Abstract

A technique is described for measuring the modulation transfer functions (MTF) of recording media. In this technique, a coherent optical system interferometrically generates a signal suitable for recording on the medium being tested. A second coherent optical system is used to obtain the MTF; spatial filters are used to remove the effects of film-grain noise, phase errors in the emulsion of the film, and extraneous light distributions. Since both systems are coherent, this technique can be used equally well to measure the MTF of phase-modulated media or bleached photographic film. A satisfying feature of this technique is that the MTF is displayed at the output of the second optical system as an easily detectable light distribution.

© 1967 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. The system must also be space-invariant; photographic film always meets this condition.
  2. In noncoherent systems, of course, the light distributions to be recorded are already expressed as intensity functions.
  3. An alternative method is to use a two-step process with a gamma product of two. Unfortunately, at high spatial frequencies an MTF for the second step of the process must also be considered.
  4. A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
    [Crossref]
  5. R. L. Lamberts, J. Opt. Soc. Am. 49, 425 (1959).
    [Crossref]
  6. L. O. Hendeberg, Arkiv Fysik 16, 457 (1960).
  7. R. L. Lamberts, J. Opt. Soc. Am. 51, 982 (1961).
    [Crossref]
  8. F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).
  9. J. Burch and D. Palmer, Opt. Acta 8, 73 (1961).
    [Crossref]
  10. F. Grum, Phot. Sci. Engr. 7, 96 (1963).
  11. E. N. Leith, Phot. Sci. Engr. 6, 75 (1962).
  12. R. E. Swing and M. C. H. Shin, Phot. Sci. Engr. 7, 350 (1963).
  13. Equation (6) is an approximation to the actual amplitude function, obtained by truncating a binomial expansion after the first two terms. This approximation clarifies the mathematical treatment without affecting its validity. As is explained in the next section, the effects of this approximation can be avoided during the reduction of the data to final form. (See also Fig. 8 and the relevant text.)
  14. The MTF is sometimes dependent on exposure (see Lamberts cited in Ref. 5). In our experiments, the average density of the film was approximately 0.4. Measurements of the MTF at higher exposures showed that the MTF varied by less than 10%, possibly because the signals we recorded had small modulation.
  15. E. N. Leith and et al., Appl. Opt. 5, 1303 (1966).
    [Crossref] [PubMed]
  16. A. L. Ingalls, Phot. Sci. Engr. 4, 135 (1960).
  17. J. H. Altman, Phot. Sci. Engr. 10, 156 (1966).
  18. Modulation Transfer Data for Kodak Films, Kodak Pamphlet No. P–49, Eastman Kodak Company, Rochester, N. Y., 1962.
  19. H. Frieser, Phot. Sci. Engr. 4, 324 (1960).
  20. A. Vander Lugt, Proc. IEEE 54, 1059 (1966).
  21. Reference 20, p. 1062.

1966 (4)

J. H. Altman, Phot. Sci. Engr. 10, 156 (1966).

A. Vander Lugt, Proc. IEEE 54, 1059 (1966).

E. N. Leith and et al., Appl. Opt. 5, 1303 (1966).
[Crossref] [PubMed]

A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
[Crossref]

1963 (3)

R. E. Swing and M. C. H. Shin, Phot. Sci. Engr. 7, 350 (1963).

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

F. Grum, Phot. Sci. Engr. 7, 96 (1963).

1962 (1)

E. N. Leith, Phot. Sci. Engr. 6, 75 (1962).

1961 (2)

J. Burch and D. Palmer, Opt. Acta 8, 73 (1961).
[Crossref]

R. L. Lamberts, J. Opt. Soc. Am. 51, 982 (1961).
[Crossref]

1960 (3)

L. O. Hendeberg, Arkiv Fysik 16, 457 (1960).

A. L. Ingalls, Phot. Sci. Engr. 4, 135 (1960).

H. Frieser, Phot. Sci. Engr. 4, 324 (1960).

1959 (1)

Altman, J. H.

J. H. Altman, Phot. Sci. Engr. 10, 156 (1966).

Burch, J.

J. Burch and D. Palmer, Opt. Acta 8, 73 (1961).
[Crossref]

Frieser, H.

H. Frieser, Phot. Sci. Engr. 4, 324 (1960).

Grum, F.

F. Grum, Phot. Sci. Engr. 7, 96 (1963).

Hendeberg, L. O.

L. O. Hendeberg, Arkiv Fysik 16, 457 (1960).

Ingalls, A. L.

A. L. Ingalls, Phot. Sci. Engr. 4, 135 (1960).

Kozma, A.

Lamberts, R. L.

Leith, E. N.

Palmer, D.

J. Burch and D. Palmer, Opt. Acta 8, 73 (1961).
[Crossref]

Scott, F.

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

Scott, R. M.

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

Shack, R. V.

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

Shin, M. C. H.

R. E. Swing and M. C. H. Shin, Phot. Sci. Engr. 7, 350 (1963).

Swing, R. E.

