Previous sections describe an initial set of scientific goals and requirements for GSMT, and are the culmination of two years of effort by a number of community-based workshops. This section describes the development of a telescope design aimed at providing performance matched to these basic requirements. At this early stage, we have not yet iterated the design to optimize its performance. Rather, we regard the concept described here as a "point design" whose primary raison d'etre is to identify technical challenges or showstoppers, and areas of significant risk or cost. The next steps (see Chapter 6) in developing a GSMT design concept involve parallel activities: further refinement of the science requirements and deeper exploration of performance-cost-risk trades that are critical precursors to adopting a requirements document and formally initiating conceptual and preliminary design activities.
We have adopted the philosophy that the design of a next generation telescope is above all a systems challenge, requiring an integrated approach that takes into account a whole range of issues: site characteristics, enclosure design, and structural design; orchestrating the active and adaptive elements with a sophisticated control system; fabricating, polishing, controlling, and maintaining the segmented primary mirror surface; and instrumentation. In other words, our approach is informed by the belief that it is no longer possible (as one example) to think of instruments as independent entities, uncoupled from the approach to Adaptive Optics (AO) systems, or, given their enormous scale, separate from the fundamental mechanical design of the telescope. Rather, the performance-cost-risk "sweet spots" can only be identified through a multi-dimensional set of systems trades.
Our goal in this design work, as in other parts of our program, is to contribute to the understanding of the common issues faced by all developers of extremely large telescopes (ELTs).
The current generation of 6-10-m optical/infrared telescopes has departed from the designs common in the earlier 4-5-m class telescopes. In the late 1970s, it was realized that the key to improving performance and reducing cost lay in reducing the relative size and mass of telescopes and their enclosures.
Because of difficulties polishing and testing fast-focal-ratio mirrors, earlier telescopes had relatively slow primary mirrors in relatively long tube structures. Limitations of passive mirror support systems led telescope builders to use thick, solid mirrors. To support these long telescopes with heavy mirrors, telescope structures had to be heavy. The result was massive telescopes, with low resonant frequencies, in large domes. Another factor limiting resonant frequencies was the indirect load paths inherent in most equatorial mount designs.
Low resonant frequencies made the telescopes susceptible to wind-buffeting, so enclosures were designed to minimize the airflow past the telescope. The high thermal inertia and minimal air flow created local seeing problems, which often were the most significant factors limiting the performance of large telescopes.
To remedy these problems, designers of the current generation of telescopes have taken advantage of advances in several fields:
- Improved computers and software have made alt-azimuth mounts practical; the resulting designs tend to have better stiffness for a given weight.
- Improvements in structural analysis techniques, particularly finite-element analysis, have made it possible to design more efficient structures, with improved stiffness-to-weight ratios.
- Development of mirror supports that can be adjusted in real time ("active optics") has made it possible to achieve excellent image quality using lightweight mirrors. Lighter mirrors allow use of lighter telescope structures.
- Advances in optical polishing and testing techniques
have made it possible to produce faster primary mirrors.
- Active optics can meet the more stringent alignment requirements for faster mirrors.
All of these developments have made it possible to build telescopes that are smaller, lighter, and stiffer, while achieving higher standards of image quality. In turn, enclosures have become relatively smaller, and can be more open to allow better ventilation. As a consequence, modern telescopes have been less expensive than standard scaling laws would indicate based on the costs of earlier 4-m class facilities.1,2
Reduced thermal inertia and better ventilation, combined with active removal of heat from electronics and other sources, have significantly reduced local seeing problems.
In the 1990s, further advances were made that are allowing these telescopes to achieve performance beyond the levels expected when they were first conceived. Dynamic compensation of disturbances, including fast steering mirrors to control image motion and AO to help control the effects of atmospheric seeing, have allowed these telescopes to produce nearly diffraction-limited images in the infrared. Use of adaptive systems also opens up new possibilities for dynamic compensation of telescope errors, such as correcting wavefront errors caused by wind-induced vibration and deformation of the mirrors.
The design of even larger telescopes such as GSMT will require an extension of the philosophies that have guided development of the current generation of telescopes, plus incorporation of features to take advantage of the dynamic compensation now available from AO systems.
