# Chapter 4, The Point Design

## Section 4.5: Optics

This section describes all aspects of the main telescope optics, including (1) optical design and performance, (2) stray light control, (3) alignment sensitivity, and (4) optomechanical considerations for the primary mirror segments, the adaptive secondary mirror, and the large folding flats.

The optical and optomechanical designs of the adaptive optics (AO) systems are described in Section 4.6.1, Section 4.7.1 and Section 4.7.6.2.

The optical and optomechanical designs of the science instruments are described in Section 4.7.1, Section 4.7.2, Section 4.7.3, Section 4.7.4, and Section 4.7.6.2.

Initially, we selected a Ritchey-Chrétien design as the baseline for the telescope optical system. However, at the f/1 primary focal ratio adopted for the point design, there is little difference between a Ritchey-Chrétien and a classical Cassegrain. The conic constant for the R- C primary mirror is -1.0004 as compared with -1.0000 for a Cassegrain design. The difference in performance is slight, and the difference in figure on a single segment would be difficult to measure. For simplicity, we adopted a paraboloidal primary mirror for the point design exercise.

Section 4.1 describes advantages and disadvantages of a short primary mirror focal length. For the point design, the primary focal ratio has been set at f/1. Section 4.1 also describes the advantages of keeping the secondary mirror as small as is practical. For the point design, the diameter of the secondary has been set at 2 m. As described in Section 4.1.3.1.7, the secondary mirror serves as the aperture stop for the telescope.

For a given size of secondary mirror, the Cassegrain focal ratio is controlled by the desired back focal distance. For the point design, the Cassegrain focus was set 9.5 m behind the primary mirror vertex, which sets the focal ratio at 18.75.

The characteristics of the primary and secondary mirrors are summarized below.

 Diameter Conic Constant Radius of Curvature Primary mirror 30 meters + -1.0000 60 meters Secondary mirror 2 meters -1.23805 4.225 meters

The optical design is illustrated in Figure 1.

The optical prescription is listed in Appendix 4.5.A. The analysis done to date assumes a notional optical design that does not have an irregular outer edge on the primary mirror. This is equivalent to assuming that the primary is sufficiently oversized so that no point in the field of view (FOV) can see the irregular edge of the primary.

Spot diagrams indicating the performance of this design are shown below. The best focus field has a 2.15-m radius of curvature of  and all spot diagrams are on a curved focal surface. Focus was re-optimized for each spot diagram.

Figure 2 shows spot diagrams at the center of the field and at a field radius of 1 arcminute. The optical design is nearly diffraction-limited in the infrared over this size of field. The linear diameter of a 2- arcminute diameter field at the Cassegrain focus is 0.33 m.

Figure 3 shows spot diagrams for a field radius of 2.64 arcminutes. This is the size of fully illuminated field that is possible with only one segment removed to provide a hole through the primary mirror. The linear size of a 5.28-arcminute diameter field at the Cassegrain focus is 0.86 m.

Figure 4 shows spot diagrams for a field radius of 6 arcminutes. The linear size of a 12-arcminute diameter field at the Cassegrain focus is 1.96 m. To use this size of field, seven segments would be removed from the center of the primary mirror. As can be seen from the spot diagrams, the telescope delivers seeing-limited images out to about a 6-arcminute radius.

The prime focus will also be used for seeing-limited imaging, with an optical corrector built into the instrument. The optical design of the prime focus instrument is described in Section 4.7.1.

Spot diagrams do not include the effects of diffraction. In a telescope with a segmented primary mirror, there are diffraction effects from several sources, including the aperture stop and the segment geometry. The effect of hexagonal segments on the image point spread function (PSF) has been well documented in the literature. (For an example, pp. 5-46 from Reference 1). The diffraction effects in the PSF have three characteristic scales related to the three characteristic scales of the primary mirror: (1) the diameter of the full aperture; (2) the size of individual segments; and (3) the width of the joints between segments. For our GSMT point design, a fourth characteristic scale will relate to the width of the secondary mirror support tripod. In the current point design, the tripod is not aligned with the joints between segments, although this may be changed in future designs.

For a perfect system with central obscuration of 7% on the diameter and without atmospheric effects, the central core of the PSF will have a radius equal to 1.2/D radians, where is the wavelength and D is the effective primary mirror diameter, 30 m. The full width half-maximum (FWHM) is equal to 1.0 /D.

The segment size of 1.153 m between centers will introduce structure into the PSF at scales of about /S, where S is the segment spacing. Even for a perfectly co-aligned mirror (no segment tilt errors), any piston errors between segments will cause light to be diffracted out of the central core.  Due to the hexagonal pattern of segments, the diffracted light will be concentrated into satellite spots in a hexagonal grid with spacing of /S. In monochromatic light, each satellite image will be a faint duplicate of the central PSF. If a range of wavelengths is present, each satellite will contain a spectrum running radially outward from the center, with the shortest wavelength closest to the center. For phasing errors that are a small fraction of the wavelength, the amount of energy diffracted out of the central core is approximately equal to:

 (1)

where is the RMS (root mean square) piston error over the aperture, normalized by wavelengths.

