Abstract

It was found experimentally that, as the relative aperture of the camera lens increases, the lens being substantially “perfect,” the measured value of the resolving power of an emulsion used with it also increases but eventually attains a maximum and then decreases. It is proposed to call this maximum the “maximum lenticular” resolving power of the emulsion. A hypothetical relation is derived for predicting the measured resolving power of a lens-emulsion combination for the maximum lenticular resolving power of the emulsion and the resolving power of the lens on the Rayleigh criterion, assuming the lens to be “perfect.”

© 1951 Optical Society of America

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Corrections

Fred H. Perrin and J. H. Altman, "Errata," J. Opt. Soc. Am. 42, 989_2-989 (1952)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-42-12-989_2

References

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  1. F. H. Perrin and J. H. Altman, J. Opt. Soc. Am. 41, 265 (1951).
    [CrossRef]
  2. F. H. Perrin and H. O. Hoadley, J. Opt. Soc. Am. 38, 1040 (1948).
    [CrossRef]
  3. P. W. Cobb and F. K. Moss, J. Franklin Inst. 205, 831 (1928).
    [CrossRef]
  4. E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. (London) 58, 493 (1946).
    [CrossRef]
  5. L. Foucault, Ann. observ. imp. Paris 5, 197 (1859).
  6. F. E. Washer, Bur. Standards J. Research 22, 729 (1939).
    [CrossRef]
  7. E. W. H. Selwyn, Phot. J. 87B, 34 (1947).
  8. S. M. J. Regnier, Rev. optique 29, 315 (1950).
  9. H. Struve, Ann. Physik u. Chem. 17, 1008 (1882).
    [CrossRef]
  10. G. M. Byram, J. Opt. Soc. Am. 34, 571 (1944).
    [CrossRef]
  11. Rayleigh, Scientific Papers (The University Press, Cambridge, 1899), Vol. I, p. 415.
  12. E. W. H. Selwyn, Proc. Phys. Soc. (London) 55, 286 (1943).
    [CrossRef]
  13. B. E. Mourashkinsky, Phil. Mag. 46, 29 (1923).
    [CrossRef]
  14. R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 40, 143 (1950).
    [CrossRef]
  15. H. W. Zieler, Am. Phot. 30, 553 (1936).
  16. J. M. Gregory, Proc. Phys. Soc. (London) 58, 769 (1946).
    [CrossRef]
  17. W. R. Dawes, Mem. Roy. Astron. Soc. 35, 137 (1867).
  18. C. Lapicque, Rev. optique 17, 297 (1938).
  19. A. E. Conrady, Monthly Notices Roy. Astron. Soc. 79, 575 (1919); Applied Optics and Optical Design (Oxford University Press, London, 1929), pp. 132–135.
  20. C. E. K. Mees, Proc. Roy. Soc. (London) 83A, 10 (1909).
    [CrossRef]
  21. E. Lihotzky, Verhandl deut. physik. Ges. 7, 30 (1926).
  22. E. W. H. Selwyn, Phot. J. 88B, 6 and 46 (1948).
  23. G. Bocchino, Ottica 5, 226 (1940).
  24. A. Couder, Cahiers phys. 3, 35 (1943).
  25. M. Marquet, Sci. Ind. Phot. 18, 129 (1947).
  26. A. H. Katz, J. Opt. Soc. Am. 38, 604 (1948).
    [CrossRef]
  27. L. P. Moroz, J. Tech. Phys. (U.S.S.R.) 14, 251 (1944).
  28. O. Sandvik, J. Opt. Soc. Am. 16, 244 (1928); Phot. J. 68, 313 (1928).
    [CrossRef]
  29. C. E. K. Mees, The Theory of the Photographic Process (Macmillan Company, New York, 1942), first edition, p. 899.
  30. A. Narath, Kinotech. 17, 91 and 107 (1935).

