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  • Journal of the Optical Society of Korea
  • Vol. 20,
  • Issue 6,
  • pp. 762-769
  • (2016)

Dynamic Modulation Transfer Function Analysis of Images Blurred by Sinusoidal Vibration

Yanlu Du, Yalin Ding, Yongsen Xu, and Chongshang Sun

Open Access Open Access

Abstract

The dynamic modulation transfer function (MTF) for image degradation caused by sinusoidal vibration is formulated based on a Bessel function of the first kind. The presented method makes it possible to obtain an analytical MTF expression derived for arbitrary frequency sinusoidal vibration. The error obtained by the use of finite order sum approximations instead of infinite sums is investigated in detail. Dynamic MTF exhibits a stronger random behavior for low frequency vibration than high frequency vibration. The calculated MTFs agree well with the measured MTFs with the slant edge method in imaging experiments. With the proposed formula, allowable amplitudes of any frequency vibration are easily calculated. This is practical for the analysis and design of the line-of-sight stabilization system in the remote sensing camera.

© 2016 Optical Society of Korea

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References

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  • Year
  • Author
  • Publication
  1. S. G. Wang, B. Q. Guan, G. B. Wang, and Q. Li, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
    [Crossref]
  2. R. Vollmerhausen, M. H. Friedman, J. Reynolds, and S. Burks, “Modeling the blur associated with vibration and motion,” Proc SPIE 6543, 65430U (2007).
  3. P. Xu, Q. Hao, C. N. Huang, and Y. T. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35, 547-552 (2003).
    [Crossref]
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    [Crossref]
  5. D. Wulich and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations,” Opt. Eng. 26, 529-533 (1987).
  6. O. Hadar, M. Fisher, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part III: numerical calculation of modulation transfer function,” Opt. Eng. 31, 581-589 (1992).
    [Crossref]
  7. O. Hadar, I. Dror, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer functions and experimental verification,” Opt. Eng. 33, 566-578 (1994).
    [Crossref]
  8. A. Friedenberg, “Simulation of the MTF due to low-frequency and correlated vibrations,” J. Mod. Opt. 55, 401-407 (2008).
    [Crossref]
  9. A. Stern and N. S. Kopeika, “Analytical method to calculate optical transfer functions for image motion and vibrations using moments,” J. Opt. Soc. Am. A 14, 388-396 (1997).
    [Crossref]
  10. Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).
  11. J. Y. Liao and X. D. Gao, “Dynamic MTF analysis and calculation of aerial camera,” Proc SPIE 7658, 765819 (2010).
  12. Photography-Electronic Still Picture Cameras-Resolution Measurements, ISO Standard 12233: 2000.
  13. S. Najafi and K. Madanipour, “Measurement of the modulation transfer function of a charge-coupled device array by the combination of the self-imaging effect and slanted edge method,” Appl. Opt. 52, 4724-4727 (2013).
    [Crossref]
  14. C. S. Sun, Y. L. Ding, D. J. Wang, and D. P. Tian, “Backscanning step and stare imaging system with high frame rate and wide coverage,” Appl. Opt. 54, 4960-4965 (2015).
    [Crossref]
  15. H. Li, C. X. Yan, and J. B. Shao, “Measurement of the modulation transfer function of infrared imaging system by modified slant edge method,” J. Opt. Soc. Korea 20, 381-388 (2016).
    [Crossref]
  16. K. Masaoka, T. Yamashita, Y. Nishida, and M. Sugawara, “Modified slanted-edge method and multidirectional modulation transfer function estimation,” Opt. Express 22, 6040-6046 (2014).
    [Crossref]

2016 (1)

2015 (1)

2014 (1)

2013 (1)

2011 (1)

2008 (1)

A. Friedenberg, “Simulation of the MTF due to low-frequency and correlated vibrations,” J. Mod. Opt. 55, 401-407 (2008).
[Crossref]

2007 (1)

S. G. Wang, B. Q. Guan, G. B. Wang, and Q. Li, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[Crossref]

2003 (1)

P. Xu, Q. Hao, C. N. Huang, and Y. T. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35, 547-552 (2003).
[Crossref]

1997 (1)

1994 (1)

O. Hadar, I. Dror, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer functions and experimental verification,” Opt. Eng. 33, 566-578 (1994).
[Crossref]

1992 (1)

O. Hadar, M. Fisher, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part III: numerical calculation of modulation transfer function,” Opt. Eng. 31, 581-589 (1992).
[Crossref]

1987 (1)

D. Wulich and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations,” Opt. Eng. 26, 529-533 (1987).

Burks, S.

R. Vollmerhausen, M. H. Friedman, J. Reynolds, and S. Burks, “Modeling the blur associated with vibration and motion,” Proc SPIE 6543, 65430U (2007).

Chen, Y. T.

Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).

Deng, Q.

Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).

Ding, Y. L.

Dong, W. D.

Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).

Dror, I.

O. Hadar, I. Dror, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer functions and experimental verification,” Opt. Eng. 33, 566-578 (1994).
[Crossref]

Feng, H. J.

Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).

Fisher, M.

O. Hadar, M. Fisher, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part III: numerical calculation of modulation transfer function,” Opt. Eng. 31, 581-589 (1992).
[Crossref]

Friedenberg, A.

