Abstract

What we believe to be a new phase-contrast technique is proposed to recover intensity distributions from phase distributions modulated by spatial light modulators (SLMs) and binary diffractive optical elements (DOEs). The phase distribution is directly transformed into intensity distributions using a 4f optical correlator and an iris centered in the frequency plane as a spatial filter. No phase-changing plates or phase dielectric dots are used as a filter. This method allows the use of twisted nematic liquid-crystal televisions (LCTVs) operating in the real-time phase-mostly regime mode between 0 and p to generate high-intensity multiple beams for optical trap applications. It is also possible to use these LCTVs as input SLMs for optical correlators to obtain high-intensity Fourier transform distributions of input amplitude objects.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. J. W. Brown and A. W. Lohmann, "Computer-generated binary holograms," IBM J. Res. Dev. 14, 160-167 (1969).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 351-361.
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    [CrossRef] [PubMed]
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    [PubMed]
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    [CrossRef] [PubMed]
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  9. D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, and E. Marom, "Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms," Appl. Opt. 36, 8427-8434 (1997).
    [CrossRef]
  10. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, "Encoding amplitude information onto phase-only filters," Appl. Opt. 38, 5004-5013 (1999).
    [CrossRef]
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    [CrossRef]
  13. L. G. Neto, D. Roberge, and Y. Sheng, "Programmable optical phase-mostly holograms with coupled-mode modulation liquid crystal television," Appl. Opt. 34, 1944-1950 (1995).
    [CrossRef] [PubMed]
  14. L. G. Neto, D. Roberge, and Y. Sheng, "Full range continuous complex modulation using two coupled-mode liquid crystal televisions," Appl. Opt. 35, 4567-4576 (1996).
    [CrossRef] [PubMed]
  15. R. W. Gerchberg and W. O. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  26. L. G. Neto, L. B. Roberto, P. Verdonck, R. D. Mansano, G. A. Cirino, and M. A. Stefani, "Multiple line generation over high angle using a hybrid difractive-refractive phase element," Appl. Opt. 40, 211-218 (2001).
    [CrossRef]
  27. J. C. Pizolato, Jr. and L. G. Neto, "The zero-order phase-contrast technique," in Diffractive Optics and Micro-Optics Topical Meeting (Optical Society of America, 2004), paper DMA4.
  28. L. G. Neto, P. S. P. Cardona, G. A. Cirino, R. D. Mansano, and P. Verdonck, "Design, fabrication and characterization of a full complex-amplitude modulation difractive optical element," J. Microlithogr. , Microfabr., Microsyst. 2, 96-104 (2003).
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2004 (1)

L. G. Neto, G. A. Cirino, R. D. Mansano, and P. Verdonck, "Implementation of Fresnel full complex-amplitude digital holograms," Opt. Eng. 43, 2640-2649 (2004).
[CrossRef]

2003 (1)

L. G. Neto, P. S. P. Cardona, G. A. Cirino, R. D. Mansano, and P. Verdonck, "Design, fabrication and characterization of a full complex-amplitude modulation difractive optical element," J. Microlithogr. , Microfabr., Microsyst. 2, 96-104 (2003).
[CrossRef]

2002 (2)

2001 (3)

1999 (1)

1998 (2)

R. D. Mansano, P. Verdonk, and H. S. Maciel, "Anisotropic reactive ion etching in silicon, using a graphite electrode," Sens. Actuators A 65, 180-186 (1998).
[CrossRef]

L. G. Neto, "Implementation of image encryption using phase contrast techniques," Proc. SPIE 3386, 284-289 (1998).
[CrossRef]

1997 (2)

1996 (2)

1995 (1)

1994 (1)

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

1993 (1)

C. Soutar, S. E. Monroe, Jr., and J. Knopp, "Complex characterisation of the Epson liquid crystal television," Proc. SPIE 1959, 269-277 (1993).
[CrossRef]

1990 (1)

1973 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).

