The 310 mm F/1.9 Schmidt camera - finally nearing completion
by Dominic-Luc Webb
1. Introduction
The main objective here was the pursuit of a new optics adventure. I
also had in the back of my mind photographic and high speed (>100 Khz)
photometric (UBVRI and spectrographic) imaging of fireballs, comets, meteor
showers, aurora borealis and other wide field objects that often have
rapid transient features. The UBVRI color difference system is defined by
Johnson (ref. 1 and references therein). The effective wavelengths of the
UBVRI system are 360, 440, 550, 700 and 880 nm, respectively. While UBVRI
was intended primarily for stellar objects, I use this for now, not yet
having constructed a proper spectrograph. There is also a 13 color Johnson
filter series (ref. 2) and I have been working on a filter changer for this.
In addition to going for a challenging design, there were some questions I
wanted to address. For instance, I wondered if it was practical to build
a precision instrument from nothing but common industrial plate glass rather
than optical glass. I also wanted to see if bee's wax could serve as a
suitable replacement for conifer pitch. You could use any glycolipid, but
bee's wax is cheaper and more widely available everywhere on the planet and
smells better than pitch. I suspect it is also much less dangerous to inhale.
If this works, I'll take up beekeeping next
Spring (wanted for other things anyway).
I wanted a very fast system, like
F/1.9, to capture in excess of 7 degrees of sky, and the opportunity arose
to experiment with slumped plate glass. Being a photographic (i.e., non-
visual) system, there was also the challenge of making and using a convex
image surface (field at focus is curved). Of course, such a
system could also be amenable to large format cinematography (i.e., 70 mm
and IMAX) and I am looking into these options. I have a design strategy to
incorporate large format movie reels despite the convex surface (maybe this is
how IMAX came to be?). Without any projection optics, the focused image
surface is 36 mm diameter; providing a nice match for 35 mm film.
The primary mirror is spherical 310 mm diameter F/1.55 slumped 19mm plate
glass (slumping compliments Richard Schwartz, Hawthorne, California). I'll post the
heating/slumping/annealing protocol later. The corrector is 250 mm diameter
"Optiwhite" (ref. 3; low iron plate glass with reduced green color) with a 6 mm axial
thickness. I consider Optiwhite to be common industrial glass since it can be
ordered from virtually any window or artwork framing shop with a price comparable
to common plate glass. Because the corrector has a somewhat smaller aperture than the
primary mirror and bends light outward, this configuration always has a larger system
focal ratio than that of the primary. As a result, the complete optical system
has a focal ratio of F/1.9. The corrector diameter is 80.6% of the primary diameter,
higher than standard 70% designs. This design offers 33% more light gathering.
Further, the corrector is complemented by a lensless configuration with a small
aperture stop, see below.
The first pic above shows the optical configuration. The second two pics are
tricolor OsloLT (ref. 3, 4) simulated spot diagrams for the "standard" 86.6%
and an "improved" 50% neutral zone (respectively) I originally selected for
the present instrument - a "rich field" Schmidt camera. I found a bug in
my simulation software (ref. 5 for debugged version), and when this was fixed,
I got the spot diagram shown in the last pic to the right which uses the
classical 86.6% neutral zone. Spots are now well under 50 microns from 340 to
900 nm (i.e., full UBVRI spectrum). This is a larger spectral range than usually
shown in spot diagrams, so spots will be a bit larger. I came to an interesting
observation. The bug in my software was calculating the curve using corrector
diameter instead of radius, so the result was just a smooth, roughly hyperbolic
curve without the steep depression around the neutral zone near the edge. It looks
like one can just as well use a rather simple convex curve and still easily get
within a 25 micron photographic criterion across most or all of the field and spectrum.
I found an optics textbook in the Berkeley (California) City Library (ref. 7) that
mentioned that a Schmidt corrector need not be terribly precise in terms of the exact
shape of the curve. As a result, molding from metal or plastic forms is sufficient,
even for some precision medical instruments. While this is design criteria dependent,
there seems to be some truth to this general statement. This fact is exploited in
the construction of the present corrector, and a simple manufacturing process for
generating and polishing a higher order corrector surface is presented.
