Optics Communications 283 (2010) 4969–4971

Contents lists available at ScienceDirect

Optics Communications

j ourna l homepage: www.e lsev ie r.com/ locate /optcom

Holographic projection based on interference and analytical algorithm

Nan Zhu, Yongtian Wang ⁎, Juan Liu ⁎, Jinghui XieSchool of optoelectronics, Beijing Institute of Technology, Beijing 100081, China

⁎ Corresponding author.E-mail addresses: wyt@bit.edu.cn (Y. Wang), juanliu

0030-4018/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.optcom.2010.07.056

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 November 2009Received in revised form 17 June 2010Accepted 21 July 2010

We propose an analytical method for holographic projection based on interference. The method to calculatethe phase hologram does not need iterative process and has great computation efficiency. Experimentalresult demonstrates the validity of this new proposed method. It is believed that this technique is useful infurther real-time video holographic projection.

@bit.edu.cn (J. Liu).

l rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Real-time video holographic projection system (VIHPS) usingphase-only Spatial Light Modulators (SLMs) as a new projectiontechnology has been developed in recent decade of years. Especially inthe applications such as new-generation pocket-sized digital videoprojectors [1] and automotive head-up displays (HUDs) [2], VIHPSexceeds conventional projection systems for its small physical size,low cost, low power consumption, and robust implementation. Thekey device in a holographic projector is a programmable phase-onlySLM which modulates an incident coherent wavefront to generate atarget pattern by diffraction. The holograms displayed on the SLM canbe changed rapidly to support high-rate dynamic applications. Unlikea conventional projector which directly displays a target image on amicro display or Liquid-Crystal panel, the key task in a holographicprojection system lies in the algorithms to calculate the phasehologram to obtain a target image. There exist various algorithmsfor designing phase-only holograms, such as Gerchberg–Saxton (GS)algorithm [3], Fienup algorithm [4], Fidoc method [5], Direct binarysearch (DBS) [6], and simulated annealing algorithm [7]. All thesealgorithms need numerical iterations and are time-consumingprocess. However, even with the simplest algorithm, such as GSalgorithm, to calculate a single iteration for a hologram with aresolution of 256×256 pixels will take 105 ms on a modern CPU [8],and to achieve a reconstructed image with acceptable quality decadeof such iterations will be needed. A modern Graphical Processing Unit(GPU) or a specialized hardware like Field Programmable Gate Arrays(FPGAs) can accelerate the computation by a factor of 10–1000 but arecomplex or expensive [9,10]. As a result, real-time VIHPS cannot berealized using the available standard PC hardware.

Recently, Zhang et al. have proposed a novel method for opticalimage encryption based on interference [11]. In their paper two phase-only masks are used to modulate the wavefronts of the incident lightbeams, in which two modulated light beams interfere with each otherafter combination with a half-mirror (HM), and finally generate anoptical imageon theoutput plane. Stimulatedby thiswork, in this paper,a novel method for holographic projection is presented. SLMs areemployed to modulate incident light beams and reconstruct the outputimage by interference. There is a great advantage of this novel methodthat the algorithm for calculation the phase patterns on SLMs does notneed iterative process, which is greatly computationally efficient andhence provides a possibility to achieve real-time video holographicprojection based on standard PC hardware. Two holographic-projectionarchitectures for this novel method are proposed.

2. Holographic projection by two SLMs

The schematic of the holographic projection system by two SLMs isillustrated in Fig.1.

A monochromatic laser beam is filtered and expanded by spatialfilters and beam expanders to generate two collimated light beams.Two SLMs are positioned in the front focal plane of the Fourier lens.They are employed to modulate the incident coherent light beams togenerate the desired wavefronts which will interfere with each otherafter combination via a half mirror. The reconstructed image will beprojected after a Fourier lens at the output screen.

