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: http://www.apo.nmsu.edu/Telescopes/eng.papers/milt/optics.html
Дата изменения: Mon Dec 13 18:48:03 1993 Дата индексирования: Sat Apr 9 23:52:23 2016 Кодировка: |
A Cassegrain system has been chosen with dual Nasmyth foci to allow simultaneous multiple instrument mounting (Figure 2.1). The primary mirror is f/1.75 and the telescope at Nasmyth will be f/TBD; (f/10 is the current working value.) Whether the Cassegrain system is to be classical with a parabolic primary, or Richey-Cretien is TBD. The initial optical design currently being pursued will include a wide field reducing camera, an atmospheric de-disperser and dummy elements corresponding to filters, windows, etc. Harland Epps (UCLA) is currently under contract to the project as its optical designer.
Locations other than the two classical Nasmyth's are being considered for small instruments. Parfocality will be enforced at the two principal Nasmyth foci but not necessarily at the others where, for instance, the focus might be displaced by the reducing camera.
Other optical fabrication experts we have consulted have been uniformly cautious about attempting an f/1.5. These include Harland Epps, Don Davidson, Rich Bingham, and Bob Parks.
In this document we have adopted the more conservative value of f/1.75 for design purposes. While this is still faster than any existing large telescope, we cannot afford to concede any more pointing error budget to wind deflection than is absolutely necessary.
Figure 2.2a shows a distribution of OBSERVED seeing values (Beckers et al. 1980). It is based on 395 rms image diameters measured from plates taken with the Solar Telescope (76 cm aperture) over a one year period.
Figure 2.2b is a somewhat more charitable plot of the same data with the effects of aperture diffraction removed, assuming that values falling within one bar of the original histogram are uniformly distributed. Presumably the corrected plot more nearly represents the intrinsic site seeing and suggests that the 90th percentile seeing diameter is less than 0.5 arc sec rms.
The consensus among ARC astronomers is that the best rms seeing disk should be sampled by no fewer than 5 detector pixels (one dimension) when the telescope is in its minimum optics 'clean' configuration (no reducing camera). With 15 x 15 micron pixels, in 0.5 arc sec seeing a minimum focal length of 31 meters is indicated; 35 meters (f/10) has been selected.
All anticipated instruments are to be fed from the 'clean' f/10 configuration at Nasmyth except wide field photographic imaging and Ronchi grating astrometry, both of which require 20-30 arc minutes of flat field. This will be provided with a reducing camera working near f/5 or 6 and perhaps located on the altitude bearing yoke at a position midway between the two standard Nasmyth foci.
In direct imaging applications this "clean" configuration offers the advantage of highest available contrast (no corrector optics are used), perfect achromatism, and a scale of 170 microns per arc second. A single CCD with 10 by 10 mm format will subtend an angle of about an arc minute. The focus gradient due to field curvature over this size detector is negligible.
It is admittedly somewhat arbitrary to single out 15 micron pixels as the sampling element in the above discussion. While such detectors currently exist, the highly developmental state of CCD detector technology implies nothing about the dependable future availability of 15-micron pixels. Correspondingly one can not reliably guess to what extent larger or smaller pixels will be available in the future. It is therefore not obvious how one should apply any currently available pixel size as a driver of telescope focal length selection.
The optics and mechanical designs are currently in a state of interation. The general approach is to anticipate all knowable applications, then design the entire optics system at the outset to serve each one.
Primary diameter 3.50 m Primary radius of curvature 12.25 m Primary f/ratio 1.75 Primary figure TBD Secondary diameter (on axis) 0.77 m Secondary radius of curvature -3.26 m Secondary figure TBD Tertiary diameter 0.65 m Tertiary figure Flat Primary-secondary spacing -4.88 m Primary-tertiary spacing (along OA) 0.41 m Nasmyth extraction distance 2.79 m
Included in the optical design will therefore be adjustable elements to de-disperse atmospherically refracted stellar images.
The 1.8 meter Tempax blank is shown in Figure 2.4. The mold cores have been removed by water blasting through access holes in the backplate.
The 3.5 meter blank will be cast in a furnace now under construction (under the grandstand of a college athletic stadium for you history buffs) that will feature continuous rotation of the mold about the nominal optical axis at a speed which holds the molten glass surface in the desired curvature until it has cooled enough to become rigid. The tops of the mold cores will be premachined to the curvature corresponding to the back of the faceplate (Figure 2.5).
The resulting curved faceplate will require only minimal generating at a saving in the cost of labor and a minimum of wasted glass.
A summary of the mechanical properties of the 3.5 meter primary is given in the following table:
Diameter 3.5 m Overall thickness 35 cm Rib thickness 12 mm Faceplate thickness 2.5 cm (concave) Backplate thickness 2.5 cm (flat) Total weight 2500 kg Material density 2.35 gm/cc Effective density ~0.7 gm/cc Coefficient of thermal expansion ~3E-6/deg c Coefficient of thermal expansion uniformity ~0.5% Young's Modulus 70E9 N/m^2
A 75 cm blank has been recently ground and polished by Norm Cole (the most likely candidate to finish our 3.5 m blank). He reports no honeycomb pattern print through despite excessive tool pressure and long polishing runs. He also noted that testing was possible nearly immediately following arun while for solid Pyrex blanks of similar size a considerable waiting period is necessary before the glass equilibrates to ambient temperature.
