Abstract

The imaging properties of an optical system can be in many cases completely specified by a function of a single variable. A convenient function is the response to a sine wave test pattern as a function of “frequency,” i.e., lines/mm. The difficulty of experimentally providing such a test pattern can be avoided by measuring the response to a square wave (bar pattern) and calculating by a simple formula the corresponding sine wave response factor. The convenience of the sine wave response factor in calculating system performance is illustrated by application to a fluoroscopic imaging system.

© 1954 Optical Society of America

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References

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  1. G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952).
  2. O. H. Schade, RCA Rev. 9, 246 (1948).
  3. E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. (London) 58, 493 (1946).
    [Crossref]
  4. E. W. H. Selwyn, Phot. J. Sect. B 88, 6–12 (1948).
  5. H. A. Klasens, Philips Research Repts.1, 241 (1946).
  6. H. Frieser, Congr. intern. phot. IXe Congr. 207 (1935).

1952 (1)

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952).

1948 (2)

O. H. Schade, RCA Rev. 9, 246 (1948).

E. W. H. Selwyn, Phot. J. Sect. B 88, 6–12 (1948).

1946 (1)

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

1935 (1)

H. Frieser, Congr. intern. phot. IXe Congr. 207 (1935).

Frieser, H.

H. Frieser, Congr. intern. phot. IXe Congr. 207 (1935).

Higgins, G. C.

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952).

Jones, L. A.

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952).

Klasens, H. A.

H. A. Klasens, Philips Research Repts.1, 241 (1946).

Schade, O. H.

O. H. Schade, RCA Rev. 9, 246 (1948).

Selwyn, E. W. H.

E. W. H. Selwyn, Phot. J. Sect. B 88, 6–12 (1948).

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

Tearle, J. L.

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

Congr. intern. phot. IXe Congr. 207 (1)

H. Frieser, Congr. intern. phot. IXe Congr. 207 (1935).

J. Soc. Motion Picture Television Engrs. (1)

G. C. Higgins and L. A. Jones, J. Soc. Motion Picture Television Engrs. 58, 277 (1952).

Phot. J. Sect. B (1)

E. W. H. Selwyn, Phot. J. Sect. B 88, 6–12 (1948).

Proc. Phys. Soc. (London) (1)

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

RCA Rev. (1)

O. H. Schade, RCA Rev. 9, 246 (1948).

Other (1)

H. A. Klasens, Philips Research Repts.1, 241 (1946).

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Figures (6)

F. 1
F. 1

Response of an imaging system to various object shapes.

F. 2
F. 2

Quantities involved in the definition of response factors.

F. 3
F. 3

Response factors for a fluoroscopic screen. The sine wave response factor R(n) is derived from the measured square wave response factor r(n) by means of Eq. (3).

F. 4
F. 4

Sine wave response factors for two fluorescent screens.

F. 5
F. 5

Calculated sine wave response for a rectangular aperture flux distribution.

F. 6
F. 6

Combining sine wave response factors.

Equations (5)

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F ( x ) = B 1 + Δ B 1 4 π [ cos 2 π n x δ 1 3 cos 3 ( 2 π n x δ ) + 1 5 cos 5 ( 2 π n x δ ) 1 7 cos 7 ( 2 π n x δ ) + ] .
r ( n ) = 4 π [ R ( n ) R ( 3 n ) 3 + R ( 5 n ) 5 R ( 7 n ) 7 + R ( 9 n ) 9 ] .
R ( n ) = π 4 [ r ( n ) + r ( 3 n ) 3 r ( 5 n ) 5 + r ( 7 n ) 7 + r ( 11 n ) 11 r ( 13 n ) 13 r ( 15 n ) 15 r ( 17 n ) 17 + r ( 19 n ) 19 + B k r ( k n ) k ] .
B k = ( 1 ) m ( 1 ) k 1 2 if r = m , B k = 0 if r < m .
R ( n ) = π 2 8 [ r ¯ ( n ) r ¯ ( 3 n ) ( 3 ) 2 r ¯ ( 5 n ) ( 5 ) 2 r ¯ ( 7 n ) ( 7 ) 2 r ¯ ( 11 n ) ( 11 ) 2 r ¯ ( 13 n ) ( 13 ) 2 + r ¯ ( 15 n ) ( 15 ) 2 r ¯ ( 17 n ) ( 17 ) 2 ] .