February 15, 2015 / Vol. 40, No. 4 / OPTICS LETTERS
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How to use a phase-only spatial light modulator as a color display Walter Harm, Alexander Jesacher, Gregor Thalhammer, Stefan Bernet,* and Monika Ritsch-Marte Division 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) without any attached color mask can be used as a full color display with white light illumination. The method is based on the wavelength dependence of the (voltage controlled) birefringence of the liquid crystal pixels. Modern SLMs offer a wide range over which the birefringence can be modulated, leading (in combination with a linear polarizer) to several intensity modulation periods of a reflected light wave as a function of the applied voltage. Because of dispersion, the oscillation period strongly depends on the wavelength. Thus each voltage applied to an SLM pixel corresponds to another reflected color spectrum. For SLMs with a sufficiently broad tuning range, one obtains a color palette (i.e., a “color lookup-table”), which allows one to display color images. An advantage over standard liquid crystal displays (LCDs), which use color masks in front of the individual pixels, is that the light efficiency and the display resolution are increased by a factor of three. © 2015 Optical Society of America OCIS 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 for computer monitors, smartphone screens, head-up displays, image projectors, or instrument displays (for an overview see [1]), to the best of our knowledge, all of them 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 which the color is adjusted by individually controlling the transmission of its different color fields. Because of absorption at the color mask, the intensity of an incident white light beam is attenuated by a factor of three, even if the pixel is programmed for maximal transmission. Furthermore, the number of actually displayed image pixels is reduced to a third of the number of electronically addressed pixels. Alternatively, there exist holographic image projection methods [2], which use SLMs as a displays for phase holograms. Color image projection is typically spatially multiplexed, displaying the RGB hologram components in different areas of the same panel [3–5], and by overlapping the projected images with different methods. The holographic approaches have, in principle, an optimal efficiency, using all incident light for image reconstruction. On the other hand, they typically suffer from speckle noise, which requires sophisticated methods for noise suppression [3]. Here we demonstrate how to utilize the dispersion of the liquid crystal layer for color image generation in a non-holographic approach. Each individual pixel can be programmed to reflect a selected color, yielding, in principle, full light efficiency at full display resolution. Parallel aligned liquid crystal on silicon (PA-LCOS) spatial light modulators (SLMs) are used typically for pure phase modulation of an incident wave front. All liquid crystal molecules are aligned parallel to each other, and parallel to the surface (x-direction). If a voltage is applied to an SLM pixel, the molecules reorient in the direction of the electric field (z-direction), i.e., 0146-9592/15/040581-04$15.00/0
perpendicularly to the surface. This changes the phase of a reflected (or transmitted) light beam, if its polarization is parallel to the initial molecule orientation (x-direction), which is the “active” optical axis. The phase shift ϕx , after transmission of a liquid crystal layer with thickness D, depends on the applied voltage U and on the readout wavelength λ, according to ϕx nλ U
2πD ; λ
(1)
where nλ U is the voltage-dependent refractive index of the liquid crystal pixel for x-polarized light. The phase shift ϕy of the y-polarization component, on the other hand, does not depend on the applied voltage. Although PA-LCOS SLMs are used typically as pure phase modulators, they can be employed also as intensity modulators. This is because of the fact that the SLM pixels act as voltage controllable birefringent cells with fixed optical axis orientations. Each SLM pixel can be individually switched from a non-birefringent state, where the phase shift differences between x- and y-polarization components are integer multiples of 2π, i.e., ϕx − ϕy 2πN (with N an integer), to a quarterwaveplate state (ϕx − ϕy 2πN π∕4), a half-waveplate (ϕx − ϕy 2πN π∕2) state, and so on, including all continuous intermediate stages. Placing a linear polarization filter in front of the display at a polarization angle of 45° with respect to the x-axis, such that the incident and reflected light pass through the same filter, one obtains a periodic modulation of the reflected intensity as a function of the applied phase shift ϕx , oscillating between the extreme situations where all intensity is reflected if the SLM pixel is in a non-birefringent state, and no reflection if it acts as a half-waveplate (which rotates the incident polarization by 90°). One intensity oscillation period thus corresponds to a 2π phase shift of ϕx . An advantageous feature of the PA-LCOS SLMs is that they allow a voltage controlled phase shift ϕx U © 2015 Optical Society of America
