> how does one calculate the max. departure? My sole resource is the
> Telescope Optics Design and Evaluation book.
Actually, if you look a bit more carefuly, it IS in the book (somewhere towards the end, where R&V discuss the design of various instruments). But in short, the Schmidt shape can be approximated by a fourth order curve
y = A*h**2 + B*h**4
where h is height of an input ray. The coefficients A and B are given as
3*D^2 1 A = ---------- , B = - --------- 32(n-1)R^3 4(n-1)R^3
where D and R are, as usual, diameter of the entrance stop (mirror has to be bigger than a corrector), and radius of the mirror (i.e. R=2*F). By varying h from 0 to D/2 you get the points of the corrector shape. n is refractive index of the glass used. I've included a short C program (it should compile and run on ANY machine) to do the calculation for you. It fits the best matching sphere (that is, you should grind in the calculated radius in order to minimize the amount of glass to be removed), and gives the depth and difference between matching sphere and corrector curve as well. Sorry, but dimensions are meant to be in millimeters only.
Bratislav
PS the fourth order is good approximation only for moderate f/ratios. That f/0.8 camera you've been planning needs a bit more than given here !
PPS I assumed BK7 or somesuch for the corrector (n1=0.517 constant in the program represents 1-n )
PPPS this calculation ONLY covers classic Schmidt cameras; for Wright or Schmidt Cassegrain you'll need a different math
PPPPS the shape calculated by this program has the neutral zone at ~86% (for minimal chromatic abberation); it can be modified for different shapes by scaling the coefficient A in the formula. I prefer to have neutral zone at ~70% because such corrector plate is MUCH easier to make, with only marginal penalties of residual chromatism
PPPPPS yes, I DO love to add these Post Scriptums at the end ! :-)
program begins here ------------------------------------------------
#include <stdio.h> #include <math.h>
main () {
double A, B, y; float h, D, D2, F, R, Rs, ys, n1=0.517;
printf("\n\nSchmidt corrector plate calculations\n\n"); printf("Diameter of entrance pupil : "); scanf("%f", &D); printf("Focal length : "); scanf("%f", &F); R = 2.0*F; D2 = D/2; A = 3.0*D*D/(32.0*n1*R*R*R); B = -0.25/(n1*R*R*R); y = (A*D2*D2 + B*D2*D2*D2*D2); Rs = D2*D2/(2*y); printf("\n"); printf(" h y y - Ysph \n" ); printf("\n"); for (h=0; h <= D2; h=h+D2/20) { y = (A*h*h + B*h*h*h*h); ys = h*h/2/Rs; printf("%4.0f %1.6f %1.6f\n", h, y, y-ys); } printf("\n"); printf(" Best matching sphere radius is %7.0f mm (saggita of %1.6f)\n", h*h/(2*y), y); printf(" Focal plane scale is %5.1f mm/deg\n", F/57.3); printf("\n");
}