Abstract

We show that by using a binary spatial filter and a square-law detector we can display all the defocused optical transfer functions (OTF’s) in a given study in a single picture. The resulting unique picture has as its horizontal coordinates the spatial frequency and as its vertical coordinates the amount of defocus. The gray-level variations are proportional to the modulus of the OTF, that is, the modulation transfer function. Numerical simulations are included.

© 1998 Optical Society of America

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References

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  1. A. R. FitzGerrell, E. R. Dowski, and W. T. Cathey, Appl. Opt. 36, 5796 (1997).
    [CrossRef] [PubMed]
  2. E. R. Dowski and W. T. Cathey, Appl. Opt. 34, 1851 (1995).
    [CrossRef]
  3. K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castañeda, Opt. Commun. 44, 323 (1983).
    [CrossRef]
  4. J. Ojeda-Castañeda, P. Andres, and E. Montes, J. Opt. Soc. Am. A 4, 313 (1987).
    [CrossRef]
  5. J. Ojeda-Castañeda, L. R. Berriel-Valdos, and E. Montes, Appl. Opt. 27, 790 (1988).
    [CrossRef]
  6. J. Ojeda-Castañeda, R. Ramos, and A. Noyola-Isgleas, Appl. Opt. 27, 2583 (1988).
    [CrossRef]
  7. P. Mouroulis and J. MacDonald, Geometrical Optics and Optical Design (Oxford University, New York, 1997).

1997

1995

E. R. Dowski and W. T. Cathey, Appl. Opt. 34, 1851 (1995).
[CrossRef]

1988

1987

1983

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castañeda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Andres, P.

Berriel-Valdos, L. R.

Brenner, K. H.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castañeda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Cathey, W. T.

Dowski, E. R.

FitzGerrell, A. R.

Lohmann, A. W.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castañeda, Opt. Commun. 44, 323 (1983).
[CrossRef]

MacDonald, J.

P. Mouroulis and J. MacDonald, Geometrical Optics and Optical Design (Oxford University, New York, 1997).

Montes, E.

Mouroulis, P.

P. Mouroulis and J. MacDonald, Geometrical Optics and Optical Design (Oxford University, New York, 1997).

Noyola-Isgleas, A.

Ojeda-Castañeda, J.

Ramos, R.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castañeda, Opt. Commun. 44, 323 (1983).
[CrossRef]

Other

P. Mouroulis and J. MacDonald, Geometrical Optics and Optical Design (Oxford University, New York, 1997).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the optical setup proposed for visualizing simultaneously all the defocused OTF’s.

Fig. 2
Fig. 2

Intermediate image with all defocused PSF’s: (a) experimental results, (b) numerical simulation, (c) profiles at different amounts of defocus.

Fig. 3
Fig. 3

Same as Fig. 2 but for the final image with all defocused MTF’s.

Equations (10)

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tx0,y0=sx0δy0,
t˜ν,μ=--tx0,y0×exp-i2πνx0+μy0dx0dy0. =s˜ν.
u˜ν,μ=t˜ν,μδμ-Aν2rectν/Ω=s˜νδμ-Aν2rectν/Ω.
ux,y=--u˜ν,μexpi2πxν+yμdνdμ=-Ω/2Ω/2s˜νexpi2πAyν2expi2πxνdν.
expi2πW2,0/λν/Ω2=expi2πAyν2,
W2,0=AΩ2λy.
Hx,y=Kux,y2.
H˜μ,y=--Hx,yexp-i2πμxdxδy-ydy=K--ux,y2exp-i2πμxdxδy-ydy.
H˜μ,y=-ΩΩs˜ν+μ/2s˜*ν-μ/2×expi2πAyμνdν rectμ/2Ω.
H˜μ;W2,0=-s˜ν+μ/2s˜*ν-μ/2×expi2πW2,0/λΩ2μνdν.

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