The image surface is convex glass ground to one half ROC of primary. In the
present configuration, with the curve obtained after fixing the bug, the system
approaches the diffraction limit for most UBVRI wavelengths (again, last pic above)
at optimal polychromatic focus. I once estimated that if built within specifications,
this system will capture in excess of 6 degrees of field of up to 14-15th magnitude
stars in 60-120 second exposures on 3200 B&W film! This system is a prototype for
two considerably larger cameras, a 500 mm single-mirror camera and a multi-mirror
array camera of 1.2 meter mirrors. I now have the glass, but am still testing some
different prototypes prior to any grinding. There is also some experimenting going
on regarding sag of large aperture correctors.
2. Design and equations
Much of the design learning can be had from one book, called "Telescope Optics"
(ref. 8). I recommend reading this.
2.1 Atmospheric scintillation considerations
One further matter I wanted to resolve was building a system
fast enough to outpace atmospheric scintillation (i.e., moving shadows).
Scintillation is caused by particulate matter in the upper atmosphere
moving around and causing stellar photons to stray from their direct
route to the ground due to reflection and refraction as well as absorbance.
This is particularly problematic for high speed photometry, like measurement
of stellar scintillation. There is a rather thorough set of 3 recent publications
on this topic with relevance to telescope design and high speed
photometry that offers some glimmer of hope in subtracting atmospheric
effects from stellar scintillation (ref. 9-11a). I would really like to
get some info on S values (scintillation factor) for Sweden if anyone
has them. Approximations would be OK. I would like to know what is mean,
minimum and maximum S, nightly and seasonal fluctuation as well as particle
size, velocity, absorbance and refractive properties. I would imagine
the intensity is wavelength specific. I have
this idea of high speed imaging that is capable of defeating the
effects of atmospheric scintillation. With enough info, I might
be able to configure the present system specifically to
accomplish this. It is widely accepted dogma that there is an optimal
magnification and aperature combination for a given level of atmospheric
scintillation, for instance. The present instrument is the fastest thing
I have ever built that will have any magnification to speak of (the 0.5
meter scope and the 1.2 meter array should both exceed this
someday). I could envisage changing the design or even using adaptive
optics to compensate for atmospheric turbulence. Come to think of it,
is this turbulence, or perhaps, sometimes really atmospheric laminar
flow? I wonder if there is a Reynold's number for this. It would also be
nice to get a hint how high elevation I would need to escape most
of this. I am concerned that Mount Everest isn't high enough. Lacking a
space-bound option, mere mortals such as myself will need creative
sampling techniques. For now, it looks like some sampling will be done
at 100 Hz, after discussions with Terry Galloway over in Berkeley.
2.2 Lensless Schmidt configuration
Above are spot diagrams for 250 and 125 mm aperture stops, 100% and 50%
of full aperture, respectively, for a system with the corrector omitted.
No originality here! Bernhard Schmidt is quoted as having stated back in
the 1930's that a functional camera (he never called it a Schmidt camera
himself) could be built without obligatory requirement for the corrector
plate if a sufficiently high focal ratio is used (by means of an aperture
stop). Since starting this project, I have found a published example of
such a telescope which has been used with great success (ref. 12). I have yet to see Schmidt's
comment in print. The only paper I possess written by Schmidt does not mention this (ref. 13),
but I'll hold Schmidt to his (alleged) word. I am going to test this lensless configuration
first, since the corrector doesn't need to be completed to do so. The primary is in the final
polishing stages. At this focal ratio, I don't even need an aluminized surface to do such a
test. The advantage this configuration offers over a Newtonian rests in the very wide field.
The Newt suffers from coma, which is a lateral aberration, increasing exponentially with
increased field. Without a corrector, the Schmidt design suffers from spherical aberration; an
axial phenomenon that can be adjusted simply by selecting an aperture stop that meets
performance criteria for a particular application. I estimate the present system will satisfy
a 25 micron photographic criteria up to several degress of field without the corrector with an
aperture stop radius of about 75-100 mm, and possibly more. This should still easily handle
13th magnitude stars within 1-2 minutes on 3200 film. Quite acceptable!
2.3 Corrector design - classic Schmidt
One needs to first solve for the deviations in thickness as a function of radius
for the corrector (the "Schmidt" curve). The present design places the (relatively)
flat side facing the stars, and the Schmidt curve facing the primary mirror.
