Abstract

After a survey of various definitions of the photometric characteristic curve of photographic emulsions, this paper reintroduces a long forgotten photometric parameter, the opacitance ω = opacity − 1 = 10D − 1 and describes its application to a characteristic function I=Aωn(n12), which is linear in log–log coordinates over the whole range of densities of practical interest in photographic photometry. In a special case n = 1 and J = I/A = ω.

© 1968 Optical Society of America

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References

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  1. G. E. Kron, I. I. Papiashvili, Pub. Astron. Soc. Pacific 79, 9 (1967).
    [CrossRef]
  2. M. F. Walker, G. E. Kron, Pub. Astron. Soc. Pacific 79, 551 (1967).
    [CrossRef]
  3. F. Hurter, V. C. Driffield, J. Soc. Chem. Ind. London 9, 455 (1890).
    [CrossRef]
  4. A. E. Baker, Proc. Roy. Soc. Edinburgh, 45, 166 (1925); Proc. Roy. Soc. Edinburgh 4734 (1926); Proc. Roy. Soc. Edinburgh 48, 106 (1928).
  5. C. E. K. Mees, Theory of the Photographic Process (The Macmillan Company, New York, 1954), 2nd ed., p. 168.
  6. G. de Vaucouleurs, J. Dragesco, P. Selme, Manuel de Photographie Scientifique (Revue d’Optique, Paris, 1956).
  7. G. de Vaucouleurs, J. des Observ. 31, 113 (1948).
  8. G. de Vaucouleurs, Ann. Astrophys. 11, 247 (1948).
  9. W. J. Albersheim. J. Motion Pict. Eng. 29, 417 (1937).
  10. W. B. Jones, D. L. Obitts, R. M. Gallet, G. de Vaucouleurs, Astronomical Surface Photometry by Numerical Mapping Techniques, Publ. Dept. Astron., Univ. Texas, (II) Nr. 8 (1967).
  11. R. A. Sampson, Mon. Not. Roy. Astron. Soc. 85, 212 (1925).
  12. G. de Vaucouleurs, Sci. Ind. Photo. 14,149, 193 (1943); Sci. Ind. Photo. 17, 257 (1946).

1967 (2)

G. E. Kron, I. I. Papiashvili, Pub. Astron. Soc. Pacific 79, 9 (1967).
[CrossRef]

M. F. Walker, G. E. Kron, Pub. Astron. Soc. Pacific 79, 551 (1967).
[CrossRef]

1948 (2)

G. de Vaucouleurs, J. des Observ. 31, 113 (1948).

G. de Vaucouleurs, Ann. Astrophys. 11, 247 (1948).

1943 (1)

G. de Vaucouleurs, Sci. Ind. Photo. 14,149, 193 (1943); Sci. Ind. Photo. 17, 257 (1946).

1937 (1)

W. J. Albersheim. J. Motion Pict. Eng. 29, 417 (1937).

1925 (2)

R. A. Sampson, Mon. Not. Roy. Astron. Soc. 85, 212 (1925).

A. E. Baker, Proc. Roy. Soc. Edinburgh, 45, 166 (1925); Proc. Roy. Soc. Edinburgh 4734 (1926); Proc. Roy. Soc. Edinburgh 48, 106 (1928).

1890 (1)

F. Hurter, V. C. Driffield, J. Soc. Chem. Ind. London 9, 455 (1890).
[CrossRef]

Albersheim, W. J.

W. J. Albersheim. J. Motion Pict. Eng. 29, 417 (1937).

Baker, A. E.

A. E. Baker, Proc. Roy. Soc. Edinburgh, 45, 166 (1925); Proc. Roy. Soc. Edinburgh 4734 (1926); Proc. Roy. Soc. Edinburgh 48, 106 (1928).

de Vaucouleurs, G.

G. de Vaucouleurs, J. des Observ. 31, 113 (1948).

G. de Vaucouleurs, Ann. Astrophys. 11, 247 (1948).

G. de Vaucouleurs, Sci. Ind. Photo. 14,149, 193 (1943); Sci. Ind. Photo. 17, 257 (1946).

W. B. Jones, D. L. Obitts, R. M. Gallet, G. de Vaucouleurs, Astronomical Surface Photometry by Numerical Mapping Techniques, Publ. Dept. Astron., Univ. Texas, (II) Nr. 8 (1967).

G. de Vaucouleurs, J. Dragesco, P. Selme, Manuel de Photographie Scientifique (Revue d’Optique, Paris, 1956).

Dragesco, J.

G. de Vaucouleurs, J. Dragesco, P. Selme, Manuel de Photographie Scientifique (Revue d’Optique, Paris, 1956).

Driffield, V. C.

F. Hurter, V. C. Driffield, J. Soc. Chem. Ind. London 9, 455 (1890).
[CrossRef]

Gallet, R. M.

W. B. Jones, D. L. Obitts, R. M. Gallet, G. de Vaucouleurs, Astronomical Surface Photometry by Numerical Mapping Techniques, Publ. Dept. Astron., Univ. Texas, (II) Nr. 8 (1967).

Hurter, F.

F. Hurter, V. C. Driffield, J. Soc. Chem. Ind. London 9, 455 (1890).
[CrossRef]

Jones, W. B.

W. B. Jones, D. L. Obitts, R. M. Gallet, G. de Vaucouleurs, Astronomical Surface Photometry by Numerical Mapping Techniques, Publ. Dept. Astron., Univ. Texas, (II) Nr. 8 (1967).

Kron, G. E.

M. F. Walker, G. E. Kron, Pub. Astron. Soc. Pacific 79, 551 (1967).
[CrossRef]

G. E. Kron, I. I. Papiashvili, Pub. Astron. Soc. Pacific 79, 9 (1967).
[CrossRef]

Mees, C. E. K.

