Abstract

We discuss some fundamental characteristics of a phase-modulating device suitable to holographically project a monochrome video frame with 1280×720 resolution. The phase-modulating device is expected to be a liquid crystal over silicon chip with silicon area similar to that of commercial devices. Its basic characteristics, such as number of pixels, bits per pixel, and pixel dimensions, are optimized in terms of image quality and optical efficiency. Estimates of the image quality are made from the noise levels and contrast, while efficiency is calculated by considering the beam apodization, device dead space, diffraction losses, and the sinc envelope.

© 2008 Optical Society of America

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    [CrossRef]
  2. A. Georgiou and W. A. Crossland, “Image projection using phase-only holograms,” Photon04 Conference Proceedings (2004).
  3. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert & Company, 2005).
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    [CrossRef]
  10. The Swedish Confederation of Professional Employees, “TCO05 notebook computers,” www.tcodevelopment.com(2005).
  11. A. Valberg, Light Vision Color (Wiley, 2005).
  12. R. D. Hamer and C. W. Tyler, “Analysis of visual modulation sensitivity. V. Faster visual response for G- than for R-cone pathway?,” J. Opt. Soc. Am. A 9, 1889-1904 (1992).
    [CrossRef] [PubMed]
  13. Digital Cinema Initiatives, “Digital Cinema System Specification” (Digital Cinema Initiatives, 2008).
  14. K. L. Tan, “Dynamic holography using ferroelectric liquid crystal on silicon spatial light modulators,” Ph.D. thesis (Cambridge University, 1999).
  15. K. L. Tan, S. T. Warr, M. G. Ilias, T. D. Wilkinson, M. M. Redmond, A. W. Crossland, and B. Robertson, “Dynamic holography for optical interconnections. II. Routing holograms with predictable location and intensity of each diffraction order,” J. Opt. Soc. Am. A 18, 205-215 (2001).
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  16. S. Winograd, “On computing the discrete Fourier transform,” Math. Comput. 32, 175-199 (1978).
    [CrossRef]
  17. R. Soneira, “LCOS display technology shootout. Part A,” http://www.displaymate.com/LCoS_ShootOut_Part_A.htm (2006).
  18. E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).
  19. M. L. Jepsen, “Why analog silicon may be best for LCOS digital TV,” in SID Symposium Digest of Technical Papers (2005).
  20. T. A. Busey, “Temporal inhibition in character identification,” Percept. Psychophys. 60, 1285-1304 (1998).
    [CrossRef] [PubMed]
  21. K. R. Dobkins, C. M. Anderson, and B. Lia, “Infant temporal contrast sensitivity functions (tCSFs) mature earlier for luminance than for chromatic stimuli: evidence for precocious magnocellular development?,” Vision Res. 39, 3223-3239 (1999).
    [CrossRef]

2008 (1)

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

2001 (1)

1999 (1)

K. R. Dobkins, C. M. Anderson, and B. Lia, “Infant temporal contrast sensitivity functions (tCSFs) mature earlier for luminance than for chromatic stimuli: evidence for precocious magnocellular development?,” Vision Res. 39, 3223-3239 (1999).
[CrossRef]

1998 (1)

T. A. Busey, “Temporal inhibition in character identification,” Percept. Psychophys. 60, 1285-1304 (1998).
[CrossRef] [PubMed]

1992 (1)

1990 (1)

1986 (1)

1978 (2)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

1971 (1)

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Akahori, H.

Anderson, C. M.

K. R. Dobkins, C. M. Anderson, and B. Lia, “Infant temporal contrast sensitivity functions (tCSFs) mature earlier for luminance than for chromatic stimuli: evidence for precocious magnocellular development?,” Vision Res. 39, 3223-3239 (1999).
[CrossRef]

Busey, T. A.

T. A. Busey, “Temporal inhibition in character identification,” Percept. Psychophys. 60, 1285-1304 (1998).
[CrossRef] [PubMed]

Christmas, J.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

Collings, N.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

Crossland, A. W.

Crossland, W. A.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

A. Georgiou and W. A. Crossland, “Image projection using phase-only holograms,” Photon04 Conference Proceedings (2004).

Dammann, H.

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Dobkins, K. R.

K. R. Dobkins, C. M. Anderson, and B. Lia, “Infant temporal contrast sensitivity functions (tCSFs) mature earlier for luminance than for chromatic stimuli: evidence for precocious magnocellular development?,” Vision Res. 39, 3223-3239 (1999).
[CrossRef]

Fienup, J. R.

Georgiou, A.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

A. Georgiou and W. A. Crossland, “Image projection using phase-only holograms,” Photon04 Conference Proceedings (2004).

A. Georgiou, “Design of liquid crystal holograms for programmable optical interconnects,” Ph.D. thesis (Cambridge University, 2005).

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert & Company, 2005).

Gortler, K.

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Hamer, R. D.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

Ilias, M. G.

Jepsen, M. L.

M. L. Jepsen, “Why analog silicon may be best for LCOS digital TV,” in SID Symposium Digest of Technical Papers (2005).

Lia, B.

K. R. Dobkins, C. M. Anderson, and B. Lia, “Infant temporal contrast sensitivity functions (tCSFs) mature earlier for luminance than for chromatic stimuli: evidence for precocious magnocellular development?,” Vision Res. 39, 3223-3239 (1999).
[CrossRef]

Moore, J.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

Redmond, M. M.

Robertson, B.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Soneira, R.

R. Soneira, “LCOS display technology shootout. Part A,” http://www.displaymate.com/LCoS_ShootOut_Part_A.htm (2006).

Tan, K. L.

Tyler, C. W.

Valberg, A.

A. Valberg, Light Vision Color (Wiley, 2005).

Warr, S. T.

