been developed to allow larger tools to be used. For example, Zeiss has developed machines that use a flexible, radial, bar-shaped lap with variable-force actuators pressing it against the glass. The Steward Observatory Mirror Laboratory has developed a stressed lap that can be warped in real-time to reduce the mismatch between the lap and mirror. However, even these polishers use localized polishing with small tools whenever they figure a mirror with any significant amount of asphericity.
The Keck mirrors were figured using a different process, however.1 As mentioned in Section 4.5, off-axis sections of a paraboloidal (or nearly paraboloidal) mirror have an aspheric departure that consists almost entirely of focus, astigmatism, and coma. These shapes can be produced relatively easily by bending a thin, flexible mirror blank. Jerry Nelson, Terry Mast, and other collaborators on the Keck project developed the "bend and polish" approach to make use of this property. A thin, meniscus mirror blank is bent into an inverse of the aspheric departure by applying forces and moments at the outer edge. It is then polished to an accurate spherical shape. If the bending has been done accurately enough, the mirror will spring back into the desired off-axis paraboloid when the stress is removed. The mirror can then be cut into a hexagon to form the off-axis segment.
In practice, an additional step was required. Because the segments warped slightly when they were cut, a deterministic figuring operation was needed to make final corrections. On the Keck project, this final operation was done by ion figuring. Because the material removal rate and profile are repeatable, they can be calibrated with good precision. It is possible with ion figuring to make predictable figure corrections right up to the edge of the mirror. This is important for a segmented-mirror telescope, where there is no opportunity to mask the edge of the mirror to cover a turned-down edge. One of the advantages of the bend and polish approach (also called stressed-mirror figuring) is that it produces an optical surface that is smooth and accurate right to the edge of the blank. Ion figuring is capable of making final corrections without degrading the edge of the aperture.
Although the stressed-mirror approach has a number of advantages, it is not particularly favored by commercial polishers. For example, REOSC is figuring the segments for the Gran Telescopio Canarias (GTC) using computer controlled polishing augmented by ion figuring.2
The segments for the Hobby-Eberly Telescope (HET) were finished by an entirely different process, one that took advantage of their spherical figure. Kodak polished the HET segments on a large continuous polishing (CP) machine, also called a planetary polisher. CP machines are normally used to polish flat mirrors. The machine has a large, stiff, circular table that revolves; often the table is made of granite. Pitch facets on the surface of the table do the polishing, and the mirror rides face-down on top, held in place by guide rollers. Round mirrors are allowed to rotate against the guide rollers, while irregularly shaped mirrors are normally held in a round septum within a cutout that matches the shape of the mirror. A large piece of granite or glass rides on top of the lap as a conditioner, to ensure that the lap maintains its shape. To help correct small figure errors in the mirrors, the opticians will sometimes place small weights on top of selected regions of the mirror as it rides on the continuously turning lap.
Mirrors polished on a CP machine can be no larger than about 1/3 of the diameter of the lap, but it is possible to polish several mirrors at the same time. Even if the mirrors are maximum size, two to three can be polished simultaneously. This type of machine is therefore very cost-effective and is the standard approach for making flat mirrors. Another reason is that CP machines can produce beautiful, smooth mirror figures right to the edge of the part.
It is possible to use the same type of CP machine to polish long-radius spheres, as Kodak did for the HET. The mirrors were polished on a 4-m CP machine until they were close to the final figure, and then finished by ion figuring. This resulted in segments whose cost was about $20,000 per square meter in 1998 dollars. This is a small fraction of the cost of the Keck segments.
In September 1999, AURA sponsored the MAXAT Workshop II, where more than 40 experts from astronomy and industry came together to develop a roadmap for technology development that would lead to ELTs of the 50-m class. At this meeting, Marc Cayrel and Eric Ruch of REOSC and Andreas Nonnenmacher of Raytheon commented on the relative costs of polishing spherical and aspherical segments. They estimated that the cost of finishing segments on a CP machine would be approximately a factor of five smaller than the cost of finishing segments one at a time using more traditional polishing techniques.
Two approaches were suggested to extend the benefits of CP machines to the production of off-axis aspheric segments. Cayrel suggested polishing spherical segments, then warping them into aspheric shape in the telescope. Jerry Nelson indicated that for the CELT project, they are proposing the reverse. Nelson proposed to do stressed-mirror figuring on a CP machine. This approach is described in detail in the literature.3
The first approach, which we will call "polish and bend," has the advantage that the mirror can be cut into a hexagonal shape before polishing. This allows the mirror to be smoothly polished right to the edge, and ensures that there is no subsequent warping when the segment is cut. The polishing operation would be simpler because no warping harness is required. Optical testing of identical spherical segments would also be much easier and cheaper to accomplish than testing more than 100 different types of aspheric mirrors.