The design of a diffraction-limited 30-m optical/infrared telescope is very challenging, and is made more difficult by the need to keep costs significantly lower than would be predicted by scaling from current 8- to 10-m designs. To simultaneously achieve cost and performance goals, all components of the telescope, including active and adaptive systems and the initial science instruments, must be developed as part of an integrated system. Careful systems engineering is required from the outset.
The starting point must be the science requirements. A conceptual design must be developed that is consistent with the science requirements and is responsive to the needs of anticipated scientific instruments. With a conceptual design in mind, the science requirements are used to derive specific error budgets. Initially, these will be "top-down" error budgets, derived simply by dividing allowable errors into a number of individual contributions assigned to appropriate subsystems. In establishing error budgets, all components should be considered as part of a dynamically interactive system, with errors of one subsystem compensated by the effects of others. As the design features are progressively elaborated, subsystems and their interactions will be modeled and their performance simulated. Based on these results, the designs and error budget will be iterated.
If GSMT is to be affordable, meeting cost goals will be as important as meeting performance goals. We will have to once again "beat the cost curve". While some additional savings are possible from the traditional approach of making the design relatively smaller and lighter, it is clear that a rigorous design-to-cost effort will be needed (see Section 5.7).
As mentioned in Chapter 3, Science Requirements, the design must consider issues of performance and construction cost, as well as operational issues such as reliability, maintainability, and life cycle cost. Estimates of annual operating costs range upwards from $25M per year. Hence, over the lifetime of GSMT, the total operating cost will be comparable to the construction cost. In cost-performance trades, evaluation of life cycle costs should have comparable weight to capital costs. Taking a systems approach that considers the operating life of the telescope is the rational path to minimizing total cost.
As mentioned in Chapter 1, one of the three parallel development paths of the New Initiatives Office (NIO) is to develop a "point design." But what exactly is a point design? It is an exercise that explores a single, plausible design consistent with the science requirements. This exercise helps to identify the key technical issues and highlight areas where additional development is necessary. It also indicates design factors important to the science requirements, and may indicate areas where some tradeoffs are required between technical feasibility and scientific goals. By working on the point design, technical staff have an opportunity to develop analytical methods that will be necessary for any GSMT design. Because a point design is a learning tool rather than a design that is being proposed for construction, it is not necessary to develop all features fully, or even in a completely consistent form. Once the key lessons have been learned, the design team can move on to explore other areas.
At this point in time, NIO has chosen to develop a point design instead of doing a "trade study" of all possible designs. Such a trade study will be appropriate at a later time, when the astronomy community has reached agreement on a firm set of science requirements. We believe that more can be accomplished at this phase by concentrating on a single point design, and that if the design is well chosen, most of the lessons learned will be transferable to later conceptual designs, even if they eventually look quite different.
At the start, certain fundamental decisions must be made about the system architecture. The following sections describe the key architectural features chosen for the point design and explain the reasons they were chosen.
The starting point for the design is choosing aperture size. Regarding the size of the GSMT, the report of the Panel on Optical and Infrared Astronomy from the Ground3 stated:
|"The ESO proposal for a 100-m-class telescope would offer even more spectacular gains for many kinds of observations, but it is the opinion of the panel that the proposal is too ambitious for the current decade, and that an intermediate step, to a 30-m telescope, would be optimal in terms of science, technology, and allocation of resources."|
Comments by Horace Babcock1 on the size of the Hale telescope:|
"The advances from Ritchey's 24-inch to the Hale 200-inch were perhaps bold but they were sufficiently conservative. One may recall that in the years between 1925 and 1928 there were strong pressures to make the next telescope of the series 300 inches in diameter. It is to the credit of Hale and his advisors that they calculated the structural limits on mirror support and consequently limited the diameter to 200 inches which was close to the practicable limit for conventional designs and materials then available."
On the same subject, Richard Learner wrote:2
"...the decision was to have a 200-inch primary mirror. This was triumphantly correct - 180 inches would have been harder to fund because this size would not have riveted people's attention; 220 might have been impossible to make."
|"The GSMT will be a filled-aperture, diffraction-limited telescope with atmospheric correction by AO down to at least 1 Ám."|
A second key decision was whether to use a spherical primary mirror, or to use an optical design requiring an aspheric primary. Several proposed concepts for ELTs use spherical primaries because spherical segments are easier to fabricate.4,5,6 However, to achieve good performance over a reasonable field of view (FOV), a telescope with a spherical primary needs at least two aspheric corrector mirrors; many designs use four-element correctors. The designs that have been proposed use correctors made of pairs of opposed concave mirrors in a "clamshell" arrangement, where the light must come to a reasonably good focus to pass through a small hole in the center of each corrector mirror. However, with a fast spherical primary mirror, the circle of least confusion becomes large. Even if you can get the entire science beam through, the light from laser guide stars focuses at a significantly different position.