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of several multiples of 2π. This feature has recently been exploited to produce (phase-only) diffractive patterns, which project pre-calculated wavefronts with an improved efficiency by reducing wrapping artifacts [6,7], to suppress the zero diffraction order of projected holograms in a broad wavelength range [8], for color hologram projection [9], and in microscopy for simultaneous steering of optical tweezers and optical image processing at different wavelengths [10]. In all of these cases, 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 range allows one to harmonically modulate the reflected light intensity over a corresponding number of periods. According to Eq. (1), the corresponding oscillation period as a function of the applied voltage strongly depends on the wavelength. Thus, if the SLM is illuminated with white light, each voltage level applied to an SLM pixel creates a different spectrum of reflected intensities, resulting in a certain color. If the phase modulation range of the SLM is sufficiently large, one obtains a color palette, which can be used to display arbitrary color images. For this purpose, one can directly calibrate the color response of the SLM by measuring the reflected color spectrum for all accessible voltage levels. This generates a “color lookup table,” i.e., a table that relates an ideal SLM 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 × 600 pixels, each with an edge length of 20 μm. In phase-only mode, the SLM offers a phase shift of 7.2π at 465 nm, of 5.9π at 532 nm, and of 4.7π at 633 nm, if the maximal voltage is applied. In front of the SLM, a linear polarizer is attached at an angle of 45° with respect to the active polarization axis. Thus, each 2π-phase shift results in a harmonic intensity modulation period of the respective wavelength. 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 “daylightwhite” field was used. The spectrum of the white emitter shows a continuous broad maximum in the red/green range with a peak (about 57% relative intensity) at 550 nm and a full width at half-maximum (FWHM) of about 150 nm, and an additional stronger blue peak (100% relative intensity) at 450 nm with a FWHM of approximately 40 nm [11]. The reflected light is recorded by a color camera (Point Grey GS3-U3-23S6C-C) with attached macro objective, which sharply images the SLM surface to the camera chip. Prior to image recording, a color calibration is performed, where the SLM is programmed to toggle sequentially between all applicable 4096 voltage levels (which are actually addressed as gray levels, sending a 12-bit grayscale image to the SLM), and the respective 4096 color images are recorded under computer control by the RGB camera. Afterward, the RGB channels of the camera images are read out individually. This yields a spectrum of the intensities of the reflected red, green, and blue intensity components as a function of the applied voltage. The results are shown in Fig. 2. The upper graph shows the relative intensities (normalized to their maximal values) of the three color components (I exp;r , I exp;g , I exp;b ) as a function of the applied voltage level U. Note that in the ideal case of a “perfect” PA-LCOS pixel, illuminated with monochromatic light, the modulations would be expected to oscillate between 0 and full intensity. In our case, where an almost continuous illumination spectrum is used, the oscillation contrast is reduced at higher voltage levels. This is because of the fact that, with increasing voltage the LC pixels act as waveplates of increasing order, which have a correspondingly higher wavelength selectivity, i.e., the desired intensity modulation applies to a shrinking wavelength band. Furthermore, the assumption that each SLM pixel acts as a birefringent crystal with a fixed orientation of its optical axis, may not be perfectly valid, because of the so-called fringing field effect [12]. Nevertheless, the modulation characteristics can be used to obtain a broad range of accessible colors. At the bottom of Fig. 2, the corresponding color-palette is displayed, i.e., the color produced by the combination of the above displayed RGB intensity components. 1
0.8
0.6
0.4
0.2
0 500
Fig. 1. Setup for color image projection. Light from a white light emitting diode (LED) passes through a linear broad band polarizer which has a 45° orientation with respect to the active optical axis of the liquid crystal layer. The SLM displays a pre-calculated pattern, which modulates the polarization of the 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 then sharply imaged with a color camera.