The third characteristic scale is the width of the joints between segments. For the point design, we are assuming 3-mm joints with 1-mm bevels, so the effective width is 5 mm. This is 0.9% of the total area of the mirror; the fraction of light scattered because of the joints is also about 0.9%. The light will be scattered primarily into six spikes radiating outwards from the core of the PSF.

A somewhat larger effect will be caused by the tripod supporting the secondary mirror. The legs of the point design tripod are 45 cm wide. The fraction of light occulted by these legs is 2.7%. They will also form six spikes radiating outwards from the central core, brighter than the spikes from the segment edges with a relative rotation of approximately 15 degrees.

In the absence of AO, atmospheric effects dominate over diffraction effects. Table 1 lists, at several wavelengths, the Airy disk diameter, diffraction-limited FWHM, and characteristic spacing of satellite images as compared to a typical seeing disk size.

Wavelength (mm) Airy disk diameter (arcsec) Diffraction FWHM (arcsec) Satellite image spacing (arcsec) Seeing disk FWHM (arcsec)(r0 = 15 cm at = 0.55 µm) Table 1 Comparison of, for several wavelengths: Airy disk diameter; FWHM of the diffraction- limited PSF; characteristic spacing of satellite images from segment geometry; and typical seeing disk FWHM. 0.5 0.008 0.003 0.089 0.69 1.0 0.017 0.007 0.179 0.63 2.0 0.033 0.014 0.358 0.53 5.0 0.083 0.034 0.894 0.43 10.0 0.165 0.069 1.789 0.38

4.5.2 DIFFERENTIAL REFRACTION AND ATMOSPHERIC DISPERSION

Differential refraction and atmospheric dispersion affect the performance of all telescopes.  Atmospheric refraction causes stars to appear farther above the horizon than they actually are, and because this effect varies approximately as the tangent of the zenith angle, at low elevation angles differential refraction can cause significant distortion of the field.  Atmospheric dispersion is caused by differences in the refractive index of air with wavelength, and at low elevation angles it causes significant spreading of light of different colors.  The design of specific atmospheric dispersion correctors is discussed in Sections 4.6.2, 4.7.1, and 4.7.6.2.

However, additional concerns about the effects of atmospheric refraction on a 30-m telescope have been raised by Pat Wallace.

First, the monochromatic image of a star will be elongated astigmatically because of the differential atmospheric refraction seen by the upper part of the aperture compared to the lower part due to the difference in air pressure. Although the astigmatism can be compensated by AO, it varies somewhat from the center to the edge of the field.

The second effect is the variation in dispersion across the field. If the dispersion is corrected at the center of the field, it will not be as well corrected at the edge.

Wallace calculated the results shown in Table 2 based on the following parameters:

Site elevation: 3000 m
Pressure: 716 mB
Temperature: 2 deg C
Relative humidity: 30 %
Mirror diameter: 30 m
Field diameter: 20 arcmin
Wavelength range: 0.35 - 0.9 micron

The differential refraction columns indicate the length of the astigmatic stretching of the monochromatic image, in milli-arcseconds, caused by the differential refraction of a star as seen from the lower and upper parts of the primary mirror. Column 2 is for a star in the center of the field, column 3 is for a star at the edge, and column 4 is the difference.

The atmospheric dispersion columns indicate the length of the image over the wavelength range of 0.35 - 0.9 micron, caused by atmospheric dispersion. These calculations do not include the effects of the 30-m aperture, that is, the monochromatic astigmatism effects are not included. Column 5 is for a star in the center of the field, column 6 is for a star at the edge, and column 7 is the difference.

Zenith distance (degrees) Differential Refraction (mas) Atmospheric Dispersion (mas)( = 350-900 nm) Center of field Edge of field Difference Center of field Table 2 Differential refraction and atmospheric dispersion as a function of Zenith distance. 0 0.0 0.0 0.0 0.0 5.1 5.1 10 3.6 3.6 0.1 309.5 314.8 5.3 20 14.4 14.6 0.1 638.8 644.6 5.8 30 33.5 33.7 0.2 1013.0 1019.8 6.8 40 62.5 62.8 0.4 1471.5 1480.2 8.7 50 105.6 106.2 0.6 2087.9 2100.2 12.3 60 173.1 174.2 1.2 3027.6 3047.9 20.3 70 295.6 298.2 2.6 4771.9 4814.5 42.6 80 613.3 622.7 9.4 9520.0 9669.9 149.9 90 3393.4 3571.9 178.5 52449.9 55209.0 2759.1

Fortunately, the difference values in column 4 indicate that for Zenith distances up to 70 degrees, an astigmatism correction based on wavefront measurements anywhere in the field will adequately correct the differential refraction over the entire field. Similarly, the difference values in column 7 indicate that out to a Zenith distance of 70 degrees, a correction for atmospheric dispersion in the center of the field will only be off by a few hundredths of an arcsecond at the edge of a 20 arcminute FOV.