1970 (3)

W. H. Lee, "Sampled Fourier transform hologram generated by computer," Appl. Opt. 9, 639-643 (1970).
[CrossRef] [PubMed]

C. B. Burckhardt, "A simplification of Lee's method of generating holograms by computer," Appl. Opt. 9, 1949 (1970).
[PubMed]

W. Kern and D. A. Puotinen, "Cleaning solution based on hydrogen peroxide for use in semiconductor technology," RCA Rev. 31, 187-206 (1970).

1969 (1)

J. W. Brown and A. W. Lohmann, "Computer-generated binary holograms," IBM J. Res. Dev. 14, 160-167 (1969).
[CrossRef]

1967 (1)

Appl. Opt. (10)

W. H. Lee, "Sampled Fourier transform hologram generated by computer," Appl. Opt. 9, 639-643 (1970).
[CrossRef] [PubMed]

C. B. Burckhardt, "A simplification of Lee's method of generating holograms by computer," Appl. Opt. 9, 1949 (1970).
[PubMed]

D. C. Chu, J. R. Fienup, and J. W. Goodman, "Multiemulsion on-axis computer generated hologram," Appl. Opt. 12, 1386-1388 (1973).
[CrossRef] [PubMed]

A. W. Lohmann and D. P. Paris, "Binary Fraunhofer holograms, generated by computer," Appl. Opt. 6, 1739-1748 (1967).
[CrossRef] [PubMed]

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, and E. Marom, "Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms," Appl. Opt. 36, 8427-8434 (1997).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, "Encoding amplitude information onto phase-only filters," Appl. Opt. 38, 5004-5013 (1999).
[CrossRef]

L. G. Neto, D. Roberge, and Y. Sheng, "Programmable optical phase-mostly holograms with coupled-mode modulation liquid crystal television," Appl. Opt. 34, 1944-1950 (1995).
[CrossRef] [PubMed]

L. G. Neto, D. Roberge, and Y. Sheng, "Full range continuous complex modulation using two coupled-mode liquid crystal televisions," Appl. Opt. 35, 4567-4576 (1996).
[CrossRef] [PubMed]

P. C. Mogensen and J. Glückstad, "Phase-only optical decryption of a fixed mask," Appl. Opt. 40, 1226-1235 (2001).
[CrossRef]

L. G. Neto, L. B. Roberto, P. Verdonck, R. D. Mansano, G. A. Cirino, and M. A. Stefani, "Multiple line generation over high angle using a hybrid difractive-refractive phase element," Appl. Opt. 40, 211-218 (2001).
[CrossRef]

IBM J. Res. Dev. (1)

J. W. Brown and A. W. Lohmann, "Computer-generated binary holograms," IBM J. Res. Dev. 14, 160-167 (1969).
[CrossRef]

J. Microlithogr. (1)

L. G. Neto, P. S. P. Cardona, G. A. Cirino, R. D. Mansano, and P. Verdonck, "Design, fabrication and characterization of a full complex-amplitude modulation difractive optical element," J. Microlithogr. , Microfabr., Microsyst. 2, 96-104 (2003).
[CrossRef]

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

Opt. Eng. (2)

C. Soutar and K. Lu, "Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell," Opt. Eng. 33, 2704-2712 (1994).
[CrossRef]

L. G. Neto, G. A. Cirino, R. D. Mansano, and P. Verdonck, "Implementation of Fresnel full complex-amplitude digital holograms," Opt. Eng. 43, 2640-2649 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (Stuttgart) (1)

R. W. Gerchberg and W. O. Saxton, "Practical algorithm for determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).

Proc. SPIE (2)

C. Soutar, S. E. Monroe, Jr., and J. Knopp, "Complex characterisation of the Epson liquid crystal television," Proc. SPIE 1959, 269-277 (1993).
[CrossRef]

L. G. Neto, "Implementation of image encryption using phase contrast techniques," Proc. SPIE 3386, 284-289 (1998).
[CrossRef]

RCA Rev. (1)

W. Kern and D. A. Puotinen, "Cleaning solution based on hydrogen peroxide for use in semiconductor technology," RCA Rev. 31, 187-206 (1970).