1000
1500
2000
2500
3000
3500
4000
Fig. 2. Red, green, and blue components of a white light beam, reflected off the SLM (with attached polarization filter) as a function of the voltage (or gray level) U applied uniformly to all of its pixels. All curves are normalized to their respective maximal values. Below, a colorbar indicates the respective RGB colors, if the three channels are recombined into one color pixel.
February 15, 2015 / Vol. 40, No. 4 / OPTICS LETTERS
To display a predefined color image, it is necessary to approach the desired color of each pixel as closely as possible within the available color-palette. For this purpose, an error metrics ΔC r;g;b I r;g;b − I exp;rgb is defined for each color channel, which calculates the deviances of the desired red (I r ), green (I g ), and blue color (I b ) intensities from the respective experimentally realizable color intensities (I exp;r U, I exp;g U, I exp;b U, respectively) generated by a certain voltage level U. The total color error of a pixel is then defined as ΔC2 ΔC r 2 ΔC g 2 ΔC r 2 :
(2)
ΔC2 is calculated for each voltage level U ranging from 0 to 4095. Thus one can find a value U, which minimizes the error ΔC 2 for a given desired RGB color triple I r ; I g ; I b . For increased data processing speed, it is advantageous to precalculate the complete color lookuptable, consisting of a 3-dimensional array, which assigns to each RGB color triple the optimal voltage-level U (between 0 and 4095). For practical purposes, we have
583
reduced the color depth of each master image to 5 bits in each color channel, resulting in a color lookup-table with 25 × 25 × 25 entries. Afterward the transformation of an input RGB image into the corresponding SLM pattern corresponds just to a table-lookup, which is done in a few ms for a 600 × 600 pixel image. It should be noted that, although we use the simple RGB model for demonstration, a different color error metrics based on a different color model, such as HSV (hue, saturation, value), or CMYK (cyan, magenta, yellow, key) might be advantageous for optimal color reproduction. The image displayed at the SLM is thus a 12-bit (4096 voltage levels) image, which is displayed as a color image when read out with white light through the attached polarizer. Because of the limited available color palette, the color reproduction is not perfect. For improvement, one can use “dithering” methods, known for printed media with a limited color spectrum, or also for standard LCD systems. There, “error-diffusion” methods are employed, transferring the residual color error of a certain pixel 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 to be displayed. The second row shows the SLM-generated images, recorded with a color camera. The corresponding SLM patterns were calculated by the direct method, searching the best match to each color pixel in the available color palette. The lowest row shows the results after dithering the displayed SLM pattern with a Floyd–Steinberg error diffusion method, i.e., there the desired color of each pixel is approached by also modifying the colors in its neighborhood.
