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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 23 — Nov. 9, 2009
  • pp: 20840–20846
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Experimental evaluation of a full-color compact lensless holographic display

Michal Makowski, Maciej Sypek, Izabela Ducin, Agnieszka Fajst, Andrzej Siemion, Jaroslaw Suszek, and Andrzej Kolodziejczyk  »View Author Affiliations


Optics Express, Vol. 17, Issue 23, pp. 20840-20846 (2009)
http://dx.doi.org/10.1364/OE.17.020840


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Abstract

An iterative phase retrieval method for a lensless color holographic display using a single light modulator is experimentally validated. The technique involves iterative calculation of a three-plane synthetic hologram which is displayed on a SLM simultaneously lit with three laser beams providing an RGB illumination. Static and animated two-dimensional flicker-free full color images are reconstructed at a fixed position and captured using a high resolution CMOS sensor. The image finesse, color fidelity, contrast ratio and influence of speckles are evaluated and compared with other techniques of holographic color image encoding. The results indicate the technique superior in a case of full-color real-life pictures which are correctly displayed by this ultra-compact and simple projection setup.

© 2009 OSA

1. Motivation and the display technique

The enduring miniaturization of handheld optical devices has encountered the fundamental problem of a diffraction limit when smaller and smaller lenses are used [1

1. A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28(23), 4996–4998 ( 1989). [CrossRef] [PubMed]

]. Especially in the field of micro-projectors it is difficult to achieve a fine bright color image with low aperture optics. The usual remedy for the limitations of the volume optics is the biologically inspired artificial compound optics [2

2. K. Hamanaka and H. Koshi, “An artificial compound eye using a microlens array and its application to scale invariant processing,” Opt. Rev. 3(4), 264–268 ( 1996). [CrossRef]

4

4. R. Shogenji, Y. Kitamura, K. Yamada, S. Miyatake, and J. Tanida, “Multispectral imaging using compact compound optics,” Opt. Express 12(8), 1643–1655 ( 2004). [CrossRef] [PubMed]

], diffractive optics and holography. The first experimental demonstration of a lensless ultra-compact holographic projection technique which could potentially be applied to micro-projection is described in this paper. The main principle of the utilized method lies in the iterative calculation of a synthetic Fresnel hologram with three object planes each corresponding to a different color component obtained from a particular photograph [5

5. M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express 16(15), 11618–11623 ( 2008). [PubMed]

7

7. M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 ( 2005). [CrossRef]

]. The iterative phase retrieval itself is based on a classic Gerchberg-Saxton algorithm [8

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

], modified by Lohmann et al. [9

9. R. Dorsch, A. Lohmann, and S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Appl. Opt. 33(5), 869–875 ( 1994). [CrossRef] [PubMed]

]. A similar method has been introduced by Haist et al. [10

10. T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 ( 1997). [CrossRef]

] and used for optical trapping by Sinclair et al. [11

11. G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. J. Laczik, M. J. Padgett, and J. Courtial, “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping,” Opt. Express 12(8), 1665–1670 ( 2004). [CrossRef] [PubMed]