The Schmidt curve presented here is calculated using the measured refractive index for
Optiwhite glass in green light (540 nm, n = 1.5211, see ref. 14). The refractive index
for this glass is much in line with that of common soda plate glass (ref. 15,16). It
can be seen from the simulations that the spot sizes for different wavelengths are
not exactly linear as function of wavelength. In other words, one would not simply
decide on what range of wavelengths are desired and choose the refractive
index of the median wavelength to calculate the curve. My simulations indicate
that spots increase in size exponentially with increasing wavelength. Thus, if
one wishes to have spots of similar small size, it might be optimal to use a refractive
index for a higher wavelength (i.e., more red) than the median wavelength for these
calculations. I'll plot spot size as a function of wavelength and refractive
index sometime, once I get the Siedel coefficients for this working as I want. Two
questions I have been asked, that I do not yet have an answer to is how homogeneous
is optiwhite and is there wedge and how much do these parameters affect performance.
The homogeneity issue likely depends on the source and specific production run. The
wedge effect could be calculated. There is slight variance in the thickness of this
glass, on the order of a couple tens of microns, at most. I do not know how to make
this calculation with Oslo and have not had time to manually calculate this. I have
no idea if optical glass would be any better in this regard. My 11.5" Mak corrector
plate (fine annealed BK-7) came to me with considerable wedge.
The first pic above, taken through a 40 cm length of the "optiwhite" corrector glass
sitting on top of common plate glass of similar length, demonstrates the reduced
green color due to low iron content. The second pic shows the transmission curve from 200
to 800 nm (accurate to 3rd decimal) by spectrophotometry compared to plate glass of same
thickness and a very thin (0.4 mm) piece of fine polished borosilicate (microscope cover
slip). This indicates that about 20% of axial light (visible) is reflected, since we do
not expect much absorbance from such a thin piece of glass. The third pic is a plot of
refractive index as a function of wavelength obtained by TIR refractometer from data in
ref. 14 (accurate to 5th decimal). The last picture is the result of my effort at
simulating the optimal
Schmidt curve for this system; some C source code to solve for the 2nd, 4th and 6th
polynomial terms and then write data to file along with a configuration file for Gnuplot
(ref. 16b) to plot the result to PS and PBM formats. See reference 6 for my source code.
The code can be edited directly for any specific design, details at the top of the file.
There are a few equations around, which may or may
not be polynomial. For my F/1.1, I solved a non-polynomial equation system for variation
in thickness and ran some Matlab code to fit the data points to a polynomial function. The
reason to do this is
partly for the purpose of entering the shape of the corrector into simulation
software (which usually expects polynomial coefficients, as I have learned). The
first three (even exponents) polynomial coefficients are probably sufficient for
most Schmidts, but I suspect that for very fast systems, perhaps the present
instrument, even more terms may be needed for optimal performance. Note that for
the F/1.1 I used a 9th order polynomial fit. In a nutshell, we need to solve the
following higher order polynomial, which ignores terms for the odd-numbered
exponents:
z[r] = Ar^2 + Br^4 + Cr^6 (Eq. 2.3.1)
where z[r], the deviation in thickness relative the axial thickness, z[0], is a function of r, the
radius. If one adds the axial thickness to this equation, the following equation describing the
thickness, T, at any point along the radius is obtained:
T[r] = z[0] + Ar^2 + Br^4 + Cr^6 (Eq. 2.3.2)
The A, B and C coefficients are each somewhat complicated equations. I'll get to
these after a few more lines. As I will demonstrate, solution of this equation is
useful not only so you can see what is possible when the coefficients
are entered into simulation software. It can been used to determine a deformation
to be used for polishing by slightly warping the corrector. After releasing the lens, it magically springs into the correct shape. Keep in
mind computers with parallel ports and precision stepper motors and drivers were not available to Schmidt.
Rather early
on I reasoned that solving for z(r) could be used to solve an equation that could be written into software to
control a stepper motor driven grinding/polishing machine to generate a very close approximation of the intended
curve by use of this equation:
t[r] = 2 * pi * r * (z[0] - z[r]). (Eq. 2.3.3)
That is, the relative amount of grinding/polishing
time, t, at a given r, is just the difference in
thickness relative that on axis, z[0], times the perimeter
for that particular distance from the axis. It should be a
piece of cake to drive a stepper motor via the parallel port,
for instance, to generate the curve, regardless of how
complex the optimal design curve ends up. That is, the computer
could in principle be programmed to control the motions of a
motor consistent with a 9th order curve if that is what one
wishes to obtain. I am tired of typing, so here comes the
scribble scrabble. This is the exact solution to the Schmidt
curve to the 6th exponent. If you're in the mood for a major
headache, feel free to try and derive this (see ref. 8):
3. Cutting, grinding and polishing
3.1 Primary mirror
The above pics are: 1) the jig showing how the tool is suspended, 2) concrete
grinding tool with tiles mounted over surface, 3) closeup indicating
just how crude the edges can be and still result in a flawless mirror,
4) bee's wax "sheets" as I purchase them. These are US 8.5x11" and not
European A4 which the wax is laying on in the pic (cue to giggle), 5) closeup
showing the hex patterns that bees use as foundation to build a new hive,
6) concrete polishing tool with a roughly 5 mm layer of bee's wax and
7) primary mirror sitting on the polishing tool (note how very slumped this
beast actually is. Just imagine getting this down to 20th wave rms!!!).