Another key point is that for mid-IR instruments, the number of warm reflections should be kept to a minimum to control the effective emissivity of the telescope. For the IR, a two-reflection Cassegrain design is preferable to a six-mirror design.
For these reasons, the point design incorporates an aspherical primary mirror.
In the current generation of large telescopes, three concepts for lightweight primary mirrors have been pursued:
- Thin, meniscus, solid mirrors made of zero-expansion glass or glass-ceramic
- Borosilicate honeycomb mirrors
- Segmented mirrors (composed of hexagonal, solid, zero-expansion meniscus segments)
Other lightweight mirror concepts are possible, but have not been developed either because they offered no real advantages (for example, thin meniscus mirrors of non-zero-expansion materials) or because they were significantly more expensive (for example, large structured ULETM mirrors, or segmented mirrors composed of lightweight structured segments).
The largest single-piece telescope mirrors are the 8.4-m diameter primary mirrors being made for the Large Binocular Telescope Project. Although somewhat larger single-piece mirrors could be made, relative costs would rise rapidly with increasing size, particularly the cost of the blank fabrication facility, polishing and testing facilities, transportation, handling equipment, and coating chambers. At the 30-m size, single-piece mirrors are unaffordable. Therefore, the only lightweight mirror approach that can be extended to this size involves the use of a segmented primary.
Three large segmented-mirror telescopes already exist: Keck I, Keck II, and Hobby-Eberly. Several others are in work or have been proposed, including:
- Gran Telescopio Canarias (GTC)
- Large Aperture Multi-Object Spectroscopic Telescope (LAMOST)
- Mexican Infrared-Optical Telescope (TIM)
- Southern African Large Telescope (SALT)
These projects serve as the starting point for the design of any ELT.
The current generation of large telescopes uses primary mirror focal ratios between f/1 and f/2. Going to a relatively faster focal ratio has the following advantages and disadvantages, as shown in Table 1:
Two types of segment geometries have been considered seriously: (1) quasi-hexagonal segments, as used in the Keck, Hobby-Eberly, and GTC telescopes; and (2) petal or sector-shaped segments, as used in some Department of Defense segmented-mirror prototypes. Figure 1 shows notional geometries for these two types of segments used in an ELT.
Hexagonal segments have the following advantages and disadvantages, as shown in Table 2:
The choice of segment size is another key decision, because the range of possible sizes is large. At this stage, it isn't important to optimize the size within a few percent, but the size should be set within about a factor of two.
The largest practical segment would be the size of the largest affordable single mirrors, about 8 meters across. At this size, only 19 segments would be required to make a 30-m telescope. At the other extreme, segments could be arbitrarily small, but at some point the number of sensors and actuators would become prohibitive.
The factors involved in the choice of segment size are described in detail in Section 4.5 but the main issues are summarized in Table 4. The optimum range appears to be 1-2 meters across.
The aperture stop is located at the secondary mirror, as is often the case in telescopes optimized for infrared observations. The primary mirror is slightly oversized to allow chopping at the secondary mirror for background subtraction. This also has the effect of reducing difficulties caused by the irregular shape of the edge of the segmented primary mirror.
A fundamental decision for the telescope design involves determining whether the secondary mirror should be convex, flat, or concave. A flat mirror would introduce an unacceptably large central obscuration. A concave (Gregorian) secondary mirror would be easier to test in the optics shop, but at the size chosen for the point design, it will also be possible to test a convex secondary by conventional means. A Gregorian secondary mirror is in a favorable location to use as an adaptive mirror, because it will be conjugate to an altitude a few hundred meters above the primary mirror. However, a Gregorian secondary must be larger for a given final focal ratio and image position, which not only produces a larger central obscuration, but also increases the difficulty of making the mirror deformable. A Gregorian secondary also requires a significantly longer telescope structure, which in turn increases the size of the enclosure. The larger size and weight of a Gregorian secondary, combined with a longer telescope structure, tend to produce larger gravity deflections and lower resonant frequencies.
