Abstract

We analyze the extension of depth of field using both amplitude and phase modulation of the pupil function. In particular, we discuss the advantages and disadvantages of each approach and establish the range of applicability of each method based on the range of spatial frequencies of interest in the imaging system. To the best of our knowledge, this is the first such report on the range of applicability of amplitude and phase modulation to extend the depth of field.

© 2008 Optical Society of America

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References

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  1. R. Martnez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, IEEE J. Display Technol. 1, 321 (2005).
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    [CrossRef] [PubMed]
  3. J. Hall, Encyclopedia of Optical Engineering (Taylor & Francis, 2003).
  4. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000).
  5. A. E. Siegman, Lasers (University Science Books, 1986).
  6. P. E. X. Silveira and R. Narayanswamy, Appl. Opt. 45, 2924 (2006).
    [CrossRef] [PubMed]
  7. H. P. Urbach and D. A. Bernard, J. Opt. Soc. Am. A 6, 1343 (1989).
    [CrossRef]
  8. S. Bagheri, D. P. de Farias, and P. E. X. Silveira, in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper CMD4.
    [PubMed]

2006 (1)

2005 (1)

R. Martnez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, IEEE J. Display Technol. 1, 321 (2005).
[CrossRef]

2000 (1)

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000).

1995 (1)

1989 (1)

1986 (1)

A. E. Siegman, Lasers (University Science Books, 1986).

Bagheri, S.

S. Bagheri, D. P. de Farias, and P. E. X. Silveira, in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper CMD4.
[PubMed]

Bernard, D. A.

Cathey, W. T.

de Farias, D. P.

S. Bagheri, D. P. de Farias, and P. E. X. Silveira, in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper CMD4.
[PubMed]

Dowski, E. R.

Hall, J.

J. Hall, Encyclopedia of Optical Engineering (Taylor & Francis, 2003).

Javidi, B.

R. Martnez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, IEEE J. Display Technol. 1, 321 (2005).
[CrossRef]

Martnez-Corral, M.

R. Martnez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, IEEE J. Display Technol. 1, 321 (2005).
[CrossRef]

Martnez-Cuenca, R.

R. Martnez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, IEEE J. Display Technol. 1, 321 (2005).
[CrossRef]

Narayanswamy, R.

Saavedra, G.

R. Martnez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, IEEE J. Display Technol. 1, 321 (2005).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Silveira, P. E. X.

P. E. X. Silveira and R. Narayanswamy, Appl. Opt. 45, 2924 (2006).
[CrossRef] [PubMed]

S. Bagheri, D. P. de Farias, and P. E. X. Silveira, in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper CMD4.
[PubMed]

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000).

Urbach, H. P.

Appl. Opt. (2)

IEEE J. Display Technol. (1)

R. Martnez-Cuenca, G. Saavedra, M. Martnez-Corral, and B. Javidi, IEEE J. Display Technol. 1, 321 (2005).
[CrossRef]

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

Other (4)

S. Bagheri, D. P. de Farias, and P. E. X. Silveira, in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper CMD4.
[PubMed]

J. Hall, Encyclopedia of Optical Engineering (Taylor & Francis, 2003).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000).

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (3)

Fig. 1
Fig. 1

MTF plots of the total-DOF-extended imaging system in which spatial frequency is proportionally preserved in all directions. (a) and (b) show the amplitude-optimized system out of focus, (c) and (d) show the phase-optimized system out of focus, and (b) and (d) show the cross sections of the MTF. Spatial frequency is normalized using cutoff frequency of the imaging system with δ = 0 .

Fig. 2
Fig. 2

Imaging system simulation based on the optimal results in Table 1 for total DOF extension problem with W ̂ 20 * = 0.5 ( 1 + δ 2 ) . (a) shows the original object. (b), (c), and (d) show the final image using the amplitude-optimized, phase-optimized, and nonoptimized imaging systems, respectively.

Fig. 3
Fig. 3

MTF plots of the partial-DOF-extended imaging system in which spatial frequency on two perpendicular line segments is preserved. (a) and (b) show the amplitude-optimized system out of focus, (c) and (d) show the phase-optimized system out of focus, and (b) and (d) show the cross sections of the MTF. Spatial frequency is normalized using cutoff frequency of the imaging system with δ = 0 .

Tables (2)

Tables Icon

Table 1 MTF Optimization Results Based on Eq. (3)

Tables Icon

Table 2 MTF Optimization Results Based on Eq. (4) a

Equations (4)

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DOF t = { d o : W ̂ 20 ( d o ) W ̂ 20 * } ,
DOF p = { d o : SNR ( u , d o ) SNR * , u U * } ,
max δ , α 3 , α 4 , α 5 { min u U 1 , d o D O F t [ SNR ( u , d o ) ] } ,
max δ , α 3 , α 4 , α 5 { min u U 2 , d o D O F p [ SNR ( u , d o ) ] } ,

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