I made a couple observations about bee's wax. As near as I can tell, the
bee's wax works out to be about 3 times cheaper than Gugolz pitch. It is
also a lot easier to get ahold of. While the Gugolz folks down in Switzerland
would quite possibly commit suicide before they'd sell you a single canister
of their precious conifer pitch, Swedish bee farmers have thus far seemed
very pleased to find a new outlet for the fruits of their bee's labor. In
terms of handling, wax versus pitch is a tossup. I was able to slowly warm
up the wax inside the house on the stove without much fumes. What smell is
given off is not very offensive, and some folks might even find it pleasant.
If it is boiled, which is unnecessary, the fumes will require that heating be
done outdoors. Pitch simply must be heated outdoors and the fumes never smell
very good. Hot bee's wax pours like water. The rim for pouring onto the
concrete needs to be watertight. If it leaks water, it will leak melted wax.
The wax hardens rather quickly, so one needs to remove the rim quickly and
start working the wax almost immediately after pouring. It was a tad
difficult to get the curve into the tool due to the deep sagitta of the
primary mirror. I ended up with a very simple solution. I litterally painted
the melted wax onto the tool with a paint brush as needed to get a
reasonably convex surface. I made this tool when I got to #400 grit. I
ground the polishing tool with #400 grit. I next poured, then painted, more
wax over the surface. I went on to #600 and #1000 SiC. In terms of polishing,
bee's wax takes a little time to get
used to because the fresh wax tend to peel as it is worked. I am presently in the polishing stages with
the primary. I have discovered that furniture clamps are very handy for pressing mirror and tool together
to get optimal contact. This works best with a little warming. However, if the wax actually gets close to
the melting point, the two surfaces will fuse. The same furniture clamps can be used sideways to pry the
two surfaces apart. In one case this was successful and I went on my way polishing. In another case, the
tool was destroyed and there was a lot of wax caked onto the mirror. I scraped this away with a piece of
wood, wiped it clean with nafta and poured a new tool. A couple hours later I was polishing again, no big deal.
And this is the great advantage to bee's wax. It is so cheap that you start from the initial order buying a
lot more than you actually need and have plenty extra for such mishaps.
I found pouring to lead to some problems. I now use a paint brush to
paint a thin layer a couple mm thick on top of the grinding tool. This
has many advantages. First it forces the wax to conform to the desired
shape. Second, an inherent artefact, brush strokes, provides for channels.
3.2 Corrector
The concept I have developed and used here does not require any
kind of vacuum deformation of the corrector. I have programmed a
PC to drive a marble over the surface of the corrector by means
of the parallel port and a stepper motor. Across a 400 mm section
of the corrector, before I cut it to size, I estimated there was
about 10-15 microns variance in thickness. I decided to start with
#400 SiC, as this should be quite adequate to quickly remove this much
error. The tool was an iron plate for the flat (shall we say flatter?)
side. The depression at the neutral zone (86.6% radius in this case)
is the deepest region of any Schmidt corrector. It is 75 microns deep
in this design, a tad more than I want to risk with vacuum
deformation. This is perhaps a good reason to test my stepper motor
and marble technique (ref. 19 for my grinding software). Glaverbel, which
manufactures Optiwhite, somehow sent my local distributor what we thought was
the incorrect glass, having a faint turquoise color. I waited over 2 months
for the local distributor to receive another shipment. The new shipment
also had a faint turquoise color. The sample glass in the local glass
shop originating from Glaverbel was completely clear. An interesting
point emerged. There is no formal definition for optiwhite and this
glass varies considerably between batches, so anything with reduced
iron content can be called "optiwhite". While I am certain it really
is within the technical means of Glaverbel to actually produce a
colorless glass, I really did not feel like waiting yet another 2
months to find out. I went ahead and used the slightly colored glass.