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standard Floyd–Steinberg algorithm [13,14], which outputs the error C r;g;b I r;g;b − I exp;r;g;b of each color channel for a certain pixel, and adds it (with certain weights according to Ref. [13]) to its neighboring pixels. This is done iteratively, starting in one corner of the image and visiting each pixel in a sequential manner. As an example, if the red color channel of a pixel is too low, this is compensated by a corresponding increase of the red color channels of its surrounding pixels. Figure 3 shows the resulting images. The first row shows the master images to be reproduced. The second row shows the resulting images obtained by the direct error optimization method explained above. Obviously, image reproduction is not perfect, i.e., there appear some abrupt color changes within almost homogeneous areas, and the colors do not perfectly match. An example for this behavior is obvious in image (f ), which does not accurately reproduce the green background (left hand side of the image). The lowest row shows the results after applying the Floyd–Steinberg error diffusion algorithm. In this case, the colors are reproduced more accurately, and abrupt color changes are avoided, however, at the cost of a somewhat reduced resolution, because of dithering. 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 times increased light efficiency and display resolution as compared to currently used displays, because of the absence of an attached RGB color mask. Readout was performed with a broadband, white light LED, which suggests that the concept can be used to produce a daylight-readable display. The principle could be already demonstrated with a non-specialized commercial SLM, which was actually designed as a phase-only modulator, which produces color images of usable quality. Better color
reproductions is possible using a dithering method based on error diffusion. Using the same principle with a more optimized panel, which should provide a broader phase modulation range, would increase the available colorpalette and provide a high quality color image display. In this case, a narrowband RGB illumination would be advantageous, providing, in principle, a high intensity contrast modulation even at high voltage levels, which results in an improved color saturation. This work was supported by the ERC Advanced Grant 247024 catchIT. References 1. Y. Koike and K. Okamoto, FUJITSU Sci. Tech. J. 35, 221 (1999). 2. M. Paturzo, P. Memmolo, A. Finizio, R. Näsänen, T. J. Naughton, and P. Ferraro, Opt. Express 18, 8806 (2010). 3. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, Opt. Express 20, 25130 (2012). 4. K. Choi, H. Kim, and B. Lee, Opt. Express 12, 5229 (2004). 5. T. Shimobaba, T. Takahashi, N. Masuda, and T. Ito, Opt. Express 19, 10287 (2011). 6. V. Calero, P. García-Martínez, J. Albero, M. M. SánchezLópez, and I. Moreno, Opt. Lett. 38, 4663 (2013). 7. J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, Opt. Lasers Eng. 51, 111 (2013). 8. A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 22, 17590 (2014). 9. A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 22, 20530 (2014). 10. A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 39, 5337 (2014). 11. http://www.ledengin.com/files/products/LZ4/LZ4‑00MD00.pdf. 12. C. Lingel, T. Haist, and W. Osten, Appl. Opt. 52, 6877 (2013). 13. R. W. Floyd and L. Steinberg, Proc. SID 17, 75 (1976). 14. P. Heckbert, Comput. Graph. 16, 297 (1982).
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How to use a phase-only spatial light modulator as a color display Walter Harm, Alexander Jesacher, Gregor Thalhammer, Stefan Bernet,* and Monika Ritsch-Marte Division 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) without any attached color mask can be used as a full color display with white light illumination. The method is based on the wavelength dependence of the (voltage controlled) birefringence of the liquid crystal pixels. Modern SLMs offer a wide range over which the birefringence can be modulated, leading (in combination with a linear polarizer) to several intensity modulation periods of a reflected light wave as a function of the applied voltage. Because of dispersion, the oscillation period strongly depends on the wavelength. Thus each voltage applied to an SLM pixel corresponds to another reflected color spectrum. For SLMs with a sufficiently broad tuning range, one obtains a color palette (i.e., a “color lookup-table”), which allows one to display color images. An advantage over standard liquid crystal displays (LCDs), which use color masks in front of the individual pixels, is that the light efficiency and the display resolution are increased by a factor of three. © 2015 Optical Society of America OCIS 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 for computer monitors, smartphone screens, head-up displays, image projectors, or instrument displays (for an overview see [1]), to the best of our knowledge, all of them 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 which the color is adjusted by individually controlling the transmission of its different color fields. Because of absorption at the color mask, the intensity of an incident white light beam is attenuated by a factor of three, even if the pixel is programmed for maximal transmission. Furthermore, the number of actually displayed image pixels is reduced to a third of the number of electronically addressed pixels. Alternatively, there