The effects of atmospheric refraction are significantly reduced at longer wavelengths.

Stray light control is important for any optical telescope. Common sources of stray light include the moon, if it is relatively near the FOV, and moonlight or other lights reflected from parts of the telescope or from the inside of the enclosure.

A first-order layout of standard-form Cassegrain baffles indicates that a 5-arcminute diameter Cassegrain focus can be baffled against a direct view of the sky, using a primary baffle extending 13.5 m from the primary mirror and a secondary baffle 3 m in diameter. This configuration is illustrated in Figure 5. The primary baffle is substantially less than 3 m in diameter, hence it can be left in place when the MOMFOS is used at prime focus, without increasing the central obscuration.

The MOMFOS will be baffled internally. For this instrument, the deformable mirror in the corrector is conjugate to the primary mirror, and is in effect the aperture stop. For the Cassegrain instruments, there are also advantages to baffling stray light inside the instrument at a reimaged pupil (an image of the aperture stop; in this case, the secondary mirror). This will have to be done in any case for IR instruments, because it is important that IR instruments not be able to see the relatively warm baffles or the hole in the primary mirror.

The large telescope baffles would add weight, and their substantial cross sectional area would contribute to wind-shake of the telescope. However, if all of the instruments have internal baffles at reimaged pupils, the main telescope baffles could be eliminated. Baffles around the light path behind the primary mirror will be used in any case. There will be other stray light issues raised by the bevels on the edges of the segments and by reflections off the secondary support legs. Once a GSMT conceptual design is firm, a full stray light analysis will be done, but it would be premature at this stage where we are only considering a point design.

Source Telescope emissivity (%) Aluminum coatings Table 3 Telescope emissivity at the Cassegrain focus, with aluminum or silver coatings. Primary mirror coating 2.0 1.3 Secondary mirror coating 2.0 1.3 Secondary mirror obscuration 0.4 0.4 Segment joints 0.9 0.9 Secondary support tripod 2.7 2.7 Total 8.0 6.6

Contributors to the telescope emissivity at the Cassegrain focus include the obstructions from the secondary mirror, the secondary mirror support tripod, and the joints in the primary, as well as the emissivity of the surfaces of the primary and secondary mirrors. Table 3 gives estimated contributions to the telescope emissivity, assuming that the mirrors are clean and have fresh coatings, and that the emissivity of the obscurations is 100%. Contamination of the mirrors could be another significant contributor to system emissivity. An effective contamination control system should be designed into the facility.

Throughput and emissivity of the telescope and the MCAO system are discussed in Section 4.2.2.

NIO Technical Report RPT-GSMT-004 (Appendix 4.5.B) describes the effects of misalignments on the image position and image quality of the point design telescope. Some representative results are repeated here.

Image motion

• Lateral translation of the secondary mirror by 1 mm results in an image shift of -6.5 arcseconds at the Cassegrain focus
• Tilt of the secondary mirror by 1 arcsecond results in an image shift of 0.133 arcseconds
• Translation of a Cassegrain instrument by 1 mm results in an image shift of -0.37 arcsecond relative to the detector
• Rotation of a Cassegrain instrument about the optical axis by 100 arcseconds would produce an image shift of 0.29 arcseconds relative to the detector at the edge of a 20-arcminute diameter FOV

Image quality

• Despace of the secondary mirror by 1 mm results in spherical aberration amounting to 0.21 arcseconds
• Lateral translation of the secondary mirror by 1 mm results in 1.28 arcseconds of tangential coma

Clearly, the design is very sensitive to alignment errors. On a structure of this size, an active alignment control system will be essential.

The effects of misalignment of individual segments are discussed in the following paragraphs.

As described in Section 4.1 , the segments for the point design are hexagonal. For simplicity, the shape of the segments has been based on projecting equal sized hexagons onto the curved surface. The segment on the optical axis is truly hexagonal. Those close to the outer edge are stretched in one direction by approximately 3%.

The issues related to segment size are summarized in Table 4 in Section 4.1 and discussed in more detail in the following paragraphs.

Fabricating, finishing, and testing equipment will all scale as the size of the segment. As long as the segments are within the range normally available at optical shops, the size of the segment is not a significant cost driver. For production of mirror blanks, sizes up to about 2 m should not drive up the cost per kilogram of the material. Beyond this size, costs will gradually increase, with costs rising significantly above a few meters diameter.