Considering these factors, particularly the size of the telescope structure and enclosure, we have chosen a convex secondary mirror for the point design.
There are several reasons to minimize the size of the secondary mirror:
- To minimize the central obscuration
- To reduce the difficulty of optical testing
- To minimize the mass that must be carried at the top end of the telescope
- To minimize the cross-sectional area at the top of the telescope that is exposed to the wind
- To reduce the difficulty of making the secondary an adaptive, deformable mirror
However, as the size of the secondary is reduced, the focal ratio required to place the Cassegrain focus at a convenient position behind the primary mirror increases, as does the image scale. This means, for example, that elements in the higher-order AO systems will get larger. As the size of the secondary mirror is decreased, the amount of astigmatism increases for a given field angle, and the entrance pupil moves farther behind the primary mirror, which increases the primary mirror diameter required to avoid vignetting.
As described in Section 4.5, the size chosen for the secondary mirror is 2 meters diameter.
Conventional AO systems have placed the adaptive components far down in the system to keep the adaptive components small. For example, in the Gemini Altair AO system, the first deformable mirror is M6. However, if the issues involved in producing a large deformable mirror can be successfully addressed, there are several advantages to using the secondary mirror as an adaptive mirror.
The GSMT point design incorporates an adaptive secondary mirror to serve the following needs:
- Correction of telescope wind-buffeting effects, including distortion of the primary mirror at frequencies higher than the bandwidth of the segment positioning system
- Adaptive Optics correction to high Strehl ratios in the mid-infrared with no further deformable elements
- Partial atmospheric correction in the visible and near-infrared, improving energy concentration even though the Strehl ratio is still low
- Serving as the first stage in higher-order AO systems
The point design telescope structure is patterned after a radio telescope design. The telescope is a lightweight steel truss structure on an alt-azimuth mounting. The secondary mirror is relatively small, and is mounted on a tripod supported directly off the primary backing structure rather than on spider vanes supported off a tube-like structure. The primary mirror is several meters above the elevation axis.
A radio telescope type of structure has several advantages. By locating the primary mirror above the elevation axis, the elevation bearings can be moved inwards behind the primary. This decreases the span between the bearings and provides a more direct load path from the main concentration of telescope mass down into the pier, resulting in a more efficient structure with less mass and higher resonant frequencies. Moving the elevation bearings inwards also makes it possible to provide large Nasmyth platforms without increasing the width of the telescope beyond that of the primary mirror. This helps reduce the size and weight of the telescope structure, and reduces the width of enclosure required if the enclosure is co-rotating (see Section 4.3).
In a more traditional design with the elevation axis above the primary mirror, the use of Nasmyth foci requires a large tertiary mirror to fold the beam along the elevation axis. The optical path distance from the secondary mirror to the focus is quite long, approximately equal to the primary mirror focal length plus half the primary mirror diameter. For a given final focal ratio, this requires a relatively large secondary mirror.
In contrast, in the GSMT point design the beam to the Nasmyth focus is relayed by additional optics sitting behind the primary mirror. The optical path distance from the secondary mirror to the first focus is just slightly more than the primary mirror focal length. For a given focal ratio, this allows use of a relatively small secondary mirror and simplifies the support of the tertiary mirror.
The point design also allows room for stationary laboratory space between the elevation bearings, where instruments can be located.
A radio telescope type of design has a couple of disadvantages, however. It requires a counterweight to balance the telescope and a greater front-to-back depth of the enclosure for a given primary mirror focal ratio. For the point design, we believe the advantages of this type of structure outweigh the disadvantages.
The advantages and disadvantages are summarized in Table 5:
The point design follows the philosophy that the optical design must be driven by the requirements of the science instruments. It should be possible to have more than one large instrument mounted and ready for use, and a range of different foci should be provided to accommodate the needs of different science instruments and observing programs. These needs include:
- Focal ratio/image scale
- Field of view
- Image quality (AO corrected, if necessary)
- Physical size of required instruments
- Instrument locations that maintain constant orientation relative to the telescope
- Locations that do not tilt with the telescope
- Foci that require minimal emissivity
The conceptual designs of the instruments themselves are described in Section 4.7.
The instrument locations incorporated in the point design include the following.
