Efficient image projection by Fourier electroholographyMichał Makowski,* Izabela Ducin, Karol Kakarenko, Andrzej Kolodziejczyk, Agnieszka Siemion,

Andrzej Siemion, Jaroslaw Suszek, Maciej Sypek, and Dariusz WojnowskiFaculty of Physics, Warsaw University of Technology, Koszykowa 75, 00 662 Warsaw, Poland

*Corresponding author: michal.makowski@if.pw.edu.pl

Received May 5, 2011; revised July 7, 2011; accepted July 11, 2011;posted July 12, 2011 (Doc. ID 147130); published August 4, 2011

An improved efficient projection of color images is presented. It uses a phase spatial light modulator with threeiteratively optimized Fourier holograms displayed simultaneously—each for one primary color. This spatial divi-sion instead of time division provides stable images. A pixelated structure of the modulator and fluctuations ofliquid crystal molecules cause a zeroth-order peak, eliminated by additional wavelength-dependent phase factorsshifting it before the image plane, where it is blocked with a matched filter. Speckles are suppressed by time in-tegration of variable speckle patterns generated by additional randomizations of an initial phase and minor changesof the signal. © 2011 Optical Society of AmericaOCIS codes: 090.1705, 090.1760, 090.2870.

The image projection methods utilizing flat and compactelectronically addressed spatial light modulators (SLMs)are a promising and actively developed alternative forbulky refractive optics. The creation of a light field byelectroholography provides aberration-free, high-con-trast images with a unique resistance to local faults ofSLMs, like dead pixels and dust. Previously, we reportedon the highly efficient method of rich-colored projection[1]. The main concerns of this concept are connectedwith the pixelated nature of the SLM, its limited fill factor,the time-domain fluctuations of the phase retardation[2,3], and the phase-only modulation. The disturbingartifacts in the projected images are spurious higher dif-fractive orders, a strong central peak from nondiffractedlight, and a speckle noise on the whole visible area intro-duced by random initial phase in the iterative optimiza-tion process. Unless an optically addressed SLM is used[4,5], the mentioned inevitable artifacts must be dealtwith, which is the main subject of this Letter.In the previously reported optical setup [1], three ex-

panded and slightly converging laser beams of primarycolors were illuminating a single full high-definitionphase-only SLM by Holoeye (Pluto VIS model). All thebeams were shaped by amplitude filters in such a waythat each one was illuminating one third of the SLM’s sur-face. After being reflected from the SLM, the beams werefocused into a common point on a screen due to theirgeometry. By addressing the appropriate areas of theSLM with iteratively optimized Fourier holograms of col-or components of a true-color input image, we achievedits projection on the screen.In this Letter, we describe how we managed to im-

prove the projection quality of this setup. The mainimprovement was the successful blocking of thezeroth diffractive order. This was done by multiplying theiterated Fourier holograms by additional wavelength-dependent phase factors T of a divergent lens:

TR;G;Bðx; yÞ ¼ SR;G;Bðx; yÞeiπ

f λR;G;Bðx2þy2Þ

; ð1Þ

where f ¼ 1000mm is the focal length of the addedlens factor, S is the aperture function that divides SLMarea into three sections, λR ¼ 633 nm, λG ¼ 532 nm, andλB ¼ 445 nm.

This technique effectively shifted the image recon-struction plane [Fig. 1(k)] behind the Fourier plane [6][Fig. 1(j)].

The inevitable light peak due to the limited fill factor(87%) and fluctuations of the SLM remained in the Four-ier plane, where we could locate and block it. This wasdone by putting a photosensitive plate (Agfa 10E56) in

Fig. 1. (Color online) Scheme of the optical setup: (a) He–Nelaser, (b) DPSS Nd:YAG laser at 532 nm, (c) laser diode at445 nm, (d) beam expander, (e) amplitude filter for partial illu-mination of the SLM, (f) mirror, (g) half-transparent mirror,(h) SLM, (i) low-pass amplitude filter, (j) high-pass amplitudefilter (see Fig. 2) placed in the geometrical Fourier plane,(k) screen with piezoelectric movements, (l) Canon EOS500D camera with 75–300 zoom lens and macro rings.

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the Fourier plane [Fig. 1(j)] and illuminating it with threelaser beams with SLM switched off. We developed andfixed the plate chemically without removing it. Then itacted as a matched high-pass amplitude filter. Theobtained transparency can be seen in Fig. 2.The images visible on the projection screen with the

blocked and unblocked zero peak are compared in Fig. 3.The artifacts from the zeroth order are clearly visible andthe take form of three separated color shapes, which isdue to the geometry of the setup. Once the zero peakhas been blocked, there is almost no trace of any dis-turbance, which can be seen in the centers of the picturesin Fig. 3. and in animated movies (Fig. 4, Media 1 and

Media 2). The central haze and residual presence ofzeroth-order spots can be suppressed by using a higher-contrast and less scattering photographic material as ahigh-pass filter.

