Dan McShane wrote:

snip

Mike,

More precisely it`s about the edge rays and how much the filter shifts to a
lower central wavelength as the AOI increases. In addition to the CWL
shifting lower, the filter bandwidth gets wider and loses some TX%. Fast
scopes have a very steep cone angle and therefore "potentially" could affect
the filter`s CWL and bandwidth more so than slower scopes.

Not so sure about the center being affected though, as it`s the one place
where at least some of the ray bundle is nearly perfectly perpendicular to
the optical axis.

This is from a similar thread "Filters and Fast scopes?" on SAA a couple of
years ago;

Here`s some spectral scans http://users.erols.com/dgmoptics/filters.htm of a
nebular filter I designed using TF Calc Thin Film software. The scans are at
0, 10, and 20 AOI. The filter is not as narrow as an OIII but it does
demonstrate that with nebular filters anything less than about a 10 AOI
doesn`t effect the filter very much. Now the OIII has narrower bandwidth but
is still not a especially narrow filter as far as interference filters go
and is therefore not effected as much by AOI.

Dan McShane


Dan,
Thanks for the more detailed response. I have access to and occasionally use TF
Calc and FilmStar for film design and performance trades, but not for nebular
filter design. Not having the exact filter stack prescriptions for various Ha,
O-III, etc. filters, I couldn't specifically analyze their AOI performance, so
thanks for the more precise value for maximum permissible incidence angle.

My comment about performance at the FOV center was that at sufficiently low
focal ratios, ray angles at the rim of the entrance pupil could be incident on
the filter at sufficient angles to shift the passband and reduce image contrast
even at FOV center. The cone half angle U for a given focal ratio is ASIN(1 /
(2f/#) ). This gives

f/# ASIN( 1 / 2(f/#) )
f/2 14.48º
f/3 9.59º
f/3.5 8.21º
f/6 4.78º
f/15 1.91º

You said that up to 10º AOI no significant passband shifts occur, which means
that the filters could give good central FOV performance down to about f/3.
This agrees well with the specifications from Astronomix. Perhaps Astronomix
was being conservative in their minimum focal ratio (maximum AOI) by limiting
the lower focal ratio to f/3.5.

Another factor limiting lower focal ratios with filters is their introduction of
overcorrected spherical and chromatic aberration. A perfectly plane-parallel
plate in a converging cone shifts the focus by a wavelength-dependent factor of
(thickness)(n-1)/n. The index "n" rises with decreasing wavelength, therefore
the filter introduces overcorrected chromatic aberration. The spherical
aberration of a plano plate is given in "Modern Optical Engineering" by W.J.
Smith as

LA' = (t/n) [ 1 - ((ncosU) / SQR(n²-sin²U)) ]

where U is the maximum cone angle given above as ASIN(1 / 2(f/#)). A quick
ZEMAX simulation shows that for a 12.5" aperture f/3 light cone used with a
0.15" thick plane-parallel plate of BK7 over F-C spectrum, at best visually
weighted RMS focus the filter introduces about 0.3 wavelengths polychromatic P-V
OPD of overcorrected spherical and chromatic aberration. At f/3.5 this values
reduces to about 0.23 wavelengths P-V, and at f/6 gives 0.08 wavelengths P-V.
Thinning the plate to 0.1" thick at f/3.5 gives about 0.15 wavelengths P-V OPD.
Best-focus RMS wavefront errors for all these values are roughly 1/3 to 1/4 the
P-V values, so except at f/3 the filters introduce little visual image
degradation or Strehl impact. I don't know how thick these filters are, but the
lower focal ratio limit of f/3.5 given by Astronomix still appears credible. Of
course all this analysis assumes the filter faces are perfectly flat and the
internal index of refraction is perfectly homogeneous, which of course isn't the
case.

Thanks as well to Pierre for initiating this interesting thread.
Mike