]. In our approach a single iteration starts in the object plane fR with a random phase and an amplitude of the red component. The wavefront is then propagated to the second object plane fG, where an amplitude of the green component is enforced without changing the phase. After a propagation to the closest object plane fB an amplitude of the blue component is applied with phase left unchanged. Then the field is propagated to the hologram plane. There an amplitude equalization is done, which ensures a phase-only hologram in every iteration. The wavefront is propagated back to the object plane fR. This loop is repeated a predefined number of times which leaves us with a phase distribution of an optimized three-plane Fresnel hologram. The object planes are designed at such distances fR, fG, fB from the hologram which ensure the appearance of a color image at a fixed plane due to the chromatic dispersion of the holographic structure. In this work a base distance of 200 mm was chosen, which is potentially suitable for handheld projectors. When an iterated phase pattern of a three plane hologram is displayed on a spatial light modulator illuminated with a plane wave of λ=632.8 nm, three images are reconstructed at distances: fB=154 mm, fG=168 mm and fR=200 mm. When the illuminating light is replaced with a plane wave of λ=532 nm, the obtained images are located at rescaled distances: 185 mm, 200 mm and 238 mm. In the last case when we used λ=428 nm, the distances were as follows: 200 mm; 218 mm and 260 mm. Therefore when we simultaneously illuminate the SLM with three beams, nine images are formed as seen in Fig. 1(b)
Fig. 1 a) An ideal scheme of the experimental setup; b) magnification of the marked area showing the locations of all reconstructed object planes with illumination from three beams.
and three of them are overlapped at a distance of 200 mm on a rotating ground glass, giving a color image. The mentioned distances fR, fG and fB satisfy the Eq. (1), where λR , λG and λB are the wavelengths of red, green and blue laser beams, respectively.

fG:fR=λB:λG,fB:fR=λB:λR,fB:fG=λG:λR
(1)

2. Alternative color encoding techniques

3. Experimental results

The images obtained from numerical simulations and different experiments are gathered in Fig. 4
Fig. 4 The results of numerical and experimental reconstructions of color images for projection distance of 200 mm.
. The column “Input RGB image” contains the input bitmaps that were split into RGB components and used in the calculation of a hologram. The column “Numerical reconstruction” shows the results of three separate numerical reconstructions of the obtained iterated holograms using the three wavelengths λR, λG and λB. Three monochromatic images were combined into a color image using GIMP. The contrast in the numerical reconstructions is inevitably lower in comparison with input bitmaps [7

7. M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 ( 2005). [CrossRef]

]. The decreased contrast is counterbalanced by a proper color reproduction.

The contrast ratio was calculated as the average intensity in the bright test region divided by the average intensity in the dark test region, shown in Fig. 5
Fig. 5 Magnification of reconstructed images: a) 3 SLMs; b) proposed method; c) multi-exposure; d) surface segmentation. The “bright” test region is marked in black, the “dark” test region is marked in white.
. The noise rate was calculated as a standard deviation of the intensity divided by an average intensity in the test region. As seen in Table 1, the proposed method provides approximately two times higher contrast and approximately 56% lower noise ratio compared to the alternative methods under the same test conditions. Please note that the numerical assessment was only conducted on the sharp “IF” test image. Clearly, our method provides better results in the case of smooth test images (“Lena”, “Parrots” and “Speed racers”), although it is difficult to confirm that using statistics. Our method provides a color image by a superposition of three RGB component images on a screen. Nevertheless the other six reconstructed images are still present in different planes along the optical axis, which is illustrated in Fig. 1 and is recorded in Fig. 6(c)
Fig. 6 Reconstruction of holograms designed on an array of: a) 1024 by 1024 (Media 1 showing animations); b) 2048 by 1024; c) 2048 by 2048 (Media 2 showing the diffractive field along the optical axis while approaching the SLM); d) 4096 by 4096 points. The non-diffracted field is visible and the presence of higher diffraction orders are marked in (d).
(Media 2).

To summarize, the achieved color reproduction and synchronization is correct. Any notable color smudges, as seen in Fig. 6(b), are caused only by imperfections of the alignment of laser beams into a beam expander. The gray levels of the SLM were optimized to achieve a 2π phase shift for λ=632.8 nm. A smaller modulation depth for green and blue beams was partly compensated by increasing their intensity. This fact combined with a 87% fill factor of the SLM caused an obstructing non-diffracted rectangular field visible in all the obtained photographs. That field inevitably decreases the contrast ratio. This issue could be overcome by the off-axis holography, but then severe misalignments in color components would be hard to suppress. This is the reason why we mainly present images with approximately the same pixel number as the phase array displayed on the SLM, i.e. 2048 by 1024 against 1920 by 1080. Larger images always exhibit non-diffracted field, as visible in Fig. 6. Additionally, since the large hologram is reconstructed from its relatively small fragment of 1920 by 1080 points, some negative effects occur. Speckles become larger and the depth of field increases thus causing the image planes to be less localized and therefore the color saturation is worse. Moreover, the large reconstructed image overlap with images from higher orders of diffraction, as visible in Fig. 6(d). These are the reasons why increasing the size of the calculation array to achieve a large image is not the optimal concept.

