Abstract

In this paper we present a new approach for obtaining all-optical axial super-resolving imaging by using a non-diffractive binary phase mask inserted at the entrance pupil of an imaging lens. The designed element is tested numerically and experimentally on various practical testing benches and eventually is inserted into the lens of a cellular phone camera.

© 2006 Optical Society of America

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References

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  1. W. T. Cathy and E. R Dowski, "Apparatus and method for extending depth of field in image projection system," US patent 6069738 (May 2000).
  2. W. T. Cathy and E. R Dowski, "Extended depth of field optical systems," PCT publication WO 99/57599 (November 1999).
  3. W. T. Cathy, "Extended depth field optics for human vision," PCT publication WO 03/052492 (June 2003).
  4. E. R Dowski and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
  5. J. van der Gracht, E. Dowski, M. Taylor, D. Deaver, "Broadband behavior of an optical-digital focus-invariant system," Opt. Lett. 21, 919-921 (1996).
    [CrossRef] [PubMed]
  6. C. M. Hammond, "Apparatus and method for reducing imaging errors in imaging systems having an extended depth of field," US patent 6097856 (August 2000).
  7. D. Miller and E. Blanko, "System and method for increasing the depth of focus of the human eye," US patent 6554424 (April 2003).
  8. N. Atebara and D. Miller, "Masked intraocular lens and method for treating a patient with cataracts," US patent 4955904 (September 1990).
  9. J. O. Castaneda, E. Tepichin and A. Diaz, "Arbitrary high focal depth with a quasi optimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2669 (1989).
    [CrossRef]
  10. J. O. Castaneda and L. R. Berriel-Valdos, "Zone plate for arbitrary high focal depth," Appl. Opt. 29, 994-997 (1990).
    [CrossRef]
  11. E. Ben-Eliezer, Z. Zalevsky, E. Marom, N. Konforti and D. Mendlovic, "All optical extended depth of field imaging system," PCT publication WO 03/076984 (September 2003).
  12. E. Ben-Eliezer, Z. Zalevsky, E. Marom and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003).
    [CrossRef]
  13. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005).
    [CrossRef] [PubMed]
  14. A. Sauceda and J. Ojeda-Castaneda, "High focal depth with fractional-power wavefronts," Opt. Lett. 29, 560-562 (2004).
    [CrossRef] [PubMed]
  15. W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett. 26, 875-877 (2001).
    [CrossRef]
  16. Z. Zalevsky, "Optical method and system for extended depth of focus," US patent application 10/97494 (August 2004).
  17. J. W Goodman, Introduction to Fourier Optics (McGraw-Hill, New York 1996) pp.126-151.
  18. T. Q. Pham and L. J. van Vliet, "Separable bilateral filtering for fast video processing," http://www.qi.tnw.tudelft.nl/~lucas.

2005 (1)

2004 (1)

2003 (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

2001 (1)

1996 (1)

1995 (1)

1990 (1)

1989 (1)

Ben-Eliezer, E.

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "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," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

Berriel-Valdos, L. R.

Castaneda, J. O.

Cathey, W. T.

Chi, W.

Deaver, D.

Diaz, A.

Dowski, E.

Dowski, E. R

George, N.

Konforti, N.

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "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," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

Marom, E.

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "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," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

Ojeda-Castaneda, J.

Sauceda, A.

Taylor, M.

Tepichin, E.

van der Gracht, J.

Zalevsky, Z.

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "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," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

Appl. Opt. (4)

J. Opt. A: Pure Appl. Opt. (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A: Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

Opt. Lett. (3)

Other (10)

C. M. Hammond, "Apparatus and method for reducing imaging errors in imaging systems having an extended depth of field," US patent 6097856 (August 2000).

D. Miller and E. Blanko, "System and method for increasing the depth of focus of the human eye," US patent 6554424 (April 2003).

N. Atebara and D. Miller, "Masked intraocular lens and method for treating a patient with cataracts," US patent 4955904 (September 1990).

