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References

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  1. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957).
  2. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).
  3. J. Macdonald, “New Analytical and Numerical Techniques in Optical Design,” Ph.D. Thesis, U. Reading, Reading, U.K. (1974).
  4. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).
  5. H. H. Hopkins, “Ray Tracing and Calculation of Aberrations for Optical Systems of Rotational Symmetry,” U. Reading, U.K.; personal communication (1983).
  6. CODE V Designer’s Manual (Optical Research Associates, Calif., 1984).
  7. ACCOS V User’s Manual (Scientific Calculations, Inc., New York, 1983).
  8. A. E. Murray, “Reflected Light and Ghosts in Optical Systems,” J. Opt. Soc. Am. 39, 30 (1949).
    [CrossRef]
  9. A. G. Naylor, “Veiling Glare due to Multiple Reflections Between Surfaces,” Can. J. Phys. 48, 2720 (1970).
    [CrossRef]
  10. G. Smith, “Veiling Glare due to Reflections from Component Surfaces: The Paraxial Approximation,” Opt. Acta 18, 815 (1971).
    [CrossRef]

1971 (1)

G. Smith, “Veiling Glare due to Reflections from Component Surfaces: The Paraxial Approximation,” Opt. Acta 18, 815 (1971).
[CrossRef]

1970 (1)

A. G. Naylor, “Veiling Glare due to Multiple Reflections Between Surfaces,” Can. J. Phys. 48, 2720 (1970).
[CrossRef]

1949 (1)

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957).

Hopkins, H. H.

H. H. Hopkins, “Ray Tracing and Calculation of Aberrations for Optical Systems of Rotational Symmetry,” U. Reading, U.K.; personal communication (1983).

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

Macdonald, J.

J. Macdonald, “New Analytical and Numerical Techniques in Optical Design,” Ph.D. Thesis, U. Reading, Reading, U.K. (1974).

Murray, A. E.

Naylor, A. G.

A. G. Naylor, “Veiling Glare due to Multiple Reflections Between Surfaces,” Can. J. Phys. 48, 2720 (1970).
[CrossRef]

Smith, G.

G. Smith, “Veiling Glare due to Reflections from Component Surfaces: The Paraxial Approximation,” Opt. Acta 18, 815 (1971).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).

Can. J. Phys. (1)

A. G. Naylor, “Veiling Glare due to Multiple Reflections Between Surfaces,” Can. J. Phys. 48, 2720 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

G. Smith, “Veiling Glare due to Reflections from Component Surfaces: The Paraxial Approximation,” Opt. Acta 18, 815 (1971).
[CrossRef]

Other (7)

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957).

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).

J. Macdonald, “New Analytical and Numerical Techniques in Optical Design,” Ph.D. Thesis, U. Reading, Reading, U.K. (1974).

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

H. H. Hopkins, “Ray Tracing and Calculation of Aberrations for Optical Systems of Rotational Symmetry,” U. Reading, U.K.; personal communication (1983).

CODE V Designer’s Manual (Optical Research Associates, Calif., 1984).

ACCOS V User’s Manual (Scientific Calculations, Inc., New York, 1983).

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Figures (4)

Fig. 1
Fig. 1

Usual reasons for ray failure: (a) ray misses the surface; (b) ray undergoes total internal reflection; (c) ray meets the surface outside the clear aperture.

Fig. 2
Fig. 2

Ray meets the same surface after refraction.

Fig. 3
Fig. 3

Transfer of the ray P k P ˜ k P k + 1 after refraction at the convex refracting surface.

Fig. 4
Fig. 4

Flow chart for the first part of the transfer check after refraction at the kth refracting surface; the kth surface is convex to the incident ray.

Equations (8)

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X 2 + Y 2 + ( 1 + Q ) Z 2 2 r Z = 0 ,
X ˜ k = X k + L k Δ k , Y ˜ k = Y k + M k Δ k , Z ˜ k = Z k + N k Δ k .
[ L k 2 + M k 2 + ( 1 + Q ) N k 2 ] Δ k 2 2 { N k r [ L k X k + M k Y k + ( 1 + Q ) N k Z k ] } Δ k + [ X k 2 + Y k 2 + ( 1 + Q ) Z k 2 2 r Z k ] = 0 .
F = c [ X k 2 + Y k 2 + ( 1 + Q ) Z k 2 ] 2 Z k , G = N k c [ L k X k + M k Y k + ( 1 + Q ) N k Z k ]
c ( 1 + N k 2 Q ) Δ k 2 2 G Δ k + F = 0 .
Δ k = G c ( 1 + N k 2 Q ) ± { [ G c ( 1 + N k 2 Q ) ] 2 F c ( 1 + N k 2 Q ) } 1 / 2 ;
G c ( 1 + N k 2 Q ) = { [ G c ( 1 + N k 2 Q ) ] 2 F c ( 1 + N k 2 Q ) } 1 / 2 ,
P k P ˜ k = Δ k = 2 G c ( 1 + N k 2 Q ) .

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