Abstract

The design of a circularly symmetric hybrid imaging system that exhibits high resolution as well as extended depth of field is presented. The design, which assumes spatially incoherent illumination, searches for an optimal “binary amplitude and phase” pupil mask, which for a certain desired depth of field, provides the largest spatial frequency band that assures a certain desired contrast value. The captured images are electronically processed by an off-line Wiener filter, to finally obtain high quality output images. Simulations as well as experimental results are provided.

© 2008 Optical Society of America

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  2. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw- Hill, New York, 1968).
  3. M. Mino and Y. Okano, "Improvement in the OTF of a Defocused Optical System Trough the Use of Shaded apertures," Appl. Opt. 10, 2219-2225 (1971).
    [CrossRef] [PubMed]
  4. T. C. Poon and M. Motamedi, "Optical Digital Incoherent Image Processing for Extended Depth of Field," Appl. Opt. 26, 4612-4615 (1987).
    [CrossRef] [PubMed]
  5. J. O. Castaneda, R. Ramos, and A. Noyola-Isgleas, "High focal depth by apodization and digital restoration," Appl. Opt. 272583-2586 (1988).
    [CrossRef]
  6. J. O. Castaneda, E. Tepichin, and A. Diaz, "Arbitrary high focal depth with a quasioptimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2669 (1989).
    [CrossRef]
  7. J. O. Castaneda and L. R. Berriel-Valdos, "Zone plate for arbitrary high focal depth," Appl. Opt. 29, 994-997 (1990).
    [CrossRef]
  8. S. Sanyal and A. Ghosh, "High focal depth with quasi-bifocus birefringent lens," Appl. Opt. 39, 2321-2325 (2000).
    [CrossRef]
  9. E. Peli and A. Lang, "Appearance of images through a multifocal intraocular lens," J. Opt. Soc. Am. A 18, 302-309 (2001).
    [CrossRef]
  10. E. R Dowski Jr and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
  11. J. van der Gracht, E. R. DowskiJr, M. G. Taylor, and D. M. Deaver, "Broadband behavior of an optical-digital focus-invariant system," Opt. Lett. 21, 919-921 (1996).
    [CrossRef] [PubMed]
  12. S. S. Sherif, W. T. Cathey, and E. R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging systems," Appl. Opt. 43, 2709-2721 (2004).
    [CrossRef] [PubMed]
  13. S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
    [CrossRef]
  14. S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
    [CrossRef]
  15. W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett. 26, 875-877 (2001).
    [CrossRef]
  16. N George and W. Chi, "Computational imaging with the logarithmic asphere: theory," J. Opt. Soc. Am. A 20, 2260-2273 (2003).
    [CrossRef]
  17. J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
    [CrossRef]
  18. E. Ben-Eliezer and E. Marom, "Aberration-free superresolution imaging via binary speckle pattern encoding and processing," J. Opt. Soc. Am. A 24, 1003-1010 (2007).
    [CrossRef]
  19. E. Ben-Eliezer, N. Konfori, and E. Marom, "Superresolution imaging with noise reduction and aberration elimination via random structured illumination and processing," Opt. Express 15, 3849-3863 (2007).
    [CrossRef] [PubMed]
  20. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Pure Appl. Opt. 5, S164-S169 (2003).
    [CrossRef]
  21. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Proc. SPIE 4829, 221-222 (2002).
  22. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental Realization of an Imaging System with an Extended Depth of Field," Appl. Opt. 44, 2792-2798 (2005).
    [CrossRef] [PubMed]
  23. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field," Appl. Opt. 45, 2001-2013 (2006).
    [CrossRef] [PubMed]
  24. R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, "Color image processing pipeline," IEEE Sig. Proc. Mag. 22, 34-43 (2005).
    [CrossRef]
  25. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1993).
  26. B. R. Hunt and O. Kubler, "Karhunen-Loeve Multispectral Image Restoration, Part I: Theory," ASSP 32, 592-600 (1984).
    [CrossRef]
  27. E. Marom, E. Ben-Eliezer, and N. Knoforti, PCT/IL2008/000527 "Optical imaging system with an extended depth-of-field and a method for designing an optical imaging system."