The presented experiment was also conducted for different base distances. Figure 7
Fig. 7 Reconstruction quality for base projection distances: 500 mm; 700 mm and 1000 mm.
shows the results of reconstruction of the same test image calculated on the array of 4096 by 4096 points for different projection ranges. Similar result were achieved for the array of 1024 by 1024 points. Larger distances introduce severe speckles in the obtained photographs, therefore the imaging distance is one of the limitations of the method, at least when using an SLM.

4. Conclusions and outlook

We have presented an experimental proof of a usefulness of our color lensless holographic display technique. The main features are a small and simple lensless optical setup, a use of only one light modulator and a flicker-free full-color image. Promising results were achieved at short working distances with various test images. The method is still under research not only by our group [15

15. J. Xia and H. Yin, “Three-dimensional light modulation using phase-only spatial light modulator,” Opt. Eng. 48(2), 020502 ( 2009). [CrossRef]

]. The quality of the obtained images seems to be limited mostly by the computational power and the used hardware, namely the pixel pitch and the fill factor of the light modulator. The important advantage of the utilized Fresnel diffuse hologram is the resistance of the output image to obstacles like dead pixels, dust, fingerprints or other obstruction on the large surface of the active area of the modulator. The future research will cover the optimization of calculation speed in order to achieve a real-time holographic encoding on a standard PC workstation. A preview of animated projection was recorded in the optical setup from pre-calculated phase distributions sequentially displayed on the SLM, see Fig. 6(a) (Media 1). Additionally, our aim will be to introduce a numeric way of enlarging the output images other then simply enlarging the hologram calculation matrix, which is extremely time-consuming.

Acknowledgements

The authors would like to thank HOLOEYE Photonics AG for a valuable support. This work has been supported by the European Union in the framework of European Social Fund through the Warsaw University of Technology Development Programme.

References and links

1.

A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28(23), 4996–4998 ( 1989). [CrossRef] [PubMed]

2.

K. Hamanaka and H. Koshi, “An artificial compound eye using a microlens array and its application to scale invariant processing,” Opt. Rev. 3(4), 264–268 ( 1996). [CrossRef]

3.

J. Duparré, P. Schreiber, A. Matthes, E. Pshenay-Severin, A. Bräuer, A. Tünnermann, R. Völkel, M. Eisner, and T. Scharf, “Microoptical telescope compound eye,” Opt. Express 13(3), 889–903 ( 2005). [CrossRef] [PubMed]

4.

R. Shogenji, Y. Kitamura, K. Yamada, S. Miyatake, and J. Tanida, “Multispectral imaging using compact compound optics,” Opt. Express 12(8), 1643–1655 ( 2004). [CrossRef] [PubMed]

5.

M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express 16(15), 11618–11623 ( 2008). [PubMed]

6.

M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikula, and J. Suszek, “Iterative design of multi-plane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 ( 2007). [CrossRef]

7.

M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 ( 2005). [CrossRef]

8.

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

9.

R. Dorsch, A. Lohmann, and S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Appl. Opt. 33(5), 869–875 ( 1994). [CrossRef] [PubMed]

10.

T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 ( 1997). [CrossRef]

11.

G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. J. Laczik, M. J. Padgett, and J. Courtial, “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping,” Opt. Express 12(8), 1665–1670 ( 2004). [CrossRef] [PubMed]

12.

M. Sypek, “Light propagation in the Fresnel region: new numerical approach,” Opt. Commun. 116(1-3), 43–48 ( 1995). [CrossRef]

13.

