Abstract

Two methods are described for testing cameras and camera lenses by utilizing the properties of the crossed cylinder lens, an ophthalmic test device. In the first, the cylinder lens is used in conjunction with a rectangular grid to defocus the star image formed by a collimator. This test permits quantitative determination of axial chromatic aberration, spherical aberration and its variations with wavelength, and coma of the lens. In the second, a segment of the cylinder lens is used as a supplementary lens attachment to the camera, which photographs a polar coordinate chart. Analysis of the photograph permits determination of the sagittal and tangential field curvatures, and also indicates errors in focal adjustment and misalignment of film plane with respect to the lens axis. Since these tests require cylinder lenses of smaller dioptric power and quality superior to that available from the ophthalmic lens industry, methods for the construction and synthesis of large-aperture, weak, cross cylinder lenses and segments thereof are given. Experimental details of the lens testing procedures, together with examples of photographic determination of the various camera and lens defects, are presented. A sensitive test for lateral chromatic aberration is included in an appendix.

© 1968 Optical Society of America

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References

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  1. J. Flügge, Die wissenschaftliche und angewandte Photographie, Das photographische Objektiv (Springer-Verlag, Vienna, 1955), Chapter 11, Vol. 1.
    [CrossRef]
  2. A. König, H. Köhler, Die Fernrohre und Entfernungsmesser, (Springer-Verlag, Berlin, 1959), Secs. 39 and 40.
  3. H. Osterberg, Optical Design, Military Standardization Handbook MIL–HDBK–141 (Standardization Division, Defense Supply Agency, Washington, D. C., 1962), Sees. 24 and 25.
  4. C. D. Reid, Photogr. Sci. Eng. 10, 241 (1966).
  5. K. Mütze, L. Fortzik, W. Krug, G. Schreiber, ABC der Optik (Verlag Werner Dausien, Hanau/Main, 1961), entry under Objectivprüfung, pp. 604–609.
  6. I. M. Borish, Clinical Refraction (The Professional Press, Chicago, 1954).
  7. G. A. Boutry, Instrumental Optics (Hilger and Watts, Ltd., London, 1961), p. 29.
  8. Ref. 7, Chap. 12.
  9. H. Naumann, Optik für Konstrukteure, (Wilhelm Knapp Verlag, Düsseldorf, 1960).
  10. A. E. Conrady, Applied Optics and Optical Design (Dover Publications, New York, 1957), p. 116.
  11. F. S. Washer, J. Res. Nat. Bur. Stand. 61, 31 (1958).
    [CrossRef]
  12. W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, Inc., New York, 1964), p. 107.
  13. Marilyn Levy, Photog. Sci. Eng. 11, 46 (1967).
  14. John Strong, Concepts in Classical Optics (W. H. Freeman and Co., Inc., San Francisco, 1958), Sec. 14–6.
  15. Ref. 5, entry under Dispersionsprismen, p. 188.
  16. A. E. H. Love, A Treatise on Mathematical Elasticity (Dover Publications, New York, 1944), p. 471.
  17. S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Chap. 2.

1967

Marilyn Levy, Photog. Sci. Eng. 11, 46 (1967).

1966

C. D. Reid, Photogr. Sci. Eng. 10, 241 (1966).

1958

F. S. Washer, J. Res. Nat. Bur. Stand. 61, 31 (1958).
[CrossRef]

Borish, I. M.

I. M. Borish, Clinical Refraction (The Professional Press, Chicago, 1954).

Boutry, G. A.

G. A. Boutry, Instrumental Optics (Hilger and Watts, Ltd., London, 1961), p. 29.

Brouwer, W.

W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, Inc., New York, 1964), p. 107.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover Publications, New York, 1957), p. 116.

Flügge, J.

J. Flügge, Die wissenschaftliche und angewandte Photographie, Das photographische Objektiv (Springer-Verlag, Vienna, 1955), Chapter 11, Vol. 1.
[CrossRef]

Fortzik, L.

K. Mütze, L. Fortzik, W. Krug, G. Schreiber, ABC der Optik (Verlag Werner Dausien, Hanau/Main, 1961), entry under Objectivprüfung, pp. 604–609.

Köhler, H.

A. König, H. Köhler, Die Fernrohre und Entfernungsmesser, (Springer-Verlag, Berlin, 1959), Secs. 39 and 40.

König, A.