Adaptive corrections may not be feasible for a significant fraction (> 20%) of the available time. It is thus important to provide the capability for frontier science observations that exploit these conditions. Section 2.1 describes such observations, which argue strongly for a wide-field, seeing-limited capability.
However, for seeing-limited observations over a wide field, the image scale at the Cassegrain focus is inconveniently large. One arcsecond is 2.7 mm wide, and a 20 arcminute field is 3.27 meters across. A more convenient image scale is available at the f/1 prime focus-6.9 arcseconds per millimeter. At prime focus, a 20 arcminute field is 175 mm across.
A prime focus corrector is necessary to provide good image quality over a wide field. The design of the prime focus corrector is described in Section 4.7.1, with a discussion of the MOMFOS (multi-object multi-fiber optical spectrograph) instrument designed to use this focus.
The prime focus instrument must be interchangeable with the secondary mirror assembly and should be relatively small (no more than about 3 meters in diameter). The installation of the MOMFOS instrument is illustrated in Figure 4.
Instruments can be mounted directly at the Cassegrain focus, where they will move with the telescope. This is useful for infrared instruments, because they can be fed with only two warm reflections. It is also useful for instruments with second-stage AO, because it preserves a fixed orientation between the adaptive secondary and the wavefront sensor and deformable mirror. This simplifies control and improves performance.
The optical performance at the Cassegrain focus is described in Section 4.5. The Cassegrain focal ratio is f/18.75.
It is possible to locate an instrument in the laboratory space between the elevation bearings, with the beam fed in by means of two flat mirrors: one to direct the beam along the elevation axis, and another to direct the beam downwards into the instrument. An upward-looking instrument can be rotated in this position on a turntable to compensate for field rotation. This provides a fixed gravity environment for alignment-sensitive instruments.
The point design includes a multi-conjugate adaptive optics (MCAO) system, located behind the primary mirror and co-rotating with it. This system is designed to feed an f/38 beam through one of the elevation bearings to instruments mounted on a Nasmyth platform. It would be possible to mount the instrument upward-looking on a turntable to compensate for image rotation, while maintaining a constant gravity orientation.
The layout and optical performance of the MCAO system are described in Section 4.6.2.
|Image scale (arcsec/mm)|
|Field of view (arcmin)|
|Field diameter (meter)|
|Image quality goal|
|Other possible instruments|
* Available field of view with one segment removed to form the central hole of the primary (the field of view of the High Order AO Coronagraph is much smaller). A larger seeing-limited field is available if required - see Section 4.5.
Section 4.6.1 describes the four adaptive optics modes that are provided in the point design. That information is summarized briefly here, to show how the adaptive optics modes have evolved from the requirements of the science instruments.
The instrument proposed for prime focus is a seeing-limited multi-object multi-fiber optical spectrograph (described in Section 4.7.1). The natural guide star AO system proposed for prime focus cannot deliver high Strehl ratios in the visible, but it should be able to improve seeing slightly. To the extent that it corrects ground-level seeing disturbances, the correction should be effective over a wide field (see Appendix 4.6.A). However, one of the main purposes for the prime focus AO system is to compensate for wind-buffeting disturbances of the primary mirror. Because it will use natural guide stars, the prime focus system will be able to exploit conditions (i.e., thin cirrus) that may not be suitable for MCAO.
The direct Cassegrain focus can be used for infrared instruments to minimize the number of warm reflections. By having an adaptive secondary mirror, it should be possible to provide nearly diffraction-limited images in the infrared, with relatively high Strehl ratios. The adaptive secondary mirror can also compensate for wind-buffeting disturbances of the primary mirror and correct dynamic alignment errors.
The diffraction-limited coronagraph will include a high-order AO system to provide high Strehl ratios in the near infrared. This high-order corrective element will likely have limited dynamic range, so it will depend on the adaptive secondary mirror to serve as a first stage to compensate for larger amplitude aberrations.
Similarly, the MCAO system will use the secondary mirror as a coarse stage. Like the diffraction-limited coronagraph, the MCAO system will extend the focal ratio to about f/38 to provide a better match between the diffraction-limited resolution and detector pixel sizes.
All four proposed AO modes are directly based on the requirements of anticipated instruments described in Section 4.7. In two of these modes, prime focus AO and narrow field high-order AO, a deformable mirror will be incorporated into the instrument. In all of these modes, on-instrument guiding/wavefront sensors will be needed.
