Abstract

The capacity of a reflecting surface to transfer contrast is governed by two parameters, “figure,” and microroughness. In the present study, highly polished surfaces were evaluated in terms of contrast or modulation transfer; it was found that only figure, not microroughness, accounts for a reduction in modulation transfer at higher spatial frequencies of object details.

© 1963 Optical Society of America

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References

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  1. S. Tanaka, N. Noguchi, M. Watanabe, and T. Takahashi, Oyobutsuri, J. Appl. Phys. (Japan) 31, No. 3 (1962).
  2. P. M. Duffieux, L’intégrale de Fourier et ses applications à l’optique (Université de Besançon, Oberthurn, Rennes, 1946).
  3. E. Diederichs and A. Lohmann, Optik 15, 751–757 (1958).
  4. R. L. Lamberts, G. C. Higgins, and R. N. Wolfe, J. Opt. Soc. Am. 48, 487–490, 490–495 (1958); E. Ingelstam, E. Djurle, and E. Sjögren, ibid.  46, 707–714 (1956); A. Lohmann, Optik 14, 510–518 (1957); F. H. Perrin, J. Soc. Motion Picture Television Engrs. 69, 151–156, 239–249 (1960).
    [CrossRef]
  5. K. Murata, Optik 17, 152–159 (1960).
  6. G. Franke, Haŭsmitteilŭngen J. Schneider (Kreuznach, Germany) 13, 34–41 (1960/61).
  7. H. E. Bennett pointed out the fact that the lens is passed by the light twice, once in the one and once in the opposite direction which tends to minimize at least some of the aberrations.
  8. H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51, 123–129 (1961).
    [CrossRef]
  9. J. R. Meyer-Arendt, J. O. Porteus, and H. E. Bennett, Stanford Meeting, American Physical Society, 27–29 December 1962.

1962 (1)

S. Tanaka, N. Noguchi, M. Watanabe, and T. Takahashi, Oyobutsuri, J. Appl. Phys. (Japan) 31, No. 3 (1962).

1961 (1)

1960 (2)

K. Murata, Optik 17, 152–159 (1960).

G. Franke, Haŭsmitteilŭngen J. Schneider (Kreuznach, Germany) 13, 34–41 (1960/61).

1958 (2)

Bennett, H. E.

H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51, 123–129 (1961).
[CrossRef]

J. R. Meyer-Arendt, J. O. Porteus, and H. E. Bennett, Stanford Meeting, American Physical Society, 27–29 December 1962.

Diederichs, E.

E. Diederichs and A. Lohmann, Optik 15, 751–757 (1958).

Duffieux, P. M.

P. M. Duffieux, L’intégrale de Fourier et ses applications à l’optique (Université de Besançon, Oberthurn, Rennes, 1946).

Franke, G.

G. Franke, Haŭsmitteilŭngen J. Schneider (Kreuznach, Germany) 13, 34–41 (1960/61).

Higgins, G. C.

Lamberts, R. L.

Lohmann, A.

E. Diederichs and A. Lohmann, Optik 15, 751–757 (1958).

Meyer-Arendt, J. R.

J. R. Meyer-Arendt, J. O. Porteus, and H. E. Bennett, Stanford Meeting, American Physical Society, 27–29 December 1962.

Murata, K.

K. Murata, Optik 17, 152–159 (1960).

Noguchi, N.

S. Tanaka, N. Noguchi, M. Watanabe, and T. Takahashi, Oyobutsuri, J. Appl. Phys. (Japan) 31, No. 3 (1962).

Porteus, J. O.

H. E. Bennett and J. O. Porteus, J. Opt. Soc. Am. 51, 123–129 (1961).
[CrossRef]

J. R. Meyer-Arendt, J. O. Porteus, and H. E. Bennett, Stanford Meeting, American Physical Society, 27–29 December 1962.

Takahashi, T.

S. Tanaka, N. Noguchi, M. Watanabe, and T. Takahashi, Oyobutsuri, J. Appl. Phys. (Japan) 31, No. 3 (1962).

Tanaka, S.

S. Tanaka, N. Noguchi, M. Watanabe, and T. Takahashi, Oyobutsuri, J. Appl. Phys. (Japan) 31, No. 3 (1962).

Watanabe, M.

S. Tanaka, N. Noguchi, M. Watanabe, and T. Takahashi, Oyobutsuri, J. Appl. Phys. (Japan) 31, No. 3 (1962).

Wolfe, R. N.

Hausmitteilungen J. Schneider (Kreuznach, Germany) (1)

G. Franke, Haŭsmitteilŭngen J. Schneider (Kreuznach, Germany) 13, 34–41 (1960/61).

J. Opt. Soc. Am. (2)

Optik (2)

K. Murata, Optik 17, 152–159 (1960).

E. Diederichs and A. Lohmann, Optik 15, 751–757 (1958).

Oyobutsuri, J. Appl. Phys. (Japan) (1)

S. Tanaka, N. Noguchi, M. Watanabe, and T. Takahashi, Oyobutsuri, J. Appl. Phys. (Japan) 31, No. 3 (1962).

Other (3)

P. M. Duffieux, L’intégrale de Fourier et ses applications à l’optique (Université de Besançon, Oberthurn, Rennes, 1946).

J. R. Meyer-Arendt, J. O. Porteus, and H. E. Bennett, Stanford Meeting, American Physical Society, 27–29 December 1962.

H. E. Bennett pointed out the fact that the lens is passed by the light twice, once in the one and once in the opposite direction which tends to minimize at least some of the aberrations.

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Figures (3)

Fig. 1
Fig. 1

Schematic view of apparatus for measuring modulation and phase transfer functions of reflecting surfaces. (1) xenon arc; (2) entrance grid; (3) rotating cube; (4) beam splitter; (5) objective lens and iris diaphragm; (6) test surface; (7) photocell with horizontal slit; (8) auxiliary light source; (9) four-prism arrangement (only two prisms are shown); (10) auxiliary telescope.

Fig. 2
Fig. 2

Rotating drum arrangement for measuring transfer functions of a reflecting surface. (1) xenon arc; (2) rotating drum with slots of increasing spatial frequency; (3) objective lens; (4) test surface; (5) slit; (6) photocell; (7) slot for phase signal.

Fig. 3
Fig. 3

Relationship between image contrast and spatial frequency for different kinds of plane first-surface mirrors.

Equations (11)

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Δ ( x , y ) = Δ a ( x , y ) + Δ m ( x , y ) .
I 0 ( x ) = b 0 ( R ) exp ( 2 π i R x ) d R ,
I i ( ξ ) = b i ( R ) exp ( 2 π i R ξ ) d R ,
D ( R ) = D a ( R ) D m ( R ) ,
D a ( R ) = 1 A p A c exp { i k [ Δ a ( x + p λ 2 R , y ) Δ a ( x λ p 2 R , y ) ] } d x d y ,
D m ( R ) = 1 A p A p exp { i k [ Δ m ( x + λ p 2 R , y ) Δ m ( x p λ 2 R , y ) ] } d x d y .
D m ( R ) 1 k 2 2 [ Δ m ( x + λ p 2 R , y ) Δ m ( x ) ] 2 ,
D m ( R ) = 1 ( k Δ m ) 2 = const . ,
γ ( I max I min ) / ( I max + I min ) .
( γ image / γ object ) ( R ) = T ( R ) .
D ( R ) = T ( R ) exp [ i θ ( R ) ] ,