A. Friedenberg, “Simulation of the MTF due to low-frequency and correlated vibrations,” J. Mod. Opt. 55, 401-407 (2008).
[Crossref]

Friedman, M. H.

R. Vollmerhausen, M. H. Friedman, J. Reynolds, and S. Burks, “Modeling the blur associated with vibration and motion,” Proc SPIE 6543, 65430U (2007).

Gao, X. D.

J. Y. Liao and X. D. Gao, “Dynamic MTF analysis and calculation of aerial camera,” Proc SPIE 7658, 765819 (2010).

Guan, B. Q.

S. G. Wang, B. Q. Guan, G. B. Wang, and Q. Li, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[Crossref]

Hadar, O.

O. Hadar, I. Dror, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer functions and experimental verification,” Opt. Eng. 33, 566-578 (1994).
[Crossref]

O. Hadar, M. Fisher, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part III: numerical calculation of modulation transfer function,” Opt. Eng. 31, 581-589 (1992).
[Crossref]

Hao, Q.

P. Xu, Q. Hao, C. N. Huang, and Y. T. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35, 547-552 (2003).
[Crossref]

Huang, C. N.

P. Xu, Q. Hao, C. N. Huang, and Y. T. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35, 547-552 (2003).
[Crossref]

Jung, Y. S.

Kim, Y. J.

Kopeika, N. S.

A. Stern and N. S. Kopeika, “Analytical method to calculate optical transfer functions for image motion and vibrations using moments,” J. Opt. Soc. Am. A 14, 388-396 (1997).
[Crossref]

O. Hadar, I. Dror, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer functions and experimental verification,” Opt. Eng. 33, 566-578 (1994).
[Crossref]

O. Hadar, M. Fisher, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part III: numerical calculation of modulation transfer function,” Opt. Eng. 31, 581-589 (1992).
[Crossref]

D. Wulich and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations,” Opt. Eng. 26, 529-533 (1987).

Lee, J. H.

Li, H.

Li, Q.

S. G. Wang, B. Q. Guan, G. B. Wang, and Q. Li, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[Crossref]

Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).

Liao, J. Y.

J. Y. Liao and X. D. Gao, “Dynamic MTF analysis and calculation of aerial camera,” Proc SPIE 7658, 765819 (2010).

Madanipour, K.

Masaoka, K.

Najafi, S.

Nishida, Y.

Reynolds, J.

R. Vollmerhausen, M. H. Friedman, J. Reynolds, and S. Burks, “Modeling the blur associated with vibration and motion,” Proc SPIE 6543, 65430U (2007).

Ryoo, S. Y.

Shao, J. B.

Stern, A.

Sugawara, M.

Sun, C. S.

Tian, D. P.

Vollmerhausen, R.

R. Vollmerhausen, M. H. Friedman, J. Reynolds, and S. Burks, “Modeling the blur associated with vibration and motion,” Proc SPIE 6543, 65430U (2007).

Wang, D. J.

Wang, G. B.

S. G. Wang, B. Q. Guan, G. B. Wang, and Q. Li, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[Crossref]

Wang, S. G.

S. G. Wang, B. Q. Guan, G. B. Wang, and Q. Li, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[Crossref]

Wang, Y. T.

P. Xu, Q. Hao, C. N. Huang, and Y. T. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35, 547-552 (2003).
[Crossref]

Wulich, D.

D. Wulich and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations,” Opt. Eng. 26, 529-533 (1987).

Xu, P.

P. Xu, Q. Hao, C. N. Huang, and Y. T. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35, 547-552 (2003).
[Crossref]

Xu, Z. H.

Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).

Yamashita, T.

Yan, C. X.

Appl. Opt. (2)

J. Mod. Opt. (1)

A. Friedenberg, “Simulation of the MTF due to low-frequency and correlated vibrations,” J. Mod. Opt. 55, 401-407 (2008).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Korea (2)

Opt. Eng. (3)

D. Wulich and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations,” Opt. Eng. 26, 529-533 (1987).

O. Hadar, M. Fisher, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part III: numerical calculation of modulation transfer function,” Opt. Eng. 31, 581-589 (1992).
[Crossref]

O. Hadar, I. Dror, and N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer functions and experimental verification,” Opt. Eng. 33, 566-578 (1994).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

P. Xu, Q. Hao, C. N. Huang, and Y. T. Wang, “Degradation of modulation transfer function in push-broom camera caused by mechanical vibration,” Opt. Laser Technol. 35, 547-552 (2003).
[Crossref]

Pattern Recogn. Lett. (1)

S. G. Wang, B. Q. Guan, G. B. Wang, and Q. Li, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[Crossref]

Other (4)

R. Vollmerhausen, M. H. Friedman, J. Reynolds, and S. Burks, “Modeling the blur associated with vibration and motion,” Proc SPIE 6543, 65430U (2007).

Q. Deng, H. J. Feng, Z. H. Xu, Q. Li, Y. T. Chen, and W. D. Dong, “Study on MTF of remote sensing imaging under arbitrary known vibration,” Proc SPIE 8420, 84200W (2012).

J. Y. Liao and X. D. Gao, “Dynamic MTF analysis and calculation of aerial camera,” Proc SPIE 7658, 765819 (2010).

Photography-Electronic Still Picture Cameras-Resolution Measurements, ISO Standard 12233: 2000.

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