1951 (1)

1950 (2)

R. N. Wolfe and F. C. Eisen, J. Opt. Soc. Am. 40, 143 (1950).
[CrossRef]

S. M. J. Regnier, Rev. optique 29, 315 (1950).

1948 (3)

1947 (2)

M. Marquet, Sci. Ind. Phot. 18, 129 (1947).

E. W. H. Selwyn, Phot. J. 87B, 34 (1947).

1946 (2)

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. (London) 58, 493 (1946).
[CrossRef]

J. M. Gregory, Proc. Phys. Soc. (London) 58, 769 (1946).
[CrossRef]

1944 (2)

L. P. Moroz, J. Tech. Phys. (U.S.S.R.) 14, 251 (1944).

G. M. Byram, J. Opt. Soc. Am. 34, 571 (1944).
[CrossRef]

1943 (2)

E. W. H. Selwyn, Proc. Phys. Soc. (London) 55, 286 (1943).
[CrossRef]

A. Couder, Cahiers phys. 3, 35 (1943).

1940 (1)

G. Bocchino, Ottica 5, 226 (1940).

1939 (1)

F. E. Washer, Bur. Standards J. Research 22, 729 (1939).
[CrossRef]

1938 (1)

C. Lapicque, Rev. optique 17, 297 (1938).

1936 (1)

H. W. Zieler, Am. Phot. 30, 553 (1936).

1935 (1)

A. Narath, Kinotech. 17, 91 and 107 (1935).

1928 (2)

O. Sandvik, J. Opt. Soc. Am. 16, 244 (1928); Phot. J. 68, 313 (1928).
[CrossRef]

P. W. Cobb and F. K. Moss, J. Franklin Inst. 205, 831 (1928).
[CrossRef]

1926 (1)

E. Lihotzky, Verhandl deut. physik. Ges. 7, 30 (1926).

1923 (1)

B. E. Mourashkinsky, Phil. Mag. 46, 29 (1923).
[CrossRef]

1919 (1)

A. E. Conrady, Monthly Notices Roy. Astron. Soc. 79, 575 (1919); Applied Optics and Optical Design (Oxford University Press, London, 1929), pp. 132–135.

1909 (1)

C. E. K. Mees, Proc. Roy. Soc. (London) 83A, 10 (1909).
[CrossRef]

1882 (1)

H. Struve, Ann. Physik u. Chem. 17, 1008 (1882).
[CrossRef]

1867 (1)

W. R. Dawes, Mem. Roy. Astron. Soc. 35, 137 (1867).

1859 (1)

L. Foucault, Ann. observ. imp. Paris 5, 197 (1859).

Altman, J. H.

Bocchino, G.

G. Bocchino, Ottica 5, 226 (1940).

Byram, G. M.

Cobb, P. W.

P. W. Cobb and F. K. Moss, J. Franklin Inst. 205, 831 (1928).
[CrossRef]

Conrady, A. E.

A. E. Conrady, Monthly Notices Roy. Astron. Soc. 79, 575 (1919); Applied Optics and Optical Design (Oxford University Press, London, 1929), pp. 132–135.

Couder, A.

A. Couder, Cahiers phys. 3, 35 (1943).

Dawes, W. R.

W. R. Dawes, Mem. Roy. Astron. Soc. 35, 137 (1867).

Eisen, F. C.

Foucault, L.

L. Foucault, Ann. observ. imp. Paris 5, 197 (1859).

Gregory, J. M.

J. M. Gregory, Proc. Phys. Soc. (London) 58, 769 (1946).
[CrossRef]

Hoadley, H. O.

Katz, A. H.

Lapicque, C.

C. Lapicque, Rev. optique 17, 297 (1938).

Lihotzky, E.

E. Lihotzky, Verhandl deut. physik. Ges. 7, 30 (1926).

Marquet, M.

M. Marquet, Sci. Ind. Phot. 18, 129 (1947).

Mees, C. E. K.

C. E. K. Mees, Proc. Roy. Soc. (London) 83A, 10 (1909).
[CrossRef]

C. E. K. Mees, The Theory of the Photographic Process (Macmillan Company, New York, 1942), first edition, p. 899.

Moroz, L. P.

L. P. Moroz, J. Tech. Phys. (U.S.S.R.) 14, 251 (1944).

Moss, F. K.

P. W. Cobb and F. K. Moss, J. Franklin Inst. 205, 831 (1928).
[CrossRef]

Mourashkinsky, B. E.

B. E. Mourashkinsky, Phil. Mag. 46, 29 (1923).
[CrossRef]

Narath, A.

A. Narath, Kinotech. 17, 91 and 107 (1935).

Perrin, F. H.

