How to use a phase-only spatial lightmodulator as a color display

Walter Harm, Alexander Jesacher, Gregor Thalhammer, Stefan Bernet,* and Monika Ritsch-MarteDivision of Biomedical Physics, Medical University of Innsbruck, Müllerstraße 44, 6020 Innsbruck, Austria

*Corresponding author: stefan.bernet@i‑med.ac.at

Received November 14, 2014; revised December 17, 2014; accepted December 17, 2014;posted January 14, 2015 (Doc. ID 226845); published February 10, 2015

We demonstrate that a parallel aligned liquid crystal on silicon (PA-LCOS) spatial light modulator (SLM) withoutany attached color mask can be used as a full color displaywith white light illumination. Themethod is based on thewavelength dependence of the (voltage controlled) birefringence of the liquid crystal pixels. Modern SLMs offer awide range over which the birefringence can be modulated, leading (in combination with a linear polarizer) to sev-eral intensity modulation periods of a reflected light wave as a function of the applied voltage. Because ofdispersion, the oscillation period strongly depends on the wavelength. Thus each voltage applied to an SLM pixelcorresponds to another reflected color spectrum. For SLMs with a sufficiently broad tuning range, one obtains acolor palette (i.e., a “color lookup-table”), which allows one to display color images. An advantage over standardliquid crystal displays (LCDs), which use color masks in front of the individual pixels, is that the light efficiency andthe display resolution are increased by a factor of three. © 2015 Optical Society of AmericaOCIS codes: (230.3720) Liquid-crystal devices; (070.6120) Spatial light modulators; (330.1715) Color, rendering and

metamerism; (260.2030) Dispersion.http://dx.doi.org/10.1364/OL.40.000581

Although there exist a variety of LCD technologies forcomputer monitors, smartphone screens, head-up dis-plays, image projectors, or instrument displays (for anoverview see [1]), to the best of our knowledge, all ofthem use a “superpixel” concept for color production.There, a pixelated color mask is attached to the display,and three adjacent LC pixels with red–green–blue (RGB)color filters are combined into a “superpixel,”with whichthe color is adjusted by individually controlling the trans-mission of its different color fields. Because of absorp-tion at the color mask, the intensity of an incidentwhite light beam is attenuated by a factor of three, evenif the pixel is programmed for maximal transmission.Furthermore, the number of actually displayed imagepixels is reduced to a third of the number of electroni-cally addressed pixels.Alternatively, there exist holographic image projection

methods [2], which use SLMs as a displays for phaseholograms. Color image projection is typically spatiallymultiplexed, displaying the RGB hologram componentsin different areas of the same panel [3–5], and by over-lapping the projected images with different methods.The holographic approaches have, in principle, an opti-mal efficiency, using all incident light for imagereconstruction. On the other hand, they typically sufferfrom speckle noise, which requires sophisticated meth-ods for noise suppression [3].Here we demonstrate how to utilize the dispersion of

the liquid crystal layer for color image generation in anon-holographic approach. Each individual pixel canbe programmed to reflect a selected color, yielding, inprinciple, full light efficiency at full display resolution.Parallel aligned liquid crystal on silicon (PA-LCOS)

spatial light modulators (SLMs) are used typically forpure phase modulation of an incident wave front. Allliquid crystal molecules are aligned parallel to eachother, and parallel to the surface (x-direction). If a volt-age is applied to an SLM pixel, the molecules reorient inthe direction of the electric field (z-direction), i.e.,

perpendicularly to the surface. This changes the phaseof a reflected (or transmitted) light beam, if itspolarization is parallel to the initial molecule orientation(x-direction), which is the “active” optical axis. Thephase shift ϕx, after transmission of a liquid crystal layerwith thickness D, depends on the applied voltage U andon the readout wavelength λ, according to

ϕx � nλ�U� 2πDλ

; (1)

where nλ�U� is the voltage-dependent refractive index ofthe liquid crystal pixel for x-polarized light. The phaseshift ϕy of the y-polarization component, on the otherhand, does not depend on the applied voltage.

Although PA-LCOS SLMs are used typically as purephase modulators, they can be employed also as intensitymodulators. This is because of the fact that the SLM pix-els act as voltage controllable birefringent cells withfixed optical axis orientations. Each SLM pixel can beindividually switched from a non-birefringent state,where the phase shift differences between x- andy-polarization components are integer multiples of 2π,i.e., ϕx − ϕy � 2πN (with N an integer), to a quarter-waveplate state (ϕx − ϕy � 2πN � π∕4), a half-waveplate(ϕx − ϕy � 2πN � π∕2) state, and so on, including allcontinuous intermediate stages. Placing a linear polariza-tion filter in front of the display at a polarization angle of45° with respect to the x-axis, such that the incident andreflected light pass through the same filter, one obtains aperiodic modulation of the reflected intensity as a func-tion of the applied phase shift ϕx, oscillating between theextreme situations where all intensity is reflected if theSLM pixel is in a non-birefringent state, and no reflectionif it acts as a half-waveplate (which rotates the incidentpolarization by 90°). One intensity oscillation period thuscorresponds to a 2π phase shift of ϕx.

