Design Schmidt–Cassegrain telescope with SYNOPSYS software

The classical Schmidt telescope is a great illustration of the power you obtain when you understand basic optics. That form consists of a spherical mirror and a spherical focal surface, with the stop at the common center of curvature. Since the system is symmetric about that center, there is no unique optical axis anywhere and every field point has the same aberrations.

Correct the spherical aberration, and the system has no off-axis aberrations either. This is a brilliant insight—but you have to correct the spherical aberration first, which is done with a thin aspheric plate located at the common center. You do not obtain perfect correction when you do that, since offaxis beams see the corrector foreshortened, but it is pretty good nonetheless. A serious drawback is the fact that you wind up with a curved image surface, which is tricky to manage with glass photographic plates. Still, this is a classic design form that is widely used in astronomy. It has the drawback that the primary mirror is much larger than the entrance pupil, which is at the corrector, if the field of view is wide, as it usually is

Adding a secondary mirror opens up more possibilities, and the system is then called a Schmidt–Cassegrain telescope. This is a highly corrected form used with a small field. The lens file below gives the input for this example

RLE 
ID CC SCHMIDT CASS ZERNIKE 
  FNAME ’SCT.RLE ’ 
WAVL .6562700 .5875600 .4861300 
  APS 1 
  GLOBAL 
  UNITS INCH 
  OBB 0.000000 0.40800 5.00000 0.00000 0.00000 0.00000 5.00000 
  MARGIN 0.050000 
  BEVEL 0.010000 
    0 AIR 
    1 CV 0.0000000000000 TH 0.25000000 
    1 N1 1.51981155 N2 1.52248493 N3 1.52859442 
    1 GTB S ’K5 ’ 
    1 EFILE EX1 5.050000 5.050000 5.060000 0.000000 
    1 EFILE EX2 5.050000 5.050000 0.000000 
    2 CV 0.0000000000000 TH 20.17115161 AIR 
    2 AIR 
    2 ZERNIKE 5.00000000 0.00000000 0.00000000 
     ZERNIKE 3 -0.00022795 
     ZERNIKE 8 0.00022117 
     ZERNIKE 15 -2.00317788E-07 
     ZERNIKE 24 -3.81789104E-08 
     ZERNIKE 35 -3.47468956E-07 
     ZERNIKE 36 3.76974435E-07 
    2 EFILE EX1 5.050000 5.050000 5.060000 
    3 CAI 1.68000000 0.00000000 0.00000000 
    3 RAD -56.8531404724216 TH -19.92114987 AIR 
    3 AIR

    3 EFILE EX1 5.204230 5.204230 5.214230 0.000000 
    3 EFILE EX2 5.204230 5.204230 0.000000 
    3 EFILE MIRROR 1.250000 
    3 REFLECTOR 
    4 RAD -23.7669696838233 TH 29.18770982 AIR 
    4 CC -1.54408563 
    4 AIR 
    4 EFILE EX1 1.555450 1.555450 1.555450 0.000000 
    4 EFILE EX2 1.545450 1.545450 0.000000 
    4 EFILE MIRROR -0.243545 
    4 REFLECTOR 
    4 TH 29.18770982 
    4 YMT 0.00000000 
     BTH 0.01000000 
    5 CV 0.0000000000000 TH 0.00000000 AIR 
    5 AIR 
END
        

Note how the vignetted rays are identified on the fan plots in PAD in following image. Switch 21 is honored there as well.

On the SPEC listing you see that surfaces 2 and 4 are aspheric, denoted by the ‘O’ after the radius column:

Surface 2 is defined as a Zernike polynomial aspheric. Let us see what that surface looks like. Type

ADEF 2 PLOT        

and you obtain the plot as following:

The black curve shows how the surface departs from the closest-fitting sphere (CFS), which in this case is very close to flat. That tells you how to figure the corrector, once you have generated a surface with the radius of the CFS.

The ray-fan curves in PAD show the system free from coma and spherical aberration, although there is a tiny bit of spherochromatism. The striking thing is the strong field curvature, indicated by the nearly parallel S- and T-fan curves shown below.

A young viewer with a good eyepiece would see a sharp image all over the field, since young eyes can accommodate for the focus shift. Without refocusing, on the other hand, an older viewer would be faced with about 1.5 waves of defocus. Let us see what that would look like over the field.

This time, start at the menu tree (EZ Menus in the top toolbar) and go down to MDI (Diffraction Image Analysis), where you have many choices. Select MPF, near the bottom (or just type MPF in the CW) Select ‘Show visual appearance’ and click ‘Execute’. You obtain the results shown below.

The image at the lower left is the on-axis image, and it is essentially perfect, while the upper right shows the image at the edge of the field. That is not too sharp. Let us examine it in a different format. Back in MPF, select the option to ‘Show as surface’, and change the ‘Height’ from the default 1 to 0.

Indeed, the image at the edge of the field is pretty smeared out, as shown below. Of course, a young observer would see a much sharper image than shown here, since he can adjust the focus of his eyethe focus of his eyes.

You can edit the Zernike terms most easily just by changing the value in the WS, but there is also a dialog that lists them by polynomial, which you can reach from the WS by clicking the ‘Curvature Dialog’ button and following the trail as you did the Aperture dialog above. You arrive at the dialog shown below, where you can change things if you want.

To design this kind of system, vary the Zernike terms with the general-purpose ‘G’ variables. For example, the PANT entry VY 2 G 8 would vary term number 8 on surface 2. The definition of the G terms depends on the current shape definition on the surface.