Abstract

We propose to improve the depth of field of Integral Imaging systems by combining an array of phase masks with the traditional lenslet array. We show that obtained elemental images are sharp over a larger range than with a regular lenslet array. We further increase the quality of elemental images by a digital restauration. Computer simulations of pickup and reconstruction are presented.

© 2007 Optical Society of America

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References

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  1. Y. Frauel, E. Tajahuerce, O. Matoba, A. Castro, and B. Javidi, "Comparison of passive ranging integral imaging and active imaging digital holography for three-dimensional object recognition," Appl. Opt. 43, 452-462 (2004).
    [CrossRef] [PubMed]
  2. B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies, (Springer Berlin, 2002).
  3. J.-S. Jang, F. Jin, and B. Javidi, "Three-dimensional integral imaging with large depth of focus by use of real and virtual fields," Opt. Lett. 28, 1421-1423 (2003).
    [CrossRef] [PubMed]
  4. J.-S. Jang and B. Javidi, "Depth and lateral size control of three-dimensional images in projection integral imaging," Opt. Express 12, 3778-3790 (2004).
    [CrossRef] [PubMed]
  5. J.-S. Jang and B. Javidi, "Large depth of focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lens and aperture sizes," Opt. Lett. 28, 1925-1926 (2003).
    [CrossRef]
  6. M. Hain, W. von Spiegel, M. Schmiedchen, T. Tschudi, and B. Javidi, "3D integral imaging using diffractive Fresnel lens array," Opt. Express 13, 315-326 (2005).
    [CrossRef] [PubMed]
  7. S. Jung, J. Hong, J. H. Park, Y. Kim, and B. Lee, "Depth-enhanced integral-imaging 3D display using different optical path lengths by polarization devices or mirror barrier array," J. Soc. Inf. Disp. 12, 461-467 (2004).
    [CrossRef]
  8. M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Integral imaging with improved depth of field by use of amplitude-modulated microlens arrays," Appl. Opt. 43, 5806-5813 (2004).
    [CrossRef] [PubMed]
  9. R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).
    [CrossRef] [PubMed]
  10. R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools," J. Disp. Technol. 1, 321-327 (2005).
    [CrossRef]
  11. J.-Y Son, V. Saveljev, J.-S. Kim, S.-S. Kim, and B. Javidi, "Viewing zones in three-dimensional imaging systems based on lenticular, parallax-barrier, and microlens-array plates," Appl. Opt. 43, 4985-4992 (2004).
    [CrossRef] [PubMed]
  12. J.-S. Jang and B. Javidi, "Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics," Opt. Lett. 27, 324-326 (2002).
    [CrossRef]
  13. A. Stern and B. Javidi, "Three-dimensional sensing, visualization, and processing using integral imaging," Proc. IEEE 94, 591-607 (2006).
    [CrossRef]
  14. A. Castro and J. Ojeda-Castañeda, "Asymmetric phase mask for extended depth of field," Appl. Opt. 43, 3474-3479 (2004).
    [CrossRef] [PubMed]
  15. J. Ojeda-Castañeda, A. Castro, and J. Santamaría, "Phase mask for high focal depth," in The 18th Congress of the International Commission for Optics A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, and T. Asakura, eds., Proc. SPIE 3749, 14 (1999).
    [CrossRef]
  16. A. Castro and J. Ojeda-Castañeda, "Increased depth of field with phase-only filters: ambiguity function," in Opto-Ireland 2005: Photonic Engineering, B. W. Bowe, G. Byrne, A. J. Flanagan, T. J. Glynn, J. Magee, G. M. O’Connor, R. F. O’Dowd, G. D. O’Sullivan, and J. T. Sheridan, eds., Proc. SPIE 5827, 1-11 (2005).
    [CrossRef]
  17. F. Okano, H. Hoshino, J. Arai and I. Yuyama, "Real-time pickup method for a three-dimensional image based on integral photography," Appl. Opt. 36, 1598-1603 (1997).
    [CrossRef] [PubMed]
  18. H. Arimoto and B. Javidi, "Integral 3D imaging with digital reconstruction," Opt. Lett. 26, 157-159 (2001).
    [CrossRef]
  19. S.-H. Hong, J.-S. Jang, and B. Javidi, "Three-dimensional volumetric object reconstruction using computational integral imaging," Opt. Express 12, 483-491 (2004).
    [CrossRef] [PubMed]
  20. D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction of three-dimensional objects in integral imaging using lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
    [CrossRef]
  21. H. H. Hopkins, "The frequency response of a defocused optical system," Proc. Roy. Soc. Lond. Series A,  231, 91-103 (1951).
    [CrossRef]
  22. J. W. Goodman, Introduction to Fourier optics, 2nd Ed. Chap. 6 (McGraw-Hill, New York, NY, 1996).
  23. A. Castro, J. Ojeda-Castañeda, and A.W. Lohmann, "Bow-tie effect: differential operator," Appl. Opt. 45, 7878-7884 (2006).
    [CrossRef] [PubMed]
  24. G. Hausler, "A method to increase the depth of focus by two step image processing," Opt. Commun. 6, 38-42 (1972).
    [CrossRef]
  25. E. R. Dowski, and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1865 (1995).
    [CrossRef] [PubMed]
  26. A. Sauceda, P. J. García Ramírez, L. García-González, J. Martínez-Castillo, L. Herrera-May, and A. Castro, "Imaging properties of phase shifting apodizers," Rev. Mex. Fis. 52, 336-341 (2006).
  27. A. Sauceda and J. Ojeda-Castañeda, "High focal depth with fractional-power wave fronts," Opt. Lett. 29, 560-562 (2004).
    [CrossRef] [PubMed]
  28. J. Ojeda-Castañeda, J. E. A. Landgrave, and H. M. Escamilla, "Annular phase-only mask for high focal depth," Opt. Lett. 30, 1647-1649 (2005).
    [CrossRef] [PubMed]
  29. K. R. Castleman, Digital image processing (Prentice-Hall, Upper Saddle River, NJ, 1996).
  30. A. E. Siegman, Lasers (University Science, Sausalito, CA, 1986).