Spurious diffractive orders greater thanþ1 (originatingfrom the pixelated nature of the SLM) were eliminatedfrom the viewing range by a simple rectangular low-passamplitude filter placed at half of the distance between theSLM and the high-pass filter, as seen in Fig. 1(i).

The speckle noise in the observed projections was thesecond issue in our experiment. Note that two kinds ofspeckles are visible: one originating from the method ofcalculating the Fourier holograms and one originatingfrom a diffuse nature of the used projection screen.The first kind is introduced by the iterative Fouriertransform algorithm (IFTA) [7], which assumes a randominitial phase distribution. This random character is gen-erally preserved in the whole iterative process and thefinal phase patterns, which will be displayed on theSLM, are also stochastic, which yields speckle noise.One can lower the amount of this noise by increasingthe number of iterations, but it is time consuming. In-stead we proposed a limited number of three iterations,and, additionally, for each input image, we calculate fiveseparate holograms, each with a different initial phasedistribution. As a result, the five images reconstructedfrom holograms on the screen have the same signal,but a different noise pattern from speckles. Therefore,by integrating them into one image, a dramatic specklesuppression occurs [1,8]. In practice, we do this by takingpictures of a projection screen with a long exposure time(1=12 s) with the mentioned five holograms displayed onthe SLM one by one in a loop. This solution lowers thespeckle noise very efficiently, but unfortunately it lowersthe effective number of frames per second (fps) of theprojector from 60 to 12 fps. Nevertheless, it can be stillpractically applied if a faster ferroelectric SLM is used,reaching thousands of hertz [9]. The additional specklesuppression was achieved by displaying holograms con-taining a slightly deformed signal. We added five moreholograms to the loop, each with the input image shiftedby one pixel to the left, right, up, and down and resized bytwo pixels in both directions. This solution theoreticallydecreases the final resolution and sharpness of the im-age, but this effect was not visible in the obtained photo-graphs. On the other hand, the speckle noise was furthereliminated. We presume that the amount of computationsfor optimizing 10 holograms in three iterations can beperformed in real-time mode with graphics processingunits (GPU). Naturally, this technique lowered the frame

Fig. 2. (Color online) Photographically obtained high-passfilter used to block the zero peak.

Fig. 3. (Color online) Exemplary projected images without(left column) and with (right column) high-pass zeroth-orderfiltering. The size of the images is approximately 15 cm ×15 cm at 2m from the SLM.

Fig. 4. (Color online) Animated movie: (a) without zero peakfiltering (Media 1) and (b) with filtering (Media 2).

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rate of the projection to 6 fps and increased the exposuretime to 1=6 s. The graph showing the amount of noiseagainst the number of integrated holograms is shownin Fig. 5. Note that the noise rate drops approximatelytwofold, while the overall contrast rate is preserved.The second origin of speckle noise lies in the diffusive

nature of our projection screen. This was overcome bypiezoelectric movements of the screen during the expo-sures of the camera. The influence of this modification onthe contrast is negligible, while it helps lower the noiselevel, which can be seen in Fig. 5 in the curves with“piezo” in their descriptions.By introducing both methods of speckle suppression,

the noise rate dropped from 19% to 7.5%. This differencecan be better seen on exemplary magnified photos,shown in Fig. 6. Note that moving the screen duringthe exposure helps to remove the finest speckles, whilemost of the noise removal happens by time integration.The statistical measures presented in Fig. 5 were cal-

culated as follows. The noise ratio is taken as a standarddeviation of the intensity divided by the average value ofthe intensity over a small test region of the image wherethe intensity should be constant in the perfect case. Thecontrast ratio was calculated as the average value ofintensity over a region of the highest brightness, dividedby the average value of the intensity over a region of thelowest brightness.To summarize, the concept of shifting the zero peak off

the Fourier plane and blocking it [6] was successfully ap-plied in a polychromatic case and combined with specklesuppression techniques, yielding near-perfect lensless

projections of color images by diffractive means. Thesimple computations are based on the fast Fourier trans-form, hence they can be easily performed in a real-timemode with GPU processing [10].

The main drawback of the presented technique is a re-sidual presence of speckles, which can be possibly over-come by adding correlated amplitude modulation [11,12].The other solution is to use the lower-coherence lightsources, like pinholed LEDs for the price of a lower lightoutput. Another problem lies in a small throwing angle ofsuch lensless projection, which is limited by the 8 μm pix-el pitch of the used SLM. Nevertheless, the newest SLMswith denser pixel patterns should greatly improve thepractical value of the presented solution of the lenslessimage projection.

This work was supported by the Polish Ministry ofScience and Higher Education under grant IP2010023570 and the European Union in the framework ofthe European Social Fund through the Warsaw Univer-sity of Technology Development Program.

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Fig. 5. Contrast and noise ratios against the number of time-integrated holograms: 1–5, created with random initial phasedistributions; 6–10, created with minor shift and rescaling ofthe signal.

Fig. 6. (Color online) Pictures obtained on a projection screenwith different speckle suppression techniques applied: (a) threeiterations of IFTA, (b) IFTA with time averaging, (c) IFTA withtime averaging and piezoelectric screen movements.

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