K. M. Johnson, M. Armstrong, L. Hesselink, and J. W. Goodman, “Multiple multiple-exposure hologram,” Appl. Opt. 24(24), 4467–4472 ( 1985). [CrossRef] [PubMed]

14.

J. Suszek, M. Makowski, M. Sypek, A. Siemion, and A. Kolodziejczyk, “Angle-dependent encoding of multiple asymmetric symbols in a binary phase hologram with a spatial segmentation,” Appl. Opt. 48(2), 270–275 ( 2009). [CrossRef] [PubMed]

15.

J. Xia and H. Yin, “Three-dimensional light modulation using phase-only spatial light modulator,” Opt. Eng. 48(2), 020502 ( 2009). [CrossRef]

OCIS Codes
(090.1760) Holography : Computer holography
(090.2870) Holography : Holographic display
(090.1705) Holography : Color holography

ToC Category:
Holography

History
Original Manuscript: August 6, 2009
Revised Manuscript: September 30, 2009
Manuscript Accepted: October 8, 2009
Published: October 29, 2009

Citation
Michal Makowski, Maciej Sypek, Izabela Ducin, Agnieszka Fajst, Andrzej Siemion, Jaroslaw Suszek, and Andrzej Kolodziejczyk, "Experimental evaluation of a full-color compact lensless holographic display," Opt. Express 17, 20840-20846 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-23-20840


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References

  1. A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28(23), 4996–4998 (1989). [CrossRef] [PubMed]
  2. K. Hamanaka and H. Koshi, “An artificial compound eye using a microlens array and its application to scale invariant processing,” Opt. Rev. 3(4), 264–268 (1996). [CrossRef]
  3. J. Duparré, P. Schreiber, A. Matthes, E. Pshenay-Severin, A. Bräuer, A. Tünnermann, R. Völkel, M. Eisner, and T. Scharf, “Microoptical telescope compound eye,” Opt. Express 13(3), 889–903 (2005). [CrossRef] [PubMed]
  4. R. Shogenji, Y. Kitamura, K. Yamada, S. Miyatake, and J. Tanida, “Multispectral imaging using compact compound optics,” Opt. Express 12(8), 1643–1655 (2004). [CrossRef] [PubMed]
  5. M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express 16(15), 11618–11623 (2008). [PubMed]
  6. M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikula, and J. Suszek, “Iterative design of multi-plane holograms: experiments and applications,” Opt. Eng. 46(4), 045802 (2007). [CrossRef]
  7. M. Makowski, M. Sypek, A. Kolodziejczyk, and G. Mikuła, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Opt. Eng. 44(12), 125805 (2005). [CrossRef]
  8. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
  9. R. Dorsch, A. Lohmann, and S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Appl. Opt. 33(5), 869–875 (1994). [CrossRef] [PubMed]
  10. T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997). [CrossRef]
  11. G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. J. Laczik, M. J. Padgett, and J. Courtial, “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping,” Opt. Express 12(8), 1665–1670 (2004). [CrossRef] [PubMed]
  12. M. Sypek, “Light propagation in the Fresnel region: new numerical approach,” Opt. Commun. 116(1-3), 43–48 (1995). [CrossRef]
  13. K. M. Johnson, M. Armstrong, L. Hesselink, and J. W. Goodman, “Multiple multiple-exposure hologram,” Appl. Opt. 24(24), 4467–4472 (1985). [CrossRef] [PubMed]
  14. J. Suszek, M. Makowski, M. Sypek, A. Siemion, and A. Kolodziejczyk, “Angle-dependent encoding of multiple asymmetric symbols in a binary phase hologram with a spatial segmentation,” Appl. Opt. 48(2), 270–275 (2009). [CrossRef] [PubMed]
  15. J. Xia and H. Yin, “Three-dimensional light modulation using phase-only spatial light modulator,” Opt. Eng. 48(2), 020502 (2009). [CrossRef]

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