When the 4m Blanco telescope at CTIO was designed in the late 1960's, it is doubtful that the designers anticipated that it would ever be used at prime focus with any detector other than photographic plates. Wide field imaging was to be done with a camera using a pair of non-achromatic triplet correctors, optimized for use in red and blue light.

The telescope has changed greatly since then, as have other large telescopes constructed during the same era. Imaging is now done almost exclusively with CCDs. Image quality has been significantly improved by careful control of environmental variables and upgrading the optics where feasible (Baldwin et al. (1996)).

A new corrector, the Prime Focus Atmospheric Dispersion Compensator (PFADC) has been installed to take advantage of the telescope's improved imaging capability. The PFADC provides high-quality, wide-field achromatic imaging at prime focus and incorporates atmospheric dispersion compensation (ADC). It is used mainly with a CCD imager and a fiber-fed, multi-object spectrograph known as Argus. Direct photography is still supported, though this option is now little used.

In principle, everything there is to know about a system like this can be computed directly from the optical design. However, there are at least 70 independent variables involved in the design and fabrication of this set of optics, such as spacing, radii, tilts, decenterings and refractive indices. Sufficient error in any one of these is capable of rendering the system's image quality unacceptable.

Each of the parameters can be measured, though always with some uncertainty. The corrector cannot be tested as a unit except on the telescope where the only variables which can be accurately measured are the image size and the optical field angle distortion (OFAD). Photographic plates are the classical and still the most appropriate method of directly measuring the OFAD. The large detector area, flatness, continuous nature of the detecting medium and high dimensional stability of plates makes them ideal for the job. Monolithic CCDs of the requisite size, flatness and number of pixels still lie in the future.

The OFAD coefficients for the old CTIO prime focus UBK-7 triplets were determined experimentally using plates by Cudworth & Rees (1991) and Guo et al. (1993). A similar photographic determination of the OFAD for the PFADC has been made recently by Guo et al. (1996).

Photographic measurements are not sufficient to fully characterize the optics. At CTIO, several instruments with differing optical configurations are used at prime focus and some of the elements of the PFADC are moveable. It is impractical to directly measure the OFAD under all possible permutations. What we have done here is to carefully compare the empirically determined OFAD under a single known set of conditions to the predicted performance under the same conditions and quantify a baseline behavior.

Monte Carlo simulations permit us to show that the observed performance of the optics is within the range which would be expected to occur as a result of normal manufacturing tolerances. This gives us confidence that we understand the corrector and allows us to make useful predictions as to how it can be expected to work in other configurations. The analysis represents a synthesis of theory and measurement and results in a better characterization of the corrector's behavior than would have been possible using the information provided by either computer modeling or direct measurement alone.

The results presented here are intrinsically interesting and not merely to potential users of this corrector. We certainly have benefitted from the exercise. Even the answer to such an apparently mundane question as "What happens when a filter is changed?" can be more interesting and significant than one might think. This kind of sub-arcsecond absolute astrometry will also be necessary for modeling a second ADC corrector now under construction. It will be used with "Hydra-CTIO" (Bardeen 1991), a new multiple object fiber-fed spectrograph now being constructed at NOAO-Tucson.

For the moment, our extrapolations of the PFADC's behavior only involve changes of the optical parameters which deal with the effect of changing filters and the corrector back focal distance. We do not yet have enough information to allow us to do comparisons of direct measurement with theoretical models of the ADC function. This is a different and more complex problem which we hope to study in the near future.

The PFADC was designed by Richard Bingham at University College London under contract to CTIO. It is important to emphasize that the values shown in Table 1 are those of the nominal design, but of the system as built and measured. The theoretical performance of the final configuration is essentially identical to that of the original design.

Table1: Optical Design of PFADC for PFCCD on 4M Blanco Telescope  

This corrector is a descendant of the triplets originally provided with the Blanco telescope (Wynne, 1968). Addition of a fourth element provides broadband color correction and significantly improves image quality. The basic optical configuration is similar to a 4-element design first described by Wynne (1967) for the Hale 5m. Though the 1967 design is for a classical Cassegrain optical system, Wynne (1987) later showed that it could be adapted for use on a Ritchey-Chretièn telescope.