3.3 Image surface and film holder
The image surface is curved, with an ROC of 480.5 mm; one half that of the primary
mirror. The entire focused beam has a cross-sectional diameter a bit more than
36 mm, so 35 mm film (measures about 35x24 mm) will capture most of the field. I
recommend beer bottles to make this, but before you shop'n guzzle a six-pack, go
for the largest bottoms you can find (I mean the beer bottle bottoms, right?)!
Bishop's Fingers is quite large and tastes pretty good. Alternatively,
Hobbgoblins or Fidler's Elbows are quite suitable in both respects. These
all have decent curves already provided, compliments the bottle manufacturer.
For the hard core drinkers, Black Death Tequila or Absolut Vodka bottles
will more than work fine, remembering that drinking and working glass don't
mix. To break out the bottoms, I wrap tape around the bottom and hit the
side with a hammer. This is followed by a bit of grinding on a concrete tool.
I recommend not polishing this surface. Leaving the surface slightly coarse,
around 600 grit, is useful for focusing without exposing any film.
I am not holding the film in place with either adhesives or vacuum; see
the picture above. Since I need a tool to grind the image surface, I decided I
may as well use that as a clamp to press the film down. Both the image
surface and the tool (now a clamp), are larger than than the image itself.
The clamp has a 38 mm hole drilled through it to permit
light to go through and hit the film that it presses from its edges
onto the image surface. The two blue objects are spacers about same thickness
as the film.
4. Optical tests
Several types of optical tests were used, or will be used, in the testing of
the present instrument, including ronchi test, star tests, Couder masks, and
sheering interferometry. I hope to someday write about the design details of
each of these. What I can say for now is that my ronchi and interference gratings
are home made, mainly with Polaroid Polagraph B&W slide film and the optical
flat for the interferometer is a 1.25" Newtonian diagonal (BTW, a newton
interferometer typically uses a full aperture flat, expensive!). Mine is cheap
and highly effective, so that's what I use! The point is to measure the
Strehl ratio, which gives an indication of quality of star images as a function
of degrees of field for the specific optic that has been produced which has its
own distinctive mapping of wavefront deformations (briefly described in ref. 17b).
4.1 Primary mirror
Before re-grinding showing more TDE than I will accept:
After re-grinding at 400 grit with very short strokes and working way to polishing with
new painted tool TDE is gone, although replaced by a new central error:
Above are ronchigrams I took very close to ROC manually holding my
webcam up to the grating (100 LPI). The images were obtained by
moving in stepwise increments away from the mirror at approximate
distances from ROC of -10, -5, 0, +5 and +10 mm. The tester has two
adjacent 35 mm frames with grating images. The light source goes
through one frame, reflects from the mirror, and returns through
the second frame about 2 cm beside the source. There is a hole in
the plate that holds up the second grating for the camera to take
a picture (or for an eyeball). This tester uses a 50 Watt Halogen
bulb, which I reason is not overkill because I use etched glass
plates and filters to condition the beam. I got the lines suggested
by these ronchigrams after about 45 minutes of polishing on bee's wax
using MicroAbrasive 2 micron Microgrit CeO. Basically, I got a
sphere, but with unacceptably high amount of TDE (turned down edge).
After some email exchanges with other ATMs indicating TDE was
inevitable with such a short F/ratio, I decided to retrace my steps
and experiment a little, believing I could do better than this, but
perhaps not by polishing. I explored two observations: 1) TDE was caused
by too much glass at the edge being removed relative the rest of the
mirror, and 2) the wax was progressively being pushed out of, rather
than into, proper shape.
I found a remedy for both of these problems. I cut out small triangular
wedges on the edge of the tool such that the result looks like a gear.
I did not want to use a subdiameter lap, reasoning that I still wanted
continuous contact with the edge, but I wanted to reduce the amount of
time spent polishing there; but only a little. This worked very well
until I broke the polishing tool when I used too much (unnecesary) force
to press the surfaces with furniture clamps. Since the lap consistently
and progressively had a tendency to move around as I worked it, and it
was now clear that the amount of TDE I had was not coming out with
polishing before the Sun goes supernova, I decided to go back to 400
grit and work my way back to polishing using very short center-over-center
strokes. When it was time to start polishing, rather than pouring onto
another concrete tool, I tried (literally) painting a thin layer of wax
over the tool and polishing with this. The result was immediately and
clearly superior.
