Abstract

A method of generating an aberration- and distortion-free wide-angle holographically projected image in real time is presented. The target projector is first calibrated using an automated adaptive-optical mechanism. The calibration parameters are then fed into the hologram generation program, which applies a novel piece-wise aberration correction algorithm. The method is found to offer hologram generation times up to three orders of magnitude faster than the standard method. A projection of an aberration- and distortion-free image with a field of view of 90x45 degrees is demonstrated. The implementation on a mid-range GPU achieves high resolution at a frame rate up to 12fps. The presented methods are automated and can be performed on any holographic projector.

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Corrections

3 August 2016: Corrections were made to the article keywords.


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References

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  1. A. J. Cable, “Real-time high-quality two and three dimensional holographic video projection using the one-step phase retrieval (OSPR) approach,” Ph.D. dissertation, Dept. Eng., Cambridge Univ., Cambridge, United Kingdom (2006).
  2. E. Buckley, “Computer generated holograms for real-time image display and sensor applications,” Ph.D. dissertation, Dept. Elect. Eng., Cambridge Univ., Cambridge, United Kingdom (2006).
  3. A. J. Cable, “Pico projectors, interactive experience,” Nat. Photonics 4(11), 750–751 (2010).
    [Crossref]
  4. A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
    [Crossref]
  5. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express 20(22), 25130–25136 (2012).
    [Crossref] [PubMed]
  6. M. Makowski, “Towards extremely efficient, lensless, holographic laser projectors,” J. Electron. Imaging 302, 4748 (2013).
  7. A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
    [Crossref]
  8. J. P. Freeman, “Visor projected helmet mounted display for fast jet aviators using a Fourier video projector,” Ph.D. dissertation, Dept. Eng., Cambridge Univ., Cambridge, United Kingdom (2009).
  9. J. P. Freeman, T. D. Wilkinson, and P. Wisely, “Visor projected HMD for fast jets using a holographic video projector,” Proc. SPIE 7690, 76901H (2010).
    [Crossref]
  10. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” Appl. Opt. Optical Eng. 11, 1–53 (1992).
  11. A. J. Cable, “Holographic image display system,” Patent application, WO2009074819 A2 (2009).
  12. Optical Design Program, User's Guide, Radiant ZEMAX, Redmond, WA, 135–138 (2002).
  13. G. Zheng, X. Ou, R. Horstmeyer, and C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013).
    [Crossref] [PubMed]
  14. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007).
    [Crossref] [PubMed]
  15. I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
    [Crossref] [PubMed]

2015 (1)

A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
[Crossref]

2013 (2)

2012 (1)

2010 (2)

A. J. Cable, “Pico projectors, interactive experience,” Nat. Photonics 4(11), 750–751 (2010).
[Crossref]

J. P. Freeman, T. D. Wilkinson, and P. Wisely, “Visor projected HMD for fast jets using a holographic video projector,” Proc. SPIE 7690, 76901H (2010).
[Crossref]

2007 (1)

1992 (1)

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” Appl. Opt. Optical Eng. 11, 1–53 (1992).

1988 (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Buckley, E.

A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
[Crossref]

Cable, A. J.

A. J. Cable, “Pico projectors, interactive experience,” Nat. Photonics 4(11), 750–751 (2010).
[Crossref]

A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
[Crossref]

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” Appl. Opt. Optical Eng. 11, 1–53 (1992).

Crossland, W. A.

A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
[Crossref]

Czerniawski, S.

A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
[Crossref]

Ducin, I.

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Freeman, J. P.

J. P. Freeman, T. D. Wilkinson, and P. Wisely, “Visor projected HMD for fast jets using a holographic video projector,” Proc. SPIE 7690, 76901H (2010).
[Crossref]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Gordon, G. S.

A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
[Crossref]

Horstmeyer, R.

Kaczorowski, A.

A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
[Crossref]

Kakarenko, K.

Kolodziejczyk, A.

Lawrence, N. A.

A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
[Crossref]

Makowski, M.

M. Makowski, “Towards extremely efficient, lensless, holographic laser projectors,” J. Electron. Imaging 302, 4748 (2013).

M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express 20(22), 25130–25136 (2012).
[Crossref] [PubMed]

Mash, P.

A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
[Crossref]

Mosk, A. P.

Ou, X.

Palani, A.

A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
[Crossref]

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Suszek, J.

Sypek, M.

Vellekoop, I. M.

Wilkinson, T. D.

A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
[Crossref]

J. P. Freeman, T. D. Wilkinson, and P. Wisely, “Visor projected HMD for fast jets using a holographic video projector,” Proc. SPIE 7690, 76901H (2010).
[Crossref]

A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
[Crossref]

Wisely, P.