An advantageous feature of the PA-LCOS SLMs isthat they allow a voltage controlled phase shift ϕx�U�

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of several multiples of 2π. This feature has recently beenexploited to produce (phase-only) diffractive patterns,which project pre-calculated wavefronts with an im-proved efficiency by reducing wrapping artifacts [6,7],to suppress the zero diffraction order of projectedholograms in a broad wavelength range [8], for colorhologram projection [9], and in microscopy for simulta-neous steering of optical tweezers and optical imageprocessing at different wavelengths [10]. In all of thesecases, the SLM was used as a pure phase modulator.In the present situation, where the SLM is employed as

an intensity modulator, its broad phase shifting rangeallows one to harmonically modulate the reflected lightintensity over a corresponding number of periods. Ac-cording to Eq. (1), the corresponding oscillation periodas a function of the applied voltage strongly dependson the wavelength. Thus, if the SLM is illuminated withwhite light, each voltage level applied to an SLM pixelcreates a different spectrum of reflected intensities, re-sulting in a certain color. If the phase modulation rangeof the SLM is sufficiently large, one obtains a color pa-lette, which can be used to display arbitrary color images.For this purpose, one can directly calibrate the colorresponse of the SLM by measuring the reflected colorspectrum for all accessible voltage levels. This generatesa “color lookup table,” i.e., a table that relates an idealSLM voltage level, which approximates the desired color,to each possible RGB color triple.For demonstration (see Fig. 1), we use a PA-LCOS-SLM

(Hamamatsu X10468-01) with a resolution of 800 × 600pixels, each with an edge length of 20 μm. In phase-onlymode, the SLM offers a phase shift of 7.2π at 465 nm, of5.9π at 532 nm, and of 4.7π at 633 nm, if the maximal volt-age is applied. In front of the SLM, a linear polarizer isattached at an angle of 45° with respect to the activepolarization axis. Thus, each 2π-phase shift results in aharmonic intensity modulation period of the respectivewavelength.The SLM is illuminated by a collimated beam from a

four-die LED (LZ4-00MD00 with four red, green, blue,

and white emitting fields), where only the “daylight-white” field was used. The spectrum of the white emittershows a continuous broad maximum in the red/greenrange with a peak (about 57% relative intensity) at550 nm and a full width at half-maximum (FWHM) ofabout 150 nm, and an additional stronger blue peak(100% relative intensity) at 450 nm with a FWHM of ap-proximately 40 nm [11]. The reflected light is recorded bya color camera (Point Grey GS3-U3-23S6C-C) with at-tached macro objective, which sharply images the SLMsurface to the camera chip. Prior to image recording, acolor calibration is performed, where the SLM is pro-grammed to toggle sequentially between all applicable4096 voltage levels (which are actually addressed as graylevels, sending a 12-bit grayscale image to the SLM), andthe respective 4096 color images are recorded undercomputer control by the RGB camera. Afterward, theRGB channels of the camera images are read out indi-vidually. This yields a spectrum of the intensities ofthe reflected red, green, and blue intensity componentsas a function of the applied voltage. The results areshown in Fig. 2.

The upper graph shows the relative intensities (nor-malized to their maximal values) of the three colorcomponents (Iexp;r , Iexp;g, Iexp;b) as a function of the ap-plied voltage level U . Note that in the ideal case of a “per-fect” PA-LCOS pixel, illuminated with monochromaticlight, the modulations would be expected to oscillate be-tween 0 and full intensity. In our case, where an almostcontinuous illumination spectrum is used, the oscillationcontrast is reduced at higher voltage levels. This is be-cause of the fact that, with increasing voltage the LC pix-els act as waveplates of increasing order, which have acorrespondingly higher wavelength selectivity, i.e., thedesired intensity modulation applies to a shrinking wave-length band. Furthermore, the assumption that eachSLM pixel acts as a birefringent crystal with a fixed ori-entation of its optical axis, may not be perfectly valid,because of the so-called fringing field effect [12]. Never-theless, the modulation characteristics can be used toobtain a broad range of accessible colors. At the bottomof Fig. 2, the corresponding color-palette is displayed,i.e., the color produced by the combination of the abovedisplayed RGB intensity components.

Fig. 1. Setup for color image projection. Light from a whitelight emitting diode (LED) passes through a linear broad bandpolarizer which has a 45° orientation with respect to the activeoptical axis of the liquid crystal layer. The SLM displays apre-calculated pattern, which modulates the polarization ofthe reflected light of each pixel individually in broad range.After passing again through the attached polarization filter,each pixel reflects a predefined color. The SLM surface is thensharply imaged with a color camera.