There was very even contact across the entire surface and the
reflectivity was spreading smoothly from the middle out towards the
edge. As seen in the first "after" image above, with tester about 5 mm
towards primary from focus, the TDE is entirely gone now, although the
outer zone is not yet as reflective. Note that the high reflectivity
region is a circle. There is a uniform error near the middle that thus
far seems to be coming out. Note that in the "before" images there is
ring shaped region of poor contact between tool and mirror, which
proves the old polishing tool that was poured and much thicker, never
really broken in. I have not made any effort to measure this exactly
yet. The TDE experiment is done. I am now polishing more and making
more precise measurements.
4.2 System with corrector
No optical test was done on the corrector alone although a spherometer
was used to get the relative difference between axis and neutral zone
prior to fine grinding and polishing. The first test employed here
tests the ronchi interference pattern appearance of the entire optical
system.
The first image above shows the system test setup. The key points to
notice are that the light source is at prime focus on-axis and ronchi
grating is directly in front of this. An image of the ronchi grating
is projected onto the primary mirror and out of the system, through
the corrector plate. From a number of ROCs away from the corrector,
a camera is placed to take a picture of the ronchi pattern for
evaluation of how the path of the photons had been affected by the
corrector plate. Obvisouly, the primary mirror needs to be completely
figured before this test can be meaningful. Through repeated cycles
of polishing and measurements, corrections can be made.
5. Silvering, aluminizing and other coatings
Consider this: fine-polished glass still reflects about, let's say,
10% of the light that strikes its surface. Actually, I suspect more,
but let us say 10%. The following equation can be used to get the
diameter for a mirror with twice as much area, and hence fully
compensates for photons lost to transmission:
Du = 2 * [(Dc/2)^2 * Rc/Ru]^0.5 (Eq. 5.1)
where Du and Dc are diameters of uncoated and coated mirrors, and Ru
and Rc are reflectivity of uncoated and coated surfaces, respectively.
It is noteworthy that in some cases, Ru/Rc is small, and as a
consequence, as little 20% more diameter could give same light
gethering capacity without need of a reflective coating. Given the
log nature of magnitudes, and the fact that aluminizing can be
the most expensive component of the optical construction, especially
as aperture increases, dispensing with it might be more than just
an acceptable alternative. The present mirror has about 3500 times
more area to collect light with than the human eye, so the bare
polished surface without any coating still collects about 350 times
more light (90% is lost) than the human eye. That's a decent number
of magnitudes. It should also be mentioned that even high quality
aluminized and silvered surfaces have residual transmission. There
is a further rationale for not silvering or aluminizing. These
practices deposit thin films of metal over the precision polished
surface. These have varying degrees of precision in thickness across
the surface, meaning there is an inherent departure from the
polished figure as a result of any coating. So what of light
reflecting back from the back side? I am trying just coarse grinding
and black paint. Time will tell how well this works. My first star
tests seem encouraging. If I coat, I will likely go with silver.
6. Film and photography
Stars per pixel or pixels per star? In the present case, it could be
stars per pixel. Consider this: Ray tracing indicates that about
100% of photons from an infinitely distant point source (a star is
pretty infinite) land in an area only 5 microns in diameter. This is
so for all visible light across the entire optical field at full
250mm aperture. The film I have chosen is 35 mm Ilford Delta 3200
B&W print film (ref. 11b), or the 120 version with a projection
lens. The rating of this film indicates it should be about 8 times
faster than conventional Tri-x 400 B&W film. Don't let the high
speed deceive you. The grain size of this particular film is 10
microns, somewhat smaller than conventional films used for
astrophotography. The spectral response of this film remains at a
plateau of about 80% or more of peak response from 380 to 680 nm,
covering most of the UBVRI. It really is upsetting that Ilford
doesn't make something like this in movie reels. I'd sure as heck
buy it! Alternatively, Ilford does make 35 mm film reels of a
400 series.
Perhaps a word is due here regarding CCD imaging. Consider that
this camera has a very large image surface. If one is to capture
the entire image surface, one would need a 2" square CCD. I think
the Kodak photometric KAF1400 2x2" chips are about 70 000 USD
(about 1 million SEK with tax). In addition, to implement this,
one would need a very specialized field flattener that would have
to be custom built. It would be a major innovation for Kodak or
Texas Instruments to come out with convex CCDs. Remember, CCD
detectors are silica based, and perhaps they could be ground and
polished to some geometry other than flat. I won't hold my breath.