exist holographic image projection methods [2], which use SLMs as a displays for phase holograms. Color image projection is typically spatially multiplexed, displaying the RGB hologram components in different areas of the same panel [3–5], and by overlapping the projected images with different methods. The holographic approaches have, in principle, an optimal efficiency, using all incident light for image reconstruction. On the other hand, they typically suffer from speckle noise, which requires sophisticated methods for noise suppression [3]. Here we demonstrate how to utilize the dispersion of the liquid crystal layer for color image generation in a non-holographic approach. Each individual pixel can be programmed to reflect a selected color, yielding, in principle, full light efficiency at full display resolution. Parallel aligned liquid crystal on silicon (PA-LCOS) spatial light modulators (SLMs) are used typically for pure phase modulation of an incident wave front. All liquid crystal molecules are aligned parallel to each other, and parallel to the surface (x-direction). If a voltage is applied to an SLM pixel, the molecules reorient in the direction of the electric field (z-direction), i.e., 0146-9592/15/040581-04$15.00/0
perpendicularly to the surface. This changes the phase of a reflected (or transmitted) light beam, if its polarization is parallel to the initial molecule orientation (x-direction), which is the “active” optical axis. The phase shift ϕx , after transmission of a liquid crystal layer with thickness D, depends on the applied voltage U and on the readout wavelength λ, according to ϕx nλ U
2πD ; λ
(1)
where nλ U is the voltage-dependent refractive index of the liquid crystal pixel for x-polarized light. The phase shift ϕy of the y-polarization component, on the other hand, does not depend on the applied voltage. Although PA-LCOS SLMs are used typically as pure phase modulators, they can be employed also as intensity modulators. This is because of the fact that the SLM pixels act as voltage controllable birefringent cells with fixed optical axis orientations. Each SLM pixel can be individually switched from a non-birefringent state, where the phase shift differences between x- and y-polarization components are integer multiples of 2π, i.e., ϕx − ϕy 2πN (with N an integer), to a quarterwaveplate state (ϕx − ϕy 2πN π∕4), a half-waveplate (ϕx − ϕy 2πN π∕2) state, and so on, including all continuous intermediate stages. Placing a linear polarization filter in front of the display at a polarization angle of 45° with respect to the x-axis, such that the incident and reflected light pass through the same filter, one obtains a periodic modulation of the reflected intensity as a function of the applied phase shift ϕx , oscillating between the extreme situations where all intensity is reflected if the SLM pixel is in a non-birefringent state, and no reflection if it acts as a half-waveplate (which rotates the incident polarization by 90°). One intensity oscillation period thus corresponds to a 2π phase shift of ϕx . An advantageous feature of the PA-LCOS SLMs is that they allow a voltage controlled phase shift ϕx U © 2015 Optical Society of America
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of several multiples of 2π. This feature has recently been exploited to produce (phase-only) diffractive patterns, which project pre-calculated wavefronts with an improved efficiency by reducing wrapping artifacts [6,7], to suppress the zero diffraction order of projected holograms in a broad wavelength range [8], for color hologram projection [9], and in microscopy for simultaneous steering of optical tweezers and optical image processing at different wavelengths [10]. In all of these cases, 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 range allows one to harmonically modulate the reflected light intensity over a corresponding number of periods. According to Eq. (1), the corresponding oscillation period as a function of the applied voltage strongly depends on the wavelength. Thus, if the SLM is illuminated with white light, each voltage level applied to an SLM pixel creates a different spectrum of reflected intensities, resulting in a certain color. If the phase modulation range of the SLM is sufficiently large, one obtains a color palette, which can be used to display arbitrary color images. For this purpose, one can directly calibrate the color response of the SLM by measuring the reflected color spectrum for all accessible voltage levels. This generates a “color lookup table,” i.e., a table that relates an ideal SLM 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 × 600 pixels, each with an edge length of 20 μm. In phase-only mode, the SLM offers a phase shift of 7.2π at 465 nm, of 5.9π at 532 nm, and of 4.7π at 633 nm, if the maximal voltage is applied. In front of the SLM, a linear polarizer is attached at an angle of 45° with respect to the active polarization axis. Thus, each 2π-phase shift results in a harmonic intensity modulation period of the respective wavelength. 