Abstract

Asymmetric spline surfaces appear useful for the design of high-quality general optical systems (systems without symmetries). A spline influence function defined as the actual surface resulting from a simple perturbation in the spline definition array shows that a subarea is independent of others four or more points away. Optimization methods presented in this paper are used to vary a reflective spline surface near the focal plane of a decentered Schmidt-Cassegrain to reduce rms spot radii by a factor of 3 across the field.

© 1984 Optical Society of America

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References

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  1. T. P. Vogl, A. K. Rigler, B. R. Canty, “Asymmetric Lens Design Using Bicubic Splines: Application to the Color TV Lighthouse,” Appl. Opt. 10, 2513 (1971).
    [CrossRef] [PubMed]
  2. A. K. Rigler, T. P. Vogl, “Spline Functions: An Alternative Representation of Aspheric Surfaces,” Appl. Opt. 10, 1648 (1971).
    [CrossRef] [PubMed]
  3. C. J. de Boor, “Bicubic Spline Interpolation,” Math. Phys. 41, 212 (1962).
  4. R. K. Tyson, D. M. Byrne, “The Effect of Wavefront Sensor Characteristics and Spatiotemporal Coupling on the Correcting Capability of a Deformable Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 228, 21 (1980).
  5. Scientific Calculations, Inc., The ACCOS V Users’ Manual (Scientific Calculations, Fishers, N.Y., 1981).
  6. G. H. Spencer, “A Flexible Automatic Lens Correction Procedure,” Appl. Opt. 2, 1257 (1963).
    [CrossRef]
  7. W. J. Smith, “Image Formation: Geometrical and Physical Optics,” in Handbook of Optics, W. G. Driscoll, W. Vaughan Eds. (McGraw-Hill, New York, 1978).

1980 (1)

R. K. Tyson, D. M. Byrne, “The Effect of Wavefront Sensor Characteristics and Spatiotemporal Coupling on the Correcting Capability of a Deformable Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 228, 21 (1980).

1971 (2)

1963 (1)

1962 (1)

C. J. de Boor, “Bicubic Spline Interpolation,” Math. Phys. 41, 212 (1962).

Byrne, D. M.

R. K. Tyson, D. M. Byrne, “The Effect of Wavefront Sensor Characteristics and Spatiotemporal Coupling on the Correcting Capability of a Deformable Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 228, 21 (1980).

Canty, B. R.

de Boor, C. J.

C. J. de Boor, “Bicubic Spline Interpolation,” Math. Phys. 41, 212 (1962).

Rigler, A. K.

Smith, W. J.

W. J. Smith, “Image Formation: Geometrical and Physical Optics,” in Handbook of Optics, W. G. Driscoll, W. Vaughan Eds. (McGraw-Hill, New York, 1978).

Spencer, G. H.

Tyson, R. K.

R. K. Tyson, D. M. Byrne, “The Effect of Wavefront Sensor Characteristics and Spatiotemporal Coupling on the Correcting Capability of a Deformable Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 228, 21 (1980).

Vogl, T. P.

Appl. Opt. (3)

Math. Phys. (1)

C. J. de Boor, “Bicubic Spline Interpolation,” Math. Phys. 41, 212 (1962).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. K. Tyson, D. M. Byrne, “The Effect of Wavefront Sensor Characteristics and Spatiotemporal Coupling on the Correcting Capability of a Deformable Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 228, 21 (1980).

Other (2)

Scientific Calculations, Inc., The ACCOS V Users’ Manual (Scientific Calculations, Fishers, N.Y., 1981).

W. J. Smith, “Image Formation: Geometrical and Physical Optics,” in Handbook of Optics, W. G. Driscoll, W. Vaughan Eds. (McGraw-Hill, New York, 1978).

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Figures (8)

Fig. 1
Fig. 1

Spline influence function of an asymmetric spline deformed at the central point of an 11 × 11 base array.

Fig. 2
Fig. 2

Profile of the decentered Schmidt-Cassegrain showing the spline surface location.

Fig. 3
Fig. 3

(a) Ray aberration maps (footprints) for the right half of the spline surface; (b) ray distribution of OPD errors.

Fig. 4
Fig. 4

Wave-front aperture map used to select the spline point spacing.

Fig. 5
Fig. 5

Composite spot diagrams before spline surface optimization. Note the difference in scale between individual spots and their spacings.

Fig. 6
Fig. 6

Composite spot diagrams after spline surface optimization.

Fig. 7
Fig. 7

rms wave-front error for image points from the on-axis point to the upper right corner of the image plane of the system with and without a splined surface.

Fig. 8
Fig. 8

Projection of the optimized spline optical surface.

Tables (1)

Tables Icon

Table I Lens Prescription of the Decentered Schmidt-Cassegrain.a

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