The easily available size of polishing machines depends on the process anticipated. Many optical finishers have machines that will polish 2-m diameter mirrors, and several can polish mirrors up to 4 m. Only three polishers are currently equipped to polish mirrors larger than 4 m. However, the most cost-effective finishing method appears to be to use a continuous polishing (CP) machine (see Section 5.4). A CP machine must be about three times larger diameter than the part being polished. At present, the largest CP machines we are aware of are just over 4-m diameter, which would accommodate parts no bigger than 1.4 m in diameter.

Several optical finishers have ion figuring equipment. The largest system we know of is the 2.5-m capacity facility at Kodak. Reportedly, a facility this size costs more than a million dollars.

Some types of optical tests use a full-size test plate, or matrix, that serves as an interferometric standard. For this type of test equipment, 1.5-m diameter is practical, and 2-m diameter is probably possible but would push technical feasibility.

There appear to be no significant cost drivers in terms of optical fabrication equipment for segments up to about 1.4-m diameter. From that size up to about 2 m, the difficulty increases somewhat depending on the particular processes anticipated. Above that size, costs for fabrication equipment will escalate.

The break point on transportation cost is at a size that will still fit into a standard shipping container. That size would be approximately 2.2 m across flats. At that size, segments can be shipped in standard containers with no special handling requirements. Above that size, costs will jump significantly.

The size of the coating chamber for GSMT will be set by the 2-m diameter of the secondary mirror.  As long as the segments are smaller than this, a chamber that can coat the secondary mirror should  be suitable for coating all of the GSMT optics.

Each segment will need at least three rigid attachment points on the telescope structure, so as the segments get larger, the number of attachment points decreases inversely with the square of the segment size. This simplifies the telescope structure.

Each segment will need three position actuators to control piston, tip and tilt, and six edge sensors to provide position feedback. As the segments get larger, the numbers of position actuators and edge sensors also decrease inversely with the square of the segment size.

However, for a given segment thickness (i.e., a given primary mirror weight), the number of support points per segment increases more or less as the square of the segment size. Depending on the type of mirror support proposed, this can be a significant complication (for example, in a whiffletree support, an additional layer of levers might be needed).

Chanan2 has calculated that the propagation of edge sensor errors increases approximately as the square root of the number of segments across the diameter of the mirror, or inversely as the square root of the segment size. While this favors larger segments, it doesn't provide a strong driver in that direction.

The hexagonal pattern of segments has six-fold symmetry, so the number of different segment types is equal to the total number of segments divided by six.

Of the six rigid body degrees of freedom of a segment, the tolerances on two get tighter as the segment size increases. This is because the aspheric departure of the segment increases as the square of the segment diameter. Because the segment asphericity also increases as the square of the segment radial position, if the segment is shifted radially, its asphericity will not match the proper mirror shape. Similarly, if the segment is rotated, its aspheric departure will no longer match the parent mirror.

The segment asphericity is mostly astigmatism, which can be described by the equation:

 (2)

where C22 is the Zernike coefficient, and Z, and are the linear, radial and angular coordinates of a cylindrical coordinate system centered on the optical surface of the segment.

The magnitude of the Zernike coefficient is given to a first approximation by:3

 (3)

where K is the conic constant, a is the segment radius, r is the radial distance between the center of the segment and the optical axis, and R is the paraxial radius of curvature of the parent mirror.

To evaluate a radial shift of the segment, differentiate equation (2) with respect to r:

 (4)

The error created by a radial shift is astigmatic, with the same orientation as the segment asphericity and an amplitude that is defined by:

 (5)

where Cr is the Zernike coefficient of the surface error from a radial movement.

In the worst case, at the edge of the aperture:

K = -1
r = 15.16 m
R = 60 m

Then:

 (6)

For example, if a = 1 meter and r = 0.001 m,
Cr = 35 nm, which results in about 29 nm RMS wavefront error.

To evaluate the effect over the entire aperture, consider that the average radial position error is r. The total area of segments at a given radial position varies as the square of the radial position, so the total error will be weighted more by the outer segments. Note that the amplitude of the wavefront error varies linearly with r, so the weighted average will equal 2/3 of the maximum at the outer edge (in this case, about 20 nm RMS).

For a segment diameter of 2 m, an average radial position error of 1 mm would slightly exceed the GSMT error budget. With slightly smaller segments, a 1 mm position error would be acceptable.

Rotational error

To evaluate the effect of a rotation of the segment, differentiate equation (2) with respect to :

 (7)

The error created by segment rotation is astigmatic, with its orientation clocked 45ş from the orientation of the segment asphericity, and an amplitude that is defined by:

 (8)

where C is the Zernike coefficient of the surface error from a segment rotation.