Sens. Actuators A (1)

R. D. Mansano, P. Verdonk, and H. S. Maciel, "Anisotropic reactive ion etching in silicon, using a graphite electrode," Sens. Actuators A 65, 180-186 (1998).
[CrossRef]

Other (5)

J. C. Pizolato, Jr. and L. G. Neto, "The zero-order phase-contrast technique," in Diffractive Optics and Micro-Optics Topical Meeting (Optical Society of America, 2004), paper DMA4.

W. Kern, ed., Handbook of Semiconductor Wafer Cleaning Technology: Science, Technology and Application (Noyes, 1993), p. 443.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 220-222.

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 351-361.

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Figures (12)

Fig. 1
Fig. 1

Phase object used to implement the zeroth-order phase-contrast technique. t ( x , y ) has M × N square pixels of size X × Y , generated from a gray-level image a ( x , y ) of M × N square pixels. Two regions that modulate different values of phase compose each pixel. One region of pixels is formed considering the information of a ( x , y ) and the other by the phase value exp(jp).

Fig. 2
Fig. 2

System that forms the zero-order phase-contrast technique based on an image-forming system such as the 4f optical correlator.

Fig. 3
Fig. 3

Numerical simulation of the zeroth-order phase-contrast technique. (a) 256 × 256 gray-level image used to generate the amplitude information a ( x , y ) . The distribution t ( x , y ) is formed from a ( x , y ) as described in Fig. 1 and Eq. (5). (b) Image of the intensity distribution S ( u , v ) on the Fourier plane. Only the delimited area is used to recover the original information a ( x , y ) . (c) Numerical recovered image.

Fig. 4
Fig. 4

Optical simulation of the zeroth-order phase-contrast technique. The intensity distribution resulting from the optical simulation of the proposed method using a CCD camera to image the output of an experimental setup similar to Fig. 2.

Fig. 5
Fig. 5

Pixel structure of a DOE. The DOE is considered a two-dimensional matrix structure with M × N rectangular cells of dimensions X × Y . In each pixel, one region is formed considering the phase value exp ( j 0 ) and the other, the phase value exp ( j p ) .

Fig. 6
Fig. 6

Schematic view of the fabrication process sequence of the DOE operating in transmittance mode. Because of the low-cost fabrication approach, a photomask that consists of a teaching-class transparency film was used. The pattern to be transferred was printed in the transparency film by a 15 μ m minimum feature-size 2400 dpi plotter Agfa Avantra 30e. No electron-beam-generated photomask is required.

Fig. 7
Fig. 7

Photography of a wafer showing the geometry of a rectangular pixel structure with the size of 15 μ m × 15 μ m .

Fig. 8
Fig. 8

Schematic view of the fabrication process sequence of the DOE operating in reflectance mode.

Fig. 9
Fig. 9

Schematic view of the experimental setup used for implementing the optical reconstruction of the zeroth-order phase-contrast technique of a DOE operating in transmittance mode.

Fig. 10
Fig. 10

Optical reconstruction of an intensity distribution image encoded in DOE transmittance mode fabricated using the steps described in Section 4. The recovered information was imaged onto a CCD camera.

Fig. 11
Fig. 11

Schematic view of the experimental setup used for implementing the optical reconstruction of the zeroth-order phase-contrast technique of a DOE operating in reflection mode.

Fig. 12
Fig. 12

Optical reconstruction from a DOE reflection mode.

