Film Slit - Testing Telescope Mirrors - Bill Thomas
(send comments to firstname.lastname@example.org)
The mask is computer scanned for the purpose of accurately measuring the hole pair spacing.
The center hole is used to align the tester with the optical axis. This is done using a ½"
reticle eyepiece. Sharpie dot the center of the mirror to align the mask. Use a level to
align the holes
The reflected slit (0.003" tester slit) images from the holes are recorded on film, which is located
in front or behind the Radius of Curvature - ROC. My exposures are done aft of ROC by about 1.250".
The ray cross each other in back of ROC and the film plane must be some amount aft of
where the two outer zones intersect:
l = (h3n-1 - h3n)/(2R(hn-1 - hn)) + some amount
The processed film is then computer scanned and the distance, Ym between the slit pair's
measured in PhotoShop.
Next Sixtests.exe is fired up in LWT
(Lateral Wire Test) fixed source mode with zone inputs of -Ym/2 (the half below the optical axis).
The film plane should be at right angles to the optical axis. Replace the
film with a plastic mirror, and then project a laser through a hole in the
plastic mirror to the center of the mirror under test. Adjust the film plane
until the second reflection returns to the center of the mirror under test.
Film Slit tester doesn't require as an elaborate tester as the one pictured above.
This tester was constructed for LWT. But due to environmental variations e.g.,
temperature it was impossible to obtain meaningful data. The Film Slit test
solves this problem in that all slit measurements are recorded at the same moment in time.
Slit images (Tmax 400, 30 second exposure. Developed 7 minutes - HC110 Dilution B - 7 parts water to one part stock). The center ray is used to
align the tester to the optical axis. Also check, to be sure that the
center slit image is very nearly equally between the slit pairs.
The full size, undistorted (953 K byte TIFF file) version of this image is available here.
Moving source: yl = (l - s)h/R; Sagitta, s = l - RYm/2h
Fixed source: yl = 2(l - s)h/R; Sagitta, s = l - RYm/4h
R = ROC
h = zone radius
sagitta, s = h2/(2R); //ignores term +h4/(4R3)
X = 3h2/(2R) or 3s
Y = 2h3/R2 or 4hs/R
y = Y/2 or 2hs/R
yl = (l - s)y/(X - s)
For fixed source double yl
yl = (l - s)2sh/R/(3s-s)
yl = (l - s)2sh/(2sR)
yl = (l - s)h/R
sagitta, s = l - Ryl/h
The Film Slit Ym's are fixed source measurements. That is yl = Ym/4 and
Sagitta, s = l - RYm/(4h)
Example (Film_Slit.xls. Besides Excel, there is a free spreadsheet, OpenOffice at http://www.openoffice.org/) is for a 12.5" f 4.7 mirror.
Optical Diameter of the mirror B2
Radius of Curvature C2
The scanned DPI J3
The mask's measured h's C6:C11
The scanned films measured slits Ym J6:K11
Rotate the image (my scanner is most accurate in the direction of scanner travel and in the center):
Enlarge the image greatly. Using the "measure tool" draw a line through the center of a slit image.
On the "Info pallet" adjust the the measure tool "H" so as to be zero. Then drag the measure tool to the center of each
slit image and read off the "Y", proceeding from the top slit to the bottom slit.
The spreadsheet does the differences to get the pixel separation and then divides by the the scanned DPI J3 e.g., 6400 pixels/inch.
Image->Rotate Canvas->Arbitrary dialog box opens "Rotate Canvas" click OK (the angle is already there to level the slits).
At first glance, computed s should be s = l - Ryl/h.
However, l depends on determining the location of ROC (center of the mirror)
which can be difficult, which in turn makes l problematic. The approach (Glen Youman's idea http://www.astrophotos.net/) taken instead,
is to base the computed s on the 94.9% zone as follows:
Ryl/h for each zone, is added to the computed s (h2/(2R) of the 94.9%
zone minus Ryl/h of the 94.9% zone ($D$11+K6 -$K$11, …………, $D$11+K11 -$K$11).
This normalizes all zone to the 94.9% zone. Notice that l is computed to be 1.33804"
(M6-M11). The value of l determined from the measured ROC was 1.3480"
(E24). A 0.010" measurement error of the ROC.
Besides the -yl/2 input (B15 - B20), Sixtests.exe also needs an accurate l This is
accomplished with the Excel's solver (Tools->solver). Cells D15 - D20 contain the
expected -yl/2 as a function of working l (F24). Solver changes working l to minimize
the sum of the weighted (h2) differences (-yl/2 - computed -yl/2) in E21.
working l and light source along with -yl/2 (B15 - B20) are then the inputs to
Sixtests.exe. Notice that the Implied l 1.3380" and Working l 1.336988" are in
very close agreement, differing by only 0.001".
Bills 12.5 inch LWT 8/5/05 film
12.344 3 Mirror, obstruction diameters (mm)
117.3440 Source distance (0=moving source)
y, mm X, mm Y, mm
0.99305 1.336988 -0.022656
1.96375 1.336988 -0.044609
3.39078 1.336988 -0.075234
4.35352 1.336988 -0.094219
5.10625 1.336988 -0.107812
5.85859 1.336988 -0.120312
-1.000 0.0 Conic targets: b, R (mm)
0.0000 Measurement std deviation, mm
116.000 Longitudinal reading bias, mm
© 2005, 2006, & 2007 Bill Thomas