Abstract

Comatic images formed by off-axis rays reflected from a good ellipsoidal mirror were studied experimentally. Horizontal and vertical knife edges were used to chop slices of these images, and the alternating current output of a photo-multiplier tube, proportional to the chopped radiation, was used to indicate the intensity distributions in the comatic images.

Calculations of intensity distributions in comatic images were made, and the experimental observations were predicted from them satisfactorily.

Infra-red detector sensitivity is inversely proportional to the square root of the detector area. Accordingly, the intensity distribution in the comatic image may be used to calculate optimum dimensions for both the exit slit and the detector in an infra-red spectrometer.

© 1950 Optical Society of America

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References

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  1. J. Rud Nielsen, J. Opt. Soc. Am. 39, 59 (1949).
    [Crossref]
  2. M. Born, Optik (Julius Springer Verlag, Berlin, 1933).
    [Crossref]

1949 (1)

Born, M.

M. Born, Optik (Julius Springer Verlag, Berlin, 1933).
[Crossref]

Rud Nielsen, J.

J. Opt. Soc. Am. (1)

Other (1)

M. Born, Optik (Julius Springer Verlag, Berlin, 1933).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Diagram of experimental apparatus.

Fig. 2
Fig. 2

(a) Horizontal slicing; (b) Vertical slicing.

Fig. 3
Fig. 3

The comatic image.

Fig. 4
Fig. 4

Horizontal intensity distribution in the comatic image.

Fig. 5
Fig. 5

Vertical intensity distribution in the comatic image.

Tables (5)

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Table I Experimental data.

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Table II Flux distribution in the X-direction.

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Table III Flux distribution in the Y-direction.

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Table IV Theoretical data (Cf. Table I).

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Table V Comparison of slit lengths.

Equations (17)

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ρ = A ψ h 2 .
I d a ~ d ρ ( d a / 2 π ρ d ρ ) = d a / 2 π ρ ,
I d x d y = B 0 2 π 1 ρ d x d y .
I d x d y = B 0 2 π ( 1 ρ 1 + 1 ρ 2 ) d x d y .
I d x d y = B 0 2 π [ 1 ρ 1 ( 2 cos φ + 1 ) + 1 ρ 2 ( 2 cos θ - 1 ) ] d x d y .
x = 2 ρ 1 + ρ 1 cos φ = 2 ρ 2 - ρ 2 cos θ .
x 3 ρ 0 , 0 φ 120° , cos φ x / ρ 0 - 2 , 0 θ 60° , cos θ 2 - x / ρ 0 .
I d x d y = B 0 2 π [ 2 + cos φ x ( 2 cos φ + 1 ) + 2 - cos θ x ( 2 cos θ - 1 ) ] d x d y .
I x d x = 2 ( B 0 2 π ) [ 2 + cos φ x ( 2 cos φ + 1 ) d y + 2 - cos θ x ( 2 cos θ - 1 ) d y ] d x .
I x d x = B 0 π [ 0 L 2 + cos φ x ( 2 cos φ + 1 ) · J | x y x φ | d φ + L 60° 2 - cos θ x ( 2 cos θ - 1 ) · J | x y x θ | d θ ] d x , I x d x = B 0 d x π [ 0 L 1 2 + cos φ d φ + L 60° 1 2 - cos θ d θ ] , I x d x = B 0 d x π { [ 2 3 arc tan ( 1 3 tan φ 2 ) ] 0 L + [ 2 3 arc tan ( 3 tan θ 2 ) ] L 60° } ,
I d x d y = B 0 2 π [ 1 ρ 1 ( 2 cos φ + 1 ) + 1 ρ 2 ( 2 cos θ - 1 ) ] d x d y .
y = ρ 1 sin φ = ρ 2 sin θ ,
y ρ 0 , 0 φ 120° , sin φ y / ρ 0 , 0 θ 60° , sin θ y / ρ 0 , I d x d y = B 0 2 π [ sin φ y ( 2 cos φ + 1 ) + sin θ y ( 2 cos θ - 1 ) ] d x d y , I y d y = B 0 2 π [ sin φ y ( 2 cos φ + 1 ) d x + sin θ y ( 2 cos θ - 1 ) d x ] d y , I y d y = B 0 d y 2 π [ L L L U sin φ y ( 2 cos φ + 1 ) · J | x y y φ | d φ + L L L U sin θ y ( 2 cos θ - 1 ) · J | x y y θ | d θ ] , I y d y = B 0 d y 2 π [ L L L U d φ sin φ + L L L U d θ sin θ ] , I y d y = B 0 d y 2 π { [ ln tan φ 2 ] L L L U + [ ln tan - θ 2 ] L L L U } ,
0 y / ρ 0 0.05.
ρ 0 = A ψ h 0 2 .
ψ = d / F i ,
A = ρ 0 / ψ h 0 2 .