Wynne and Worswick (1988) then demonstrated that an ADC version could be built by putting a pair of rotating, curved, zero-deviation, Risley-like prisms with an oiled mating surface in front of the basic 4-element configuration. Bingham (1988) soon produced a simpler design in which a pair of rotating ADC prisms with an oiled, flat, rotating contact surface served as the first element of a 4-element corrector. This reduced the number of elements from 8 to 7. Glass-air interfaces were decreased from 10 to 8.

While designing the PFADC for CTIO and a similar corrector for the WHT, Bingham was able to further improve the design by replacing both of the front two elements of the 4-element configuration with doublets having shapes similar to those in the corresponding elements of the basic 4-element corrector. Each doublet is made of glasses (LLF1 and PSK3) which have almost the same indices of refraction but different dispersions. The cemented surfaces of the doublets are slightly inclined, so both act like zero-deviation prisms with a small dispersive power. When the axes of the prisms are 180° out of phase, their dispersions cancel and the system has essentially the same image quality as the basic 4-element design. The final optical system contains 6 pieces of glass and 8 glass-air interfaces. The rotating surfaces are not in contact.

Both doublets can rotate independently over 360°, allowing an artificial dispersion of variable magnitude to be added in any direction. This permits the corrector to compensate for atmospheric distortion with very little image degradation at any azimuth and at zenith angles to 70°. The optical design provides excellent unvignetted images at all wavelengths from 3400A to past 10000A over 48 arcmin field. There is little image shift with ADC. Chromatic effects are small. The quality of imaging at all air masses is primarily seeing-limited.

The four surfaces on the two singlets have been coated with broad-band anti-reflection coatings having high transmission from 3500- 10000A. The four surfaces of the doublets were coated with MgF₂ instead of the broad-band coatings. Use of these new coatings was felt to involve too much risk because their long-term characteristics were not well known. So far they appear to be stable and robust.

Transmission of the corrector including coatings and glasses is 85% or higher at all wavelengths from 3700A to 8700A, falling to 75% at 3650A and 10000A and 54% at 3500A. Excellent BVRI photometry can be done using the PFADC. The short wavelength transmission limit makes photometric calibrations somewhat more difficult in U, though good results have been obtained in this band.

The original design specification called for image quality of .25'' full width half maximum (fwhm) in the center of the field and .5'' fwhm at the edge. The corrector meets this specification. However, the images produced by ADC correctors tend to have irregular profiles which often makes fwhm a misleading representation of image size. In the rest of this paper, we will refer to image size by specifying the diameter of a circle in which 70% of the incident energy is contained (D₇₀). This is a somewhat more stringent specification for image quality than the original. For various reasons, we believe that D₇₀ provides as accurate a quantification of the useful image quality of the instrument as can be provided by a single number. For the purpose of theoretical OFAD modeling, the images are considered to lie at the centroid of the spot diagram.

The PFADC was planned with a CCD imager as the default instrument. The design assumed that a 4mm BK7 filter would normally be placed within the back focal space (distance 11 in Table 1 [1]) in front of a 6mm window of fused silica. With the corrector as built, theory predicts the best imaging with the focal plane of the detector 91.9mm behind the rear face of the nominal corrector. Under these conditions, the focal plane is very nearly flat and the system is achromatic. So long as the surfaces of the window and filter are flat, their precise locations within the back focal distance have almost no effect on the optical behavior of the system.

Argus places its fiber tips directly in the image plane. As a result, there is 10mm less refractive material in the system than the design calls for, which causes an image shift and a small amount of chromatism. To maintain the same optical distance between corrector and detector, the Argus fibers must be placed closer (88.6mm at 4400A) to the rear surface of the nominal corrector. Over the entire field, more than 90% of the transmitted light at all wavelengths from 3500A to 10000A falls into a .7 arcsecond circle when the system is focussed through a B filter. This image quality is sufficient to do efficient broadband spectroscopy through Argus' 1.86'' diameter fibers.

The nominal thickness of the filters used in the Prime Focus Camera is 2mm. For best imaging with 2mm filters, the film surface should be 89.3mm from the nominal corrector. The filters normally used for photography have different thicknesses and compositions. The image quality is much better than was achievable with the old triplet correctors.

In all three cases, the instruments have been mounted with back focal distances which are nearly optimum for the respective configurations in the nominal design. The actual "as built'' and measured distances (+/-.1mm) between the rear of the corrector and detector plane are 91.6mm, 88.5mm and 89.2mm respectively for the PFCCD, Argus and the PF Camera.