2007 (2)

2006 (1)

2005 (2)

2004 (4)

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
[CrossRef]

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

S. S. Sherif, W. T. Cathey, and E. R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging systems," Appl. Opt. 43, 2709-2721 (2004).
[CrossRef] [PubMed]

2003 (2)

N George and W. Chi, "Computational imaging with the logarithmic asphere: theory," J. Opt. Soc. Am. A 20, 2260-2273 (2003).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

2002 (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Proc. SPIE 4829, 221-222 (2002).

2001 (2)

2000 (1)

1996 (1)

1995 (1)

E. R Dowski Jr and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt 34, 1859-1866 (1995).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (1)

1987 (1)

1984 (1)

B. R. Hunt and O. Kubler, "Karhunen-Loeve Multispectral Image Restoration, Part I: Theory," ASSP 32, 592-600 (1984).
[CrossRef]

1971 (1)

Ben-Eliezer, E.

Berriel-Valdos, L. R.

Castaneda, J. O.

Cathey, W. T.

Chi, W.

Deaver, D. M.

Diaz, A.

Dowski, E. R.

Drew, M. S.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, "Color image processing pipeline," IEEE Sig. Proc. Mag. 22, 34-43 (2005).
[CrossRef]

George, N

George, N.

Ghosh, A.

Hunt, B. R.

B. R. Hunt and O. Kubler, "Karhunen-Loeve Multispectral Image Restoration, Part I: Theory," ASSP 32, 592-600 (1984).
[CrossRef]

Konfori, N.

Konforti, N.

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field," Appl. Opt. 45, 2001-2013 (2006).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental Realization of an Imaging System with an Extended Depth of Field," Appl. Opt. 44, 2792-2798 (2005).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Proc. SPIE 4829, 221-222 (2002).

Kubler, O.

B. R. Hunt and O. Kubler, "Karhunen-Loeve Multispectral Image Restoration, Part I: Theory," ASSP 32, 592-600 (1984).
[CrossRef]

Lang, A.

Marom, E.

Mino, M.

Motamedi, M.

Narayanswamy, R.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

Noyola-Isgleas, A.

Okano, Y.

Pauca, V. P.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

Paul Pauca, V.

S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
[CrossRef]

Peli, E.

Plemmons, R.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

Plemmons, R. J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
[CrossRef]

Poon, T. C.

Prasad, S.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
[CrossRef]

Ramanath, R.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, "Color image processing pipeline," IEEE Sig. Proc. Mag. 22, 34-43 (2005).
[CrossRef]

Ramos, R.

Sanyal, S.

Setty, H.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

Sherif, S. S.

Snyder, W. E.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, "Color image processing pipeline," IEEE Sig. Proc. Mag. 22, 34-43 (2005).
[CrossRef]

Taylor, M. G.

Tepichin, E.

Torgersen, T.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

Torgersen, T. C.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
[CrossRef]

van der Gracht, J.

S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
[CrossRef]

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

J. van der Gracht, E. R. DowskiJr, M. G. Taylor, and D. M. Deaver, "Broadband behavior of an optical-digital focus-invariant system," Opt. Lett. 21, 919-921 (1996).
[CrossRef] [PubMed]

Yoo, Y.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, "Color image processing pipeline," IEEE Sig. Proc. Mag. 22, 34-43 (2005).
[CrossRef]

Zalevsky, Z.

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field," Appl. Opt. 45, 2001-2013 (2006).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental Realization of an Imaging System with an Extended Depth of Field," Appl. Opt. 44, 2792-2798 (2005).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Proc. SPIE 4829, 221-222 (2002).