Rayleigh,

Rayleigh, Scientific Papers (The University Press, Cambridge, 1899), Vol. I, p. 415.

Regnier, S. M. J.

S. M. J. Regnier, Rev. optique 29, 315 (1950).

Sandvik, O.

O. Sandvik, J. Opt. Soc. Am. 16, 244 (1928); Phot. J. 68, 313 (1928).
[CrossRef]

Selwyn, E. W. H.

E. W. H. Selwyn, Phot. J. 88B, 6 and 46 (1948).

E. W. H. Selwyn, Phot. J. 87B, 34 (1947).

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. (London) 58, 493 (1946).
[CrossRef]

E. W. H. Selwyn, Proc. Phys. Soc. (London) 55, 286 (1943).
[CrossRef]

Struve, H.

H. Struve, Ann. Physik u. Chem. 17, 1008 (1882).
[CrossRef]

Tearle, J. L.

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. (London) 58, 493 (1946).
[CrossRef]

Washer, F. E.

F. E. Washer, Bur. Standards J. Research 22, 729 (1939).
[CrossRef]

Wolfe, R. N.

Zieler, H. W.

H. W. Zieler, Am. Phot. 30, 553 (1936).

Am. Phot. (1)

H. W. Zieler, Am. Phot. 30, 553 (1936).

Ann. observ. imp. Paris (1)

L. Foucault, Ann. observ. imp. Paris 5, 197 (1859).

Ann. Physik u. Chem. (1)

H. Struve, Ann. Physik u. Chem. 17, 1008 (1882).
[CrossRef]

Bur. Standards J. Research (1)

F. E. Washer, Bur. Standards J. Research 22, 729 (1939).
[CrossRef]

Cahiers phys. (1)

A. Couder, Cahiers phys. 3, 35 (1943).

J. Franklin Inst. (1)

P. W. Cobb and F. K. Moss, J. Franklin Inst. 205, 831 (1928).
[CrossRef]

J. Opt. Soc. Am (1)

O. Sandvik, J. Opt. Soc. Am. 16, 244 (1928); Phot. J. 68, 313 (1928).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Tech. Phys. (U.S.S.R.) (1)

L. P. Moroz, J. Tech. Phys. (U.S.S.R.) 14, 251 (1944).

Kinotech. (1)

A. Narath, Kinotech. 17, 91 and 107 (1935).

Mem. Roy. Astron. Soc. (1)

W. R. Dawes, Mem. Roy. Astron. Soc. 35, 137 (1867).

Monthly Notices Roy. Astron. Soc. (1)

A. E. Conrady, Monthly Notices Roy. Astron. Soc. 79, 575 (1919); Applied Optics and Optical Design (Oxford University Press, London, 1929), pp. 132–135.

Ottica (1)

G. Bocchino, Ottica 5, 226 (1940).

Phil. Mag. (1)

B. E. Mourashkinsky, Phil. Mag. 46, 29 (1923).
[CrossRef]

Phot. J. (2)

E. W. H. Selwyn, Phot. J. 87B, 34 (1947).

E. W. H. Selwyn, Phot. J. 88B, 6 and 46 (1948).

Proc. Phys. Soc. (London) (3)

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. (London) 58, 493 (1946).
[CrossRef]

E. W. H. Selwyn, Proc. Phys. Soc. (London) 55, 286 (1943).
[CrossRef]

J. M. Gregory, Proc. Phys. Soc. (London) 58, 769 (1946).
[CrossRef]

Proc. Roy. Soc. (London) (1)

C. E. K. Mees, Proc. Roy. Soc. (London) 83A, 10 (1909).
[CrossRef]

Rev. optique (2)

C. Lapicque, Rev. optique 17, 297 (1938).

S. M. J. Regnier, Rev. optique 29, 315 (1950).

Sci. Ind. Phot. (1)

M. Marquet, Sci. Ind. Phot. 18, 129 (1947).

Verhandl deut. physik. Ges. (1)

E. Lihotzky, Verhandl deut. physik. Ges. 7, 30 (1926).

Other (2)

C. E. K. Mees, The Theory of the Photographic Process (Macmillan Company, New York, 1942), first edition, p. 899.

Rayleigh, Scientific Papers (The University Press, Cambridge, 1899), Vol. I, p. 415.