2006

A. Stern and B. Javidi, "Three-dimensional sensing, visualization, and processing using integral imaging," Proc. IEEE 94, 591-607 (2006).
[CrossRef]

A. Castro, J. Ojeda-Castañeda, and A.W. Lohmann, "Bow-tie effect: differential operator," Appl. Opt. 45, 7878-7884 (2006).
[CrossRef] [PubMed]

A. Sauceda, P. J. García Ramírez, L. García-González, J. Martínez-Castillo, L. Herrera-May, and A. Castro, "Imaging properties of phase shifting apodizers," Rev. Mex. Fis. 52, 336-341 (2006).

2005

J. Ojeda-Castañeda, J. E. A. Landgrave, and H. M. Escamilla, "Annular phase-only mask for high focal depth," Opt. Lett. 30, 1647-1649 (2005).
[CrossRef] [PubMed]

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools," J. Disp. Technol. 1, 321-327 (2005).
[CrossRef]

D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction of three-dimensional objects in integral imaging using lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

M. Hain, W. von Spiegel, M. Schmiedchen, T. Tschudi, and B. Javidi, "3D integral imaging using diffractive Fresnel lens array," Opt. Express 13, 315-326 (2005).
[CrossRef] [PubMed]

2004

S. Jung, J. Hong, J. H. Park, Y. Kim, and B. Lee, "Depth-enhanced integral-imaging 3D display using different optical path lengths by polarization devices or mirror barrier array," J. Soc. Inf. Disp. 12, 461-467 (2004).
[CrossRef]

M. Martínez-Corral, B. Javidi, R. Martínez-Cuenca, and G. Saavedra, "Integral imaging with improved depth of field by use of amplitude-modulated microlens arrays," Appl. Opt. 43, 5806-5813 (2004).
[CrossRef] [PubMed]

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004).
[CrossRef] [PubMed]

Y. Frauel, E. Tajahuerce, O. Matoba, A. Castro, and B. Javidi, "Comparison of passive ranging integral imaging and active imaging digital holography for three-dimensional object recognition," Appl. Opt. 43, 452-462 (2004).
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, "Depth and lateral size control of three-dimensional images in projection integral imaging," Opt. Express 12, 3778-3790 (2004).
[CrossRef] [PubMed]

S.-H. Hong, J.-S. Jang, and B. Javidi, "Three-dimensional volumetric object reconstruction using computational integral imaging," Opt. Express 12, 483-491 (2004).
[CrossRef] [PubMed]

J.-Y Son, V. Saveljev, J.-S. Kim, S.-S. Kim, and B. Javidi, "Viewing zones in three-dimensional imaging systems based on lenticular, parallax-barrier, and microlens-array plates," Appl. Opt. 43, 4985-4992 (2004).
[CrossRef] [PubMed]

A. Castro and J. Ojeda-Castañeda, "Asymmetric phase mask for extended depth of field," Appl. Opt. 43, 3474-3479 (2004).
[CrossRef] [PubMed]

A. Sauceda and J. Ojeda-Castañeda, "High focal depth with fractional-power wave fronts," Opt. Lett. 29, 560-562 (2004).
[CrossRef] [PubMed]

2003

J.-S. Jang and B. Javidi, "Large depth of focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lens and aperture sizes," Opt. Lett. 28, 1925-1926 (2003).
[CrossRef]

J.-S. Jang, F. Jin, and B. Javidi, "Three-dimensional integral imaging with large depth of focus by use of real and virtual fields," Opt. Lett. 28, 1421-1423 (2003).
[CrossRef] [PubMed]

2002

2001

1997

1995

1972

G. Hausler, "A method to increase the depth of focus by two step image processing," Opt. Commun. 6, 38-42 (1972).
[CrossRef]

1951

H. H. Hopkins, "The frequency response of a defocused optical system," Proc. Roy. Soc. Lond. Series A,  231, 91-103 (1951).
[CrossRef]

Appl. Opt.