R. E. Swing and M. C. H. Shin, Phot. Sci. Engr. 7, 350 (1963).

Vander Lugt, A.

A. Vander Lugt, Proc. IEEE 54, 1059 (1966).

Appl. Opt. (1)

Arkiv Fysik (1)

L. O. Hendeberg, Arkiv Fysik 16, 457 (1960).

J. Opt. Soc. Am. (3)

Opt. Acta (1)

J. Burch and D. Palmer, Opt. Acta 8, 73 (1961).
[Crossref]

Phot. Sci. Engr. (7)

F. Grum, Phot. Sci. Engr. 7, 96 (1963).

E. N. Leith, Phot. Sci. Engr. 6, 75 (1962).

R. E. Swing and M. C. H. Shin, Phot. Sci. Engr. 7, 350 (1963).

F. Scott, R. M. Scott, and R. V. Shack, Phot. Sci. Engr. 7, 345 (1963).

H. Frieser, Phot. Sci. Engr. 4, 324 (1960).

A. L. Ingalls, Phot. Sci. Engr. 4, 135 (1960).

J. H. Altman, Phot. Sci. Engr. 10, 156 (1966).

Proc. IEEE (1)

A. Vander Lugt, Proc. IEEE 54, 1059 (1966).

Other (7)

Reference 20, p. 1062.

Modulation Transfer Data for Kodak Films, Kodak Pamphlet No. P–49, Eastman Kodak Company, Rochester, N. Y., 1962.

Equation (6) is an approximation to the actual amplitude function, obtained by truncating a binomial expansion after the first two terms. This approximation clarifies the mathematical treatment without affecting its validity. As is explained in the next section, the effects of this approximation can be avoided during the reduction of the data to final form. (See also Fig. 8 and the relevant text.)

The MTF is sometimes dependent on exposure (see Lamberts cited in Ref. 5). In our experiments, the average density of the film was approximately 0.4. Measurements of the MTF at higher exposures showed that the MTF varied by less than 10%, possibly because the signals we recorded had small modulation.

The system must also be space-invariant; photographic film always meets this condition.

In noncoherent systems, of course, the light distributions to be recorded are already expressed as intensity functions.

An alternative method is to use a two-step process with a gamma product of two. Unfortunately, at high spatial frequencies an MTF for the second step of the process must also be considered.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Typical curve of amplitude transmittance vs exposure for photographic film.

Fig. 2
Fig. 2

Interference of a plane wave and a wave of radius R.

Fig. 3
Fig. 3

Analyzing system.

Fig. 4
Fig. 4

Unfiltered light distribution in the output plane.

Fig. 5
Fig. 5

Filtered light distribution in the output plane.

Fig. 6
Fig. 6

Practical system for generating and analyzing test films.

Fig. 7
Fig. 7

Interferometric optical system.

Fig. 8
Fig. 8

Instantaneous frequency vs space coordinate.

Fig. 9
Fig. 9

Photograph of the MTF’s for six films.

Fig. 10
Fig. 10

Modulation transfer functions. (a) Plus-X Pan, D-19, 4 min. (b) Tri-X Pan, D-19, 4 min. (c) Pan-X, D-19, 4 min. (d) Panchromatic Separation, D-76, 6.5 min. (e) High Contrast Copy, D-19, 4 min. (f) 649-F, D-19, 5 min.

Fig. 11
Fig. 11

Modulation transfer function for 649-F film. (a) Unbleached. (b) Bleached. (c) Bleaching transfer function.