E. Ben-Eliezer, Z. Zalevsky, E. Marom, N. Konforti and D. Mendlovic, "All optical extended depth of field imaging system," PCT publication WO 03/076984 (September 2003).

W. T. Cathy and E. R Dowski, "Apparatus and method for extending depth of field in image projection system," US patent 6069738 (May 2000).

W. T. Cathy and E. R Dowski, "Extended depth of field optical systems," PCT publication WO 99/57599 (November 1999).

W. T. Cathy, "Extended depth field optics for human vision," PCT publication WO 03/052492 (June 2003).

Z. Zalevsky, "Optical method and system for extended depth of focus," US patent application 10/97494 (August 2004).

J. W Goodman, Introduction to Fourier Optics (McGraw-Hill, New York 1996) pp.126-151.

T. Q. Pham and L. J. van Vliet, "Separable bilateral filtering for fast video processing," http://www.qi.tnw.tudelft.nl/~lucas.

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Figures (6)

Fig. 1.
Fig. 1.

(a). A cross section of the designed element. (b). The OTF versus spatial frequency without the EDOF. (c). -(e). The OTF versus spatial frequency with the EDOF for objects at 50cm, 15cm and infinity respectively. (f). The through focus OTF without the EDOF element for frequency of 80cycles/.mm for object at 50cm. (g).-(h). The through focus OTF with the EDOF element for frequency of 80cycles/.mm for object at 15cm and at infinity respectively.

Fig. 2.
Fig. 2.

(a). The images were captured when the object is in focus. Left part is without the EDOF element and the right part is with it. (b). The same as Fig. 2(a) but this time the object is positioned in an out of focus plane in which ψ=17 (shift of +2mm aside from the in focus plane).

Fig. 3.
Fig. 3.

2-D test grating positioned at out of focus planes of ψ=±13 (shift of ±1.5mm aside from the in focus plane). (a). Without element and for ψ=13 and (b). Without element and for ψ=-13. (c). and (d). Shows the same as Figs. 3(a) and 3(b) but this time with the EDOF element.

Fig. 4.
Fig. 4.

2-D test grating positioned at out of focus plane of ψ=15. (a). Without element and for ψ=15 and (b). With element and for ψ=15. (c). Without element in focus. (d). With element in focus.

Fig. 5.
Fig. 5.

Close and far range all optical experiments with television resolution target. (a). The optical setup. (b). Without EDOF element and object at 15cm. (c). Zoom of Fig. 5(b). (d). With EDOF element and object at 15cm. (e). Zoom of Fig. 5(d). (f). Without EDOF element and object at 150cm. (g). With EDOF element and object at 150cm.

Fig. 6.
Fig. 6.

(a). Without EDOF element. (b). With EDOF element but without digital processing. (c). The image of Fig. 6(b) after applying digital processing.

Equations (27)