J. P. Freeman, T. D. Wilkinson, and P. Wisely, “Visor projected HMD for fast jets using a holographic video projector,” Proc. SPIE 7690, 76901H (2010).
[Crossref]

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” Appl. Opt. Optical Eng. 11, 1–53 (1992).

Yang, C.

Zheng, G.

Appl. Opt. Optical Eng. (1)

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” Appl. Opt. Optical Eng. 11, 1–53 (1992).

J. Disp. Technol. (1)

A. Kaczorowski, G. S. Gordon, A. Palani, S. Czerniawski, and T. D. Wilkinson, “Optimization-based adaptive optical correction for holographic projectors,” J. Disp. Technol. 11(7), 596–603 (2015).
[Crossref]

J. Electron. Imaging (1)

M. Makowski, “Towards extremely efficient, lensless, holographic laser projectors,” J. Electron. Imaging 302, 4748 (2013).

Nat. Photonics (1)

A. J. Cable, “Pico projectors, interactive experience,” Nat. Photonics 4(11), 750–751 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref] [PubMed]

Proc. SPIE (1)

J. P. Freeman, T. D. Wilkinson, and P. Wisely, “Visor projected HMD for fast jets using a holographic video projector,” Proc. SPIE 7690, 76901H (2010).
[Crossref]

Other (6)

A. J. Cable, “Holographic image display system,” Patent application, WO2009074819 A2 (2009).

Optical Design Program, User's Guide, Radiant ZEMAX, Redmond, WA, 135–138 (2002).

J. P. Freeman, “Visor projected helmet mounted display for fast jet aviators using a Fourier video projector,” Ph.D. dissertation, Dept. Eng., Cambridge Univ., Cambridge, United Kingdom (2009).

A. J. Cable, E. Buckley, P. Mash, N. A. Lawrence, T. D. Wilkinson, and W. A. Crossland, “Real-time binary hologram generation for high-quality video projection applications,” SID Symposium Digest of Technical Papers35(1), 1431–1433 (2004).
[Crossref]

A. J. Cable, “Real-time high-quality two and three dimensional holographic video projection using the one-step phase retrieval (OSPR) approach,” Ph.D. dissertation, Dept. Eng., Cambridge Univ., Cambridge, United Kingdom (2006).

E. Buckley, “Computer generated holograms for real-time image display and sensor applications,” Ph.D. dissertation, Dept. Elect. Eng., Cambridge Univ., Cambridge, United Kingdom (2006).

Supplementary Material (1)

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» Visualization 1: MP4 (13048 KB)      Visualisation 1

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Figures (18)

Fig. 1
Fig. 1 Aberrations of a holographic system: (a) ideal situation with no aberrations, (b) aberration-free spot, (c) real scenario with aberrations, and (d) the resultant aberrated spot.
Fig. 2
Fig. 2 Concept of the holographic aberration correction: a wavefront is modified to ideally cancel out the system's aberration.
Fig. 3
Fig. 3 Spatial variation of aberrations. The small white dotted circle in the inset figure shows the exact position where the correction was made. However, the correction is also valid for the nearby points. The approximate boundaries of correction are indicated by the two red circles.
Fig. 4
Fig. 4 The layout of a projector inputted into ZEMAX ray-tracing software: (a) without Zernike correction and (b) with Zernike correction. L1, L2 and L3 indicate the lenses: L1 – beam-expanding lens, f = 5mm. L2 – collimating lens f = 150mm. L3 – 3mm Sapphire ball lens, f = 3.4mm. Wavelength of light is 532nm (green).
Fig. 5
Fig. 5 Spatial variation of Zernike correction for the fourth Zernike Polynomial - defocus. The points represent the appropriate field positions and the line is the polynomial fit of this function.
Fig. 6
Fig. 6 A schematic view of the feedback loop mechanism: an image of a single point is displayed on a projector, the replay field is then fed back through the webcam to the computer, which performs the correction.
Fig. 7
Fig. 7 Image of concentric circles used as an input to the distortion correction algorithm. In order to improve the performance of the algorithm, many images of the same target with different corrections were averaged to get a sharp image.
Fig. 8
Fig. 8 Measured distortion curve. The line is tangential to y = x at x = 0, indicating that no distortion is present close to the centre, but curves upwards as y rises, indicating pincushion distortion, which drags distorted points outwards.
Fig. 9
Fig. 9 (a) A target image of a grid, and (b) Grid predistorted to counteract distortions.
Fig. 10
Fig. 10 (a) Grid of single pixels with one of the corrections applied, (b) The selection of contiguous points for which this correction is best, and (c) an assigned correction region.
Fig. 11
Fig. 11 A schematic view of the holographic projector used. Lenses L1-L3 have the same parameters as indicated in Fig. 4, the laser wavelength is 532 nm
Fig. 12
Fig. 12 Grid of single pixels (a) without and (b) and with distortion correction.
Fig. 13
Fig. 13 (a) Target image given as an input to the hologram generation script, indicating correction points, (b) uncorrected replay field, (c) Zemax correction and (d) Adaptive Optical correction.
Fig. 14
Fig. 14 Boundary masks: different shades of gray indicate different regions of the image.
Fig. 15
Fig. 15 An example of correction in region 6: (a) an uncorrected and (b) a corrected image.
Fig. 16
Fig. 16 Execution time of different algorithms. The PWPS and PC-OSPR routines has been tested using both: CUDA and MatLAB implementations.
Fig. 17
Fig. 17 Correction of a real image: (a) a target image, (b) an uncorrected replay field using the OSPR algorithm, and (c-e) Corrected replay fields: (c) Zemax PWPS, (d) Adaptive-optical piecewise-corrected PWPS, (e) Adaptive-optical PC-OSPR. The green line at the bottom center of (b)-(e) is zero-order diffraction caused by light specularly reflecting off the glass SLM cover. This could be reduced with improved anti-reflection coatings or by using off-axis holographic projection.
Fig. 18
Fig. 18 Real-time projection of a YouTube video (see Visualization 1): (a) an uncorrected replay field, (b) a fully-corrected replay field. The bright vertical line is zero-order diffraction light, while the horizontal line is a YouTube loading bar.

