Abstract

Artmann formulas were used for determining the influence of total internal reflection on the imaging quality of the reflected beam. The differential equation that describes the meridian of the wavefront corresponding to the totally reflected bundle of rays was derived. It was shown that for the Artmann equations one obtains results very similar to those for the Renard formulas presented in our paper [J. Opt. Soc. Am. A 22, 168 (2005) ], and the difference between the two formulas is not significant for the value of the Strehl definition.

© 2006 Optical Society of America

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References

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  1. A. Miks, J. Novak, and P. Novak, "Influence of total reflection on the imaging quality of optical systems," J. Opt. Soc. Am. A 22, 168-173 (2005).
    [CrossRef]
  2. R. H. Renard, "Total reflection: a new evaluation of the Goos-Hänchen shift," J. Opt. Soc. Am. 54, 1190-1197 (1964).
    [CrossRef]
  3. A. A. Stahlhofen, "Influence of total reflection on the imaging quality of optical systems: comment," J. Opt. Soc. Am. A 23, 146-147 (2006).
    [CrossRef]
  4. K. Artmann, "Berechnung der Seitenversetzung des totalreflektierten Strahles," Ann. Phys. 6, 87-102 (1948).
    [CrossRef]

2006

2005

1964

1948

K. Artmann, "Berechnung der Seitenversetzung des totalreflektierten Strahles," Ann. Phys. 6, 87-102 (1948).
[CrossRef]

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Equations (10)

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d λ 1 = sin ϵ π sin 2 ϵ n 2 = x λ 1 cos ϵ ,
d λ 1 = n 2 sin ϵ ( 1 n 2 ) π ( n 4 cos 2 ϵ + sin 2 ϵ n 2 ) sin 2 ϵ n 2 = x λ 1 cos ϵ ,
d x d p + P ( p ) x + Q ( p ) = 0 ,
P ( p ) = P ( p ) = 1 p ( 1 + p 2 ) , L = λ 1 n 2 π
Q ( p ) = p 2 L n 2 ( 1 + p 2 ) 3 [ p 2 1 + p 2 n 2 ] 3 2 ,
Q ( p ) = p 2 L [ 3 ( p 2 n 2 ) 2 n 4 ( 1 + p 2 ) ] ( p 2 n 2 ) 2 ( 1 + p 2 ) 2 [ p 2 1 + p 2 n 2 ] 3 2 .
A ( p ) = 1 p , B ( p ) = L n 2 p 2 1 + p 2 n 2 ,
A ( p ) = 1 p , B ( p ) = L ( 1 + p 2 ) ( p 2 n 2 ) p 2 1 + p 2 n 2 .
Renard : S D = 0.9985 , S D = 0.9904 ,
Artmann : S D = 0.9985 , S D = 0.9895 .

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