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OPTICS

General Description

The AAT primary mirror has a clear aperture of about 3.9m (more precisely 3893mm) and a focal length of 12.7m. The focal ratio at prime focus is therefore about f/3.3. The primary and the largest of the secondary mirrors together form an f/7.9  Ritchey-Chrétien system; i.e. they give a coma-free field. For this purpose, the cross section of the primary is hyperbolic, so correction is needed at prime focus even for on-axis work. Without correction the circle of least confusion would be about 8 arc sec in diameter. Three prime focus correcting systems are available, an aspheric plate, a doublet and a triplet.

The primary mirror is made of Cervit, a glass-ceramic material with a thermal expansion coefficient less than 10-7/°C, which makes it practically immune to thermal distortion. To maintain focus when the steel framework changes length with changes in attitude and temperature, the distance between the primary mirror cell and the fixed top ring is compared against a tensioned invar wire. In respose to changes in this distance, computer-derived corrections are made to the focus drive which moves the whole top end structure. The corrections applied are up to about 0.5mm with changing attitude and about 0.1mm/°C.

Prime Focus Correctors

General features

Since the aspheric plate and doublet are made of uncoated fused silica, the UV response is good down to the atmospheric cutoff, while the IR performance deteriorates only slowly beyond the 1000nm indicated in the spot plots. Both the aspheric plate and the doublet are suitable for work well into the IR region. The triplet is made of UBK7 glass and has a single layer anti-reflection coating on each surface of the first two elements and multi-layer coatings on the third.

Details of the three prime focus correctors are shown in Fig. 1.1 and optical designs are provided for each of the correctors. Spot plots have been generated for each corrector at appropriate wavelengths throughout their usable range and at its extremities. Throughout this manual the effective wavelengths for the photographic U, B, V, R and I bands are taken to be 365, 425, 550, 650 and 830 nm respectively.

The correctors are mounted within the prime focus camera pedestal and are interchanged by crane with the prime focus cage removed from the telescope, so it is not practicable to change from one to another during an observing night.

Fig. 1.1 The optical configurations and field sizes of the three prime focus correctors, drawn to the same scale. The figure of the aspheric plate has been exaggerated in this diagram.

Aspheric plate

The aspheric plate produces images with diameters of less than 0.5 arc sec over a flat field of 7 arc min (25mm) diameter and over a curved field 10 arc min (37mm) diameter. The curvature of the wider field is concave to the primary mirror, with radius 1.308m. Fig. 1.2 shows the performance of the aspheric plate at these angles. There is some chromatic difference in focus with this corrector. When focus is found at 550nm ( i.e. at V) the values of focus offset ( i.e. top end movement) given in Table 1.1 may be used to correct for this effect.

 

The plate scale with the aspheric plate is approximately 16.2 arc sec/mm.

TABLE 1.2

Figure 1.2 Spot diagrams for the aspheric plate from 320 to 1000nm. The axes are labelled in millimeters. Image quality is good well beyond the spectral range indicated here.

Figure 1.3 The image quality of the aspheric plate, 15 arc min off axis. Axes in millimeters. This image has been refocused to the optimum, but is not good enough for guiding.

Without some special provision, the main difficulty in the use of the aspheric plate is the poor quality of the images at the minimum field angle accessible to the offset guider without having the probe shadow affect some part of the usable field. Fig. 1.3 shows that the image at 15 arc min radius is more than 4 arc sec across, largely due to astigmatism. This is the case even when the focus is readjusted to an optimum, as was done for this spot diagram. As a consequence of these difficulties the aspheric plate has been virtually unused.

Doublet

Fig. 1.4 illustrates the performance of the doublet. It produces images under 0.5 arc sec diameter over its 25 arc min diameter unvignetted field. As indicated by the ray diagram spots for the 320 and 1000nm wavelengths, the doublet performs well over a very wide range of colours and has a flat field. The spot plots, apart from those at 30 arc min radius, are set at the optimum focus for the centre of the field at 550nm, as would be the case for an observer focusing with the knife-edge (with allowance for a filter). There is nothing to be gained by re-focusing for each wavelength. Despite the increasing vignetting beyond 12.5 arc min radius, the doublet gives images very suitable for guiding out to 1° diameter. The spot plots at 30 arc min radius are re-focused to an optimum and include 54 rays, compared with the 100 transmitted on axis. Note that the spot diagrams reveal some radial shift in image position with changing colour.

The two uncoated fused silica elements of the doublet give it a transmission of about 86% from below 300nm to beyond 2um.