Equations (18)

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t ( x , y ) 1 + j a ( x , y ) .
I ( x , y ) | 1 + j a ( x , y ) | 2 1 .
I ( x , y ) | exp [ j ( π / 2 ) ] + j a ( x , y ) | 2 1 + 2 a ( x , y ) .
t ( x , y ) = { exp [ j a ( x , y ) ] I I I [ x / X , ( y Y / 4 ) / Y ] + exp ( j π ) I I I [ x / X , ( y + Y / 4 ) / Y ] } *   rect ( x / X , 2 y / Y ) ,
t ( x , y ) { [ 1 + j a ( x , y ) ] I I I [ x / X , ( y Y / 4 ) / Y ] + exp ( j π ) I I I [ x / X , ( y + y / 4 ) / Y ] } *   rect ( x / X , 2 y / Y ) .
I ( x , y ) { [ 1 + j a ( x , y ) ] I I I [ x / X , ( y Y / 4 ) / Y ] + exp ( j π ) I I I [ x / X , ( y + Y / 4 ) / Y ] }  *  rect ( x / X , 2 y / Y ) 2 1 .
S ( u , v ) X Y { j A ( u , v ) * [ I I I ( X u , Y v ) exp ( j π Y v / 2 ) ] + I I I ( X u , Y v ) exp ( j π Y v / 2 ) I I I ( X u , Y v ) exp ( j π Y v / 2 ) } × [ ( X Y / 2 ) sinc ( X u , Y v / 2 ) ] .
S ( u , v ) ( X 2 Y 2 / 2 ) { j A ( u , v ) * [ I I I ( X u , Y v ) × exp ( j π Y v / 2 ) ] + I I I ( X u , Y v ) exp ( j π Y v / 2 ) I I I ( X u , Y v ) exp ( j π Y v / 2 ) } × [ sinc ( X u , Y v / 2 ) rect ( X u , Y v ) ] .
S ( u , v ) ( X 2 Y 2 / 2 ) [ j A ( u , v ) * δ ( u , v ) + δ ( u , v ) δ ( u , v ) ] sinc ( X u , Y v / 2 ) j A ( u , v ) sinc ( X u , Y v / 2 ) A ( u , v ) .
I ( x , y ) = a ( x , y ) 2 .
e z e r o t h = { [ M X 2 ( M 2 1 ) X N Y 2 ( N 2 1 ) Y S ( u , v ) 2 d u d v ] / [ S ( u , v ) 2 d u d v ] } × 100 % .
g ( x , y ) = k = M / 2 M / 2 1 l = N / 2 N / 2 1 rect [ ( x k X ) / X ] [ H ( y Y / 2 ) H ( y Y / 2 ) + sgn ( y + a k l ) ] × rect ( x / M X , y / N Y ) ,
G ( u , v ) = M N X 2 Y 2 ( k = M / 2 M / 2 1 l = N / 2 N / 2 1 sinc ( X u ) × exp ( j 2 π k X u ) { [ δ ( v ) / 2 + j / 2 π v ] × exp ( j π Y v ) [ δ ( v ) / 2 j / 2 π v ] exp ( j π Y v ) ( j / π v ) exp ( j 2 π a v ) } ) * sinc ( M X u , N Y v ) ,
G ( u , v ) = M N X 2 Y 2 { k = M / 2 M / 2 1 l = N / 2 N / 2 1 [ exp ( j 2 π k X u ) ] [ ( j / π v ) cos ( π Y v ) ( j / π v ) cos ( 2 π a k l v ) + ( 1 / π v ) sin ( 2 π a k l v ) ] } .
G ( u , v ) = 2 M N X 2 Y 2 [ k = M / 2 M / 2 1 l = N / 2 N / 2 1 a k l   exp ( j 2 π k X u ) ] ,
g ( x , y ) = T F 1 [ G ( u , v ) ] = 2 M N X 2 Y 2 a k l ,
t h ( x , y ) = [ λ g ( x , y ) ] / [ 2 π ( n 1 ) ] ,
t h ( x , y ) = [ λ   cos ( θ ) ] / 4 ,

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