In the worst case, at the edge of the aperture, this error would be:

 (9)

One mm of tangential motion at the corner of a 2-m diameter segment is a one mrad rotation. This would produce an astigmatic error with a Zernike coefficient of about 530 nm, or a wavefront error of about 435 nm RMS. This type of error varies as the square of the radial position, so the weighted average over the aperture is ˝ the maximum value, or in this case, about 220 nm RMS wavefront. This exceeds the GSMT error budget allocation by more than an order of magnitude.

A comparison of equations (3) and (6) makes it clear why the error caused by rotation is so much larger. The rotational error d can be thought of as a tangential movement at the edge of the segment, divided by the radius a. Comparing equations (3) and (6), it is apparent that for a given linear error (dr or ), the divisor in the case of a radial shift is r, and in the case of a rotational shift, the divisor is a. For the segment sizes under consideration, r/a > 10. The positional accuracy required to control segment rotation needs to be more than an order of magnitude tighter than that required to control segment radial position.

As the segment radius a increases, the amplitude of error from a radial movement increases approximately as a2, and the amplitude of error from segment rotation increases approximately as a. These provide strong incentives to keep the segments smaller.

Several factors argue for larger segments, including the reduction in the number of position actuators and edge sensors, simplification of the telescope structure, and reduction of edge sensor noise propagation. Other factors argue for smaller segments, including several cost factors related to fabrication equipment, transportation and coating chambers, simplicity of support mechanisms, and in particular, the control of segment position errors.

The optimum range for segment size seems to be 1- to 2-m diameter, although the tight rotational position tolerances drive the choice toward the lower end of that range. For the point design, the size of the segments has been chosen so that, in the worst case, they have approximately the same magnitude of aspheric departure as the worst-case Keck segments. This produces segments about 1.15-m across flats (but see box below).

 Filling the aperture The pattern and size of the point design segments were originally chosen to have equivalent area to a 30-m solid mirror. However, because of the irregular edge of the mirror, the largest completely filled circle is just under 29 m. Because the aperture stop is at the secondary mirror, the primary mirror must be larger than the entrance pupil to accommodate the field angle. To have an unvignetted FOV of 2 arcmin diameter, with a 30-m diameter round entrance pupil, the primary must be filled to a radius of 15.08 m. Using the same pattern as the point design, this would require segments 1.20 m across flats. As an alternative, the number of segments could be increased.

4.5.6.2 Properties of Segments

The nominal segment dimensions are 1.15 m across flats, 1.33 m point to point, and 50 mm thick. As discussed above, these dimensions vary slightly from the center of the aperture to the edge. The gap between segments is nominally 3 mm. The bevels on the edges are nominally 1 mm wide. The point design has 618 segments; the total projected area of the 618 segments is 711 square meters.

The segments in the current design are solid meniscus mirrors. The nominal material for the segments is Zerodur, although other low-expansion glass and glass-ceramic materials will be given equal consideration. The average mass of each segment is 157 kg (133 kg if the segments are made of Corning ULE). The average area of each segment is 1.2 square m, so the areal density, if Zerodur, would be 130 kg/m2. The total mass of the 618 segments is 97 metric tonnes.

The segments are nearly flat; the sagitta of the curve is less than 4 mm. The maximum aspheric departure of the edge segments is an astigmatism coefficient of 115 microns (230 microns peak- to-valley), and a coma coefficient of 10 microns (20 microns peak-to-valley).

A notional design for a segment support system is described in Appendix 4.5.C. The design uses an 18-point whiffletree for the axial support and a six-flexure design for the lateral support. The lateral support design follows an approach proposed by Jerry Nelson. Pairs of flexures are used to apply loads having a virtual center at the midsurface of the material, avoiding the need to bore holes into the glass. Figure 6 illustrates this segment support design.

One of the advantages of a whiffletree support is that it reacts wind loads at all the support points, not just three. Because the anticipated wind loads are two orders of magnitude lower than the weight of the mirror, there is no significant print-through effect caused by wind pressure.

Performance of the design has been verified by finite-element analysis, both zenith pointing and horizon pointing. Further analysis is planned, as described in Appendix 4.5.C. Results to date are consistent with the error budget.

In this design, the mirror support incorporates an active optics system to provide control of the segment figure. This will be accomplished by applying moments to the pivots of the whiffletree, in a manner similar to that used by the Gran Telescopio Canarias.4 It is envisioned that 15 degrees of freedom will be controlled, so it will be possible to adjust the segment to correct several low- order bending modes.

The main purpose for the active optics systems will be to correct small errors in the mirror supports as a function of zenith angle, using a look-up table. This will help accommodate the small differences in the shape of segments from the center to the edge, without requiring custom hardware for each set of segments.

Having active control capability for each segment may also make it possible to have fewer unique segment types, because segments close to each other have aspheric departures that differ primarily by small changes in the magnitude and direction of the astigmatic and comatic terms. Within a moderate range, segment figure variations can be implemented with the active optics system without introducing significant print-through bumps at the 18 points where the forces are applied.

