Abstract

We discuss a class of phase computer-generated holograms for the encoding of arbitrary scalar complex fields. We describe two holograms of this class that allow high quality reconstruction of the encoded field, even if they are implemented with a low-resolution pixelated phase modulator. In addition, we show that one of these holograms can be appropriately implemented with a phase modulator limited by a reduced phase depth.

© 2007 Optical Society of America

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References

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  1. A. W. Lohmann and D. P. Paris, 'Binary Frauhofer holograms generated by computer,' Appl. Opt. 6, 1739-1748 (1967).
    [CrossRef] [PubMed]
  2. C. K. Hsueh and A. A. Sawchuk, 'Computer-generated double-phase holograms,' Appl. Opt. 17, 3874-3883 (1978).
    [CrossRef] [PubMed]
  3. W. J. Dallas, 'Computer-generated holograms,' in The Computer in Optical Research, B.R.Frieden, ed. (Springer-Verlag, 1980), pp. 4156-4165.
  4. N. Mait and K.-H. Brenner, 'Dual-phase holograms: improved design,' Appl. Opt. 26, 4883-4892 (1987).
    [CrossRef] [PubMed]
  5. O. Bryngdahl and F. Wyrowski, 'Digital Holography-Computer-Generated Holograms,' in Progress in Optics, Vol. XXVIII, E.Wolf, ed. (North-Holland, 1990), pp. 1-86.
    [CrossRef]
  6. R. W. Cohn and M. Liang, 'Approximating fully complex spatial modulation with pseudorandom phase-only modulation,' Appl. Opt. 33, 4406-4415 (1994).
    [CrossRef] [PubMed]
  7. V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, 'Zeroth-order coding of complex amplitude in two dimensions,' J. Opt. Soc. Am. A 14, 808-815 (1997).
    [CrossRef]
  8. 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]
  9. 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]
  10. M. A. A. Neil, T. Wilson, and R. Juskaitis, 'A wavefront generator for complex pupil function synthesis and point spread function engineering,' J. Microsc. 197, 219-223 (2000).
    [CrossRef] [PubMed]
  11. V. Arrizón, 'Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices,' Opt. Lett. 28, 2521-2523 (2003).
    [CrossRef] [PubMed]
  12. V. Arrizón, G. Méndez, and D. Sánchez-de-La-Llave, 'Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators,' Opt. Express 13, 7913-7927 (2005).
    [CrossRef] [PubMed]
  13. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1922), p. 22.
  14. A. Ashkin and J. M. Dziedzic, 'Optical trapping and manipulation of single living cells using infrared-laser beams,' Ber. Bunsenges. Phys. Chem. 93, 254-260 (1989).
  15. A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, 'Force generation of organelle transport measured in vivo by an infrared laser trap,' Nature (London) 348, 346-348 (1990).
    [CrossRef]
  16. W. H. Wright, G. J. Sonek, Y. Tadir, and M. W. Berns, 'Laser trapping in cell biology,' Int. J. Quantum Chem. 26, 2148-2157 (1990).
  17. I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, 'Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,' Jpn. J. Appl. Phys., Part 1 34, 6423-6434 (1995).
    [CrossRef]
  18. R. Ponce, A. Serrano-Heredia, and V. Arrizón, 'Simplified optimum phase-only configuration for a TNLCD,' Proc. SPIE 5556, 206-213 (2004).
    [CrossRef]
  19. H. Kim and Y. H. Lee, 'Unique measurement of the parameters of a twisted-nematic liquid-crystal display,' Appl. Opt. 44, 1642-1649 (2005).
    [CrossRef] [PubMed]

2005 (2)

2004 (1)

R. Ponce, A. Serrano-Heredia, and V. Arrizón, 'Simplified optimum phase-only configuration for a TNLCD,' Proc. SPIE 5556, 206-213 (2004).
[CrossRef]

2003 (1)

2000 (1)

M. A. A. Neil, T. Wilson, and R. Juskaitis, 'A wavefront generator for complex pupil function synthesis and point spread function engineering,' J. Microsc. 197, 219-223 (2000).
[CrossRef] [PubMed]

1999 (1)

1997 (2)

1995 (1)

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, 'Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,' Jpn. J. Appl. Phys., Part 1 34, 6423-6434 (1995).
[CrossRef]

1994 (1)

1990 (2)

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, 'Force generation of organelle transport measured in vivo by an infrared laser trap,' Nature (London) 348, 346-348 (1990).
[CrossRef]

W. H. Wright, G. J. Sonek, Y. Tadir, and M. W. Berns, 'Laser trapping in cell biology,' Int. J. Quantum Chem. 26, 2148-2157 (1990).

1989 (1)

A. Ashkin and J. M. Dziedzic, 'Optical trapping and manipulation of single living cells using infrared-laser beams,' Ber. Bunsenges. Phys. Chem. 93, 254-260 (1989).

1987 (1)

1978 (1)

1967 (1)

Appl. Opt. (7)

Ber. Bunsenges. Phys. Chem. (1)

A. Ashkin and J. M. Dziedzic, 'Optical trapping and manipulation of single living cells using infrared-laser beams,' Ber. Bunsenges. Phys. Chem. 93, 254-260 (1989).

Int. J. Quantum Chem. (1)

W. H. Wright, G. J. Sonek, Y. Tadir, and M. W. Berns, 'Laser trapping in cell biology,' Int. J. Quantum Chem. 26, 2148-2157 (1990).