The first actual telescope test will occur later this winter when John McGraw assembles the Baker-Paul transit telescope (McGraw 1982) using the 60 cm sphere as its tertiary.
s = 6.5 * n * z * sqr(E)
where E is the fraction of the total image intensity contained inside some circle whose diameter is s airy disk diameters, n is the mirror diameter divided by the spatial period of the irregularity (ie. the number of 'bumps' across the 3.5 meter aperture) and z is the rms amplitude of the irregularity in fractions of a wavelength.
If we then adopt a goal to concentrate geometrically 80% of the light of a point source image within a circle 0.3 arc sec, in diameter then
n * z = 0.73
Now if any size scale of surface bumpiness can dominate in a honeycomb mirror it will most likely be that corresponding to the structural cell width. Barnes (1969) has already pointed out that for a 2.5 cm thick faceplate this spacing should not exceed about 20 cm in order to sustain polishing tool pressures without 'quilting'.
Using 20 cm as the cell size, n for the 3.5 meter will be about 17 corresponding to an amplitude z of about lambda/20 or about 0.04 micron RMS. The MMT mirrors are figured to approximately this level of quality.
The fractional change in mirror thickness dt for some temperature change dT is just
dt = C * dT
where C is the coefficient of thermal expansion of the material. We assume the resulting figure error is divided equally between the front and rear surfaces.
The MMT mirrors currently exhibit inherent peak to valley surface errors on the order of 0.06 microns over distance of a few tens of centimeters. For a30 cm thick Pyrex mirror in which two adjacent ribs are different in temperature by dT degrees, (Figure 2.6) then for C = 3E-6/deg C, the 0.06 micron surface error corresponds to
dT = 2 * 0.06 / (3E-6 * 30 * 10000) = 0.13 deg C
If such a mirror were otherwise perfect then this temperature gradient alone would impose figure errors similar to those inherent in the existing MMT mirrors which limit their performance to about 0.5 arc second in the best seeing.
Even for a perfectly isothermal mirror however, variations in C can be important, especially since all telescope mirrors are polished and tested in shops near 23 C but will be used during winter temperatures perhaps 30 or so degrees cooler.
Again, using the mirror dimensions above and the current MMT surface quality criterion of 0.06 microns peak-to-valley we can estimate the allowable fractional range in C that could just be tolerated for a 30 degree C operating range.
If C varies by a fractional amount kC then for a 30 deg C temperature change dT
k = d(dt) / ( t * dT * C )
= 0.06 / (30 * 10000 * 30 * 3E-6) = 0.002
Values of C for a large number of melted and refrozen samples of Ohara E6 have been measured by Angel (personal communication) and are found to vary over a range corresponding to k = 0.005 or about 0.5%. Based on the previous calculations this is only marginally tolerable and it would be unfortunate to find values of k much larger than this in the finished mirror blank.
A typical sunset ambient cooling rate for the MMT is about -1.5 deg C per hour (Woolf 1979). Thus it seems clear that a ventilated mirror will always track ambient at these cooling rates to better than 0.5 deg C and mirror temperature gradients at least as small as 0.13 deg C (see above) over a few tens of centimeters seem realistic.
Residual errors are characterized by 0.012 micron rms errors with peak to valley extremes of 0.06 micron. The same mirror pointed toward the horizon performs considerably better than this. A mirror with this performance would be better than those currently in the MMT.
A larger number of supports will be needed, approximately in proportion to the additional mirror weight, for the 3.5 meter mirror. Unless a more suitable alternative develops before design freeze, we will probably adapt this support design since engineering has already been done and a field test will have been completed before we need to make a final decision.
There is a serious possibility that we may receive the 3.5 meter Pyrex blank free in consideration of our efforts to design a telescope system that fully demonstrates its advantages for the benefit of future projects.
Such a fortuitous windfall will not of course benefit future telescope projects quite so handsomely but still represents, even at full cost, a very substantial saving over quartz and other expensive low expansion materials.
This sort of failure potential does not however, distinguish our project among telescope projects. Every telescope now in existence larger than 3 meters has a "glass" mirror, was subject to the same single point failure potential at all stages of its creation (including the proposal stage), and REMAINS this way throughout its useful life.
In recent years at least one project (IRTF) suffered a broken primary in the grinding stage. The blank was replaced and the project finished.
If there are exposed bubbles, then there must be bubbles throughout the blank. In the Mt. Wilson mirror there are enormous internal voids. Richey was warned by "experts" that it could never work. He didn't agree and was vindicated (Woodbury 19xx). Observers with experience at Mt. Wilson consider the seeing there to be better than most. The mirror, bubbles and all obviously works well.
Bubbles do exist in the Angel mirrors, but in numbers no greater than one would expect normally for most telescope mirrors.
Poor annealing can lead to stored stresses and unmanageable astigmatism. No existing major telescope mirror suffers this problem in practice.
Annealing of a honeycomb mirror has to be more effective than for a solid one simply because large thermal gradients cannot be supported across such thin dimensions.
Finally, the uniformity of CTE over the blank has been challenged as unlikely to be good enough to guarantee acceptable performance (section 2-5). Again the 200 inch is an example of a successful Pyrex mirror cast under the most disadvantageous circumstances. Individual melts of Pyrex were ladled by hand into the mold. Little mixing could have occurred. Roger Angel distributes the shuffled fragments from several melts evenly over the mold before heating. While mixing still only occurs locally this seems to be at worst a more satisfactory technique than was used for the Palomar blank.