The phase holograms φ1 and φ2 on two SLMs can be calculated byanalytic algorithm as follows. If the target image is a nonnegativedistributiont(m,n), the object function t′(m,n) can be constructed byadding a random phase distribution,

t ′ m;nð Þ =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit m;nð Þ

pexp i2πrand m;nð Þ½ �; ð1Þ

where rand(m,n) generates a random distribution between 0 and 1.This constructed field distribution can be expressed as the

Fig. 1. Schematic of holographic projection system by two SLMs (SF: spatial filter, BE:beam expander, HM: half mirror).

Fig. 2. Schematic of holographic projection system using a single SLM.

4970 N. Zhu et al. / Optics Communications 283 (2010) 4969–4971

interference of optical fields generated by phase distributions φ1 andφ2,

t ′ m;nð Þ = g0FTfexp iφ1ð Þg + g0FTfexp iφ2ð Þg; ð2Þ

where FT{…} expresses the Fourier transform, and g0 is a function of theincident wavelength and the focal length of the Fourier lens. Since theexistence of g0 does not change the relative distribution of the objectfunction t′(m,n), we can always take g0 as unity by scaling t′(m,n). If wedefine Q = FT−1ft ′ m;nð Þg, where FT−1{...} expresses the inverseFourier transform, we can have

exp iφ1ð Þ = Q− exp iφ2ð Þ: ð3Þ

Since φ1 and φ2 are consist of phase-only values, we can have

jQ− exp iφ2ð Þj2 = jQ− exp iφ2ð ÞjjQ− exp iφ2ð Þj� = 1: ð4Þ

At last, we obtain two phase distributions as

φ1 = arg Qð ÞF arccos abs Qð Þ= 2½ �; ð5Þ

φ2 = arg Q− exp iφ1ð Þ½ �; ð6Þ

where arg(Q) and abs(Q) denote the phase angles and the amplitudeof element Q, respectively.

In theory, using the holographic-projection architecture men-tioned above, there will be no loss in the quality of the reconstructedimage. Precise alignment for two SLMs is needed. Since SLM is pixel-structured the accuracy of the alignment need to be in the scale of onetenth of a pixel's dimension, i.e. from less than one micro to severalmicro depends on specific devices. On the other hand, the aboveholographic-projection system can be integrated into a firm singlepackage which can be assembled in optical shop. Once the accuracy ofthe alignment of two SLMs is achieved during assembling process, theprojection system can be employed conveniently by a general user.Compare with other holographic-projection technologies, the need ofa second SLM and extra optical alignment in this novel architectureincrease the cost of the system. On the other hand, the prices of SLMsdrop significantly in recent time, this novel architecture still have anadvantage over the VIHPS using complex GPU and expensive FPGA.

3. Holographic projection by a single SLM

The above architecture of holographic projection system can alsobe simplified by using a single SLM, as shown in Fig. 2(a). Amonochromatic laser beam is filtered and expanded by a spatial filterand a beam expander to generate a collimated beam. A SLM is

employed tomodulate the incident light beam to generate the desiredwavefront. After transmitting a Fourier lens the generated wavefrontwill reconstruct the target image and project it on the output screen.

The frame area by dashed line in Fig. 2(a) is illustrated by Fig. 2(b)in detail. The SLM is positioned in the front focal plane of the Fourierlens. The phase hologram loaded on the SLM is vertically divided intotwo divisions with equal area. Phase distributions φ1' and φ2' areloaded on the upper and lower divisions of the SLM, respectively, witha vertical displacement d to the center of the SLM, as

φ′1 x; yð Þ = φ1 x; y−dð Þ; ð7Þ

φ′2 x; yð Þ = φ2 x; y+dð Þ: ð8Þ

And we have:

FTfexp iφ′1 x; yð Þ� �g = exp −i2πdfη� �

FTfexp iφ1 x; yð Þ½ �g; ð9Þ

FTfexp iφ′2 x; yð Þ� �g = exp i2πdfη� �

FTfexp iφ2 x; yð Þ½ �g: ð10Þ

After passing through a Fourier lens the Fourier transformdistribution on the output screen is

F fξ; fη� �

= g0FTfexp iφ′1 x; yð Þ� �g + g0FTfexp iφ′2 x; yð Þ� �g

= g0 exp −i2πdfη� �

FTfexp iφ1 x; yð Þ½ �g

+ g0 exp i2πdfη� �

FTfexp iφ2 x; yð Þ½ �g:

ð11Þ

Compared with the amplitude distribution of the target imageexpressed in Eq. (2), the additional exp(− i2πdfη) and exp(i2πdfη) inEq. (11) will bring noise in the projection image, but the quality of theprojection image can still be maintained in an acceptable range. Theoptical experiment below will demonstrate this point.

