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Corrections

U. W. Ludwig, "Erratum: Special Ray-Trace Equations for Conic Surfaces," J. Opt. Soc. Am. 62, 303_1-303 (1972)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-62-2-303_1

References

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  1. D. Feder, J. Opt. Soc. Am. 52, 177 (1962).
    [Crossref] [PubMed]
  2. G. Spencer, private communication.

1962 (1)

Feder, D.

Spencer, G.

G. Spencer, private communication.

J. Opt. Soc. Am. (1)

Other (1)

G. Spencer, private communication.

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Figures (1)

Fig. 1
Fig. 1

Ray path from A to B is a real ray path to the second intersection. Ray path from A to C does not exist. Ray path from D to E is a real ray path to the first intersection. Ray path from D to F does not exist.

Equations (15)

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X T = X + i S / N , Y T = Y + j S / N , Z T = Z + k S / N - T H ,
i X T + j Y T + k Z T = 0.
S / N = - [ i X + j Y + k ( Z - T H ) ] / N 2 ,
N 2 = i 2 + j 2 + k 2 .
C [ X s 2 + Y s 2 + ( 1 - K ) Z s 2 ] - 2 Z s = 0 ,
X S = X T + i Q Y S = Y T + j Q Z S = Z T + k Q ,
C [ X T 2 + 2 i Q X T + i 2 Q 2 + Y T 2 + 2 j Q Y T + j 2 Q 2 + ( 1 - K ) ( Z T 2 + 2 k Q Z T + k 2 Q 2 ) ] - 2 Z T - 2 k Q = 0 ,
Q = D / { B + [ sgn of B ( B 2 = A D ) 1 2 ] V } ,
A = C ( N 2 - K M 2 ) ,
B = - C [ i X T + j Y T + ( 1 - K ) k Z T ] + k ,
D = C [ X T 2 + Y T 2 + ( 1 - K ) Z T 2 ] - 2 Z T ,
V = 1 for first intersection V = - 1 for second intersection ,
( i R , j R , k R ) = [ - C X S , - C Y S , 1 - ( 1 - K ) C Z S ] .
S = S + N X T = X T + i Y T = Y T + j Z T = Z T + k .
Q = [ - B - sgn of B ( B 2 - A D ) 1 2 ] / A .