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A
flat-field Schmidt camera for CCD imaging Mike Harlow |
1 Introduction
In
an article written in 2006 for Orwell Astronomical Society, ‘CCD Imaging with a Schmidt Camera’, I described the
upgrade of my 1985-built Schmidt camera from film to CCD imaging. In the
present article I describe a further upgrade involving the addition of a
field-flattening lens and a larger CCD detector.
2 The field-flattener
2.1 Lens design
For
large CCDs, or short focal lengths, the field curvature of the Schmidt camera
blurs images significantly at the edges of the flat field of the CCD. In this
case a field-flattening lens is required just in front of the CCD. This lens
is typically plano-convex with the convex side (facing the mirror) having a
radius of curvature, R, given
by:[1] R
= F(n–1)/n where
F is the focal length of the
Schmidt camera, and n is the
refractive index of the glass used for the field-flattening lens. More
generally, for any shape of field-flattening lens, the focal length of the
lens, flens, is given by:[2] flens
= F/n where
again, F is the focal length
of the Schmidt camera, and n
is the refractive index of the glass used for the field-flattening lens. Note
that the first equation is just a special case for plano-convex lenses
derived from the second, general equation. The
detailed theory of the Schmidt camera is provided by Linfoot in his book Recent
Advances in Optics.[3] In Chapter 3 Section 5 of this book the
field-flattened Schmidt is fully discussed. Equations are given showing how
chromatic aberration and coma introduced by the field-flattening lens can be
minimised by modifying the shape of the corrector plate and moving it towards
the mirror. For the modestly sized camera discussed here these modifications
are unnecessary. |
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6-inch Schmidt
camera with 4-inch finder/guidescope |
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2.2 Making the field-flattening
lens The
plano-convex lens for the field-flattener is the smallest optical component I
have made (so far). The glass substrate used was the plane parallel clear
window from my first, 1992 vintage, CCD camera, and was just 2 mm thick at
the start of grinding. It was ground against a preformed template of the
correct curvature, both to minimise the amount of glass removed and to make
measuring the radius of curvature easier. The radius of
curvature of the convex side of the lens is derived from the first equation
given above. In this case the focal length of the Schmidt is 400 mm and the
refractive index of the glass is 1.52. Therefore, R is given by: R
= F(n–1)/n R
= 400 mm(0.52)/1.52 R
= 137 mm This
curvature will result in a lens with a focal length of ~263 mm, or about +3.8
dioptre in terms of lens power.[4] The glass
template was ground as illustrated at right, against a spare piece of glass
– the central core from my 36-cm Cassegrain mirror. This very thick
piece of glass was ideal, as good clearance was required to prevent the top
piece of glass – the template – from grounding on the top of the
grinding stand. The
curvature was measured in the early stages of grinding using curves of
different radii cut from pieces of card. Curves from 130 mm to 170 mm in
10-mm intervals were cut out and placed against the ground-glass surface to
check progress. In this way the curvature could be estimated to within 5 mm
of the desired value. Once the curve on the template had been generated with
80-grade carborundum it was smoothed with 180 grade, and final measurements
were made of the curvature. These were made using an illuminated slit and a
ruler, as illustrated at right. The ground surface was sufficiently smooth
when wetted to form a good image of the slit, allowing measurements of the
curvature to within 1 or 2 mm. Once
the curvature of the template was as close as possible to the required 137
mm, grinding of the field-flattening lens was started. The lens was mounted
on the cap of a 35-mm film canister with double-sided tape to make handling
easier and to prevent scratching the already flat, polished back surface. The
lens was easily demounted between abrasive grades using nail vanish remover
(acetone). Because
of the small size of the lens – just 35 mm diameter by 2 mm thick
– and the relatively small amount of glass to be removed, grinding was
started with 280-grade carborundum. Changing the surface from flat to the
desired curvature took just nine wets, illustrating how fast grinding is on
such small lenses. After every three wets grinding the field-flattening lens,
the template was reground against its grinding tool to preserve the correct
radius and spherical shape. Grinding was completed with 400, 600 and
1000-grade abrasives, and polishing was carried out with a conventional, if
rather small, polishing lap. As can be seen in the picture below, it only