500 1000 1500 2000 2500 3000 3500 40000

0.2

0.4

0.6

0.8

1

Fig. 2. Red, green, and blue components of a white light beam,reflected off the SLM (with attached polarization filter) as afunction of the voltage (or gray level) U applied uniformly toall of its pixels. All curves are normalized to their respectivemaximal values. Below, a colorbar indicates the respectiveRGB colors, if the three channels are recombined into one colorpixel.

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To display a predefined color image, it is necessary toapproach the desired color of each pixel as closely aspossible within the available color-palette. For this pur-pose, an error metrics ΔCr;g;b � Ir;g;b − Iexp;rgb is definedfor each color channel, which calculates the deviances ofthe desired red (Ir), green (Ig), and blue color (Ib) inten-sities from the respective experimentally realizable colorintensities (Iexp;r�U�, Iexp;g�U�, Iexp;b�U�, respectively)generated by a certain voltage level U . The total colorerror of a pixel is then defined as

�ΔC�2 � �ΔCr�2 � �ΔCg�2 � �ΔCr�2: (2)

�ΔC�2 is calculated for each voltage level U rangingfrom 0 to 4095. Thus one can find a value U , which min-imizes the error ΔC2 for a given desired RGB color triple�Ir; Ig; Ib�. For increased data processing speed, it is ad-vantageous to precalculate the complete color lookup-table, consisting of a 3-dimensional array, which assignsto each RGB color triple the optimal voltage-level U(between 0 and 4095). For practical purposes, we have

reduced the color depth of each master image to 5 bitsin each color channel, resulting in a color lookup-tablewith 25 × 25 × 25 entries. Afterward the transformationof an input RGB image into the corresponding SLM pat-tern corresponds just to a table-lookup, which is done ina few ms for a 600 × 600 pixel image. It should be notedthat, although we use the simple RGB model for demon-stration, a different color error metrics based on a differ-ent color model, such as HSV (hue, saturation, value), orCMYK (cyan, magenta, yellow, key) might be advanta-geous for optimal color reproduction.

The image displayed at the SLM is thus a 12-bit (4096voltage levels) image, which is displayed as a color imagewhen read out with white light through the attachedpolarizer. Because of the limited available color palette,the color reproduction is not perfect. For improvement,one can use “dithering” methods, known for printed me-dia with a limited color spectrum, or also for standardLCD systems. There, “error-diffusion” methods are em-ployed, transferring the residual color error of a certainpixel into its near surrounding. In our case, we use a

Fig. 3. Test color images (600 × 600 pixels) recorded with the setup displayed in Fig. 1. The upper row shows the master images tobe displayed. The second row shows the SLM-generated images, recorded with a color camera. The corresponding SLM patternswere calculated by the direct method, searching the best match to each color pixel in the available color palette. The lowest rowshows the results after dithering the displayed SLM pattern with a Floyd–Steinberg error diffusion method, i.e., there the desiredcolor of each pixel is approached by also modifying the colors in its neighborhood.

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standard Floyd–Steinberg algorithm [13,14], which out-puts the error Cr;g;b � Ir;g;b − Iexp;r;g;b of each color chan-nel for a certain pixel, and adds it (with certain weightsaccording to Ref. [13]) to its neighboring pixels. This isdone iteratively, starting in one corner of the image andvisiting each pixel in a sequential manner. As an example,if the red color channel of a pixel is too low, this is com-pensated by a corresponding increase of the red colorchannels of its surrounding pixels.Figure 3 shows the resulting images. The first row

shows the master images to be reproduced. The secondrow shows the resulting images obtained by the directerror optimization method explained above. Obviously,image reproduction is not perfect, i.e., there appear someabrupt color changes within almost homogeneous areas,and the colors do not perfectly match. An example forthis behavior is obvious in image (f ), which does notaccurately reproduce the green background (left handside of the image). The lowest row shows the results afterapplying the Floyd–Steinberg error diffusion algorithm.In this case, the colors are reproduced more accurately,and abrupt color changes are avoided, however, at thecost of a somewhat reduced resolution, because of dith-ering. For example, the green background missing in (f )is now better approximated in (i).In summary, we demonstrated a method to present

color images at an LC display, which has a three timesincreased light efficiency and display resolution as com-pared to currently used displays, because of the absenceof an attached RGB color mask. Readout was performedwith a broadband, white light LED, which suggests thatthe concept can be used to produce a daylight-readabledisplay. The principle could be already demonstratedwith a non-specialized commercial SLM, which wasactually designed as a phase-only modulator, whichproduces color images of usable quality. Better color

reproductions is possible using a dithering method basedon error diffusion. Using the same principle with a moreoptimized panel, which should provide a broader phasemodulation range, would increase the available color-palette and provide a high quality color image display.In this case, a narrowband RGB illumination would beadvantageous, providing, in principle, a high intensitycontrast modulation even at high voltage levels, whichresults in an improved color saturation.

This work was supported by the ERC Advanced Grant247024 catchIT.

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