The properties of the site must be factored into the systems engineering approach to the design of the telescope and enclosure, and site selection criteria should be based on an understanding of the effects of site characteristics on system performance. Several site-related characteristics must be considered, including:
- Cloud cover
- Temperature range
- Wind speed and direction
- Precipitable water vapor
- Seismic activity
- Snow loading
- Dust levels
- Light pollution levels
- Sodium layer height
Section 5.2 describes the ongoing program of site testing studies for a GSMT.
Section 4.3 describes a number of enclosure concepts under consideration for a GSMT. The design of the enclosure will be based on systems engineering considerations. In addition to meeting support function requirements, the design will be optimized to allow good ventilation while protecting the telescope from windloading, based on our ongoing studies to characterize windloading (see Section 5.5). Within these design constraints, the primary emphasis will be on minimizing the cost of the enclosure.
At the 30-m scale, glass and steel alone can't deliver diffraction-limited images at optical/IR wavelengths without extensive active and adaptive systems to correct internal inaccuracies and compensate for external disturbances. Our point design control system concepts are based on a hierarchical approach, where active and adaptive elements make corrections over a range of spatial and temporal frequencies. Some of these corrections are described below and summarized in Table 7.
Figure errors in individual primary mirror segments will be corrected by the segment active optics (warping) systems. Alignment and co-phasing of the primary mirror segments will be accomplished by the segment positioners and will be maintained using feedback from edge sensors and wavefront sensors.
Tracking errors and atmospheric image motion will be corrected on short time scales by fast tip-tilt of the secondary mirror; over longer time scales consistent with the response bandwidth of the mount structure, tracking errors will be corrected by the main drives and instrument rotators. For diffraction-limited observations at shorter wavelengths, image motion will be further corrected by the higher-stage AO system.
Gravity sag and thermal expansion of the telescope structure will be corrected by repositioning the primary mirror segments and the secondary mirror. It may also be necessary to include active elements in the telescope structure. Gravity sag and thermal warping of the primary mirror segments will be corrected by the segment AO systems.
Wind-buffeting of the primary mirror will be corrected on short time scales by the deformable secondary mirror or the deformable mirror in the prime focus corrector. On longer time scales consistent with the response bandwidth of the segment positioning system, quasi-static windloading will be compensated by moving the primary mirror segments.
Atmospheric seeing effects, including local "dome" seeing, will be compensated to the extent possible by the AO systems.
The control of these active and adaptive systems will be complex, requiring integrated hierarchical control systems layered by subsystem bandwidth. Point design control system concepts are described in detail in Section 4.8.
The features that have been chosen for the fundamental system architecture of the GSMT point design are:
- Filled aperture
- Aspherical, segmented, f/1primary mirror
- Hexagonal segments-1.15 meters across flats
- Aperture stop located at secondary mirror
- Convex, adaptive secondary mirror - 2 meters diameter
- Radio telescope type of structural design
- Four instrument locations:
- Prime focus
- Co-moving Cassegrain focus
- Gravity-invariant Cassegrain focus
- MCAO-corrected Nasmyth focus
- Four AO modes based on instrument requirements
- Prime focus corrector
- Adaptive secondary
- Narrow field high-order AO
- Multi-conjugate AO
- Hierarchical control system
These systems are described in detail in later sections.
Thanks to Rick Robles for producing the color figures in this section.
- Meinel, Aden B. "Cost scaling laws applicable to very large optical telescopes". Proc SPIE 172, pp. 2-7.
- Schmidt-Kaler, Theodor; Rucks, Peter. "Telescope costs and cost reduction". Proc SPIE 2871, pp. 635-640.
- Report of the Panel on Optical and Infrared Astronomy from the Ground, Astronomy and Astrophysics in the New Millenium: Panel Reports, p. 67. National Academy Press, 2001.
- Dierickx, Philippe; Gilmozzi, Roberto. "Progress of the OWL 100-m Telescope Conceptual Design". Proc SPIE 4004, pp. 290-299.
- Ray, Frank B.; Bash, Frank N.; Ramsey, Lawrence W.; Sebring, Thomas. "Issues in scaling the ELT up to 100 meters". Proc SPIE 4004, pp. 405-419.
- Owner-Petersen, M.; Andersen, T.; Ardeberg, A. "Optical Design of a 25 m Telescope for Optical Wavelengths". Proc SPIE 2199, pp. 945-949.