In an astrograph, the spherical sky is presumed to be projected onto a flat plate perpendicular to the beam of the astrograph. In this ideal case, the distance r₀ from the optical axis to a point on a plate is given by  r₀=f tan(A), where f is the focal length of the astrograph and A the angular distance from the optical axis to the same point.

Correctors such as the PFADC deviate from this model via radial pincushion distortion, called optical field angle distortion (OFAD), which varies as a function of the distance from the optical axis. We will represent distortion using the model in Chiu's 1976 paper

r = f tan(A)[1+d₃ tan²(A) +d₅ tan⁴(A)]

Here, r is the measured distance from the center of the field to the image in the detector plane. Distortion is modeled via the third and fifth order dimensionless distortion coefficients d₃ and d_5.

The inverted model

r₀ = r b₃ r³ +b₅ r⁵

is usually preferred for analyzing plates, along with the image scale S, usually expressed in arcsec/mm. The two models are equivalent for our purpose and easily interchangeable via the simple relations

f = 206265/S,   d₃ = -b₃f² and d_{5 =} (3b_3² -b₅) f⁴

In Table 2, results of theoretical analysis of the OFAD for the "as built'' PF camera using Zemax tm are presented along with the values empirically determined by Guo et al.(1996) from plates taken in 1995. In both cases, the two ADC doublets were set in a "neutral'' position with their dispersive axes opposed in the north-south direction. UBVRI bands in the observations are approximated respectively by the conventional wavelengths of 3600A, 4400A, 5500A, 7000A and 9000A.

Table 2: Theoretical and Experimental OFAD Coefficients for the PF Camera

The photographic exposures were made through UG-5, GG385 and GG485 filters with thicknesses of 2.73mm, 1.96mm and 1.84mm respectively. The focal lengths in Table 2 have been corrected to the values they would have had if the filters had all been 2mm thick and made of BK7.

These two sets of models predict star positions with an rms difference between theoretical and empirical positions of less than 13µ over the field in all three colors. Nowhere does the predicted position of a star image differ from its measured location by more than 17µ (.31 arcsec). Still, the measured focal lengths of the system are slightly greater than the theoretical values. The rms difference between measured and predicted positions can be reduced to 4µ by adjusting the focal lengths of the system to be 1.8mm greater than predicted. As we will show, an adjustment of this order is what might be expected as a result of manufacturing tolerances.

Theory and experiment agree that there is a gradual increase in f with increasing wavelength while d₃ and d₅ decrease. Most of this variation of the OFAD is caused by secondary chromatism coming from color dependencies in the image distortion. Moving away from the optical axis, the blue images at first fall slightly closer to the center than those in the red so the focal lengths are lower in the blue. Farther out in the field, the shorter wavelength images begin to be displaced more because of larger values of d₃ and d_5, passing the longer wavelength images near the edge. The U images are as much as .36'' from the I images in parts of the field. This shift is the reason the broad band images often required by Argus are somewhat larger than the narrower band images generally used for CCD exposures. With Argus and the PF Camera, there is a small additional shift of image position with color resulting from primary chromatism caused by the incorrect filter thickness.

The photographic calibrations used here are based on eight plates of two fields, all taken on the night of February 23/24, 1995. These fields are called LP543 and M68 by Guo et al. The measured OFAD coefficients in Table 2 [2] are averages in which equal weight is given to all plates.

The focal lengths measured from the LP543 plates are approximately 3mm longer than those derived from the M68 series while the focal length determined from plates taken in the same color of the same field differed by less than a millimeter. This difference is difficult to explain since the images were taken in uninterrupted sequence during the same night. The air mass at which the LP543 plates were exposed is somewhat higher than for those of M68 so an error may have been made in correcting for atmospheric refraction.

The errors can be put into perspective by observing that the models determined for each plate predict measured image positions on that particular plate with an rms precision of 1.5-2micron. The measured values of the OFAD fluctuate between plates within the same series by approximately 3-4micron of position uncertainty, roughly the same as the difference between the theoretical and experimental models one a correction has been applied to the focal length. The rms position difference caused by the 3mm focal length difference between the LP543 and M68 plates is 14micron . This means that uncertainty in focal length is the principal source of error in our knowledge of the corrector's behavior. The experimental focal lengths in Table 2 [2] are an average of the two plate sets.

The values for the paraxial focal lengths predicted by Zemax at all wavelengths were taken to be the "f'' terms in the predicted OFAD. Values for d₃ and d₅ were then obtained by fitting the OFAD model to the positions given by Zemax for the centroids of a number of images distributed uniformly throughout the field. This procedure yields models which predict Zemax's theoretical image locations with an rms error of less than 4µ in U and 2µ in all other colors.