just survived the polishing process. The pitch was very hard, so adhesion to
the glass template was rather poor. After polishing, the focal length of the
lens was measured and found to be 268 mm – within 2% of the required
value. |
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Grinding the
template curve
Large curvature
requires good clearance
Measuring the
radius of curvature |
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The field-flattening lens during grinding with 280-grade abrasive |
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The polisher (believe it or not) |
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The field-flattening lens polished |
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Another view |
2.3
Mounting the field-flattening lens in the CCD camera head
The CCD used with the field-flattened Schmidt is the
Starlight Xpress SXVF-H16. This is a monochrome camera with 2048 x 2048
pixels each 7.4 µm square. This gives a chip size of just over 15 x 15
mm with a diagonal dimension of just over 21 mm. The optical window in the
original camera is replaced by the field-flattening lens as follows. An
aluminium adaptor ring was made to fit into the recess in the spare front
plate of the CCD head. This was sealed in place using silicone sealant and
then spray-painted on the outside with matt black paint. The field-flattening
lens was then sealed onto the back of the adaptor ring, again using silicone
rubber sealant. This new front-end assembly was then swapped with the
front-end supplied with the camera. When assembled, the field-flattening lens
was within 2 mm of the front surface of the CCD chip. |
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SXV-H16 camera, spare front-end adaptor ring and field-flattening
lens |
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The partly dismantled camera |
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The field-flattened camera assembled and ready for action |
3 First test images: before and after
The
images below show the effect of adding a field-flattening lens. Blurring at
the edge of the 2.1 x 2.1-degree field of the H16 CCD is completely
eliminated by adding the simple plano-convex lens. (Focusing still has to be
perfected to achieve the ultimate image quality.) |
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First terrestrial image to set focus : no field-flattening lens |
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Field of M81 and M82 without the field-flattening lens |
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Field of M101 with the field-flattening lens |
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Slice of the above field of M81 and
M82
without the field-flattening lens (The white lines are due to a fault with the CCD as supplied by the
manufacturer) |
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Slice of the above field of M101 with the
field-flattening lens |
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The corners compared |
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Appendix
: The Schmidt corrector plate
In my original 1986 article for
Orwell Astronomical Society, ‘Construction of a Schmidt Camera’,
I mentioned using a petal-shaped polishing lap but did not show any pictures
of it. At right is shown one of the petal laps used to generate the corrector
profile where the amount of pitch in contact with the corrector at a given
radius is proportional to the amount of glass to be removed. The lap is made
by hot-pressing a template of the desired profile, made of thin card, into a
flat polishing lap. After cooling, the card is easily removed by soaking it
in soapy water. Conventional
techniques were initially used to make the corrector plane-parallel with flat
surfaces on both sides. Only then was figuring attempted with the petal lap
using very short strokes across the centre of the corrector to polish in the
aspheric curve. Regular testing was carried out by placing the corrector on
an optical flat and illuminating it with monochromatic light. The resulting
interference patterns were checked against the theoretical profile, and
figuring continued until they matched to within ¼ wavelength. Half the
correction was placed on each side of the corrector plate. The interference
pattern of the completed corrector, shown at right, was produced by a green
laser pointer used as the monochromatic source at a wavelength of 532 nm. A small
residual wedge between the corrector and the optical flat produces the
slightly asymmetric profile. Note: The corrector has a shape factor A = 1.0,
producing a neutral zone at ~71% of the radius. References
1 Buchroeder, R., private
communication. Questions
and comments can be directed to the author |
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Petal polishing lap for generating the corrector profile
Interference test of the corrector plate |
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