Appl. Opt (1)

E. R Dowski Jr and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt 34, 1859-1866 (1995).
[CrossRef] [PubMed]

Appl. Opt. (9)

T. C. Poon and M. Motamedi, "Optical Digital Incoherent Image Processing for Extended Depth of Field," Appl. Opt. 26, 4612-4615 (1987).
[CrossRef] [PubMed]

J. O. Castaneda, R. Ramos, and A. Noyola-Isgleas, "High focal depth by apodization and digital restoration," Appl. Opt. 272583-2586 (1988).
[CrossRef]

S. Sanyal and A. Ghosh, "High focal depth with quasi-bifocus birefringent lens," Appl. Opt. 39, 2321-2325 (2000).
[CrossRef]

J. O. Castaneda and L. R. Berriel-Valdos, "Zone plate for arbitrary high focal depth," Appl. Opt. 29, 994-997 (1990).
[CrossRef]

J. O. Castaneda, E. Tepichin, and A. Diaz, "Arbitrary high focal depth with a quasioptimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2669 (1989).
[CrossRef]

S. S. Sherif, W. T. Cathey, and E. R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging systems," Appl. Opt. 43, 2709-2721 (2004).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental Realization of an Imaging System with an Extended Depth of Field," Appl. Opt. 44, 2792-2798 (2005).
[CrossRef] [PubMed]

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "A Radial Mask for Systems that exhibit High Resolution and Extended Depth of Field," Appl. Opt. 45, 2001-2013 (2006).
[CrossRef] [PubMed]

M. Mino and Y. Okano, "Improvement in the OTF of a Defocused Optical System Trough the Use of Shaded apertures," Appl. Opt. 10, 2219-2225 (1971).
[CrossRef] [PubMed]

ASSP (1)

B. R. Hunt and O. Kubler, "Karhunen-Loeve Multispectral Image Restoration, Part I: Theory," ASSP 32, 592-600 (1984).
[CrossRef]

IEEE Sig. Proc. Mag. (1)

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, "Color image processing pipeline," IEEE Sig. Proc. Mag. 22, 34-43 (2005).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (3)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Proc. SPIE 4829, 221-222 (2002).

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

S. Prasad, V. Paul Pauca, R. J. Plemmons, T. C. Torgersen and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," Proc. SPIE 5559,335-345 (2004).
[CrossRef]

Pure Appl. Opt. (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-Optical Extended Depth of Field Imaging System," Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

Other (4)

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1993).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw- Hill, New York, 1968).

E. Marom, E. Ben-Eliezer, and N. Knoforti, PCT/IL2008/000527 "Optical imaging system with an extended depth-of-field and a method for designing an optical imaging system."

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Figures (12)

Fig. 1.
Fig. 1.

An illustration of a binary phase mask, with two annular phase rings in red. The rings introduce a π phase difference for a central wavelength within the illumination light bandwidth.

Fig. 2.
Fig. 2.

Schematic of the combined binary amplitude and phase mask (2Rc case), as well as an illustration of the optimization process (green arrows).

Fig. 3.
Fig. 3.

OTF radial cross-sections. The red and the blue curves denote the OTF of the optimal phase masks with one phase ring, which were designed for ψmax=10 and desired contrast values of 5% and 10% respectively, while the black curve stands for the OTF, provided by the clear aperture. (a)- in-focus position (b)- defocus parameter of ψ=5. (c)- defocus parameter of ψ=10.

Fig. 4.
Fig. 4.

OTF radial cross-sections. The red and the blue curves denote the OTF of the optimal phase mask with two annular phase rings, which were designed for ψmax=14 and desired contrast values of 5% and 10% respectively. (a)- in-focus position (b)- defocus parameter of ψ=7. (c)- defocus parameter of ψ=14.

Fig. 5.
Fig. 5.