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 “daylightwhite” field was used. The spectrum of the white emitter shows a continuous broad maximum in the red/green range with a peak (about 57% relative intensity) at 550 nm and a full width at half-maximum (FWHM) of about 150 nm, and an additional stronger blue peak (100% relative intensity) at 450 nm with a FWHM of approximately 40 nm [11]. The reflected light is recorded by a color camera (Point Grey GS3-U3-23S6C-C) with attached macro objective, which sharply images the SLM surface to the camera chip. Prior to image recording, a color calibration is performed, where the SLM is programmed to toggle sequentially between all applicable 4096 voltage levels (which are actually addressed as gray levels, sending a 12-bit grayscale image to the SLM), and the respective 4096 color images are recorded under computer control by the RGB camera. Afterward, the RGB channels of the camera images are read out individually. This yields a spectrum of the intensities of the reflected red, green, and blue intensity components as a function of the applied voltage. The results are shown in Fig. 2. The upper graph shows the relative intensities (normalized to their maximal values) of the three color components (I exp;r , I exp;g , I exp;b ) as a function of the applied voltage level U. Note that in the ideal case of a “perfect” PA-LCOS pixel, illuminated with monochromatic light, the modulations would be expected to oscillate between 0 and full intensity. In our case, where an almost continuous illumination spectrum is used, the oscillation contrast is reduced at higher voltage levels. This is because of the fact that, with increasing voltage the LC pixels act as waveplates of increasing order, which have a correspondingly higher wavelength selectivity, i.e., the desired intensity modulation applies to a shrinking wavelength band. Furthermore, the assumption that each SLM pixel acts as a birefringent crystal with a fixed orientation of its optical axis, may not be perfectly valid, because of the so-called fringing field effect [12]. Nevertheless, the modulation characteristics can be used to obtain a broad range of accessible colors. At the bottom of Fig. 2, the corresponding color-palette is displayed, i.e., the color produced by the combination of the above displayed RGB intensity components. 1
0.8
0.6
0.4
0.2
0 500
Fig. 1. Setup for color image projection. Light from a white light emitting diode (LED) passes through a linear broad band polarizer which has a 45° orientation with respect to the active optical axis of the liquid crystal layer. The SLM displays a pre-calculated pattern, which modulates the polarization of the 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 then sharply imaged with a color camera.
1000
1500
2000
2500
3000
3500
4000
Fig. 2. Red, green, and blue components of a white light beam, reflected off the SLM (with attached polarization filter) as a function of the voltage (or gray level) U applied uniformly to all of its pixels. All curves are normalized to their respective maximal values. Below, a colorbar indicates the respective RGB colors, if the three channels are recombined into one color pixel.
February 15, 2015 / Vol. 40, No. 4 / OPTICS LETTERS
To display a predefined color image, it is necessary to approach the desired color of each pixel as closely as possible within the available color-palette. For this purpose, an error metrics ΔC r;g;b I r;g;b − I exp;rgb is defined for each color channel, which calculates the deviances of the desired red (I r ), green (I g ), and blue color (I b ) intensities from the respective experimentally realizable color intensities (I exp;r U, I exp;g U, I exp;b U, respectively) generated by a certain voltage level U. The total color error of a pixel is then defined as ΔC2 ΔC r 2 ΔC g 2 ΔC r 2 :
(2)
ΔC2 is calculated for each voltage level U ranging from 0 to 4095. Thus one can find a value U, which minimizes the error ΔC 2 for a given desired RGB color triple I r ; I g ; I b . For increased data processing speed, it is advantageous to precalculate the complete color lookuptable, consisting of a 3-dimensional array, which assigns to each RGB color triple the optimal voltage-level U (between 0 and 4095). For practical purposes, we have
583
reduced the color depth of each master image to 5 bits in each color channel, resulting in a color lookup-table with 25 × 25 × 25 entries. Afterward the transformation of an input RGB image into the corresponding SLM pattern corresponds just to a table-lookup, which is done in a few ms for a 600 × 600 pixel image. It should be noted that, although we use the simple RGB model for demonstration, a different color error metrics based on a different color model, such as HSV (hue, saturation, value), or CMYK (cyan, magenta, yellow, key) might be advantageous for optimal color reproduction. The image displayed at the SLM is thus a 12-bit (4096 voltage levels) image, which is displayed as a color image when read out with white light through the attached polarizer. Because of the limited available color palette, the color reproduction is not perfect. For improvement, one can use “dithering” methods, known for printed media with a limited color spectrum, or also for standard LCD systems. There, “error-diffusion” methods are employed, transferring the residual color error of a certain pixel 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 to be displayed. The second row shows the SLM-generated images, recorded with a color camera. The corresponding SLM patterns were calculated by the direct method, searching the best match to each color pixel in the available color palette. The lowest row shows the results after dithering the displayed SLM pattern with a Floyd–Steinberg error diffusion method, i.e., there the desired color of each pixel is approached by also modifying the colors in its neighborhood.