I'll use a B&W webcam and grab only a small part of the optical
field on those rare occasions when I must use a CCD. I am
presently working on another solution.
7. Thermal stability
Everyone asks me about this and I am not sure what to make of thermal stability in the
present case. On the one hand, plate glass is not precision annealed, so it is not terribly
homogeneous, suggesting instability. On the other hand, this glass is very thin, meaning it
should equilibrate more quickly. Being so thin, it is lightweight, so motion control should
be far easier than with a traditional 1:6 thickness. I am banking on thin plate glass
equilibrating with ambiant temperature so much better that it will exceed 1:6 thicknes
borosillicate. Amateur astronomers, as opposed to pros, tend to move their scopes from warm
homes to the freezing outdoors, so there is a serious temperature differential. However,
thermal expansion is extremely low for any glass; industrial or optical grade. I am more
concerned about precision motion control, particularly tracking, which is easier in the
present case, simply less weight for the stepper motor to push if the mounting is not
perfectly gravity centered. I'll try and think of some cute tests in this regard.
8. Mounting and motion control system
For the mount, I poured a concrete block with the base tilted approximately 30 degrees consistent
with my local latitude of nearly 60 degrees north. This seems like an excellent solution for my
location since the block serves as my polar axis and points nearly vertically. A wooden fork
mount is bolted through a spacer (for a worm), a worm gear and chair bearing into the concrete
mount. I still have some stabilizing to do before I feel this is rock steady. The second pic
above shows a closeup of the clock drive worm and gear purchased from Andy Saulietis of the
ATM list. Third pic above shows the plywood tube on the right and the primary mirror in its
holder for the optical tester on the left. Note that the tube is considerably shorter than
the book shelves in the background; one of the great advantages of a low focal ratio. In the
background to the left is a camera tripod with one of my homemade stand-alone stepper motor
based clock drives. The Schmidt camera also need not be driven by a computer, as I am building
another stand alone stepper motor driver that is tuned from a timer IC and drives the motors
via a Johnson counter and a Darlington array. Mainly, I plan to use the computer, actually, but
this is sometimes faster and easier, not requiring a computer.
For computerization of motion, I will use my usual STP software setup. Basically: the stepper
motors from the stand alone circuit interface with, and get pulse information from, the
parallel port of a PC running any flavor of UNIX. I wanted to run the drive from a Sun, but
this turned out to be a real headache. Sun does not offer much info on how to program via the
parallel port of a Sparc Station other than you cannot get direct access as with Linux on a
PC by directly opening a port and writing bits to it after ioperm. One has to go through Sun's
proprietary drivers BPPIOC_SETOUTPINS and/or BPPIOC_SETPARMS ioctl for which they offer no
example code. If anyone knows how to write such code, I would really appreciate an example. I
am looking into replacing the SunOS with Linux to get direct access, and some other reasons.
My STP software, which presently runs on a PC, drives the motors using coordinates from Xephem
ephemeris software. Importantly, STP was
designed to run autonomously over a radio network and is happy working side-by-side with
AX.25 ham radio (data mode) using TCP/IP protocol. In essence, the scope can be on a
mountain top, or some other cold place, like Marsta, Sweden, or even Mars, and the user can
be sunbathing on Santa Monica beach sitting behind a computer choosing what part of the sky
to image. Obviously, this is not compatible with photographic imaging. Just wait till you see
the digital imaging system I worked out for this! I still do not have an FTP site for my
software, but I am slowly submitting it to Image Reduction and Analysis Facility (IRAF, ref. 12).
The main packages are STP, PMTI and PRISM.
9. Real application: photographic tests and evaluation
9.1 Lensless configuration
9.1.1. Rainbow and other wierd optical effects
I have gotten rainbow. It really is not hard to get with such a
mirror. When properly aligned, a collimated Schmidt camera
behaves as it should, with all wavelengths converging at the same
point. However, when misaligned, the mirror begins to act more
and more like a prism, placing different wavelengths at different
off-axis coordinates. My first experience with this was when I
made my first Schmidt and immediately after 15 minutes of
polishing, when the mirror surface was looking just barely
reflective when dry, I rushed out to take a look at a reflection
of the Moon. I just propped the mirror up and stuck my eye into
the optical path. Obviously, there would be substantial
instability in this case and a lot of tilt. What was seen was a
grey Moon with a blue semi-disk on one side and a red semi-disk
on the other side running along the radius. It is an interesting
effect to look at, seeing the Moon in a couple of different
segregated colors. Once the fun is over, careful alignment
eliminates this problem.