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Figures (9)

Fig. 1
Fig. 1

Light distribution in the diffraction patterns of tricolumnar test objects on a logarithmic scale. The “periods” represented by the curves are 50 and 175 lines/mm, and the Rayleigh limit of the lens is 1/328 mm. The illuminance for a plane of infinite extent is taken as unity, and the abscissas represent relative distances normal to the axis, one unit being the center-to-center distance of the images of the columns.

Fig. 2
Fig. 2

Light distribution in the diffraction patterns of tripunctiform, trilinear, and tricolumnar test objects whose geometrical images are separated according to the Rayleigh criterion for two points (3.02μ). The maximum illuminance in the pattern of a single element is taken as unity.

Fig. 3
Fig. 3

Ratio of illuminance (maximum in outside columns to minimum in spaces) in the diffraction pattern of a tricolumnar test object as a function of the “period” of the test object when photographed with an f/5, 150-mm lens in light of λ=500 mμ. Solid line, theoretical curve computed from diffraction theory; dotted line, Eq. (7), taken as an approximate analytical representation. The Rayleigh limit for points is indicated as well as the illuminance ratio for points and for lines at this limit.

Fig. 4
Fig. 4

Resolving power of six materials as a function of the resolving power of the camera lens in light of λ=546 mμ. The curves are described in the text.

Fig. 6
Fig. 6

Two families of curves for deriving the relation giving the resolving power of lens-emulsion combinations. One gives the illuminance ratio in the pattern of a tricolumnar test object as a function of the “period” when the “period” corresponding to the Rayleigh limit (indicated by the vertical dotted line) has the value RL. (These curves are replotted from the broken curve of Fig. 3.) The other family gives the illuminance ratio required to produce the value of resolving power read on the scale of ordinates when the measured value for a ratio of infinity is RS, according to Sandvik. The intersections of the families give the measured value RSL to be expected when a lens whose Rayleigh limit is RL is used with an emulsion whose maximum lenticular resolving power is RS.

Fig. 5
Fig. 5

Resolving power of materials tested by Sandvik as a function of the reciprocal of the luminance ratio in the test object. The resolving power of each material for a ratio of infinity as determined from similar plots of the individual materials is taken as 100.

Fig. 7
Fig. 7

Comparison of new relation for predicting RSL with experimental values obtained in this laboratory. ● Micro-File Film; ○ Fine Grain Release Positive Film (5302); + Aerographic Super-XX Film, all in f/5 camera. □ Kodalith Ortho Plate in high-aperture camera. × Spectroscopic Type V-G Plate in both cameras.

Fig. 8
Fig. 8

Comparison of new relation with Bocchino’s and Couder’s data. ○ Couder’s data, unmodified (RS=52); × same, modified (RS=70); ● Bocchino’s data.

Fig. 9
Fig. 9

Comparison of new relation with other relations. The exponential law, Eq. (8), is represented by isolated points instead of a curve to avoid confusing the figure.

Tables (4)

Tables Icon

Table I Ratio of illuminance of outer peaks of tricolumnar lucicoles to illuminance of intervening valleys for a wavelength of 500 mμ.

Tables Icon

Table II Plates used to study resolving power as a function of the aperture of the camera lens. The developer formulas and development times are also given, as well as the values of resolving power obtained with the f/5 camera when the luminance ratio in the test object is practically infinite.

Tables Icon

Table III Characteristics of objectives used for measuring resolving power as a function of the aperture of the camera lens. The values of resolving power are for λ=546 mμ.

Tables Icon

Table IV “Maximum lenticular” resolution in lines per millimeter of selected emulsions compared with the values obtained with a highly corrected f/5 camera when the luminance ratio in the object is 1000 or more.

Equations (8)

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x 0 = 0.61 λ / θ
x 0 = K λ / θ
R = R [ 1 - exp ( - α D ) ] ,
R = R [ 1 - ( 1 / ρ ) α / k ] ,
α S L / α L = ( α S / α L ) [ 1 - exp ( - α S / α L ) ] - 1 .
R S L / R L = ( R S / R L ) [ 1 - exp ( - R L / R S ) ] .
log ρ = 1.8323 - 0.0950 R + 0.001553 R 2 - 8.11 × 10 - 6 R 3 .
R S L / R L = [ 1 - exp ( - R S / R L ) ]