This has implications on the provision of spare segments. Because there are 103 different types of segments, there would need to be 103 spares to provide replacements for each segment during recoating. If the number of unique segment types is reduced by taking advantage of the segment-warping capabilities of the active optics system, the number of spares can also be reduced.

Another type of active optics system is required to control segment positions to maintain a continuous mirror surface of the correct figure. The GSMT point design approach to this system is based on the work done by Keck1 and CELT.2,5 Two edge sensors will be used along each segment edge to measure the relative position of the segments. Three position actuators below the segment support system will control the mirror position in piston, tip, and tilt. A preliminary set of requirements for the position actuators is listed in Table 4.

Characteristic Requirement Table 4 Preliminary specifications for segment position actuators. Stiffness 12 N/micron Range 10 mm Resolution 5 nm Mass 5 kg Response time 0.2 seconds for 50 nm steps Load capacity 50 kg

We have had preliminary discussions with actuator manufacturers, and we have received assurances that these specifications are readily attainable with actuators that are only slightly modified versions of actuators developed for other programs.

The control bandwidth of the segment positioning system will be limited to about 0.5 Hz, to avoid exciting telescope structural resonances (see Section 4.8).

As described by Chanan et al., simple edge sensors are not sensitive to low-order bending modes of the segmented mirror. The large number of segments in the GSMT point design causes the edge sensors to be insensitive to several dozen modes. To control these modes, feedback from wavefront sensors will be combined with information from the edge sensors.

A characteristic problem of this type of segmented mirror is to control the position of the segments so that the global radius of curvature of the mirror matches the radius of curvature of the individual segments. At the Keck telescopes, Shack-Hartmann tests are performed using the fine screen mode of the Phasing Camera System to locate the focus of the individual segments, in order to set the secondary mirror in the proper position relative to the primary. This establishes the global focus position to which all the segments are adjusted.

One concept to facilitate this type of measurement on GSMT is to incorporate a larger reference mirror as an expanded central segment. Figure 7 illustrates this concept. The central raft would be replaced with a single solid segment having the same outline. The center of curvature of this segment would then define the optical axis and the global radius of curvature of the mirror. One advantage of this approach is that the central hole in the primary mirror could then be made circular, and would not need to be the same size as a single segment. A disadvantage is that the central raft would be the largest optic in the facility, and would drive the size of the coating chamber. However, there are other operational advantages to having a larger chamber so that several normal-sized segments could be coated in a single operation.

Further analysis of the solid central raft concept is needed. For example, we have not evaluated the effect of the central obscuration from the secondary mirror or multi-object multi-fiber optical spectrograph (MOMFOS), which will obscure much of the central raft if the segments are sized as in the current point design. However, we think the approach is worth pursuing because of the advantages it offers to maintaining the global curvature of the primary mirror.

Co-alignment is the process of adjusting the tilt of the segments to superimpose all of the images in the focal surface. Co-phasing is the adjustment of the piston positions of the segments so that all are in phase within a fraction of a wavelength of light.

Co-alignment can be accomplished relatively easily. For example, Keck uses its Phasing Camera System in passive tilt mode.6 This mode works like a Shack-Hartmann test with one large subaperture per segment. An array of small prisms is placed in a pupil plane conjugate to the primary mirror. The prisms deviate the direction of light from each segment so that the segment images are separated on the detector and can be easily identified. The position of each image is compared to the position obtained when a reference beam is put through the same instrument, and the difference is used to calculate the required tilt adjustments of the segments.

This approach has the advantage that it measures all of the segment tilts simultaneously. A series of eight 20-second exposures is taken on a ninth-magnitude star. The corrections are calculated and accomplished, and then a second set of exposures is taken for confirmation. The entire process takes about 20 minutes. Typically, the segments are co-aligned to about 0.018 arcsecond RMS measured in one direction.7 This leaves a residual segment edge error of approximately 24 nm RMS.

On GSMT, co-alignment alone will produce an image limited by diffraction to about 0.1 arcsecond FWHM. Because MOMFOS will operate at optical wavelengths under seeing-limited conditions, with image quality limited by the atmosphere to about 0.5 arcseconds, co-alignment will be sufficient when using MOMFOS. This is important, because it is planned that the phasing instrument will be located at a bent Cassegrain focus, and would not be available when MOMFOS is in use.

Co-phasing is accomplished at Keck by two different methods. At the f/15 optical focus, the Phase Camera System is used in segment phasing mode,8 and at the f/25 focus, an infrared camera is used to record out-of-focus images for a curvature-sensing approach called phase discontinuity sensing.9

The Phase Camera System performs a Hartmann-like test in which each subaperture is across the joint between adjacent segments . Each subaperture is 12-cm diameter on the primary mirror, which is sufficient when used with a fourth-magnitude star. The relative phasing of the two segments produces changes in the appearance of the image formed by each subaperture. This technique has a capture range of approximately 30 microns, and in its most sensitive mode, it can consistently reduce the RMS piston error to about 30 nm.