OTF radial cross-sections. The red and the blue curves denote the OTF of the optimal amplitude-phase binary masks, which were designed for desired contrast values of 5%, with one and two phase rings respectively, while the black curve stands for the OTF, provided by the clear aperture with lateral dimension of 80% of the full aperture size, which provides the same light throughput. (a)- in-focus position (b)- defocus parameter of ψ=4. (c)-defocus parameter of ψ=8.

Fig. 6.
Fig. 6.

MTF curves of the optimal mask (blue curve) for several defocus positions, along with the corresponding MTF curves provided by a full size open aperture in the same defocus conditions (black curve). (a)- defocus parameter ψ=0; (b)- ψ=5; (c)- ψ=10; (d)- ψ=15; (e)- ψ=20; The contrast values of 5% and 10% are marked with green and red horizontal lines respectively.

Fig. 7.
Fig. 7.

Obtained theoretical contrast values with respect to the object distance from the lens (in-focus position in d=0.3 m), for (a)- red, (b)- green and (c)-blue channels, for open aperture (blue curve) as well as for the mask (dash-green curve), assuming normalized frequency value of 0.1 in the image plane.

Fig. 8.
Fig. 8.

Obtained theoretical contrast values with respect to the object distance from the lens (in-focus position in d=0.3 m), for (a)- red, (b)- green and (c)-blue channels. Open aperture (blue curve) as well as for the mask-equipped aperture (dash-green curve), are plotted for a normalized frequency value of 0.2 in the image plane.

Fig. 9.
Fig. 9.

A block diagram of a digital restoration filter for color images.

Fig. 10.
Fig. 10.

A natural outdoor scene (in-focus position in d=0.3 m from the lens). (a)- Clear aperture, (b) - Mask only (c) - Output with mask and restoration. Areas in black rectangle are magnified in the right.

Fig. 11.
Fig. 11.

A personal card, located 15 cm from the lens at the DOF edge (in-focus position in d=0.3 m from the lens). (a)- Clear aperture, (b) - Mask only (c) - Output with mask and restoration. Areas in black rectangle are magnified in the right.

Fig. 12.
Fig. 12.

A spoke target, located 15 cm from the lens at the DOF edge (in-focus position in d=0.3 m from the lens). (a)- Clear aperture, (b) - Mask only (c) - Output with mask and restoration. The finest line width in the middle is 7.5 mil, while widths of 10, 13, 20 and 30 mil on successive annular black rings are presented

Tables (12)

Tables Icon

Table 1. Optimization results for a phase mask with only one annular phase ring for different DOF ranges, defined by ψmax. The normalized radial phase transition locations are r1 and r2 and the normalized PCF, denoted by νmax, is provided for a desired contrast value of Cd=5%.

Tables Icon

Table 2. Optimization results for a phase mask with only one annular phase ring for different DOF ranges, defined by ψmax. The normalized radial phase transition locations are r1 and r2 and the normalized PCF, denoted by νmax, is provided for a desired contrast value of Cd=10%.

Tables Icon

Table 3. Optimization results for a mask with only one annular phase ring as well as an opaque central circle with a normalized radius of r1. Different DOF ranges were considered, defined by the ψmax values. The normalized radial phase transition locations are r2 and r3 and the normalized PCF, denoted by νmax, is provided for a desired contrast value of Cd=5%.

Tables Icon

Table 4. Optimization results for a mask with only one annular phase ring as well as an opaque central circle with a normalized radius of r1. Different DOF ranges were considered, defined by the ψmax values. The normalized radial phase transition locations are r2 and r3 and the normalized PCF, denoted by νmax, is provided for a desired contrast value of Cd=10%.

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Table 5. Optimization results for a binary phase mask with two annular phase rings designed for a desired contrast value of Cd=5%. Different DOF ranges were considered, defined by their ψmax values. The normalized radial phase transition locations are r1 … r4 and the normalized PCF, is denoted by νmax.

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Table 6. Optimization results for a binary phase mask with two annular phase rings designed for a desired contrast value of Cd=10%. Different DOF ranges were considered, defined by their ψmax values. The normalized radial phase transition locations are r1 … r4 and the normalized PCF, is denoted by νmax.