With the doublet, the effective focal length is slightly less than that of the primary alone. Near the optical axis it is about 12.58m, yielding a scale about 16.4 arc sec per mm. It has pincushion distortion, so that images of stars at the edge of the field are displaced outwards with respect to the undistorted case near the centre of the field. The distortion reaches about 0.2% 12.5 arc min off axis, and has been satisfactorily modelled by a simple cubic function of the radius (Argue and Sullivan, 1980). The doublet has given good astrometric results well beyond its unvignetted field, though on deep plates the varying sky background may not be acceptable on some measuring machines.

There is provision in the mounting of the doublet to raise it axially 30mm from its standard position in the camera pedestal to suit image detectors (such as CCDs) which cannot be placed near the nominal focal plane. Without this provision, spherical aberration due to the displacement of the required focus position with respect to the primary mirror would cause an image blur of about 1.2 arc sec diameter. With the doublet raised in this way, a supplementary lens must be fitted to the guider probe to bring focus within its range.

Table 1.1: Optical Parameters of the Doublet
Curvature
(/m)
Diameter
(m)
Seperation
(m)
Material
Comments
-0.039370 3.893 Primary Mirror b=-1.1717
12.161500 air
1.573622 0.252
0.007620 fused silica
2.610630 0.249
0.017780 air
0.406693 0.249
0.015240 fused silica
-0.684646 0.248
0.490000 air
0 0.254
0.002 filter glass
0
0.013 air
FOCAL SURFACE

Figure 1.4 Spot diagrams for the doublet corrector, with the axes labelled in millimeters. Like the aspheric plate, the doublet is usable well beyond the spectral range indicated here.

Triplet

The triplet was designed to give an unvignetted field of 1° diameter over a wavelength range of 380 to 600nm to include the B and V wavebands, but the performance from U through I is acceptable, as shown by the ray tracing spot plots in Fig. 1.5. For the B, V and R bands, focus can be left at the V value as normally found by an observer with the knife-edge. However, slightly improved performance can be gained for U and I by re-focusing from the V position, as was done for these plots. The top end movement required is given in Table 1.4.

 

Table 1.4: Triplet Corrector Best Focus
to use at change from V
(ie 5500Å)
by
3200Å increase 0.13 mm
U increase 0.11 mm
B,V,R no change needed
I decrease 0.08 mm
1um decrease 0.11 mm
2um decrease 0.33 mm

Table 1.5: Optical Parameters of the Triplet
Curvature
(/m)
Diameter
(m)
Seperation
(m)
Material
Comments
-0.039370 3.893 Primary Mirror b=-1.1717
11.894600 air
0.900917 0.455
0.027610 UBK7
0.134768 0.453
0.186385 air
0.582268 0.361
0.007366 UBK7
2.520169 0.346
0.424434 air
1.631041 0.304
0.023546 UBK7
0.184635 0.302
0.172147 air
0 0.254
0.002 filter glass
0
0.013 air
0 FOCAL SURFACE

A central doughnut-shaped ghost, about 60mm in diameter, appears as an enhancement of a few percent above the sky background if the triplet is used in either the U or I bands or if O or J sensitized emulsions are used without a filter. The ghost arises from a reflection from the emulsion and from the colour filter, returned to the focal plane by the second last surface of the corrector. This, and the last surface of the corrector have been multilayer anti-reflection coated to minimise the ghost in the B and V wavebands and most filters are also anti-reflection coated. In practice, the ghost image is completely undetectable in the B, V and R passbands. The spectral reflectance of the multi-layer coated surface which contributes to the ghost is shown in Fig. 1.6. With its coated surfaces and 58.5mm thickness of UBK7 on axis, the triplet has a spectral transmission approximately as shown in Fig. 1.7.

The triplet appreciably enlarges the image scale, giving an effective focal length near the axis of about 13.54m, corresponding to an image scale of 15.2 arc sec per mm. It also has pincushion distortion, reaching about 1.4%, 30 arc min off axis, which is a little less at a given radius than the doublet. The distortion can be very closely fitted by a simple polynomial. For spot diagrams calculated at wavelength 550nm, the radius, r, to an image centre is given by:-

where:-
= angle off axis, A = 2.310 x 103   and B = 2.003 x 106, in metres.

Note that the spot diagrams indicate some radial shift in images with changing colour.

Figure 1.5 Spot diagrams for the triplet corrector. Images are usable for guiding at all the wavelengths illustrated here, even at the edge of the 1 field. Axes are in millimeters.

Figure 1.6 . Optical properties of the anti-reflection coatings on the triplet corrector.

