Abstract

Modulation-transfer-function (MTF) measurement often involves the use of three- and four-bar resolution targets. In the conversion of three- and four-bar image data to MTF, biased results can occur when we use series-expansion techniques appropriate for square-wave targets of infinite extent. For systems where the image data are digitally recorded, a convenient and accurate conversion of bar-target data to MTF can be performed using a Fourier-domain method.

© 1995 Optical Society of America

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References

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  1. H. Osterberg, Military Standardization Handbook - Optical Design, “Evaluation phase optical tests,” Ch. 26, pp. 1–8. Defense Supply Agency, Washington, D.C. (1962).
  2. FLIR92 Thermal Imaging Systems Performance Model—Analyst’s Reference Guide, U.S. Army Night Vision and Electronic Sensors Directorate, Ft. Belvoir, Va., (1993), p. 2.
  3. J. W. Coltman, “The specification of imaging properties by response to a sine wave input,” J. Opt. Soc. Am. 44,468471 (1954).
    [CrossRef]
  4. D. H. Kelly, “Spatial frequency, bandwidth, and resolution,” Appl. Opt. 4,435437 (1965).
    [CrossRef]
  5. S. E. Reichenbach et al., “Characterizing digital image acquisition devices”, Opt. Eng. 30, 170–177 (1991).
  6. A. Daniels et al., “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34:3 (1995).

1995 (1)

A. Daniels et al., “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34:3 (1995).

1991 (1)

S. E. Reichenbach et al., “Characterizing digital image acquisition devices”, Opt. Eng. 30, 170–177 (1991).

1965 (1)

1954 (1)

J. W. Coltman, “The specification of imaging properties by response to a sine wave input,” J. Opt. Soc. Am. 44,468471 (1954).
[CrossRef]

Coltman, J. W.

J. W. Coltman, “The specification of imaging properties by response to a sine wave input,” J. Opt. Soc. Am. 44,468471 (1954).
[CrossRef]

Daniels, A.

A. Daniels et al., “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34:3 (1995).

Kelly, D. H.

Osterberg, H.

H. Osterberg, Military Standardization Handbook - Optical Design, “Evaluation phase optical tests,” Ch. 26, pp. 1–8. Defense Supply Agency, Washington, D.C. (1962).

Reichenbach, S. E.

S. E. Reichenbach et al., “Characterizing digital image acquisition devices”, Opt. Eng. 30, 170–177 (1991).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. W. Coltman, “The specification of imaging properties by response to a sine wave input,” J. Opt. Soc. Am. 44,468471 (1954).
[CrossRef]

Opt. Eng. (2)

S. E. Reichenbach et al., “Characterizing digital image acquisition devices”, Opt. Eng. 30, 170–177 (1991).

A. Daniels et al., “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34:3 (1995).

Other (2)

H. Osterberg, Military Standardization Handbook - Optical Design, “Evaluation phase optical tests,” Ch. 26, pp. 1–8. Defense Supply Agency, Washington, D.C. (1962).

FLIR92 Thermal Imaging Systems Performance Model—Analyst’s Reference Guide, U.S. Army Night Vision and Electronic Sensors Directorate, Ft. Belvoir, Va., (1993), p. 2.

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Figures (2)

Figure 1
Figure 1

Comparison of IMDs for three- and four-bar targets, and CTFs for infinite-square-wave targets, given the following MTFs: 1a) a diffraction-limited circular-aperture MTF with cutoff frequency ξ0; 1b) a Gaussian MTF = exp{−2(ξ/ξ0)2} (both IMD curves are identical to the CTF); 1c) an exponential MTF = exp{−2(ξ/ξ0)}; and 1d) a diffraction-limited annular-aperture MTF (50% diameter obscuration) with cutoff frequency ξ0

Figure 2
Figure 2

Measured output spectrum magnitude for a three-bar target (dashed line) and calculated input spectrum magnitude (solid line).

Equations (11)

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M = [ I max - I min I max + I min ] ,
MTF ( ξ ) = [ M output ( ξ ) M input - sine - wave ( ξ ) ] .
CTF ( ξ f ) = [ M output ( ξ f ) M input - square - wave ( ξ f ) ] .
CTF ( ξ f ) = 4 π { MTF ( ξ = ξ f ) - MTF ( ξ = 3 ξ f ) 3 + MTF ( ξ = 5 ξ f ) 5 - MTF ( ξ = 7 ξ f ) 7 + MTF ( ξ = 9 ξ f ) 9 } .
MTF ( ξ ) = π 4 { CTF ( ξ f = ξ ) + CTF ( ξ f = 3 ξ ) 3 - CTF ( ξ f = 5 ξ ) 5 + CTF ( ξ f = 7 ξ ) 7 + CTF ( ξ f = 11 ξ ) 11 } .
IMD ( ξ f ) = [ M output ( ξ f ) M input - bar - target ( ξ f ) ] ,
S input , three - bar - target ( ξ ) = | X sinc ( X 2 ξ ) [ cos ( 2 π X ξ ) + 1 2 ] | ,
ξ first zero , 3 - bar = 1 3 1 X = ξ f 3 .
S input , four - bar - target ( ξ ) = | X sinc ( X 2 ξ ) [ cos ( 3 π X ξ ) + cos ( π X ξ ) ] | ,
ξ first zero , 4 - bar = 1 4 1 X = ξ f 4 .
MTF ( ξ = ξ f ) = [ S output ( ξ = ξ f ) S input - bar - target ( ξ = ξ f ) ] ,

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