The polish and bend approach has serious disadvantages, however. The segment bending would occur in the telescope, where there is no clearance at the edge of the segment to attach levers. The segment bending would also have to be on a hexagonal segment rather than on a round blank. And finally, if the bending is not perfectly smooth, there is no opportunity to correct it with ion figuring.
By comparison, the bend and polish approach is more difficult to accomplish in the optics shop. The warping harness would likely place additional weight at the outer edge of the mirror, which could result in uneven polishing. It is also likely to be relatively tall, which could interfere with the operation of the machine and could produce uneven loading because of the high center of mass and the low position of the guide rollers. However, once the segments are polished and ion-figured, they are in the correct shape when in a relaxed state. This makes it easier to control their figure in the telescope, because no large stressing forces are present. With bend and polish, the warping harness can be adjusted several times if necessary, until the mirror figure is good in the optical test. With polish and bend, the warping would have to be adjusted in the telescope, where there is no easy way to accurately test the segment shape in situ.
For these reasons, NIO favors the bend and polish approach proposed by CELT (however, see comments under Summary and Conclusions).
Following discussions held at the AURA-sponsored workshop on enabling GSMT technologies, Jerry Nelson, Larry Stepp, and Eric Hansen visited several optical finishers to discuss segment fabrication for GSMT and CELT in November 2000. These discussions are summarized in an NIO technical report;4 part of the information from that report is reproduced below.
The optical parameters of the GSMT point design are described in Section 4.5. The optical design proposed for the 30-m CELT is somewhat different.5 Some of the optical and optomechanical parameters of its design are summarized in Table 1.
The maximum amount of astigmatic departure from a sphere in the CELT segments is a Zernike coefficient of 19 microns (38 microns peak-to-valley). The maximum amount of comatic departure from the sphere is a Zernike coefficient of 0.4 microns (0.8 microns peak-to-valley).
Nelson has commented that for CELT, he would recommend some changes from the approach that was used for Keck. For example, he would prefer minimizing the number of holes that must be bored into the blanks (each Keck segment has several dozen holes).
The Keck segments are 0.9 m along each side (1.8 m point-to-point) and 75 mm thick. To get an adequate mirror figure, the Keck segments are supported on 36-point whiffletree structures. Nelson said these were difficult to adjust, and that he would prefer smaller segments that could be adequately supported on an 18-point whiffletree.
Smaller segments also have less overall asphericity. The worst-case astigmatism coefficient varies as the square of the segment radius. The worst-case coma coefficient varies as the cube of the segment radius, but the coma tends to be an order of magnitude smaller than the astigmatism.
A desire to limit segment asphericity also affects the choice of primary mirror focal ratio. The segment asphericity varies essentially as the inverse cube of the radius of curvature.
The most critical alignment sensitivity is rotation of the segment, which can be thought of in terms of the change in surface height with rotation angle dZ/d. This depends primarily on the amount of astigmatism in the segment.
CELT scientists have proposed primary mirror segment fabrication techniques based on the stressed-mirror approach used for the Keck segments.3 In our discussions with optical finishers, this approach was taken as a starting point. CELT's proposed sequence of fabrication operations is listed below.
CELT Fabrication Approach
- Acquire generated circular mirror blanks; diameter 1.1 m.
- Grind and polish back surface spherical.
- Install stressing fixture on perimeter and back region.
- Stress blank to desired deformation, test with profilometer.
- Grind front surface spherical, test with profilometer.
- Polish front surface using planetary polisher, test with profilometer, polish to within ~100 nm RMS (root mean square) of desired surface.
- Optical test of circular mirror.
- Cut to desired hexagon (some warping expected, ~ 100 nm RMS).
- Stress relieve the cut edge (polishing, etching, etc.).
- Install passive support system. This should require gluing only, on the back.
- Optical test of hexagonal segment.
- Ion figure out residual errors.
- Optical test of hexagonal segment, with and without warping harnesses.
- Ion figure if needed.
- Ship to site.