Figure 1.7 The optical transmittance of the triplet corrector on axis, with and without the anti-reflection coatings.

The Cassegrain focus

Photographs may also be made at the wide field Ritchey-Chrétien Cassegrain focus; the design parameters are given in Table 1.6. Working at f/7.9, a fully-illuminated, coma-free field of 39 arc minutes diameter is obtained on 14 inch square plates. The plate scale is 6.7 arc sec per millimeter and the focal plane is curved, concave to the sky, with a radius of 4.369m, thus requiring the plates to be bent by a vacuum plateholder during exposure.

Image quality, as shown in Fig. 1.8, degrades to about 1 arc second at the edge of the field, due mainly to astigmatism. Naturally, there is no chromatic aberration in the all-mirror system.

Fig. 1.8 Spot diagrams for the f/8  focus. The larger circles are one arc sec diameter. The on-axis spot is very small and may not be visible in this reproduction.

Table 1.6: Optical Parameters of the f/8 Cassegrain focus
Curvature
(/m)
Diameter
(m)
Seperation
(m)
Asphericity Comments
-0.039370 3.893 -1.1717 Primary Mirror
8.4416
0.068975 1.419 -8.3086 Secondary Mirrot
10.2916
0 0.355
0.003 filter glass
0 0.355
0.028
-0.228885 focal surface

Sub-Beam Prism

A fused silica prism of 145mm clear aperture diameter and about 55 arc sec apex angle can be fitted in the beam approaching the primary mirror to extend the range of photometric calibrations to fainter images. The prism is readily and reproducibly attached to one of the northern top end support vanes. It produces a faint secondary image displaced about 26 arc sec at position angle 260° from the main image and about 7 magnitudes fainter (Couch and Newell 1980) There is no measurable chromatic effect over the BJ- RF waveband.

 

Filters

A wide range of filters is available for the prime focus camera and these fall conveniently into two types, coloured glass and multilayer interference. The coloured glass filters are all 10 inches square and almost all are 2mm thick. All the glass filters except the UG1 have been coated to eliminate the reflections associated with the triplet mentioned in Section 1.2.4.

The standard range of 2mm filters, with optical thickness 0.70mm comprises Schott types:
UG1, GG385, GG395, GG475, GG495, GG530, GG590, RG610, RG630, RG665, RG695, and RG715. We also have an RG9 filter of 3mm thickness, corresponding to an optical thickness of 1.05mm.

There are also two special filters, designed by Dr Elizabeth M. Green, which approximately yield the standard photometric B and V bands on the Eastman Kodak IIIaJ and F emulsions. They are anti-reflection coated cemented doublets consisting nominally of 2mm GG395 + 1mm BG37 (BJ) and 2mm GG495 + 1.25mm BG18 (VF). The optical thickness of both filters has been found by the knife edge test to be 0.97mm.

The interference filters (except one Halpha) are all 5 x 5 inch squares and are usually mounted in special holders to fit the 10 x 10 inch slot in the prime focus camera. These filters are listed in Table 1.7.

To a first approximation, the focus setting must be increased ( i.e. the top end raised) by an amount equivalent to the optical thickness. However, because the corrector and plateholder are moved by the focus drive, and the correctors have some power as lenses, the adjustment for true focus differs slightly, but significantly, from that implied by the optical thickness. For the triplet, the motion required is a factor of 0.90x,  for the doublet 1.04x  and the aspheric plate (just) 1.01x  the optical thickness.

Such problems are largely avoided by setting focus through one of the visually clear filters, such as GG495, and adopting that value for the other filters having the same thickness (most of the coloured glass filters). However, for the triplet and aspheric plate, there is some advantage in re-focusing for different wavelengths. (see  the sections on the Triplet and Aspheric plate).

The required top end movement can be calculated as follows:

where

To sufficient accuracy, most Schott filters have a refractive index around 1.54 so this expression simplifies to 0.35kT.

Note 1:   Bandpass and central wavelength of interference filters are from manufacturer's data as seen
in f/3.3 converging beam.
Note 2:  Add `Top end Movement' to focus reading with 2mm filter. Figures in parentheses should be confirmed by focus test in good seeing.

Figure 1.9 The focal plane of the AAT. This diagram shows (1) The field covered by a 2.6 x 4.2 arc min CCD. (2) The 25 arc min unvignetted field of the doublet. (3) The 1° unvignetted field of the triplet. (4) The area of sky masked by the calibrator sky baffle. (5) The area of the focal plane available to the autoguider short probe. (6) The total area exposed on a 10 x 10 inch plate.



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