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The discussion of the relative merits of filled arrays, with
instantanous Nyquist sampling, and sparsely sampled arrays, with
``fully efficient'' pixels, lingers on in the bolometer community. A
fully efficient pixel is one that has optimum coupling to a point
source, representing the well known compromise between aperture and
beam efficiency for coherent receivers. The bolometer group at MPIfR
kept favouring the latter approach.
Fully efficient pixels have a spacing that is about four times that
required for Nyquist sampling. They therefore require scanning in
order to achieve Nyquist-sampled maps. However, scanning is necessary
anyway if the area to be mapped is larger than that of the array. For
a large hexagonal array, each subscan will provide Nyquist sampling,
exept for a very narrow angular range around the lattice directions.
The situation is even more favorable for a Cassegrain telescope, where
the array can be oriented for optimum sampling in a single subscan.
Several authors derived a factor of two speed (i.e. time) advantage of
the filled array. In a much simpler argument, it can be shown that
the aperture efficiency of a closely packed array of fully efficient
pixels is about 70%, leading to a 50% speed disadvantage compared with
filled arrays. However, such arguments do not address the problem
rigorously. S. Withington of Cambridge University, UK, convincingly
argues that the coherence properties of the fields must also be taken
into account, but he has not yet completed this task.
Even if one accepts the value for the speed advantage, one must
realize that a filled array has 16 times the number of pixels on the
same area of the focal plane, a non-trivial increase in complexity.
Furthermore, the thermal background per pixel is only 1/16 of that of
the fully efficient pixel, requiring an noise-equivalent power (NEP)
per pixel that is four times lower to reach equivalent sensitivity.
This is also not a trivial task to achieve, and might require lower
operating temperatures, which again adds cryogenic complexity.
The filled array has no intrinsic selectivity with regard to the
acceptance angle. The beam definition has to be provided externally
by a cold Lyot stop. This means that after the first large (warm)
re-imaging mirror, a cold stop (aperture) will be placed at the image
of the pupil. The stop and all following optical elements must be
at low temperature inside the cryostat. The cryostat window is near
the stop and must be necessarily larger than if it were at the final
focus, compounding the IR filter problem.
In summary, we do not see any realistic advantages of filled arrays
over fully efficient arrays for mapping observations.
Next: Sensitivity limits
Up: Technical considerations
Previous: Technical considerations
Frank Bertoldi
2002-08-21