TN89 and hints on optical vignetting and stray light

["Richard Miles" <rmiles@baa.u-net.com>]

 Have corresponded with Michael Richmond, who has asked me to post some
information on the TASS Mailing List which may be of general interest.
Michael - I have expanded here somewhat on my original mailing.

Have also expressed interest in seeing a similar analysis of the 7x7 data by
Michael using only the dark-subtracted, non-flat-fielded image data since I
am interested in the nature of the focal plane illumination, vignetting
included.  This was also raised by Arne in his note to the List of 31st Dec.

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On the subject of vignetting, these are my comments, which were prompted
after seeing the response characteristics across the MkIV field as detailed
in Technical Note 89.  I know that this analysis deals with flat-fielded
image data but care must be taken when generating flat-fields if the degree
of vignetting of the sky background is different to that of point sources -
this can be a serious limitation of the 'light-box' technique.  The general
rule is to design optics, baffles and dew-shield so that vignetting is
virtually absent - easier said than done.

First what does vignetting look like.  If you analyse response across the
frame (as was done by the methodology used in TN89) in terms of a contour
plot, you see that sensitivity is a maximum at some point and that expressed
as polar coordinates centered on that point, the response varies approx. as
the second power of the radial distance, r, across the frame when the entire
frame is suffering from vignetting.  When partial vignetting is present (the
usual case), response is constant for the central region, radius, a, and
then decreases by approx. the second power of (r - a).

Now to the practice - vignetting can arise from one (or indeed all) of three
sources.  These listed in order of likelihood are:

1.  Undersized / off-centered dew-shield.
For the MkIV optical configuration (100mm aperture, 400mm focal length, 40mm
diagonal across CCD frame), the dew-shield must be oversized relative to the
front element by at least [(40/400) x (distance from tip of dew-shield to
front element)].
For example if you have a dew-shield which is 200mm in length, then you need
it to be oversized by 20mm, i.e. a diameter of 120mm minimum.
In practice the dew-shield should be fairly rigid and larger than this (say
125-130mm in diameter) to allow for lack of concentricity of the shield with
the optical axis.

If indeed the dew-shield (light shield as described by Tom) is about the
same length as the focal length of the scope (400mm), then the front opening
of the shield will need to be about 150-160mm in diameter and should be
fairly rigid so that it does not flop when at different zenith distances -
clearly this would otherwise be disastrous for all-sky photometry.

2.  Undersized internal baffle stop.
Sometimes blackened circular apertures are interposed at one or more
positions along the optical axis.  It is common to design systems for visual
observers working on-axis.  Since you need an unvignetted field some 40mm in
diameter then care has to be taken, if baffles are used, that they are
adequate in size.
This can be checked by pointing the optics at a bright daytime sky, placing
one's eye at the focal plane and moving it laterally across the focal plane.
You should be able to see the circular entrance aperture but if there is an
obstructing baffle, then when you move the eye back and forth say 40mm
across the plane then the circular entrance aperture should be vignetted
first on one side and then on the opposite side, i.e. the edge of the
circular aperture is obstructed.  Indeed, if the dew-shield
is in place and this is undersized then this too will create the same
effect.

3.  Undersized internal optical element.
Can be the case either if there are additional lenses positioned along the
optical axis (as used in some apochromatic systems) or say a telecompressor
is used which is too small, or that a filter element is likewise too small.

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Returning to the concept of unvignetted, uniform focal plane
illumination, to achieve this for increasingly large focal planes (e.g.
across the 40mm diagonal as per the MkIV) requires increasingly oversized
baffles and dew-shields.  This makes it increasingly inefficient at cutting
down on stray light, (eg. from a nearby Moon or light pollution source
reflecting light of the internal blackened surfaces, etc.) and
makes flat-fields generated using averaged sky flats under conditions of
stray light increasingly approximate.  However, applying the methodology
used in TN89 but applying it to only the dark-subtracted images entirely
avoids this approximation of averaged sky flats since it is based directly
on point-source signal data.  Furthermore, if the TN89 methodology (applied
to only dark-subtracted image data) can utilise an even greater number of
frames and star measures, then coverage may be sufficient to even correct
for response variations having relatively high spatial frequency such as
caused by dust located near to, or on the window of the CCD chip.

And finally - diffuse reflections originating from stray light will
generally only alter the sky background in a gradual fashion across the
frame and this is easily compensated for by taking sky background measures
in close proximity to stellar images.

I know that TASS people are well aware of most, if not all of the above but
I wouldn't like to think that any of the above points may have been
inadvertently overlooked and so I do hope that this note is helpful.

Happy New Year to all,
Richard Miles