Effect of Changing the Back Focal Distance

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.

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.