Abstract

The Schmidt camera is particularly advantageous in certain astronomical and spectrographic studies. This paper gives an exact derivation for the equation of the correcting surface, together with some approximations rather more precise than those previously available. Performance of actual instruments made according to the old and new equations will differ significantly if the surfaces are figured with exceptional care.

© 1940 Optical Society of America

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References

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  1. B. Schmidt, Cent.-Zeitg. f. Optik u. Mechanik 52, Heft 2 (1931), or Mitt. Hamburger Sternwarte Bergedorf 7, Nr. 36 (1932).
  2. B. Strömgren, Vierteljahrss. d. Astronom. Ges. 70, 65 (1935).
  3. O. Struve, Astrophys. J. 86, 613 (1937).
    [Crossref]

1937 (1)

O. Struve, Astrophys. J. 86, 613 (1937).
[Crossref]

1935 (1)

B. Strömgren, Vierteljahrss. d. Astronom. Ges. 70, 65 (1935).

1931 (1)

B. Schmidt, Cent.-Zeitg. f. Optik u. Mechanik 52, Heft 2 (1931), or Mitt. Hamburger Sternwarte Bergedorf 7, Nr. 36 (1932).

Schmidt, B.

B. Schmidt, Cent.-Zeitg. f. Optik u. Mechanik 52, Heft 2 (1931), or Mitt. Hamburger Sternwarte Bergedorf 7, Nr. 36 (1932).

Strömgren, B.

B. Strömgren, Vierteljahrss. d. Astronom. Ges. 70, 65 (1935).

Struve, O.

O. Struve, Astrophys. J. 86, 613 (1937).
[Crossref]

Astrophys. J. (1)

O. Struve, Astrophys. J. 86, 613 (1937).
[Crossref]

Cent.-Zeitg. f. Optik u. Mechanik (1)

B. Schmidt, Cent.-Zeitg. f. Optik u. Mechanik 52, Heft 2 (1931), or Mitt. Hamburger Sternwarte Bergedorf 7, Nr. 36 (1932).

Vierteljahrss. d. Astronom. Ges. (1)

B. Strömgren, Vierteljahrss. d. Astronom. Ges. 70, 65 (1935).

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Figures (1)

Fig. 1
Fig. 1

Portion of meridian section through a Schmidt camera. Left shaded region is the transparent correcting plate, right shaded region is the first-surface spherical mirror. For focal ratios of f:1 to f:3, the curvatures of mirror and correcting surfaces will be very much less.

Equations (24)

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x = α h 2 - β h 4 + ,
π 0 = n t 0 + 2 - f ,
P s C = ϕ s . alt. int. s = . F P s C = ϕ s . incidence = reflection.
θ s = 2 ϕ s .             ext. = sum of opp. int. s.
f = L s / cos 2 ϕ s .
f = ( 2 cos ϕ s ) - 1 .
θ = tan - 1 [ sin ϕ / ( cos ϕ - f ) ] .
F P ¯ = ( cos ϕ - f ) / cos tan - 1 [ sin ϕ / ( cos ϕ - f ) ] .
F P ¯ = ( 1 - 2 f cos ϕ + f 2 ) 1 2 .
π = x + n t / cos δ 1 + cos ϕ / cos ( δ 1 + δ 2 ) + ( 1 - 2 f cos ϕ + f 2 ) 1 2 ;
x ( n / cos δ 1 - 1 ) = cos ϕ / cos ( δ 1 + δ 2 ) + ( 1 - 2 f cos ϕ + f 2 ) 1 2 + f - 2 - n t 0 ( 1 - 1 / cos δ 1 ) ,
d x = 2 α h d h - 4 β h 3 d h + .
x s α h s 2 - α h s 2 / 2 α h s 2 / 2.
x 2 x s h 2 / h s 2 - x s h 4 / h s 4 .
x s = ( cos ϕ s + sec ϕ s - 2 ) / ( n - 1 ) .
x s = ϕ s 4 / 4 ( n - 1 ) + ϕ s 6 / 12 ( n - 1 ) + .
( n - 1 ) x ( 1 - 2 f cos ϕ + f 2 ) 1 2 × [ 1 + 1 / ( 1 - f cos 2 ϕ / cos ϕ ) ] + f - 2 ,
θ = tan - 1 [ sin ϕ / ( cos ϕ - f ) ] ,
h s / h e = Y ,
0 h e h s 2 h 2 - h 4 d h = minimum
0 h s ( h s 2 h 2 - h 4 ) d h - h s h e ( h s 2 h 2 - h 4 ) d h = min.
Y = ( 1 2 ) 1 3 = 0.79.
x = 5.86 · 10 - 3 h 2 - 6.25 · 10 - 2 h 4 .
x = 5.903 · 10 - 3 h 2 - 6.302 · 10 - 2 h 4 .