Abstract

In a ray trace calculation of the rms radius of the spot formed in the image plane of an optical system by a point source object, a decision must be made as to how many rays will be traced to obtain the result. As the number of rays is increased, the rms spot radius is generally found to decrease, apparently approaching a definite lower limit as the number of rays becomes very large. This paper examines the question of how many rays must be traced and what their geometrical distribution within the aperture should be to approach the limiting value of the rms spot radius for an infinite number of rays within an accuracy of approximately 1%.

© 1974 Optical Society of America

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References

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  1. J. D. Mangus, J. H. Underwood, Appl. Opt. 8, 95 (1969).
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1969

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Figures (3)

Fig. 1
Fig. 1

Plot of the dimensionless constant α in the relation Γ = α R vs NR.

Fig. 2
Fig. 2

Plot of the rms spot radius Γ in microns vs NR, using data obtained by use of the x-ray telescope ray trace program.

Fig. 3
Fig. 3

Plot of the rms spot radius Γ in microns vs ΔӨ.

Tables (3)

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Table I Values of α in the Relation Γ = αR as a Function of NR, and Percentage Errors Compared with the Limiting Value for NR = ∞

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Table II Values of Γ vs NR with ΔӨ = 10°, Obtained by Use of the X-Ray Telescope Ray Trace Program and Percentage Errors Compared with the Value for NR = 100

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Table III Values of Γ vs ΔӨ with NR = 20. NӨ is the Number of Rays Traced Around Each Ring to Fill Half the Aperture

Equations (4)

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x o = N 1 i = 1 N x i y o = N 1 i = 1 N y i .
Γ = ( N 1 i = 1 N R i 2 ) 1 / 2 ,
Γ = ( o R r 2 d r / o R d r ) 1 / 2 = 3 1 / 2 R .
α = [ ( 2 N R 1 ) / 6 ( N R 1 ) ] 1 / 2 .

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