brainwagon

I mentioned that I was searching for my 6″ f/12 that I made years ago. Still have not found it, but I was wondering: how good is a 6″ f/12 sphere? I recall hours of polishing to try to get to a nice, smooth null, but don’t remember if I ever quantitatively figured out how good such a mirror would actually perform. So, I used tex, the same program that I used yesterday to analyze the real test data for a 6″ f/6.4, but instead entered the data for a 6″ f/12. To simulate a perfect sphere, I set all the zones to be zero: all measuring the same. Here’s the output:

	TEXEREAU MIRROR TEST SHEET

           Comments: six inch   Optical diameter: 6
  Readings per zone: 1
Radius of curvature: 144
                f/D: 12.00
   Diffraction disc: 0.000316224

 1 ZONE                1          2          3          4          5      
 2 h(x)              1.3416     1.8974     2.3238     2.6833     3.0000
 3 h(m)              0.6708     1.6195     2.1106     2.5035     2.8416
 4 hm**2/R           0.0031     0.0182     0.0309     0.0435     0.0561
 5 hm/4f             0.0023     0.0056     0.0073     0.0087     0.0099
 6 D1                0.0000     0.0000     0.0000     0.0000     0.0000
 7 D2                0.0000     0.0000     0.0000     0.0000     0.0000
   D3                0.0000     0.0000     0.0000     0.0000     0.0000
 8 D123              0.0000     0.0000     0.0000     0.0000     0.0000
 9 D123 +  0.0423     0.0423     0.0423     0.0423     0.0423     0.0423
10 Lamda c           0.0392     0.0241     0.0114    -0.0012    -0.0137
11 Lamda f * 1e5       9.13      13.56       8.35      -1.04     -13.56
12 Lamda f / rho      0.289      0.429      0.264     -0.033     -0.429
13 u * 1E6            -1.27      -1.88      -1.16       0.14       1.88
14 Wavefront          -1.18      -1.71      -1.69      -1.12       0.00
	Reference parabola: y = -0.288278 * x**2 + 0

Maximum wavefront error = 1 / 12.6 wave at zone 2

Not bad at all. The wavefront error is around 1/13 wave, and the transverse aberrations compared to the Airy disc sizes are all less than one (read from line 12 of the output above). A good null for a 6″ f/12 is indeed a very good telescope: even Texereau would be happy.

What about the classic 6″ f/8? We can do the same experiment here.

	TEXEREAU MIRROR TEST SHEET

           Comments:    Optical diameter: 6
  Readings per zone: 1
Radius of curvature: 96
                f/D:  8.00
   Diffraction disc: 0.000210816

 1 ZONE                1          2          3          4          5      
 2 h(x)              1.3416     1.8974     2.3238     2.6833     3.0000
 3 h(m)              0.6708     1.6195     2.1106     2.5035     2.8416
 4 hm**2/R           0.0047     0.0273     0.0464     0.0653     0.0841
 5 hm/4f             0.0035     0.0084     0.0110     0.0130     0.0148
 6 D1                0.0000     0.0000     0.0000     0.0000     0.0000
 7 D2                0.0000     0.0000     0.0000     0.0000     0.0000
   D3                0.0000     0.0000     0.0000     0.0000     0.0000
 8 D123              0.0000     0.0000     0.0000     0.0000     0.0000
 9 D123 +  0.0635     0.0635     0.0635     0.0635     0.0635     0.0635
10 Lamda c           0.0588     0.0362     0.0171    -0.0018    -0.0206
11 Lamda f * 1e5      20.55      30.51      18.79      -2.34     -30.51
12 Lamda f / rho      0.975      1.447      0.891     -0.111     -1.447
13 u * 1E6            -4.28      -6.36      -3.91       0.49       6.36
14 Wavefront          -3.99      -5.77      -5.69      -3.76       0.00
	Reference parabola: y = -0.972966 * x**2 + 0

Maximum wavefront error = 1 / 3.7 wave at zone 2

As you can see, this would not meet Texereau’s exacting standards. Even at f/8, we need to exert some work to turn it into an excellent performer.

Addendum: I took the source code for Lindner and Phillips’ program, and cleaned it up a bit, and added it to my source repository. You can get the code here. I like that it duplicates the calculations that are done in Texereau’s book, even though it’s not the most sophisticated program in the world.