Wilkinson, T. D.

Winograd, S.

S. Winograd, “On computing the discrete Fourier transform,” Math. Comput. 32, 175-199 (1978).
[CrossRef]

Wyrowski, F.

Appl. Opt. (1)

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

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A Pure Appl. Opt. 10, 035302 (2008).
[CrossRef]

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

Math. Comput. (1)

S. Winograd, “On computing the discrete Fourier transform,” Math. Comput. 32, 175-199 (1978).
[CrossRef]

Opt. Commun. (1)

H. Dammann and K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Opt. Lett. (1)

Optik (Jena) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Percept. Psychophys. (1)

T. A. Busey, “Temporal inhibition in character identification,” Percept. Psychophys. 60, 1285-1304 (1998).
[CrossRef] [PubMed]

Vision Res. (1)

K. R. Dobkins, C. M. Anderson, and B. Lia, “Infant temporal contrast sensitivity functions (tCSFs) mature earlier for luminance than for chromatic stimuli: evidence for precocious magnocellular development?,” Vision Res. 39, 3223-3239 (1999).
[CrossRef]

Other (10)

A. Georgiou and W. A. Crossland, “Image projection using phase-only holograms,” Photon04 Conference Proceedings (2004).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Robert & Company, 2005).

R. Soneira, “LCOS display technology shootout. Part A,” http://www.displaymate.com/LCoS_ShootOut_Part_A.htm (2006).

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

M. L. Jepsen, “Why analog silicon may be best for LCOS digital TV,” in SID Symposium Digest of Technical Papers (2005).

The Swedish Confederation of Professional Employees, “TCO05 notebook computers,” www.tcodevelopment.com(2005).

A. Valberg, Light Vision Color (Wiley, 2005).

A. Georgiou, “Design of liquid crystal holograms for programmable optical interconnects,” Ph.D. thesis (Cambridge University, 2005).

Digital Cinema Initiatives, “Digital Cinema System Specification” (Digital Cinema Initiatives, 2008).

K. L. Tan, “Dynamic holography using ferroelectric liquid crystal on silicon spatial light modulators,” Ph.D. thesis (Cambridge University, 1999).

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Figures (9)

Fig. 1
Fig. 1

Optical arrangement of a holographic projector. Additional optical components are usually used to illuminate the LCOS device on axis.

Fig. 2
Fig. 2

Hologram and its reconstruction. Note that the hologram is rectangular, but the horizontal and vertical pixel pitch has 2 3 ratio. This forms equal spacing of image pixels on the horizontal (u) and vertical (v) directions.

Fig. 3
Fig. 3

Image quality in terms of contrast and RMS noise improve as the number of phase levels increases. The improvement is apparent for up to 64 phase levels. Then the improvement observed is minimal and does not justify the use of more complex digital-to-analog converter under pixels.

Fig. 4
Fig. 4

Proposed solution uses (a) hologram repetition to improve efficiency and (b) do not care areas to reduces noise. (c) Image oversampling and (d) zero/noise circumscribe require substantially more pixels, making them unsuitable for near future devices.

Fig. 5
Fig. 5

Contrast and RMS errors improve as the size of the do not care areas increase. A 1536 × 1024 unit hologram is considered a sufficiently good balance. For this simulation 256 phase levels were used.

Fig. 6
Fig. 6

(a) Geometry of the proposed device. The hologram is repeated twice to minimize apodization losses. (b) Resolution of the image with the pixel spacing. Pixels must have a 2 3 aspect ratio so the reconstruction has a 3 2 aspect ratio.

Fig. 7
Fig. 7

Four main sources of optical power losses in a holographic projector: (a) beam apodization, (b) interpixel gap absorption, (c) do not care areas, and (d) sinc envelope, arising from the square pixel shape. Values for these losses for two different devices are given in Table 3.

Fig. 8
Fig. 8

(a) Target image. (b) Single frame reconstruction. The loss associated with the do not care areas (not shown) in this image is 7.8%.

Fig. 9
Fig. 9

Detail from (a) the target image and (b) the single frame reconstruction. (c) Three and (d) 37 frame averaging.

Tables (3)

Tables Icon

Table 1 Contrast and RMS Noise Improvement Is Negligible above 64 Phase Levels a

Tables Icon

Table 2 Increasing the LCOS Pixels Improves Image Quality a

Tables Icon

Table 3 Estimated Theoretical Losses for a VIHPS Projector for Two Different Devices a

Equations (11)

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

r 256 = 1 2 8 × ( e = 1 / 2 e = 1 / 2 e 2 d e ) 1 / 2 = 1 256 12 ,
δ θ U = θ U U R , δ θ V = θ V V R .
θ U = λ 2 Δ X , θ V = λ 2 Δ Y ,
Δ X Δ Y = θ V θ U = δ θ V δ θ U U R V R .
L X L Y = Δ X U R Δ Y V R = δ θ V δ θ U .
Δ Y Δ X = U R V R = 1536 1024 = 3 2 , L X = L Y ,
I ( u , v ) = F sinc 2 ( K U u ) sinc 2 ( K V v ) ,
K U = ( π 2 U R ) ( Δ X Δ X g ) , K V = ( π 2 V R ) ( Δ Y Δ Y g ) , F = ( Δ X Δ X g ) ( Δ Y Δ Y g ) ,
η = F u = U I u = U I v = V I v = V I sinc 2 ( K U u ) sinc 2 ( K V v ) d u d v ,
u = 0 u sinc 2 ( u ) d u 1 1 9 u 2 + 2 225 u 4 1 5040 u 6 + 1 129600 u 8 .
Δ X = 4 μm , Δ Y = 6 μm , g = 0.35 μm , U I / U R = 1280 / 1536 , V I / V R = 720 / 1024 ,

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