Abstract

One-dimensional templates, such as the U.S. Air Force resolution target or the circular spoke target, are commonly used for the characterization of imaging systems via the modulation transfer function response. It is shown in this paper that one needs a new family of templates for a true characterization of imaging systems that acquire two-dimensional (2D) high-density images or handle 2D information, such as 2D bar code detection and identification. The contrast provided by the newly defined 2D templates is the “true” contrast of the acquired image that the electronic processors are challenged with.

© 2010 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996) 126–151.
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    [CrossRef]
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    [CrossRef] [PubMed]
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  9. S. M. Backman and A. J. Makynen, “Random target method for fast MTF inspection,” Opt. Express 12, 2610–2615 (2004).
    [CrossRef] [PubMed]

2004 (1)

1998 (1)

1995 (2)

1976 (1)

1971 (1)

1923 (1)

V. Ronchi, “Le frange di combinazioni nello studio delle superficie e dei sistemi ottici [Combination fringes in the study of surfaces and optical systems],” Riv. Ottica Mecc. Precis. [J. Opt. Prec. Mech.] 2, 9–35 (1923).

Backman, S. M.

Bhogra, R. K.

Boreman, G. D.

Ferrell, R. K.

Goddard, J. S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996) 126–151.

Grimes, D. N.

Jaiswal, A. K.

Makynen, A. J.

Rogers, G. L.

Ronchi, V.

V. Ronchi, “Le frange di combinazioni nello studio delle superficie e dei sistemi ottici [Combination fringes in the study of surfaces and optical systems],” Riv. Ottica Mecc. Precis. [J. Opt. Prec. Mech.] 2, 9–35 (1923).

Sitter, D. N.

Yang, S.

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Figures (15)

Fig. 1
Fig. 1

Modulation transfer function curves of (a) 1D slit pupil and (b) 2D circular pupil, in focus.

Fig. 2
Fig. 2

Spoke target images (a) in focus and (b) out of focus.

Fig. 3
Fig. 3

Modulation transfer function curves of (a) 1D pupil and (b) 2D pupil, for the out-of-focus condition, ψ = 5 .

Fig. 4
Fig. 4

Typical 2D bar code.

Fig. 5
Fig. 5

Suggested 2D templates: (a) Cartesian and (b) polar.

Fig. 6
Fig. 6

(a) Standard 1D resolution chart versus (b) 2D suggested resolution chart.

Fig. 7
Fig. 7

(upper) 1D and (lower) 2D spoke templates. The red circle indicates the spatial frequency chosen for comparison. Signal traces at this selected spatial frequency (right).

Fig. 8
Fig. 8

Images of the 1D resolution target (left) and the 2D Resolution target (right) for different out-of-focus conditions: (a) ψ = 0 (in focus), (b) ψ = 2 , and (c) ψ = 5 .

Fig. 9
Fig. 9

Images of the 1D spoke target 2D (left) and the polar resolution chart (right) for different out-of-focus conditions: (a) ψ = 0 (in-focus), (b) ψ = 2 , and (c) ψ = 5 .

Fig. 10
Fig. 10

(a) 1D spoke template and (b) 2D spoke template, at focus, Ψ = 0 . The RGB circles represent three selected spatial frequencies.

Fig. 11
Fig. 11

Signal traces along the three circles drawn in Fig. 10 represent the response at three selected spatial frequencies. The RGB traces correspond to the 1D template, and the black traces correspond to the 2D template.

Fig. 12
Fig. 12

Modulation transfer function of an optical system in focus is drawn (magenta). The dashed curve represents the corresponding experimentally measured values. The RGB dots represent the contrast at the selected test frequencies.

Fig. 13
Fig. 13

(a) 1D spoke template and (b) the 2D spoke template, out of focus, Ψ = 5 . The RGB circles represent three selected spatial frequencies.

Fig. 14
Fig. 14

Signal traces along the three circles drawn in Fig. 13 represent the response at three selected spatial frequencies. The RGB traces correspond to the 1D template, and the black traces correspond to the 2D template. Note the almost lost contrast for green and phase reversal for blue.

Fig. 15
Fig. 15

Optical transfer function of an optical system out of focus, for the Ψ = 5 case, is drawn (magenta). The dashed curve represents the corresponding experimentally measured values. The RGB dots represent the contrast at the selected test frequencies.

Equations (3)

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ψ = π D 2 4 λ ( 1 d obj + 1 d img 1 f ) .
contrast = I max I min I max + I min ,
radial step = [ 2 S π 2 S + π ] N ,

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