J. Microsc. (1)

M. A. A. Neil, T. Wilson, and R. Juskaitis, 'A wavefront generator for complex pupil function synthesis and point spread function engineering,' J. Microsc. 197, 219-223 (2000).
[CrossRef] [PubMed]

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

Jpn. J. Appl. Phys., Part 1 (1)

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, 'Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,' Jpn. J. Appl. Phys., Part 1 34, 6423-6434 (1995).
[CrossRef]

Nature (London) (1)

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, 'Force generation of organelle transport measured in vivo by an infrared laser trap,' Nature (London) 348, 346-348 (1990).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

R. Ponce, A. Serrano-Heredia, and V. Arrizón, 'Simplified optimum phase-only configuration for a TNLCD,' Proc. SPIE 5556, 206-213 (2004).
[CrossRef]

Other (3)

W. J. Dallas, 'Computer-generated holograms,' in The Computer in Optical Research, B.R.Frieden, ed. (Springer-Verlag, 1980), pp. 4156-4165.

O. Bryngdahl and F. Wyrowski, 'Digital Holography-Computer-Generated Holograms,' in Progress in Optics, Vol. XXVIII, E.Wolf, ed. (North-Holland, 1990), pp. 1-86.
[CrossRef]

G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1922), p. 22.

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Figures (10)

Fig. 1
Fig. 1

Function f ( a ) versus a for the CGHs of types 1 (solid curve), 2 (dashed curve), and 3 (dotted curve).

Fig. 2
Fig. 2

Double-Fourier transform optical setup for the generation of scalar complex fields employing a CGH.

Fig. 3
Fig. 3

Schematic spatial distribution of the CGH spectra terms H q ( u q u 0 , v q v 0 ) when u 0 = v 0 .

Fig. 4
Fig. 4

Function log ( ρ ) versus a, where ρ = c Q R + 1 a 2 c 1 a 2 (for Q = 6 ) for the CGHs of types (a) 1, (b) 2, and (c) 3. The values of index R are 1 (solid curve) and 2 (dashed curve).

Fig. 5
Fig. 5

Phase distributions of CGHs of (a) type 2 and (b) type 3 that encode a Laguerre–Gauss beam of indices ( p , l ) = ( 1 , 1 ) .

Fig. 6
Fig. 6

(a) Spectrum modulus of a complex Laguerre–Gauss beam with indices ( p , l ) = ( 1 , 1 ) , and signal spectrum modules obtained with CGHs of types (b) 2, (c) 3, and (d) 1 that encode this beam.

Fig. 7
Fig. 7

Function log ( SNR ) versus the normalized waist w 0 δ x for CGHs of types 1 (circles), 2 (squares), and 3 (triangles) designed to encode a Laguerre–Gauss beam of indices ( p , l ) = ( 2 , 2 ) .

Fig. 8
Fig. 8

(a) Phase and (b) amplitude modulations provided by a translucent twisted nematic LC device (LC2002 of HoloEye Photonics LG) configured as a phase-mostly modulator.

Fig. 9
Fig. 9

Experimentally recorded intensity distributions of nondiffracting Bessel beams of orders (a) 1, (b) 2, and (c) 4 generated by type 3 CGHs employing the SLM modulation displayed in Fig. 8.

Fig. 10
Fig. 10

Experimentally recorded intensity distributions of Laguerre–Gauss beams of indices (a) ( p , l ) = ( 0 , 2 ) , (b) ( p , l ) = ( 0 , 4 ) , and (c) ( p , l ) = ( 2 , 4 ) generated by type 3 CGHs employing the SLM modulation displayed in Fig. 8.

Equations (23)

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s ( x , y ) = a ( x , y ) exp [ i ϕ ( x , y ) ] ,
h ( x , y ) = exp [ i ψ ( a , ϕ ) ] ,
h ( x , y ) = q = h q ( x , y ) ,
h q ( x , y ) = c q a exp ( i q ϕ ) ,
c q a = ( 2 π ) 1 π π exp [ i ψ ( ϕ , a ) ] exp ( i q ϕ ) d ϕ .
c 1 a = A a
π π sin [ ψ ( ϕ , a ) ϕ ] d ϕ = 0 ,
π π cos [ ψ ( ϕ , a ) ϕ ] d ϕ = 2 π A a .
ψ ( ϕ , a ) = f ( a ) ϕ ,
c q a = sinc [ q f ( a ) ] ,
sinc [ 1 f ( a ) ] = a ,
ψ ( ϕ , a ) = ϕ + f ( a ) sin ( ϕ ) .
exp [ i f ( a ) sin ( ϕ ) ] = m = J m [ f ( a ) ] exp ( i m ϕ ) ,
c q a = J q 1 [ f ( a ) ] .
J 0 [ f ( a ) ] = a .
ψ ( ϕ , a ) = f ( a ) sin ( ϕ ) .
c q a = J q [ f ( a ) ] ,
J 1 [ f ( a ) ] = A a .
h c ( x , y ) = q = h q ( x , y ) exp [ i 2 π ( q u 0 x + q v 0 y ) ] .
H c ( u , v ) = q = H q ( u q u 0 , v q v 0 ) ,
H p i x ( u , v ) = E ( u , v ) n = m = H c ( u n Δ u , v m Δ u ) ,
H c ( u n Δ u , v n Δ u ) = q = H q [ u ( n Q P + q ) u 0 , v ( n Q P + q ) u 0 ] .
u ( r , θ ) = C ( 2 r w 0 ) l L p l ( 2 r 2 w 0 2 ) exp ( r 2 w 0 2 ) exp ( i l θ ) .

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