As previously mentioned, the parameters given in Table 2 [2]are not those of the corrector as it was designed, but come from measurements made after construction. To estimate the effect of any error in these measurements, Monte Carlo (MC) calculations were done during which the mechanical and optical parameters of the system were varied at random within the tolerances which were maintained during manufacture and final assembly. Every MC iteration creates a new, slightly different optical system which represents the way the corrector might have been put together. Each MC design was modeled in the same way as the nominal configuration, optimizing the image quality by refocussing after each iteration.

Image quality after a MC perturbation always remained within or very near to the design specifications, i.e. with the monochromatic D₇₀ not exceeding .25'' in the center and .50'' at the edge. The image center moved by as much as several hundred µs as a result of tilts introduced by the Monte Carlo process, but after recentering, a new OFAD model could always be found which was able to predict the new theoretical positions to an rms precision of 6µ or less. The system focal length varied from the nominal value by an average of +/-5mm from after each Monte Carlo calculation. The MC perturbations changed d₅ by an average of 30,000 units. Increases of d₅ were seen more often than decreases. Changes in d₅ were usually accompanied by changes of d₃ in the opposite sense.

Theory should accurately predict the shape of the distortion curve, yet the measured values of d₅ were consistently approximately 100,000 units smaller than expected. According to the Monte Carlo calculations, d₅ is unlikely to have decreased as a result of manufacturing.

A difference of 100,000 in values of d₅ causes a maximum difference in image positions of 17micron (.3 arcsec) at the edge of the field. When the theoretical and empirical models are adjusted to coincide as well as possible, larger values of theoretical d₅ produce the best fit with slightly lower, compensating values of f and d₃, reducing the residual errors to about rms 4micron, roughly the same as the intrinsic errors of the measuring process. Thus, the difference between the experimental and theoretical values of d₅ is not significant here and can be safely ignored for the present, but it is unclear why this discrepancy exists. The most likely explanation is that it is some kind of systematic difference in how positions are predicted with a computer and measured photographically.

The MC calculations indicate that due to fabrication tolerances, the measured focal length might vary by be as much as 5mm from the predicted values. As previously mentioned, the best agreement occurs when the focal lengths are shortened by 1.8mm. The fact that a correction of this degree is sufficient to minimize the difference between experiment and theory strongly suggests that the corrector was assembled within specifications.

Adjusting the focal length by reduces the rms difference between the predicted and measured image positions to less than 4micron (.08 arcsec), which is comprable to the experimental error in the positions predicted by the measured OFAD. Once this adjustment has been made, the measured and predicted values tabulated for the OFAD of the PF camera in Table 2 [2] are essentially indistinguishable.

This focal length adjustment can be put into further perspective by noting that the theoretical focal length agrees almost perfectly with the plate scale derived from the M68 plates while it differs by 3mm from the scale on the LP543 plates. This provides some support to the supposition that the M68 scale is more likely to be correct and that an error may have been made correcting for refraction on the LP543 plates.

Summarizing, the theoretical OFAD coefficients are probably the more reliable, certainly for determining how d₃ and d₅ vary with wavelength. The photographic modeling gives us assurance that the true image scale is within the expected range. However the errors in fabrication appear to have been smaller than those made in the measurement of the OFAD. The theoretical values appear to be the best predictors we have of the corrector's behavior until we can obtain another, more accurate measurement of the paraxial focal length.

Table 3: OFAD Coefficients for Nominal PFCCD

Zemax can now be used to calculate the OFAD to use for the PFCCD and Argus. The OFAD for the nominal PFCCD with a 4mm BK7 filter and 6mm fused silica window are given in Table 3. Argus should be focused through a blue filter and the B band OFAD used, i.e. f=11466.5mm, d₃ = 357.9 and d₅ =835000.

The focal lengths for the nominal PFCCD are approximately 1.5mm longer than for the PF Camera while d₃ and d₅ are negligibly different. The focal length difference is because the PFCCD is .3mm from the nominal position while the PF Camera is within .1mm of the best location. It is also interesting to note that there is a slightly greater variation of focal length with color for the PF camera. As previously mentioned, this comes from a small amount of chromatic aberration in Argus and the photographic camera caused by the incorrect thickness of the filters.