9.1.2 Photographs in lensless configuration
The pics above indicates the remarkable quality of this camera system without
any corrector plate whatsoever. The first pic is Orion, and I believe the Orion
officienados will agree these came out spectacular!
Current dogma states that the
Newtonian telescope is the "simplest telescope to construct" and this is what
virtually every newby first
attempts. Given that the lensless Schmidt has only one optical surface, and this is
spherical (the easiest of all optical surfaces to produce and test), this design is
much simpler than a Newtonian. Much could be said about the natural baffling of this
system as well, given that the tube is at least as long as the ROC of the primary. A
typical newt tube would only extend perhaps 10-20% beyond the focal point.
9.2 System with corrector
Above is a series of pictures taken with the corrector. Compare these to the ones above
in the lensless configuration
9.3 System evaluation
10. Concluding remarks
Thus far, I find no reason not to use plate glass for either a primary mirror, even in this
extreme case, or for a corrector, albiet, colorless low iron glass should be used. Bee's wax
has provem acceptable as a polishing substrate with the proviso that it takes some
getting used to. There are a number of other interesting substrates that I have considered,
such as shellac and polyurethane.
11. References and Links (I don't have all as PDFs, so use ref. 28 for those articles):
- 1. Johnson, H.L. Interstellar extinction in the galaxy. Ap. J. 923-42. 1965
- 2. Paper on 13 color Johnson series
- 3. Glaverbel - Belgian manufacturer of Optiwhite
- 4. OsloLT Optical design software
- 5. Len file from Oslo-edu (Linux Slackware kernel 2.6.19, KDE3.5), last checked 16 Mar 2008
- 6. C source code for determining all 3 polynomial coefficients for Schmidt curve + gnuplot output
- 7. General Optics, Berkeley.
- 8. Telescope Optics: Design and Evaluation. Willman Bell Publishers
- 9. Dravins, D., Lindegren, L., Mezey, E., Young, A.T. Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties. PASP. 173-207. 1997.
- 10. Dravins, D., Lindegren, L., Mezey, E., Young, A.T. Atmospheric intensity scintillation of stars. II. Dependence on optical wavelength. PASP. (109)725-737. 1997.
- 11. Dravins, D., Lindegren, L., Mezey, E., Young, A.T. Atmospheric intensity scintillation of stars. III. Effects for different telescope apertures. PASP. (110)610-633. 1998.
- 11a. Dravins, D., Lindegren, L., Mezey, E., Young, A.T. Erratum. PASP. (110)610-633. 1998.
- 12. Fawdon, P., Gavin, M. A lensless Schmidt camera. J. Br. Astron. Assoc. 99(6):292-95. 1989
- 13. Schmidt, B. Zentral Zeitung fur optik und mechanik, 52 Jahrgang Heft 2; Mitt. d. Hamb. Sternw. in Bergedorf, 7, 15, 1931-32 (No. 36). English translation by Mayall. 1946.
- 14. Refractive index data for "Optiwhite" low iron plate glass
- 15. Anthony Stillman's table of plate glass refractive indexes
- 16. More info on plate glass refractive index
- 16b. GNU Project & Free Software Foundation
- 17. Polaroid website about Polagraph HC B&W slides and autodeveloper (need new link)
- 18. 100 LPI grating image (add image)
- 19. C source code to drive grinder
- 20. Ilford Films
- 21. IRAF - Image reduction and Analysis Facility
- 22. Biredskapsfabriken i Toreboda (Sweden). Tel:Int+46-0506-10273, Fax:Int+46-0506-10004
- 23. Dave Rowe on Schmidt math
- 24. ATM page info on making/testing Schmidt correctors
- 25. Short explanation of Strehl ratio
- 26. Willstrop, R.V. A simplified null test for a Schmidt camera aspheric corrector. Mon. Not. R. astr. Soc. 192. P455-66. 1980
- 28. NASA ADS Astronomy Archives, download above article here
Dominic-Luc Webb dlwebb@canit.se
http://www.canit.se/dlwebb/catadioptric/310schmidt/310schmidt.html