Abstract

A coding error was found in calculating the optimal packing distribution of our geodesic array. The error was corrected and the new optimization results in slightly improved packing density. The overall approach and algorithm remain unchanged.

© 2013 Optical Society of America

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References

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  1. H. S. Son, D. L. Marks, J. Hahn, J. Kim, and D. J. Brady, “Design of a spherical focal surface using close-packed relay optics,” Opt. Express19(17), 16132–16138 (2011).
    [CrossRef] [PubMed]
  2. H. Kenner, Geodesic Math and How to Use It, 2nd ed. (University of California 2003).

2011

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Figures (1)

Fig. 3
Fig. 3

(a) Packing densities as a function of N. Blue line is baseline geodesic, red line is the distorted geodesic with 1st order correction, and black dashed line is the theoretical maximum. (b) Chord ratios as a function of N. Blue line is baseline geodesic and red line is the distorted geodesic with 1st order correction.

Tables (1)

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Table 1 First order distortion coefficient

Equations (3)

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x 1 = x sin ( 72 ° )
y 1 = y + x cos ( 72 ° )
z 1 = ν / 2 + 2 z / ( 1 + 5 )

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