CELT has proposed the following manufacturing tolerances:
Optical figure accuracy: <: 20 nm RMS (some active optics warping allowed)
Surface finish: <: 2 nm RMS
Machining tolerances: <: 0.1 mm
Edge bevels: <: 1 mm
The companies visited by Hansen, Stepp, and Nelson are listed below (not all of the vendors were visited by all three):
- Brashear LP
- Eastman Kodak
- Rayleigh Optical
- Space Optics Research Labs
Each company was asked to comment on the stressed-mirror fabrication approach proposed by CELT. Their comments are summarized below. They were also asked to comment on a number of other fabrication issues; the specific questions and associated answers are listed in Section 18.104.22.168, Answers to Questions About Segment Fabrication.
Acquire generated circular mirror blanks; diameter 1.1 m
In general, the polishers prefer to procure the blanks themselves rather than have the project supply them. This gives them more direct control of quality and schedule.
We were told that Schott is now producing up to 1-m diameter Zerodur blanks in Durier, Pennsylvania. The quality of the material they are producing there is reportedly excellent.
One polisher commented that the amount of material required to make the segments would be comparable to the total amount of zero-expansion glass currently made by one of the large glass suppliers in a year. Therefore, a significant expansion of production would be required to deliver all of the segment blanks over a period of just a few years, although this is not expected to pose a problem.
The polishers all agreed with the desire to minimize the number of holes that must be bored into each blank, to control cost and minimize risk. However, they don't see this as a significant problem if holes are needed.
Grind and polish back surface spherical
More than one of the polishers asked if it would be acceptable to leave the back of the segments flat. For example, the (spherical) segments of the HET primary mirror have flat backs. Nelson said this would be acceptable; he could make appropriate allowances in the stressing calculations.
Some of the polishers suggested acid etching the backs of the segments rather than polishing them. They suggested that this could reduce cost, and they believe it would be adequate to remove sub-surface damage left over from grinding. It would also provide a good surface to bond to support mechanisms.
Install stressing fixture on perimeter and back region
Virtually all vendors had concerns about the design of the stressing fixture, concerning whether it would work reliably and be compatible with their CP machines.
On a CP machine, the edge of the optic must be free so that the septum of the machine can bear against it to move it laterally. Several of the polishers commented that it would be better if the stressing fixture were not attached on the edge of the mirror blank.
Several polishers also expressed a desire for the stressing fixture to be as low as possible on the back of the mirror blank, to ensure adequate clearance and keep the center of mass of the blank plus fixture as low as possible.
One polisher pointed out the need to provide uniform pressure between the part and the lap by making sure that any loading on the blank is spread out evenly. This will be difficult if the stressing fixture is attached only at the outer edge of the blank. The design of the fixture may need to allow clearance so that additional weights can be distributed on the back of the blank during polishing.
Stress blank to desired deformation, test with profilometer
Nelson reported that the amplitude of warping of the Keck segments was accurate to 1% based only on their calculations. It was routinely adjusted to within 0.1% with feedback from the profilometer used by ITEK.
Depending on the specific process flow the polishers had in mind and the number of parts that would be in work at one time, the number of stressing fixtures could vary from a few to several dozen. This highlights the need to keep the design simple and inexpensive.
Grind front surface spherical, test with profilometer
Some polishers considered grinding the segments on a CP machine, while others anticipated using different machines to do the grinding.
The polishers had different ideas about the best type of profilometer to use, but all of their ideas were based on the use of multiple linear variable differential transformers (LVDTs) in a configuration similar to that used by Steward Mirror Lab to calibrate their stressed lap. The measurements would be relative to a standard reference surface.
One polisher mentioned that there is a type of speckle interferometer used in the automotive industry to measure large surfaces with fairly large departures (for example, measuring a 12" x 12" area with a height range of 40 microns). This type of device might be used to measure the warping of the segments. The area covered by the device is defined by the size of beam expander used.
Polish front surface using planetary polisher, test with profilometer, polish to within ~100 nm RMS of desired surface
Kodak reported that they were able to hold the 26.18-m radius of curvature on the 97 HET segments constant within ± 0.5 mm.
A CP machine uses a large stone or glass conditioner plate, about half the diameter of the table, to help maintain the shape of the pitch surface. The largest mirrors that can be polished on a CP machine are about 1/3 of the diameter of the table. Therefore, to polish the size of segments anticipated by the CELT design would require at least a 3.5-m diameter CP machine. The segment size envisioned by the GSMT point design would require about a 4.5-m diameter table if the mirrors were polished as discs and then cut to hexagons. It would require a 4.1-m table if the segments were polished as pre-cut hexagons.