Recent measurements indicate that .70'' fwhm images have been observed with the PFADC in the center of the field under very good conditions of seeing. These images are undersampled because the CCD currently used has a scale of .43"/mm. At present we are unable to determine if the actual image size is smaller than this reported value.

This observation implies that with perfect seeing the PFADC is probably capable of producing central images with D₇₀ well under .5''. The images are clearly very good, though we are unable to measure how closely the central images approach the level of D₇₀ < .25" that theory predicts they should.

Changing a filter is generally equivalent to moving the instrument with respect to the corrector because different filters will generally have different optical thicknesses. Obviously the system has to be adjusted to compensate. One naturally reaches for the "focus" control to perform this operation.

Focusing the Blanco telescope moves the prime focus pedestal up and down. The pedestal is a rigid assembly which moves the corrector and detector as a unit. This is an inappropriate way to adjust for an error in back focal distance.

Such a movement forces a change in the back focal distance by relocating the corrector assembly with respect to the primary mirror. This refocusses the images, but does so by moving the corrector away from the optimum location. This degrades image quality and makes a significant change in the telescope's effective focal length.

This is not a serious problem with Argus nor with the Prime Focus camera. Argus is permanently mounted with its fiber tips in the correct plane. Observations with the prime focus camera are made with a set of filters which are nominally 2mm thick. Even though these filters actually vary in thickness from 1.8 to 3mm, the variation is small enough so there is no significant image degradation, though there is a noticeable change in focal length with wavelength and filter thickness.

The Prime Focus CCD (PFCCD) is another matter. Currently, the detector is permanently mounted 91.6mm behind the corrector. This is close to the optimum distance (91.9mm) assuming it has the 4mm filter and 6mm window for which the corrector was designed. However, the system as built uses a fused silica window 8.85mm thick. The window is a meniscus lens which compensates for curvature of the CCD. This lens acts as a Barlow, significantly increasing the focal length. With the nominal dimensions, this predicts an increase of 66.5mm in the focal length to 11542.9mm in V with a 5.1mm filter. The measured value of the focal length is 11531.5mm, the difference in the offset coming from the fact that we currently lack precise knowledge of all the dimensions, including the exact CCD pixel size at the working temperature. For the rest of this paper, we will consider the dewar window to be a plane quartz window 8.85mm thick with a flat detector.

The PFCCD normally uses filters which are between 5mm and 10mm thick, meaning further excess material is placed in the back focal space. This extra material moves the detector optically closer to the corrector. Compensating for these back focus errors by moving the pedestal causes image degradation and a substantial change in the effective focal length of the telescope.

In principle, the proper way to compensate for the problems introduced by changing filters would be to have two focussing mechanisms; one like the present pedestal height control to focus the telescope and a second adjustment which moves the detector with respect to the corrector to maintain the back focal distance at the optimum value. There is no mechanism like this currently on the PFCCD, nor are there any plans to install one.

Table 4 shows what happens when back focal distance is wrong and has been corrected by moving the pedestal. Image size and focal length as a function of back focus error (BFE) are listed. The table begins by showing the behavior of the main instruments as they now exist. As can be seen, Argus and the photographic camera are mounted in very nearly the optimal locations, while the PFCCD has a rather substantial BFE.

Table 4: Image Quality

In the second part of the table, the theoretical behavior of the PFCCD is shown with the detector at incremental locations one mm apart, beginning with the detector 3mm farther from the corrector than optimum and ending with it 3mm closer. This listing clearly shows that BFE greater than 1mm should be avoided and BFE of more than 3mm causes serious image degradation.

As can be seen in Table 4, theory predicts a linear change in effective focal length as a function of BFE at a rate of -7.67 mm of focal length change per mm change in BFE. This change could either be produced directly by physical change in BFE or by the insertion of an extra thickness of a refractive material within the back focal space. For a material of thickness T and refractive index n, this causes a back focal shift of T(1-1/n) and a change in focal length of 7.67 times this value. The variation in n with wavelength can cause significant chromatism. About .5mm of the 4.4mm focal shift with wavelength in Table 2 is caused by this effect.

This -7.67mm difference in focal length per mm of back focus change should not be confused with the classical shift in the "focus" of the telescope. The two are strictly proportional, but the pedestal only needs to move by -.86mm to cause one mm of back focus change, which in turn changes the focal length of the telescope by 7.67mm. This is probably the reason no one seems to have paid attention to this problem in the past. It is not intuitively obvious that refocussing by moving the pedestal by 1mm will cause the focal length of the telescope to change by almost 9mm. This relationship was used to calculate the effect on focal length caused by differences in the thicknesses of the filters used to measure the values in Table 2 [2].