Equations (22)

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

Ψ ( u , v ) = [ B ( x , y ) × H ( x , y ) × e i ϕ ( x , y ) ]
ϕ ( x , y ) = i = 4 N a i × Z i ( x , y )
H ( x , y ) = H u n c o r r ( x , y ) × e i ϕ ( x , y )
Ψ ( u , v ) = [ B ( x , y ) × { H u n c o r r ( x , y ) × e i ϕ ( x , y ) } × e i ϕ ( x , y ) ] = [ B ( x , y ) × H u n c o r r ( x , y ) ]
Ψ ( u , v ) = [ B ( x , y ) × { H u n c o r r ( x , y ) × e i ϕ ( x , y , u , v ) } × e i ϕ ( x , y , u 0 , v 0 ) ] = [ B ( x , y ) × H u n c o r r ( x , y ) × e i [ ϕ ( x , y , u , v ) ϕ ( x , y , u 0 , v 0 ) ] ]
H ( x , y ) = A ( u , v ) × e i Φ p i x e l u v ( x , y )
Φ p i x e l u v = 2 π ( u u max x + v v max y + ϑ ( u , v ) )
H p i x e l u v ( x , y ) = A ( u , v ) × e i Φ p i x e l u v ( u , v ) × e i ϕ ( x , y )
H ( x , y ) = u = 0 , v = 0 u = u m a x , v = v m a x A ( u , v ) × e i Φ p i x e l u v ( u , v ) × e i ϕ ( x , y , u , v )
h ( x , y ) = { 1 1 i f i f r e a l ( H ( x , y ) ) 0 r e a l ( H ( x , y ) ) < 0
ϕ ( x , y , u , v ) = 2 π i = 4 N z m a p i ( u , v ) × Z i ( x , y )
T ( u , v ) = A ( u , v ) × e i 2 π × ϑ ( u , v )
H ( x , y ) = 1 [ T ( u , v ) ]
H c o r r ( x , y ) = H ( x , y ) × e i ϕ ( x , y )
ϕ ( x , y , u , v ) = { ϕ 1 ( x , y ) ϕ 2 ( x , y ) ϕ n ( x , y ) i f i f i f ( u , v ) R 1 ( u , v ) R 2 ( u , v ) R n
H ( x , y ) = u = 0 , v = 0 u = u max , v = v max A ( u , v ) × e i Φ p i x e l u v ( x , y ) × e i ϕ ( x , y , u , v ) = q = 1 q = n { ( u , v ) R q A ( u , v ) × e i Φ p i x e l u v ( u , v ) } × e i ϕ q ( x , y )
H ( x , y ) = q = 1 q = n 1 [ M q ( u , v ) × A ( u , v ) × e i 2 π × ϑ ( u , v ) ] × e i ϕ q ( x , y )
M q ( u , v ) = { 1 0 i f ( u , v ) R q o t h e r w i s e
T ( u , v ) = A ( u , v ) × e i 2 π × ϑ ( u , v )
T q ( u , v ) = T ( u , v ) × M q ( u , v )
H q ( x , y ) = 1 [ T q ( u , v ) ] × e i ϕ q ( x , y )
H ( x , y ) = q = 1 q = n H q ( x , y )

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