Kodak currently has a 4-m CP machine, as well as several slightly smaller ones. Tinsley currently has a 4-m CP machine. Zygo has three 4.3-m CP machines. Other polishers reportedly have similarly large machines.
Optical test of circular mirror
Several possible optical test methods have been proposed by CELT.3 However, the polishers have their own ideas about testing the segments. Several of the polishers favor tests using computer-generated holograms to produce the required asphericity in the test setup. The polishers expressed confidence that they would be able to test the segments to the level of accuracy specified.
Cut to desired hexagon (some warping expected, ~ 100 nm RMS)
Nelson said that Keck allowed the location of the hexagon within the circular blank to be adjusted when the mirror was cut, which made it easier to meet tolerances. This could be an important factor in reducing the average length of time each segment needs to be worked.
The polishers discussed different methods to cut the hexagons, including the use of diamond saws or a water jet. They indicated that meeting the mechanical tolerances should not be a problem.
The polishers would prefer to have larger bevels than 1 mm, but they can work to that tolerance if necessary. We discussed the possibility that there might inevitably be a few edge chips because of the small bevels allowed. The specifications should be written with this possibility in mind.
Fiducials must be placed on the mirrors at the time the hexagon is cut.
Ion figure out residual errors
Kodak has direct experience ion figuring the Keck segments and the segments for the HET. They have an existing chamber with 2.5-m diameter capacity. Most of the other polishers we visited do not have existing ion figuring chambers large enough for the segments, although some other polishers do (for example, REOSC).
Kodak recommends minimizing the amount of material to be removed by ion figuring to save time and cost. Also, it takes a long time to remove material with a narrow ion beam, so it will be important to avoid high-spatial frequency errors in the polished surface.
The segments will need to be supported downward-looking in the chamber, and it probably does not make sense to remove them from their mounts to install them on a separate support in the chamber. This implies that the design of the mirror mount should be vacuum-compatible, and that the mount should work well upside-down (neither of which is expected to be a significant problem).
There is at least one competing technology to ion figuring: magneto-rheological finishing (MRF). Although we don't know of a polisher with the capability currently to finish 1-m segments by MRF, MRF should compare favorably to ion figuring for the following reasons:
- It appears to be as deterministic as ion figuring.
- It does not require a vacuum chamber, so it should be less expensive to set up and run.
- It should be relatively easy to scale up in terms of the part size.
- It is a polishing process, so it improves the surface finish rather than degrading it.
- 1. Various sets of parameters have been discussed for hexagonal segments, ranging (for example) from approximately 1000 segments 1 m across and 40 mm thick that are part of an f/1.5 parent paraboloid, to approximately 700 segments 1.2 m across and 50 mm thick that are part of an f/1 parent. Within this range, how would you estimate the variation of difficulty and total cost with the following parameters?
- Segment width
- Segment thickness
- Mirror focal ratio
Within this parameter space, where would you guess the minimum cost solution would lie?
- All of the polishers we talked to preferred segments in the size range we were discussing, between 0.8 m and 1.2 m. The consensus is that segment size is not a strong cost driver within this range.
The range of segment thickness between 40 and 50 mm was considered acceptable for this size of part.
The job will be easier if the segments are less aspheric, so the polishers generally favor a longer focal ratio.
- 2. Do you think it is worth the effort to correct coma by stressed-mirror polishing, or should it be corrected entirely by ion figuring?
- To minimize the amount of material to be removed by ion figuring, the polishers generally thought it would be good to correct at least some of the coma by stressed-mirror polishing, at least on the more aspheric segments.
- 3. Can the blanks be cut into hexagons before polishing, or do they need to be polished as circles and then cut?
- Nelson explained that it is very difficult to predict the warping effects when the segments are cut. The direction of stress in the material that will warp a mirror when it is cut does not cause birefringence when measured through the thickness, so there is no good way to predict the shape of the warping by measuring the residual stress before cutting.
Most of the polishers would prefer to polish the segments as hexes to minimize problems caused when the segments are cut. However, they also expressed concern over whether a warping fixture could be designed to avoid local distortion where the levers are attached. In general, they are not confident that the stressed-mirror approach will work if you don't start with oversized circular blanks.
- 4. Would it be economically feasible to equip a dedicated facility just for making these aspheric segments?
