Abstract

We measured the modulation transfer function (MTF) of a lens in the visible region using a random test target generated on a computer screen. This is a simple method to determine the entire MTF curve in one measurement. The lens was obscured by several masks so that the measurements could be compared with the theoretically calculated MTF. Excellent agreement was obtained. Measurement noise was reduced by use of a large number of targets generated on the screen.

© 1999 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1991).
  2. S. K. Park, R. Schowengredt, M. Kaczynsky, “Modulation transfer function analysis for sampled image systems,” Appl. Opt. 23, 2572–2582 (1984).
    [CrossRef]
  3. W. Hon-Sum, “Effect of knife-edge skew on MTF measurement of CCD images employing a scanning knife edge,” Opt. Eng. 30, 1394–1398 (1991).
    [CrossRef]
  4. A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
    [CrossRef]
  5. H. Kubota, H. Ohzu, “Method of measurement of response function by means of random chart,” J. Opt. Soc. Am. 47, 666–667 (1957).
    [CrossRef]

1995 (1)

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

1991 (1)

W. Hon-Sum, “Effect of knife-edge skew on MTF measurement of CCD images employing a scanning knife edge,” Opt. Eng. 30, 1394–1398 (1991).
[CrossRef]

1984 (1)

1957 (1)

Boreman, G. D.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1991).

Daniels, A.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Ducharme, A. D.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Hon-Sum, W.

W. Hon-Sum, “Effect of knife-edge skew on MTF measurement of CCD images employing a scanning knife edge,” Opt. Eng. 30, 1394–1398 (1991).
[CrossRef]

Kaczynsky, M.

Kubota, H.

Ohzu, H.

Park, S. K.

Sapir, E.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Schowengredt, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1991).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

W. Hon-Sum, “Effect of knife-edge skew on MTF measurement of CCD images employing a scanning knife edge,” Opt. Eng. 30, 1394–1398 (1991).
[CrossRef]

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1991).

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Figures (8)

Fig. 1
Fig. 1

(a) Band-limited white-noise random target. (b) PSD i of a random target.

Fig. 2
Fig. 2

Block diagram for the experimental method.

Fig. 3
Fig. 3

(a) Block diagram for the generation of random targets. (b) Discrete filter transfer function. This filter is the convolution (*) of comb (f/5.8 - 1/2) * trg(f/1.45), where trg(x) = 1 - |x| or zero if 1 - |x| < 0.

Fig. 4
Fig. 4

Discrete random target.

Fig. 5
Fig. 5

(a) NAS obtained by a homogenous gray target. (b) MTFsys, the measurement of which was carried out with the full aperture of the lens.

Fig. 6
Fig. 6

Continuous MTF of (a) a single-slit aperture and (b) a double-slit aperture: experimental results (circles) and theoretical curve (solid curve).

Fig. 7
Fig. 7

Discrete PSD measurements (circles) compared with the continuous measurements (upper curve) shown in Fig. 5(b) and the NAS (lower curve) in Fig. 5(a). The discrete measurements sample the continuous MTF at the peaks.

Fig. 8
Fig. 8

Same as Fig. 7(a) for a single-slit aperture and (b) a double-slit aperture.

Equations (7)

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fmax=1/2l=28.4 cycles/mm,
l=hobjM/N=0.0176 mm,
PSDff=MTFtot2fPSDif,
PSDff=MTFsysfMTFtestf2PSDif+NASf, MTFtest2f=PSDff-NASfMTFsys2fPSDif.
MTF=1-|f/fa|for|f|fa0for|f|>fa; fa=dFλ,
MTF=1-|f/fa|for|f|fa|f/2fa|-fb+fa/2faforfa+fb|f|2fa+fb3fa+fb/2fa-|f/2fa|for2fa+fb|f|3fa+fb0forelse; fb=d1-dFλ,
ASFff=OTFASFif.

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