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H ( μ x , μ y ; Z i ) = P ( x + λ Z i μ x 2 , y + λ Z i μ y 2 ) P * ( x λ Z i μ x 2 , y λ Z i μ y 2 ) dxdy P x y 2 dxdy
P x y = P x y exp [ ikW x y ]
W x y = W m ( x 2 + y 2 ) b 2
W m = Ψλ 2 π
Ψ = π b 2 λ ( 1 Z i + 1 Z o 1 F )
1 Z i + 1 Z o = 1 F
H ( μ ; Z i ) = P ( x + λ Z i μ 2 ) n = 1 N exp ( ia n rect ( x + λ Z i μ 2 nΔx Δx ) ) P * ( x λ Z i μ 2 ) n = 1 N exp ( ia n rect ( x λ Z i μ 2 nΔx Δx ) ) dx P ( x ) 2 dx
max a n , Δx { min μ x { H ( μ x ; Z i , W m ) } + min μ x { H ( μ x ; Z i , 0 ) } }
H μ W m sin c ( 4 π W m Z i μ b ) 2 b { δ ( μ ) + 2 sin c ( 2 π W m Z i μΔx b 2 ) [ cos ( 2 π W m λ Z i 2 μ 2 b 2 Δϕ ) cos ( 2 π W m λ Z i 2 μ 2 b 2 ) ] }
cos α cos β = 2 sin ( α + β 2 ) sin ( β α 2 )
H μ W m sin c ( 4 π W m Z i μ b ) 2 b + 4 sin ( Δϕ 2 ) 2 b sin c ( 4 π W m Z i μ b ) { sin c ( 2 π W m Z i μΔx b 2 ) sin ( 2 π W m λ Z i 2 μ 2 b 2 Δϕ 2 ) }
H μ 0 = 1 2 b rect ( x + λ Z i μ / 2 Δx ) rect ( x λ Z i μ / 2 Δx ) exp [ iΔϕ rect ( x + λ Z i μ / 2 Δx ) ]
exp [ iΔϕ rect ( x λ Z i μ / 2 Δx ) ] dx
H μ 0 = { 1 3 λ Z i μ 2 b + λ Z i μ cos Δϕ b μ < Δx λ Z i 1 Δx b λ Z i μ 2 b + Δx cos Δϕ b Δx λ Z i < μ < b λ Z i Δx λ Z i λ Z i μ 2 b Δx 2 b + ( b λ Z i μ + Δx / 2 ) cos Δϕ b b λ Z i Δx / 2 λ Z i < μ < b λ Z i + Δx / 2 λ Z i 1 λ Z i μ 2 b b λ Z i + Δx / 2 λ Z i < μ < 2 b λ Z i
f S ( x ) = f ( x ) a x′ f ( x′ ) K ( x x′ )
exp [ ( x x′ ) 2 2 σ D 2 ] exp [ ( f ( x ) f ( x′ ) ) 2 2 σ R 2 ]
H μ W m = P ( x + λ Z i μ 2 ) p * ( x λ Z i μ 2 ) dx P ( x ) 2 dx = A ( μ ) exp [ ik W m 2 λ Z i μx b 2 ] dx 2 b
H μ W m A ( 0 ) exp [ ik W m 2 λ Z i μx b 2 ] dx 2 b = b b exp [ 4 πi W m Z i μx b 2 ] dx 2 b
= 1 2 b rect ( x 2 b ) exp [ 4 πi W m Z i μx b 2 ] dx = sin c ( 4 W m πμ Z i b ) 2 b
H μ W m 1 2 b b b exp [ 4 πi W m Z i μx b 2 ] exp [ iΔϕ rect ( x + λ Z i μ / 2 Δx ) ]
exp [ iΔϕ rect ( x λ Z i μ / 2 Δx ) ] dx
exp [ iΔϕ rect ( x + λ Z i μ / 2 Δx ) ] exp [ iΔϕ rect ( x λ Z i μ / 2 Δx ) ]
1 + [ exp ( iΔϕ ) 1 ] rect ( x + λ Z i μ / 2 Δx ) + [ exp ( iΔϕ ) 1 ] rect ( x λ Z i μ / 2 Δx )
H μ W m 1 2 b rect ( x 2 b ) { 1 + [ exp ( iΔϕ ) 1 ] rect ( x + λ Z i μ / 2 Δx ) +
+ [ exp ( iΔϕ ) 1 ] rect ( x λ Z i μ / 2 Δx ) } exp [ 4 πi W m Z i μx b 2 ] dx
H μ W m 1 2 b { δ ( μ ) + [ exp ( iΔϕ ) 1 ] sin c ( 2 π W m Z i μΔx b 2 ) exp ( 2 πi W m λ Z i 2 μ 2 b 2 ) +
[ exp ( iΔϕ ) 1 ] sin c ( 2 π W m Z i μΔx b 2 ) exp ( 2 πi W m λ Z i 2 μ 2 b 2 ) } sin c ( 4 π W m Z i μ b )

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