Filters, Snell's law, and the SBIG CFW-8 Color
Wheel
I am using the SBIG CFW-8 color wheel in order to
take the Luminance, Red, Green and Blue frames. The CFW-8
comes with Red, Green and Blue interference filters and a clear filter.
I discovered something that I had not expected when I bought a
Lumicon Deep-sky filter and installed it into the fifth filter slot.
I was using the Meade f/3.3 focal reducer which essentially makes
the image at the CCD chip smaller and brighter. This also causes
the light-cone between the Focal Reducer and the CCD chip to become
shorter so you have a cone that is still the same size at one end but
shorter. The angle between opposite sides of the cone is
increased. Now the filters in the CFW-8 are in this cone.
The surprise is this: If the filters have different
thicknesses (or different refractive indices), the focal length will
change! This is due to Snell's law which is n1*Sin(theta1) =
n2*Sin(theta2) where n1 and n2 are
the refractive indices of the two materials that form the interface and
theta1 and theta2 are the angle between the incident ray and a normal
to
the interface surface.
Here is how significant this effect is for the two filters I was
(inadvertently) experimenting with:
The image on the left was taken through the clear
filter that came with the CFW-8 and is in focus. The image
on the right resulted from merely switching to the Lumicon filter
without making any focus adjustments. Since focusing is usually
a major effort, refocussing simply to compensate for filters of
different
thickness is a major inconvenience. I do not have a micrometer
(and it might damage the filters to use one) so my measurements so
far are "eyeball" measurements. I removed all of my filters from
their holders and discovered that the Lumicon H-beta filter that I have
appears to be 1.5 times thicker than the Lumicon Deep Sky filter which
in turn appears to be 1.5 times thicker than the Meade 80A filter,
which
in turn appears to be1.5 times thicker than the SBIG filters that came
with the CFW8. So the Lumicon Deep Sky filter appears to be
1.5*1.5
or 2.25 times thicker than the SBIG provided filters and results in the
defocussing effect shown in the images above when the filters are used
with a 100" focal length, f/10 scope and an f/3.3 focal reducer.
Note that it WAS possible to focus while using the Deep Sky
Filter but then
the filters provided by SBIG were then out of focus by the same amount
shown above.
The upshot of this is that to minimize focussing effort, you need to
use filters that are the same thickness and the same refractive index
if possible. There does not appear to be any
standard for filter thickness. SBIG appears to be aware of this
and their filters appear to be matched. Note that this is another
reason for them to provide a clear filter along with the red, green
and blue filters. If you were to use red, green, blue, and
"empty",
the filters would extend the focus but the "empty" slot would not so
it would have a different focal plane and would require extra focussing
effort.