- All of the polishers felt that some dedicated equipment would be necessary, but some would use parts of their existing facilities for certain process steps. Some of the vendors could modify their existing facilities to do this work; others would need new facilities. Several vendors emphasized the need to carefully design the entire facility to factor in the handling and storage of the segments, to ensure an efficient process flow, and to safeguard the parts in work. In general, the polishers would need one to two years after the start of the contract to set up an efficient facility.
- 5. Will it be more cost-effective to perform the final optical acceptance tests on individual segments, or on a raft of seven or 19 segments?
- The polishers we talked to would all prefer to test individual segments to avoid holding up the tests while waiting for multiple segments to be finished. However, several of the polishers emphasized the utility of having a test setup that could be used for more than one type of segment (for example, by having an aspheric compensator that could cover a range of off-axis radii).
In contrast, REOSC is planning to test the segments for the Gran Telescopio Canarias in groups of seven segments.6
- 6. If the segments were manufactured in radial order (that is, with the segments closest to the center produced first), followed by the next ones out, etc., would it be possible to adjust the radius of curvature of the lap slightly between each set of six segments so that it would not be necessary to bend power into the segments?
- All of the polishers generally agreed with the idea of adjusting the radius of curvature of the lap over time, to minimize the amount of curvature that would need to be bent into the segments. However, they would not adjust the radius between each set of six.
The stressing fixtures would still need to be able to control the focus term. This could be important if a segment were scratched and had to be reworked out of sequence, for example.
- 7. Would it be cost-effective to equip the vacuum chamber used for the final ion figuring run with a coating capability so that the coating could be applied to the pristine ion-figured surface?
- The polishers were uniformly negative about this approach. They said it could be done, but they saw no advantages to it. The ion-figuring chamber will be an expensive facility whose throughput should be maximized. Also, there would be issues of controlling contamination from the coating material.
- 8. There would likely be some advantages and disadvantages to making the segments sector-shaped instead of hexagonal, as illustrated. How do you think the fabrication difficulty and cost would compare between sectors and hexagons?
- Most of the polishers would prefer to produce hexagons, although they felt they could produce sectors if required. They said there would be more wasted material to produce sectors, and it would be difficult to control the mirror figure at the relative sharp (90°) corners. In general, from the polishing standpoint, the closer the blanks can be to round disks, the better.
They predict it would be cheaper to produce hexagons.
These polishers routinely work on mirrors 1-2 m in diameter; several of them had work of this size ongoing when we visited.
Some of the polishers were interested in developing the stressed-mirror process. However, a couple of them were openly skeptical; one said that the process is not economically viable, or optical shops would already be using it routinely. These vendors have other techniques that they would favor for finishing the segments.
In defense of the stressed-mirror approach, Nelson pointed out that it will tend to converge on the proper figure the longer polishing continues, as opposed to other approaches that wear away the glass differentially and require careful control of pressure and dwell time.
One polisher made the point that the optics industry is quite busy right now, and there will be a significant opportunity cost if they assign people to work on proposals or technology development efforts for telescopes that have not yet been funded. On the other hand, some of the smaller vendors would be happy to do development work for us if there were funding available to cover their costs.
One reason that several of the polishers are busy is that they have contracts to produce large numbers of flat optical elements for the National Ignition Facility (NIF). Some of these parts (the amplifier slabs) are nearly a meter long and have length-to-thickness ratios similar to the proposed GSMT segments. Their surface figure specifications are also similar to the requirements for GSMT. The NIF needs more than 7500 large optical elements (larger than 30 cm across) to be produced within the next five years, so the production rates in terms of square meters of polished surfaces per month are similar to the requirements of GSMT.
We were told that in some cases NIF was able to reduce the cost per part by approximately a factor of five by working with the polishers in advance. NIF funded some development work, allowed enough time for special machines to be fabricated and experiments to be run, and then solicited new bids based on highly optimized production schemes. This approach required significant funding in advance, involved a certain amount of financial risk, and took two to three years to accomplish, but the resulting cost savings paid for the effort many times over.
In France, there are similar laser fusion development programs. For example, last year REOSC produced a batch of 158 amplifier slabs that are 81 x 45 cm in size on their 4-m CP machine for the Laser MegaJoule (LMJ) project.2
Our discussions with polishers have confirmed that the production of off-axis aspheric segments for the GSMT primary mirror is not beyond the current state-of-the-art and could be completed within a reasonable time frame. It is clear that there are several polishers who would be well-qualified to bid on this work. The principal risk area is cost.