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OPTICS LETTERS / Vol. 40, No. 4 / February 15, 2015
standard Floyd–Steinberg algorithm [13,14], which outputs the error C r;g;b I r;g;b − I exp;r;g;b of each color channel for a certain pixel, and adds it (with certain weights according to Ref. [13]) to its neighboring pixels. This is done iteratively, starting in one corner of the image and visiting each pixel in a sequential manner. As an example, if the red color channel of a pixel is too low, this is compensated by a corresponding increase of the red color channels of its surrounding pixels. Figure 3 shows the resulting images. The first row shows the master images to be reproduced. The second row shows the resulting images obtained by the direct error optimization method explained above. Obviously, image reproduction is not perfect, i.e., there appear some abrupt color changes within almost homogeneous areas, and the colors do not perfectly match. An example for this behavior is obvious in image (f ), which does not accurately reproduce the green background (left hand side of the image). The lowest row shows the results after applying the Floyd–Steinberg error diffusion algorithm. In this case, the colors are reproduced more accurately, and abrupt color changes are avoided, however, at the cost of a somewhat reduced resolution, because of dithering. 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 times increased light efficiency and display resolution as compared to currently used displays, because of the absence of an attached RGB color mask. Readout was performed with a broadband, white light LED, which suggests that the concept can be used to produce a daylight-readable display. The principle could be already demonstrated with a non-specialized commercial SLM, which was actually designed as a phase-only modulator, which produces color images of usable quality. Better color
reproductions is possible using a dithering method based on error diffusion. Using the same principle with a more optimized panel, which should provide a broader phase modulation range, would increase the available colorpalette and provide a high quality color image display. In this case, a narrowband RGB illumination would be advantageous, providing, in principle, a high intensity contrast modulation even at high voltage levels, which results in an improved color saturation. This work was supported by the ERC Advanced Grant 247024 catchIT. References 1. Y. Koike and K. Okamoto, FUJITSU Sci. Tech. J. 35, 221 (1999). 2. M. Paturzo, P. Memmolo, A. Finizio, R. Näsänen, T. J. Naughton, and P. Ferraro, Opt. Express 18, 8806 (2010). 3. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, Opt. Express 20, 25130 (2012). 4. K. Choi, H. Kim, and B. Lee, Opt. Express 12, 5229 (2004). 5. T. Shimobaba, T. Takahashi, N. Masuda, and T. Ito, Opt. Express 19, 10287 (2011). 6. V. Calero, P. García-Martínez, J. Albero, M. M. SánchezLópez, and I. Moreno, Opt. Lett. 38, 4663 (2013). 7. J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, Opt. Lasers Eng. 51, 111 (2013). 8. A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 22, 17590 (2014). 9. A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 22, 20530 (2014). 10. A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 39, 5337 (2014). 11. http://www.ledengin.com/files/products/LZ4/LZ4‑00MD00.pdf. 12. C. Lingel, T. Haist, and W. Osten, Appl. Opt. 52, 6877 (2013). 13. R. W. Floyd and L. Steinberg, Proc. SID 17, 75 (1976). 14. P. Heckbert, Comput. Graph. 16, 297 (1982).