C. E. K. Mees, Theory of the Photographic Process (The Macmillan Company, New York, 1954), 2nd ed., p. 168.

Obitts, D. L.

W. B. Jones, D. L. Obitts, R. M. Gallet, G. de Vaucouleurs, Astronomical Surface Photometry by Numerical Mapping Techniques, Publ. Dept. Astron., Univ. Texas, (II) Nr. 8 (1967).

Papiashvili, I. I.

G. E. Kron, I. I. Papiashvili, Pub. Astron. Soc. Pacific 79, 9 (1967).
[CrossRef]

Sampson, R. A.

R. A. Sampson, Mon. Not. Roy. Astron. Soc. 85, 212 (1925).

Selme, P.

G. de Vaucouleurs, J. Dragesco, P. Selme, Manuel de Photographie Scientifique (Revue d’Optique, Paris, 1956).

Walker, M. F.

M. F. Walker, G. E. Kron, Pub. Astron. Soc. Pacific 79, 551 (1967).
[CrossRef]

Ann. Astrophys. (1)

G. de Vaucouleurs, Ann. Astrophys. 11, 247 (1948).

J. des Observ. (1)

G. de Vaucouleurs, J. des Observ. 31, 113 (1948).

J. Motion Pict. Eng. (1)

W. J. Albersheim. J. Motion Pict. Eng. 29, 417 (1937).

J. Soc. Chem. Ind. London (1)

F. Hurter, V. C. Driffield, J. Soc. Chem. Ind. London 9, 455 (1890).
[CrossRef]

Mon. Not. Roy. Astron. Soc. (1)

R. A. Sampson, Mon. Not. Roy. Astron. Soc. 85, 212 (1925).

Proc. Roy. Soc. Edinburgh (1)

A. E. Baker, Proc. Roy. Soc. Edinburgh, 45, 166 (1925); Proc. Roy. Soc. Edinburgh 4734 (1926); Proc. Roy. Soc. Edinburgh 48, 106 (1928).

Pub. Astron. Soc. Pacific (2)

G. E. Kron, I. I. Papiashvili, Pub. Astron. Soc. Pacific 79, 9 (1967).
[CrossRef]

M. F. Walker, G. E. Kron, Pub. Astron. Soc. Pacific 79, 551 (1967).
[CrossRef]

Sci. Ind. Photo. (1)

G. de Vaucouleurs, Sci. Ind. Photo. 14,149, 193 (1943); Sci. Ind. Photo. 17, 257 (1946).

Other (3)

W. B. Jones, D. L. Obitts, R. M. Gallet, G. de Vaucouleurs, Astronomical Surface Photometry by Numerical Mapping Techniques, Publ. Dept. Astron., Univ. Texas, (II) Nr. 8 (1967).

C. E. K. Mees, Theory of the Photographic Process (The Macmillan Company, New York, 1954), 2nd ed., p. 168.

G. de Vaucouleurs, J. Dragesco, P. Selme, Manuel de Photographie Scientifique (Revue d’Optique, Paris, 1956).

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Figures (7)

Fig. 1
Fig. 1

Conventional H and D curve D(log I) is roughly linear in a narrow range x at medium a densities near D ≃ 1.

Fig. 2
Fig. 2

Dependence of photographic density on (a) convergence angle Ω and (b) divergence angle Ω′ (in steradians) for a coarsegrained emulsion, after G. A. Boutry (1935).

Fig. 3
Fig. 3

Characteristic curve t(log I) is roughly linear in a small range of low densities near D ≃ 0.3.

Fig. 4
Fig. 4

Characteristic curve D(I2) is roughly linear in a short range of very low densities D < 0.2.

Fig. 5
Fig. 5

Characteristic curves ω(I) are linear in log–log coordinates over a large range of densities D < 2. The relation I = n is shown for various common values of n = 0.4 to 0.7. The relation between opacitance ω and density D is illustrated by the two scales of ordinates.

Fig. 6
Fig. 6

Examples of linear characteristic curves in log ω–log I coordinates for various batches of Kodak 103a–0 and IIa–0 emulsions used at several observatories between 1954 and 1967.

Fig. 7
Fig. 7

Effect of local errors on characteristic curve. The distortion of the charateristic curve is immediately obvious in the linear ω(I) or logω–(log I) representation (a), but it is not evident in the S-shaped H and D curve whose correct curvature is not known a priori (b). The true characteristic is shown by the dashed curves, the apparent characteristic by the full line, The corresponding observed calibration points are plotted on each graph for this fictitious example.

Equations (20)

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t = ϕ / ϕ ,
O = 1 / t = ϕ / ϕ ,
D = log O = colog t = log ϕ / ϕ
y ( I ) = f ( δ / Δ 0 ) .
y I ( I ) = h 1 ( D )
y 1 ( I ) = log I ,
f 1 ( δ ) = log Δ 0 / δ = D ,
f s ( δ ) = log Δ s / δ = d ,
y 2 = log I = h 2 ( t ) = h 2 [ f 0 ( δ ) ] .
f 1 ( δ ) = D = a I 2 + ,
f 3 ( δ ) = [ ( Δ 0 / δ ) - 1 ] 1 2 = ω 1 2
I = j = 1 m A j ω i / 2 .
I = A ω n = A f 4 ( δ ) ,
ω = ( Δ 0 / δ ) - 1 = O - 1 ,
D 1 = log 10 ( 10 D - 1 ) = D + log 10 ( 1 - 10 - D )
( log ω ) / ( log I ) = n - 1 = γ * γ = D / ( log I ) .
I = A ω .
J = I / I 1 = ω ;
( I + I 1 ) / I 1 = O = Δ 0 / δ ,
I 1 / ( I + I 1 ) = t = 1 / ( J + 1 ) .

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