Due to a fortuitous error, we are able to demonstrate that these predictions are accurate. Plates were first taken in 1993 to measure the OFAD. After our observations, we realized that the camera had been incorrectly mounted with a back focus of 91.5mm. The focal plane was lowered by 2.11mm before a second run in 1995. This increased the measured focal length by 15.9mm. This change is almost exactly the 16.2mm predicted for the increase by the BFE/focal length relationship, indicating that the focal length shift occurred as predicted. As expected, the change did not change the measured distortion coefficients.

The quality of the images also varies with wavelength. An estimate of the magnitude of this effect is also given in Table 4. These estimates are only approximate because image shape varies wildly, but they are nonetheless interesting. The values shown are based on theoretical analysis of the spot diagrams combined with some subjective weighting to attempt to make them reflect the real situation as well as is possible in a single number.

In summary, our results are consistent with the hypothesis that the corrector was fabricated and assembled quite well. The 2m difference between the measured and predicted focal lengths is a slight focal change caused by random manufacturing variations of the parameters of the optics within the specified tolerances. Image quality is excellent, as far as we are able to tell, with intrinsic image quality in perfect seeing of .5" or better in the center of the field.

Table 3 [3] gives the final OFAD to use for the PFCCD in the default location with the correct window and filter thicknesses. It is straightforward to extrapolate these results to determine the focal length and estimate image quality for other configurations by using the offsets from the B focal lengths in Table 4 [4] and the -7.67 mm/mm relationship between e.f.l. and BFE. These changes should not have a significant effect on d₃ and d₅.

The image plane of the PFCCD in its proper configuration is achromatic even though there is a 3.7mm shift in focal length from U to I. This is a manifestation of chromatic difference in distortion, not change in focal plane. No focus change with color is required if the filters are all the standard thickness and composition. In Table 2 [2] the PF Camera has a 4.4mm focal length shift over the same range, of which .5mm is a color shift in the focal plane caused by the filter and the window being thinner than the design calls for. With filters of differing thicknesses and composition the focal length shifts will be different from those shown here. The proper values are easy to compute if filter thicknesses and indices of refraction are known.

It is clear from Table 4 [4] that the image plane of the PFCCD should be moved to a better location. Installing a spacer 2.1mm thick will keep the BFE to under 1mm with any filter in current use and not cause significant image degradation, though the focal length will obviously change as filter thickness is varied. This solution to the back focus problem is reliable and easy to implement. It will significantly improve image quality and will provide a new fixed focal plane location which can be used to attempt a more precise determination of the system's focal length than we have been able to obtain so far.

Moving the detector farther from the corrector in this way will change the telescope's focal length to a value very near to the optimum for filters 7.5mm thick. There will be a very slight focal shift with color. This shift will have the opposite sign of the shift in the photographic camera because the PFCCD has too much refractive material in the beam rather than too little, as is the case from the PF camera.

Acknowledgments:

The author would like to thank members of the CTIO staff, especially Daniel Maturana, John Filhaber, Gabriel Pérez, Nick Suntzeff and Alistair Walker for their invaluable help in accumulating and presenting the data given here.

1
Baldwin, J. et al. NOAO Newsletter 45, Mar. 1996

2
Bardeen, S. et al.

3
Bingham, R.G. 1988, Proceedings of the ESO Conference on Very Large Telescopes and Their Instrumentation, ed. L.B. Robinson (Springer-Verlag, New York), 1167

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Cudworth, K. M., & Rees, R. F. 1991, PASP, 103, 470

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Chiu, L.-T. G. 1976, PASP, 88, 803

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Guo, X. 1995, PhD Thesis, Yale University

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Guo, X., Girard, T. M., van Altena, W. F., & López, C. E. 1993, AJ, 105, 2182

8
Guo, X. et al. To be published in PASP, 1996 as a companion paper to this one.

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Wynne, C.G. 1967, Ap. J., 152, 675

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Wynne, C.G. 1968, Ap. J., 152, 675

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Wynne, C.G. 1987, Observatory, 107, 31

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Wynne, C.G. and Worswick, S.P. 1998, MNRAS, 230, 457

Empirical and Theoretical Modeling of the PFADC Corrector on the Blanco 4m Telescope

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