Abstract

In a recent paper by Lin and Tsai [J. Opt. Soc. Am. A 29, 174 (2012)] there is presented a rather complicated method for derivation of the unit normal vectors of an aspherical surface given the knowledge of the unit directional vectors of the incoming and outgoing rays. In our comment we present a much simpler method that leads to compact equations suitable for practical implementation.

© 2012 Optical Society of America

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References

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  1. P. D. Lin and Ch.-Y. Tsai, “Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays,” J. Opt. Soc. Am. A 29, 174–178 (2012).
    [CrossRef]
  2. M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

2012

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Figures (1)

Fig. 1.
Fig. 1.

Reflection and refraction at the interface between two optical media with different refractive indices.

Equations (10)

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nsinε=nsinε,
n(s×g)=n(s×g),
s=μs+g1μ2[1(gs)2]μg(gs),
s=s2g(gs),
g=ss2(gs).
(gs)=1(ss)2.
g=ss2[1(ss)],
g=sμs1μ2[1(gs)2]μ(gs).
μ(gs)2+ssμ=(gs)1μ2[1(gs)2].
(gs)=|(ss)μ|1+μ22μ(ss).

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