The phase discontinuity sensing approach has the advantage that it only requires an infrared detector looking at the image of a bright star (V magnitude 3-4). The method takes about 45 minutes to perform. Its repeatability is about 40 nm RMS, and the accuracy relative to the Phase Camera System is about 66 nm RMS. Much of this difference is believed to be the result of residual segment figuring errors.

Keck has had good stability in their segmented mirror control. With its segment control system operating, it can maintain phasing between segments for about a month. However, when the operation of the system is interrupted (for example, when equipment is changed on the telescope), the co-phasing operation must be repeated. Reference 7 reports that 76 phasing operations were performed on the two Keck telescopes in 1997. This highlights the need for a fast, efficient co-phasing procedure.

Several other methods have been proposed for co-phasing segmented mirrors; some of these are discussed in Reference 10.

The point design telescope structure groups the segments into 91 seven-segment rafts, including some partial rafts at the edge of the mirror. Figure 8 illustrates the 15 rafts outside the central raft that are repeated six times each to make up the primary mirror.

To minimize handling when recoating the mirrors, an entire raft will be replaced by a spare raft. If the mirrors are recoated on an approximate two-year cycle, one raft of mirrors will need to be replaced nearly every week of telescope operation. Allowing time for disassembly and reassembly would require the capability to recoat segments at the rate of at least two per day.

Considering the length of time required to populate the mirror during the initial integration of the telescope, it may be cost-effective to provide coating chamber capacity sufficient to coat up to one raft per day. It also may be cost-effective to deposit more durable coatings so that the segments do not have to be recoated every two years.

Special handling equipment will be required to (1) remove and reinstall the rafts, (2) transport the rafts to the coating facility, (3) remove and reinstall segments on the rafts, (4) strip and wash the segments prior to recoating, (5) transfer the segments to and from the coating chamber, and (6) support the segments during the coating operation. These operations must be done quickly and safely, with a minimum of personnel.

Clean storage areas will be required for the spare segments. One approach would be to store 15 spare rafts in assembled form. An alternative approach that can be followed if the raft structures are identical involves storing spare segments, but only having a few spare rafts onto which segments would be assembled just in time to swap with the raft being removed from the telescope.

The secondary mirror in the GSMT point design is adaptive. The prototype for this is the adaptive secondary mirror currently under development for the Multiple Mirror Telescope (MMT).11,12,13 That mirror is 642 mm in diameter, with 336 actuators. The deformable mirror facesheet is 2-mm thick, and its position and shape are referenced to a machined Zerodur backing structure. The backing structure is supported by an aluminum plate that also serves as a heat exchanger for the actuators.

The proposed design for the GSMT adaptive secondary mirror is 2 m in diameter, with 2400 actuators. This has an actuator density slightly less than the MMT design.

The zero-expansion backing structure allows the system to maintain an absolute figure reference, but this structure must be supported in a manner that minimizes flexure just as would be required for a passive secondary mirror. This will be a challenge; for example, the largest secondary mirror currently in service is the 1.4-m diameter secondary of Keck I, which is made of Zerodur. If the backing structure flexes significantly with gravity, it will be necessary to characterize the deformation so that the flexure can be corrected with the facesheet by means of a look-up table.

The structure of the secondary mirror must be as light and as rigid as possible. One option is to use a non-zero expansion material such as silicon carbide for the backing structure. Silicon carbide has high thermal diffusivity and should exhibit minimal thermal distortion, but might still require look-up table compensation of the facesheet figure to account for expansion of the silicon carbide with changing temperature. The secondary mirror will be supported on a mechanism that provides fast piston, tip, and tilt motions, and slower lateral translations. The position control of the mirror will be challenging. To stabilize the image at the Cassegrain focus for diffraction-limited observing in the near infrared, tilt of the secondary mirror must be controlled to a precision of about 0.007 arcseconds. The required range of fast motion is about 20 arcseconds, and the bandwidth will need to be about 5 Hz, based on the results of the tests run at the Nobeyama radio telescope, for example (see Appendix 5.5.A).

The secondary mirror will be designed as a lightweight structure, but it will be difficult to get the mass below 500 kg. Existing large fast-tilt secondary mirrors, such as the 1.02-m diameter Gemini secondary mirrors, are an order of magnitude less massive. Moving a 500 kg mirror at 5 Hz with a precision of 0.007 arcseconds will be challenging.

Another challenge will be to design a switching mechanism that allows efficient interchange of the secondary mirror assembly with the MOMFOS prime focus instrument. If the secondary mirror assembly is compact (i.e., shorter than about 2 m axially), it could be installed in front of the MOMFOS instrument without removing the instrument. In that arrangement, however, the central obscuration would be set by the 3-m diameter of the instrument.