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Table 7. Optimization results for a binary phase mask with central opaque circle and two annular phase rings designed for a desired contrast value of Cd=5%. Different DOF ranges were considered, defined by their ψmax values. The normalized radius of the opaque center is r1 while the normalized radial phase transition locations are r2 … r5. The normalized PCF is denoted by νmax.

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Table 8. Optimization results for a binary phase mask with central opaque circle and two annular phase rings designed for a desired contrast value of Cd=10%. Different DOF ranges were considered, defined by their ψmax values. The normalized radius of the opaque center is r1 while the normalized radial phase transition locations are r2 … r5. The normalized PCF is denoted by νmax.

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Table 9. Performance comparison when design for a contrast of Cd=5% is assumed. The normalized PCF (bold), as well as the light throughput for several defocus conditions, denoted by ψmax are shown. The notation 1R means “one ring.” The notation 1RC means “one ring and opaque center”. Similar notations are used for two rings

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Table 10. Performance comparison when design for a contrast of Cd=10% is assumed. The normalized PCF (bold), as well as the light throughput for several defocus conditions, denoted by ψmax are shown. The notation 1R means “one ring”. The notation 1RC means “one ring and opaque center”. Similar notations are used for two rings.

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Table 11. Optimization results for an amplitude annular ring, defined by an inner normalized radius of r1. Different DOF ranges were considered, defined by the ψmax values. The normalized PCF, denoted by νmax, is provided for a desired contrast value of Cd=5%.

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Table 12. Optimization results for an amplitude annular ring, defined by an inner normalized radius of r1. Different DOF ranges were considered, defined by the ψmax values. The normalized PCF, denoted by νmax, is provided for a desired contrast value of Cd=10%.

Equations (16)

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G ( u , v ; ψ ) = exp [ j ψ ( u 2 + v 2 ) ] ,
ψ = π R 2 λ ( 1 d obj + 1 d img 1 f )
P ( u , v ) = P ( u , v ) exp [ j ψ ( u 2 + v 2 ) ]
I out ( x , y ) = h ( x x , y y ) 2 I g ( x , y ) dx dy
OTF ( ν x , ν y ) = Ω P ˉ ( u ν x 2 ; v ν y 2 ) P ( u + ν x 2 ; v + ν y 2 ) du dv Ω P ˉ ( u ; v ) P ( u ; v ) du dv
ν max = max r 1 r 2 N min ψ DOF [ ν ( r 1 r 2 N ) : MTF ( ν , ψ ) = C d ]
P ( ρ ; a ) = p ( ρ ) e j a 2 ρ 2
where : ρ = u 2 + v 2 ; ψ = a 2
p ( ρ ) = { 1 ; ρ < 1 0 ; else
U 1 ( a , w ) = n = 0 ( 1 ) n ( a w ) 2 n + 1 J 2 n + 1 ( w )
U 2 ( a , w ) = n = 0 ( 1 ) n ( a w ) 2 n + 2 J 2 n + 2 ( w )
h ( r ) = e j a 2 a [ U 1 ( a , w ) j U 2 ( a , w ) ] ,
where : w = 2 π R λ d img r
P ph ( ρ ) e i ψ ρ 2 = P ( ρ ; 2 ψ ) + 2 n = 1 2 N ( 1 ) n + 1 P ( ρ n ; 2 ψ r n 2 R 2 )
OTF = 0 h ( r ) 2 J 0 ( 2 π ρ r ) r dr 0 h ( r ) 2 r dr
P amp_ph ( ρ ) e i ψ ρ 2 = P ( ρ ; 2 ψ ) P ( ρ 1 ; 2 ψ r 1 2 R 2 ) + 2 n = 2 2 N + 1 ( 1 ) n P ( ρ n ; 2 ψ r n 2 R 2 )

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