To produce the required number of segments in just a few years' time and at an affordable cost will require a well-structured production operation in which every detail has been optimized to control quality and improve efficiency. This involves not only consideration of techniques for figuring and optical testing of the segments, but also handling, storing, labeling, cleaning, coating, packaging, and transport of segments, bonding of attachment points, calibration of instruments, maintenance of machines, automatic generation of reports, and so on. This operation will have to run efficiently week after week, year after year.
This type of operation is more industrial than academic. Even though we believe that stressed-mirror polishing is promising, it is the optical finishers who truly understand what types of processes will be most cost-effective in the entire production operation. Therefore, we believe that the best way to proceed is to involve the commercial optical finishers in developing production approaches, and to support these efforts with funding and academic research programs where sensible.
The following section describes our plans for continued development.
Many organizations are developing plans to build ELTs, and several of these concepts use aspheric primary mirrors with segments in the 1-2 m range. Because this is an area where collaboration on technology development could be very productive, NIO will work to set up collaborations with interested astronomical organizations and commercial optical finishers. Two of these collaborative activities are described below.
NIO hosted a workshop on Cost-Effective Fabrication of Mirror Segments, on May 30-31, 2002, in Tucson, Arizona. The workshop was aimed to involve as many ELT study groups and optical finishers as possible.
The workshop agenda included a presentation by each telescope study group, in which its telescope design concept, mirror segment requirements, segment support ideas, and anticipated schedule were described. The program also included technical presentations from academic groups that have already completed studies about fabrication and testing of segments. The optical finishers discussed their concerns and indicated types of studies or prototype programs that would be most useful. Some of these studies can be carried out by the telescope programs, but others will need to be done by industry.
Workshop participants agreed the forum was useful and expressed a desire for further meetings of this type.
A key concern is the development of highly repeatable optical test methods that can measure the radius of curvature, quantify the aspheric departure, and characterize the figuring errors of each segment. These test methods must be affordable and must provide rapid turnaround.
One testing approach has been proposed by Burge.7 It uses a full-aperture spherical test plate in combination with interchangeable computer-generated holograms to test the different segment types interferometrically. The test appears to offer excellent ability to match the required radius of curvature, and should allow highly accurate registration of the segment position.
With partial support from the NIO, the University of Arizona Optical Sciences Center has conducted a systematic study of this test method to understand design tradeoffs and sensitivity to errors. The study includes a demonstration on smaller, off-axis aspheric mirrors, as well as a full tolerance study related to the parameters of the GSMT point design.
Thanks are due to Jerry Nelson, Eric Hansen, and the engineers and managers at Brashear LP, Eastman Kodak, Rayleigh Optical, Space Optics Research Labs, Tinsley, and Zygo for very helpful discussions of the GSMT optical fabrication requirements. Thanks also to Bob Parks for Figure 1.
- Jerry E. Nelson, George Gabor, Leslie K. Hunt, Jacob Lubliner, Terry S. Mast, Stressed mirror polishing. 2: Fabrication of an off-axis section of a paraboloid, Applied Optics Vol. 19, No. 14, pp. 2341-2352, 1980.
- Roland GEYL, Marc CAYREL, REOSC approach to ELT's and segmented optics, SPIE 4003, Optical Design, Materials, Fabrication, and Maintenance, Munich, Germany, pp. 59-64, 2000.
- Terry S. Mast, Jerry E. Nelson, Gary E. Sommargren, Primary Mirror Segment Fabrication for CELT, SPIE 4003, Optical Design, Materials, Fabrication, and Maintenance, Munich, Germany, pp. 43-58, 2000.
- Larry Stepp, Fabrication of GSMT Optics, AURA New Initiatives Office technical report RPT- GSMT-002, 2001.
- J. E. Nelson, Design Concepts for the California Extremely Large Telescope (CELT), Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, Ed. T. A. Sebring and T. Andersen, SPIE Proc. 4004, pp. 282-289, Munich, Germany, 2000.
- F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo and L. Cavaller, The status of the design and fabrication of the GTC Mirrors, Optical Design, Materials, Fabrication, and Maintenance, Ed. P. Dierickx, SPIE Proc. 4003, pp. 24-33, Munich, Germany, 2000.
- J. H. Burge, Efficient testing of off-axis aspheres with test plates and computer-generated holograms, Optical Manufacturing and Testing III, Ed. H. P. Stahl, SPIE Proc. 3782, pp.348-357, 1999.