A. König, H. Köhler, Die Fernrohre und Entfernungsmesser, (Springer-Verlag, Berlin, 1959), Secs. 39 and 40.

Krug, W.

K. Mütze, L. Fortzik, W. Krug, G. Schreiber, ABC der Optik (Verlag Werner Dausien, Hanau/Main, 1961), entry under Objectivprüfung, pp. 604–609.

Levy, Marilyn

Marilyn Levy, Photog. Sci. Eng. 11, 46 (1967).

Love, A. E. H.

A. E. H. Love, A Treatise on Mathematical Elasticity (Dover Publications, New York, 1944), p. 471.

Mütze, K.

K. Mütze, L. Fortzik, W. Krug, G. Schreiber, ABC der Optik (Verlag Werner Dausien, Hanau/Main, 1961), entry under Objectivprüfung, pp. 604–609.

Naumann, H.

H. Naumann, Optik für Konstrukteure, (Wilhelm Knapp Verlag, Düsseldorf, 1960).

Osterberg, H.

H. Osterberg, Optical Design, Military Standardization Handbook MIL–HDBK–141 (Standardization Division, Defense Supply Agency, Washington, D. C., 1962), Sees. 24 and 25.

Reid, C. D.

C. D. Reid, Photogr. Sci. Eng. 10, 241 (1966).

Schreiber, G.

K. Mütze, L. Fortzik, W. Krug, G. Schreiber, ABC der Optik (Verlag Werner Dausien, Hanau/Main, 1961), entry under Objectivprüfung, pp. 604–609.

Strong, John

John Strong, Concepts in Classical Optics (W. H. Freeman and Co., Inc., San Francisco, 1958), Sec. 14–6.

Timoshenko, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Chap. 2.

Washer, F. S.

F. S. Washer, J. Res. Nat. Bur. Stand. 61, 31 (1958).
[CrossRef]

Woinowsky-Krieger, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Chap. 2.

J. Res. Nat. Bur. Stand.

F. S. Washer, J. Res. Nat. Bur. Stand. 61, 31 (1958).
[CrossRef]

Photog. Sci. Eng.

Marilyn Levy, Photog. Sci. Eng. 11, 46 (1967).

Photogr. Sci. Eng.

C. D. Reid, Photogr. Sci. Eng. 10, 241 (1966).

Other

K. Mütze, L. Fortzik, W. Krug, G. Schreiber, ABC der Optik (Verlag Werner Dausien, Hanau/Main, 1961), entry under Objectivprüfung, pp. 604–609.

I. M. Borish, Clinical Refraction (The Professional Press, Chicago, 1954).

G. A. Boutry, Instrumental Optics (Hilger and Watts, Ltd., London, 1961), p. 29.

Ref. 7, Chap. 12.

H. Naumann, Optik für Konstrukteure, (Wilhelm Knapp Verlag, Düsseldorf, 1960).

A. E. Conrady, Applied Optics and Optical Design (Dover Publications, New York, 1957), p. 116.

W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, Inc., New York, 1964), p. 107.

J. Flügge, Die wissenschaftliche und angewandte Photographie, Das photographische Objektiv (Springer-Verlag, Vienna, 1955), Chapter 11, Vol. 1.
[CrossRef]

A. König, H. Köhler, Die Fernrohre und Entfernungsmesser, (Springer-Verlag, Berlin, 1959), Secs. 39 and 40.

H. Osterberg, Optical Design, Military Standardization Handbook MIL–HDBK–141 (Standardization Division, Defense Supply Agency, Washington, D. C., 1962), Sees. 24 and 25.

John Strong, Concepts in Classical Optics (W. H. Freeman and Co., Inc., San Francisco, 1958), Sec. 14–6.

Ref. 5, entry under Dispersionsprismen, p. 188.

A. E. H. Love, A Treatise on Mathematical Elasticity (Dover Publications, New York, 1944), p. 471.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Chap. 2.

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Figures (19)

Fig. 1
Fig. 1

Arrangement of optical elements of the apparatus for the first test method.

Fig. 2
Fig. 2

Cross sections of the astigmatic bundle showing distortion of the shadow image of the grid caused by shift in focus.