J. Disp. Technol.

R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, "Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools," J. Disp. Technol. 1, 321-327 (2005).
[CrossRef]

J. Soc. Inf. Disp.

S. Jung, J. Hong, J. H. Park, Y. Kim, and B. Lee, "Depth-enhanced integral-imaging 3D display using different optical path lengths by polarization devices or mirror barrier array," J. Soc. Inf. Disp. 12, 461-467 (2004).
[CrossRef]

Jpn. J. Appl. Phys.

D.-H. Shin, E.-S. Kim, and B. Lee, "Computational reconstruction of three-dimensional objects in integral imaging using lenslet array," Jpn. J. Appl. Phys. 44, 8016-8018 (2005).
[CrossRef]

Opt. Commun.

G. Hausler, "A method to increase the depth of focus by two step image processing," Opt. Commun. 6, 38-42 (1972).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

A. Stern and B. Javidi, "Three-dimensional sensing, visualization, and processing using integral imaging," Proc. IEEE 94, 591-607 (2006).
[CrossRef]

Proc. Roy. Soc. Lond. Series A

H. H. Hopkins, "The frequency response of a defocused optical system," Proc. Roy. Soc. Lond. Series A,  231, 91-103 (1951).
[CrossRef]

Rev. Mex. Fis.

A. Sauceda, P. J. García Ramírez, L. García-González, J. Martínez-Castillo, L. Herrera-May, and A. Castro, "Imaging properties of phase shifting apodizers," Rev. Mex. Fis. 52, 336-341 (2006).

Other

J. W. Goodman, Introduction to Fourier optics, 2nd Ed. Chap. 6 (McGraw-Hill, New York, NY, 1996).

K. R. Castleman, Digital image processing (Prentice-Hall, Upper Saddle River, NJ, 1996).

A. E. Siegman, Lasers (University Science, Sausalito, CA, 1986).

J. Ojeda-Castañeda, A. Castro, and J. Santamaría, "Phase mask for high focal depth," in The 18th Congress of the International Commission for Optics A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, and T. Asakura, eds., Proc. SPIE 3749, 14 (1999).
[CrossRef]

A. Castro and J. Ojeda-Castañeda, "Increased depth of field with phase-only filters: ambiguity function," in Opto-Ireland 2005: Photonic Engineering, B. W. Bowe, G. Byrne, A. J. Flanagan, T. J. Glynn, J. Magee, G. M. O’Connor, R. F. O’Dowd, G. D. O’Sullivan, and J. T. Sheridan, eds., Proc. SPIE 5827, 1-11 (2005).
[CrossRef]

B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies, (Springer Berlin, 2002).

Supplementary Material (3)

» Media 1: AVI (218 KB)     
» Media 2: AVI (214 KB)     
» Media 3: AVI (407 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Modulation Transfer Function for various amounts of defocus for (a) a regular lenslet (b) a lenslet with an quartic phase mask.

Fig. 2.
Fig. 2.

Central elemental image of a point object (PSF). (a)–(d) correspond to a regular lenslet, (e)–(h) to a lenslet with a quartic phase mask, (i)–(l) to a lenslet with a quartic phase mask and digital restauration. The first, second, third and fourth rows are for a point object located at z=z0 =-100 mm (in focus), z=-87 mm, z=-80 mm, and z=-70 mm respectively.

Fig. 3.
Fig. 3.

Central elemental images of a scene with four E charts at various distances. (a) Regular lenslet. (b) Lenslet with a quartic phase mask. (c) Lenslet with a quartic phase mask and digital restauration.

Fig. 4.
Fig. 4.

Peak value of the elemental PSF versus distance of the object point. (a) Regular lenslet. (b) Lenslet with a quartic phase mask.

Fig. 5.
Fig. 5.

Movie of simulated reconstruction for the E chart: (a) regular lenslet array (218 KB) [Media 1], (b) lenslets with a quartic phase mask (213 KB) [Media 2], (c) lenslets with a quartic phase mask and digital restauration (407 KB) [Media 3].

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

1 z = 1 z + 1 f ,
P ( x , y ) = φ ( x ) φ ( y ) Q ( x , y ) ,
φ ( x ) = exp [ i 2 π α sgn ( x ) x w k ] ,
𝓟 ( x , y ) = P ( x , y ) exp [ i 2 π W 20 λ ( x 2 + y 2 w 2 ) ] ,
W 20 = 1 2 ( 1 z 0 1 z 1 f ) w 2 ,
W 20 = 1 2 ( 1 z 0 1 z ) w 2 .
P ( x , y ) = m = 1 M n = 1 N φ ( x x m ) φ ( y y n ) Q ( x x m , y y n ) ,

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