Development of the adaptive secondary is a crucial and very challenging part of the GSMT point design approach.

Large flat mirrors will be required to direct the beam into the MCAO system, and into Cassegrain instruments at gravity invariant locations (see Section 4.1). The largest of these currently envisioned is the first flat mirror for the MCAO, which would be 1-m minor axis, 1.4-m major axis. Figure 9 illustrates the use of large flat mirrors to direct the beam to different instrument locations.

Although these mirrors are relatively large, they are similar in size to large folding flats produced for other telescopes and are not expected to present significant problems in manufacture, mounting, or coating. For example, for the Very Large Telescope (VLT), Schott has produced four 1.25-m by 0.88-m Zerodur elliptical flat mirrors that have been 65% lightweighted by machining and have areal densities of 125 kg per square meter.14 Scaled to the 1.4-m by 1-m for the point design, the mass of the largest GSMT flat mirror would be about 160 kg if it were of similar construction.

The flat mirrors need to be in optomechanical mountings that have three degrees of freedom for initial adjustment - tip, tilt, and piston - and will need to be deployable so that they can be introduced into or removed from the beam in a repeatable manner. The first folding flat for the MCAO system may also need to be able to rotate about the optical axis, to direct the Cassegrain beam to co-alignment and co-phasing instruments as described in 4.5.6.5 above.

Thermal control will be required to minimize local seeing degradation in the observatory, and to avoid thermo-elastic deformation of precision telescope components.

Local seeing effects have been a concern of astronomers and telescope builders for decades, and our understanding of the causes of these effects has improved significantly in the past decade.15 The primary cause of local seeing is heat sources in the enclosure that cause turbulent fluctuations in the index of refraction of the air in the light path of the telescope. Heat sinks, such as cryogenically cooled instruments, can also cause seeing problems, but the cold air they create tends to move downwards and they are seldom above the light path.

In the GSMT point design, there are many potential sources of heat. Some of the most important sources include:

• The secondary mirror assembly, with fast tip-tilt-focus actuators and a 2400-actuator adaptive mirror
• The prime focus instrument, with its adaptive mirror, tip-tilt mirror, and control electronics
• The primary mirror segment control electronics, including the position actuators
• The MCAO system located behind the primary mirror

Because some of these systems could dissipate thousands of watts, it will be important to insulate them and provide a flow of coolant to remove the heat. Coolant lines should also be insulated.

In addition, warm parts of the telescope can lag behind as the air cools at the start of the night. Traditional thick primary mirrors have suffered from this effect, which causes significant degradation known as "mirror seeing." Structural parts of the telescope can also contribute to local seeing degradation. One remedy for this is to refrigerate the enclosure during the day to maintain it at night-time temperatures. If the temperature difference is only a degree or two, the 50-mm-thick facesheets of the point design segments will equilibrate fairly quickly with the air, particularly if there is some natural ventilation. Ventilation also helps to reduce the effects of local seeing by blowing away the convection cells in the light path.

The other thermal control concern is thermo-elastic distortion of precision parts. The error budget contains a term for the bowing of the ultra-low-expansion mirror segments caused by temperature gradients through their thickness. In sizing the gaps between segments, an allowance needs to be made for expansion and contraction of the steel telescope structure. Similarly, the connection of the whiffletree segment supports to the glass must be through flexible couplings that can accommodate thermal expansion.

The backing structure of the adaptive secondary mirror will contain approximately 2400 actuators that will dissipate hundreds or thousands of watts of heat. If that structure is to remain stable enough to be used as an absolute figure reference, it not only needs to be of "zero-expansion" material, but also will require careful heat transfer analysis to optimize its design. Alternative materials with higher conductivity (such as example silicon carbide) might be suitable if the design allows paths for efficient heat conduction and if the global thermal expansion can be accommodated by corrections of the adaptive mirror.

Further studies are needed in a number of areas. Some of these include:

1. Full diffraction analysis of the optical design, including the effects of the segmented mirror, M2 support legs, and central obscuration

2. Diffraction analysis of cases including segment position errors

3. Stray light analysis as described in [Section 3, Science Requirements ]

4. Studies of alternative segment materials or configurations

5. Full mechanical design of the segment support system

6. Development of the segment control system

7. Development of the segment co-alignment and co-phasing system

8. Development of technology for the adaptive secondary

9. Development of conceptual designs for the secondary mirror assembly

10. Development of a mechanism to switch between the MOMFOS and the secondary mirror assembly

11. Development of conceptual designs for segment handling equipment

The optical design listed here was prepared by Richard Buchroeder, based on earlier work by Jim Oschmann. The solid model illustrations were prepared by Rick Robles.

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