Fig. 3
Fig. 3

Distortion of the image of the grid calculated for pure coma.

Fig. 4
Fig. 4

Collimator test assembly permitting simulation of weak, large-aperture cross cylinder lens. Spacings between elements are adjustable.

Fig. 5
Fig. 5

Results of test of 250-mm telephoto lens for three wavelengths: 6300 Å, 5000 Å, 4480 Å. Shift of focus with wavelength and pronounced spherical aberration at shorter wavelengths are apparent. The grid element spacing is 48 sec of arc.

Fig. 6
Fig. 6

Graph showing combined axial chromatic aberration of 250-mm telephoto lens and collimator lens determined from measurements of parallelogram distortion of the grid.

Fig. 7
Fig. 7

Results of test with bent negative meniscus supplementary lens. The spherical aberration that this lens generates causes the axes of the grid to approximate cubic curves.

Fig. 8
Fig. 8

Test of Maksutov, 500-mm catadioptric lens. The spacing between the elements of the grid is 33 sec of arc.

Fig. 9
Fig. 9

Photograph showing distortion of the grid caused by coma (compare with Fig. 3).

Fig. 10
Fig. 10

Arrangement of apparatus for second test method. The camera photographs a polar chart through a supplementary cylinder lens and slit attachment.

Fig. 11
Fig. 11

Appearance of chart as photographed with supplementary lens attachment: (a) camera focused on chart; (b) camera focused in front of chart; (c) camera focused beyond the plane of the chart.

Fig. 12
Fig. 12

Calculated distortion of the horizontal arm of cruciform pattern caused by different amounts of tangential field curvature.

Fig. 13
Fig. 13

(a) Result of 5° vertical misalignment of the axis of the lens with respect to the film plane. (b) Results of simulated horizontal misalignment of the axis of the lens with respect to the film plane. (c) Test of antique lens having pronounced curvature of field. (d) Test of antique lens exhibiting strong curvature of radial field only. (e) Test of modern lens showing astigmatism. Radial and tangential focal surfaces are curved in opposite directions.

Fig. 14
Fig. 14

Diagram showing vector resolution of spectral dispersions caused by analyzer prism and lateral chromatic aberration.

Fig. 15
Fig. 15

Zenker prism which minimizes distortion of geometrical space.

Fig. 16
Fig. 16

Two square optical glass plates, taped to contain epoxy casting resin, are stressed in torsion by external clamps and internal rubber shims.

Fig. 17
Fig. 17

Test of entire aperture of cylinder lens of new construction. A perfect lens would image the grid without distortion.

Fig. 18
Fig. 18

Comparison of cross cylinder lenses of same dioptric powers and differing constructions: (a) lens of new construction, (b) ophthalmic lens.

Fig. 19
Fig. 19

Epoxy gluing of flat glass disk to a rectangular prism of optical glass deformed by torsion. Flexible couplings minimize bending moments.

Equations (27)

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Δ = F 2 C ,
δ = F 2 C tan ϕ ,
δ = F 2 C cot ϕ .
θ = 2 ϕ + ( π / 2 ) .
τ F ( λ / D ) ,
η = 1.22 F ( λ / A ) ,
x 1 = m x 0 + k ( 3 y 0 2 + x 0 2 ) ,
y 1 = m y 0 + 2 k x 0 y 0 ,
Δ = K t ρ 2 .
cot ϕ = Δ / F 2 C = ( K t / F 2 C ) ρ 2 .
ϕ = θ + ( π / 2 ) ,
tan θ = - ( K t / C F 2 ) ρ 2 .
cot θ = ( K r / C F 2 ) ρ 2 ,
δ - t x .
cot ϕ = y / x .
cot ϕ = ( 1 / F 2 C ) δ ,
y = ( t / F 2 C ) x 2 .
sin ψ = h ρ / v .
θ = - ψ .
sin θ = - h ρ / v .
z = k x y .
α = [ 1 / ( 2 ) 1 2 ] ( x + y ) ,
β = [ 1 / ( 2 ) 1 2 ] ( x - y ) ,
x 2 + y 2 = α 2 + β 2 = r 2 .
z = k x y = ( k / 2 ) [ x 2 + y 2 - ( x - y ) 2 ] ,
z = ( k / 2 ) r 2 - k β 2 .
z = y tan ( x ) .

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