4. Experimental result

An experiment is implemented to verify the validity of this novelholographic projection system with a single SLM. A phase-only liquid

Fig. 3. The results by a single SLM: (a) the target image, (b) phase distribution loaded onSLM (c) experimental result of the reconstructed image.

4971N. Zhu et al. / Optics Communications 283 (2010) 4969–4971

crystal SLM (Boulder Nonlinear Systems, USA) is employed, whichconsists of 512×512squarepixels. Thedimensionof eachpixel is 15 μm.The target image is a gray picture of a cameraman, as shown in Fig. 3(a).

Thewavelength of the illuminating light is 633 nm, and the focal lengthof the Fourier lens is 147 cm. The movement in vertical direction d is1.92 mm. The phase hologram on SLM is shown in Fig. 3(b).Theexperiment result of reconstructed image is shown in Fig. 3(c).

It can be seen that the speckle noise is themain source of the imagenoise. Since the experiment is implemented by using a single SLM, thespeckle noise maintains a normal level compared with otherholographic projection systems.

5. Conclusions

In summary, two new architectures for holographic-projectionsystem based on interference are proposed. The phase retrievalprocess does not need the iterative algorithm hence the computationcan be simply processed. The computation process can be acceleratedby using programming language with higher process efficiency whichprovides these new architectures the potential for applications instandard-PC-based real-time VIHPS.

Acknowledgements

This work was supported by the National Basic Research Programof China (Grant No. 2011CB301801) and the Innovation TeamDevelopment Program of the Chinese Ministry of Education (GrantNo. IRT0606).

References

[1] E. Buckley, Holographic Laser Projection Technology, information display 24, 4,2008.

[2] E. Buckley, Colour holographic laser projection technology for heads-up andinstrument cluster displays, in SID Conference 14th Annual Symposium on VehicleDisplays, , 2007 Dearborn MI.

[3] R.W.G.a.W.O. Saxton, A practical algorithm for the determination of phase fromimage and diffraction plane pictures, Optik 35 (1972) 237–246 (Jena).

[4] J.R. Fienup, Reconstruction of an object from the modulus of its Fourier transform,Opt. Lett. 3 (1978) 27–29.

[5] H. Akahori, Spectrum leveling by an iterative algorithm with a dummy area forsynthesizing the kinoform, Appl. Opt. 25 (1986) 802–811.

[6] M.A. Seldowitz, J.P. Allebach, D.W. Sweeney, Synthesis of digital holograms bydirect binary search, Appl. Opt. 26 (1987) 2788–2798.

[7] C.D.G.S. Kirckpatrick Jr., M.P. Vecchi, Optimization by simulated annealing, Science220 (1983) 671–680.

[8] J.C.A. Georgiou, N. Collings, J. Moore, W.A. Crossland, Aspects of hologramcalculation for video frames, J. Opt. A: Pure Appl. Opt. 10 (9) (2008).

[9] A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, T. Ito,Simplified electroholographic color reconstruction system using graphics proces-sing unit and liquid crystal display projector, Opt. Express 17 (2009)16038–16045.

[10] Y. Abe, N. Masuda, H. Wakabayashi, Y. Kazo, T. Ito, S.-i. Satake, T. Kunugi, K. Sato,Special purpose computer system for flow visualization using holographytech-nology, Opt. Express 16 (2008) 7686–7692.

[11] Y. Zhang, B. Wang, Optical image encryption based on interference, Opt. Lett. 33(2008) 2443–2445.