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

N ( p ) = - n ( x ) exp ( j p x ) d x ,
a ( x ) = a - b t i ( x ) ,
a ( x ) = a - b t - i ( u ) n ( x - u ) d u .
A ( p ) = δ ( p ) - b t I ( p ) N ( p ) ,
A ( p ) = - b t I ( p ) N ( p ) ;             p 0.
f ( x ) = a 1 + a 2 exp ( j k x 2 / 2 R ) ,
i ( x ) = f ( x ) 2 = a 1 2 + a 2 2 + a 1 a 2 exp ( j k x 2 / 2 R ) + a 1 a 2 exp ( - j k x 2 / 2 R ) = a 1 2 + a 2 2 + 2 a 1 a 2 cos ( k x 2 / 2 R ) .
a ( x ) = a - b t [ a 1 2 + a 2 2 + a 1 a 2 exp ( j k u 2 / 2 R ) + a 1 a 2 exp ( - j k u 2 / 2 R ) ] n ( x - u ) d u .
a ( x ) = a - b t { a 1 2 + a 2 2 + a 1 a 2 exp [ j ( α u - k u 2 / 2 R ) ] + a 1 a 2 exp [ - j ( α u - k u 2 / 2 R ) ] } × n ( x - u ) d u ; u < 2 R α / k = 0 ; u 2 R α / k ,
A ( ξ ) = A 3 exp [ j k ( F - D ) ξ 2 / 2 F 2 ] sinc ( 2 R α ξ / F ) + A 4 N ( k ξ / F ) exp [ - j k ( D + 1 2 R - F ) ξ 2 / F 2 ] × exp ( j α R ξ / F ) ;             ξ 0 = A 3 exp [ j k ( F - D ) ξ 2 / 2 F 2 ] sinc ( 2 R α ξ / F ) + A 4 N ( k ξ / F ) exp [ - j k ( D - 1 2 R - F ) ξ 2 / F 2 ] × exp ( - j α R ξ / F ) ;             ξ 0 ,
a ( x ) = b t a 1 ( x ) a 1 ( u ) a 2 ( u ) × exp ( - j k u 2 / 2 R ) n ( x - u ) d u ,
A ( ξ ) = A 1 ( ξ ) * ( N ( k ξ / F ) { A 1 ( ξ ) * A 2 ( ξ ) * exp [ - j k ( D - 1 2 R - F ) ξ 2 / F 2 ] } ) ,
a ( x ) = b t e j ϕ ( x ) a 1 2 a 2 exp ( - j k u 2 / 2 R ) n ( x - u ) d u ,
A ( ξ ) = A 4 Φ ( ξ ) * { N ( k ξ / F ) × exp [ - j k ( D - 1 2 R - F ) ξ 2 / F 2 ] } .
g ( x ) = a ( x ) e j c a ( x ) ,
g ( x ) = a ( x ) + j c a 2 ( x ) .
g ( x ) = a ( 1 + j c a ) - b t ( 1 - j 2 c a ) ( a 1 2 + a 2 2 ) + j c b 2 t 2 ( a 1 2 + a 2 2 ) 2 + j 2 c b 2 t 2 a 1 2 a 2 2 - b t a 1 a 2 × [ 1 + j 2 c a - j 2 c b t ( a 1 2 + a 2 2 ) ] exp [ j ( α x - k x 2 / 2 R ) ] - b t a 1 a 2 [ 1 + j 2 c a - j 2 c b t ( a 1 2 + a 2 2 ) ] × exp [ - j ( α x - k x 2 / 2 R ) ] + j c b 2 t 2 a 1 a 2 × exp [ 2 j ( α x - k x 2 / 2 R ) ] + j c b 2 t 2 a 1 a 2 × exp [ - 2 j ( α x - k x 2 / 2 R ) ] .
g ( x ) = 1 + j c a ( x ) - c 2 a 2 ( x ) / 2 ! +
a ( x ) = a - b t - 2 R α / k 2 R α / k ( a 1 2 + a 2 2 ) n ( x - u ) d u - b t - 2 R α / k 2 R α / k a 1 a 2 exp [ j ( α u - k u 2 2 R ) ] n ( x - u ) d u - b t - 2 R α / k 2 R α / k a 1 a 2 exp [ - j ( α u - k u 2 2 R ) ] n ( x - u ) d u .
F ( ξ ) = exp [ j k ( F - D ) ξ 2 2 F 2 ] - 2 R α / k 2 R α / k f ( x ) × exp ( - j k ξ x F ) d x ,
F 1 ( ξ ) = A 3 exp [ j k ( F - D ) ξ 2 2 F 2 ] sinc ( 2 R α F ξ ) ,
F 2 ( ξ ) = exp [ j k ( F - D ) ξ 2 2 F 2 ] - 2 R α / k 2 R α / k n ( x ) × exp ( - j k ξ x F ) d x = exp [ j k ( F - D ) ξ 2 2 F 2 ] N ( k ξ F ) .
F 3 ( ξ ) = b t exp [ j k ( F - D ) ξ 2 2 F 2 ] - 2 R α / k 2 R α / k a 1 a 2 × exp [ j ( α x - k x 2 2 R ) ] exp ( - j k ξ x F ) d x .
F 3 ( ξ ) = b t exp [ j k ( F - D ) ξ 2 2 F 2 ] - 2 R α / k 2 R α / k a 1 a 2 × exp ( - j k x 2 2 R ) exp { - j [ k F x ( ξ - α F k ) ] } d x ,
F 3 ( ξ ) = b t a 1 a 2 exp [ j k ( F - D ) ξ 2 2 F 2 ] × exp [ j k R 2 F 2 ( ξ - α F k ) 2 ] h ( ξ - α F k ) ,
h ( ξ - α F R ) = - ( k R / π ) 1 2 ( A / R + ξ / F - α / k ) ( k R / π ) 1 2 ( A / R - ξ / F + α / k ) exp [ j ( π 2 ) t 2 ] d t ,
F 2 ( ξ ) F 3 ( ξ ) = A 4 exp [ - j k ( D - 1 2 R - F ) ξ 2 / F 2 ] × exp [ - j ( α R / F ) ξ ] N ( k ξ / F ) ,
A 4 exp [ - j k ( D + 1 2 R - F ) ξ 2 / F 2 ] × exp [ j ( α R / F ) ξ ] N ( k ξ / F )