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This work presents color holographic display, which is based on a single phase only spatial light modulator (SLM). In the display entire area of the SLM is illuminated by an on-axis white light beam generated by a single large LED. The holographic display fully utilizes SLM bandwidth and has capability of full-color, full frame rate imaging of outstanding quality. This is achieved through: (i) optimal use of the source coherence volume, (ii) application of the single white light LED source, (iii) a development of a novel concept of color multiplexing technique with color filter mask in Fourier plane of the SLM, (iv) and a complex coding with improved diffraction efficiency. Within experimental part of the paper we show single color, full-color holographic 2D and 3D images generated for reconstruction depth exceeding 10 cm.
© 2016 Optical Society of America
1. Introduction
Holographic display technology provides a possibility of reconstruction of three-dimensional images, which appear to float in the air, and provide natural viewing experience with all the physiological depth cues with no conflict among them. Current developments in holographic displays include: possibility of color imaging [1–4], wide angle imaging [5,6], development of multiplexing methods [7,8], computer holography [9,10], high resolution spatial light modulators [11], pupil tracking systems [12], content capture and processing [13–17], complex wave coding [18,19], holographic television [20], color holographic projection [21,22], holographic printing [23], and others.
Most of the holographic display designs employ laser illumination because this provides images of the highest resolution, and what is even more important of the large depth. However, the use of a laser source is also disadvantageous. An image is distorted by a coherent noise of high contrast. Laser may be a cause of eye hazard. The direct way of overcoming these obstacles is to build holographic display with incoherent light source.
One known color holographic display architecture is based on white light illumination and three SLMs for corresponding RGB channels. In this solution each of the SLMs is illuminated with light of different wavelength giving three separate color holographic images, which when combined form a single full-color frame [24–26]. Holographic displays having capability of full-color imaging with single SLM were also realized. Such a capability is achieved by using a time-division method (TDM) [27,28], a space-division method (SDM) [29], or by exploiting full phase modulation range (FPMR) of the SLM [30]. In the TDM approach the SLM is reconstructing single color holographic images in a time sequence. The time sequential color reconstructions, which are realized by synchronizing LED sources with the SLM, are forming single full-color frame. Thus, in the TDM approach display frame rate is reduced. On the contrary the SDM approach, where the SLM is illuminated by three LED sources from different angular directions, offers capability of full-color reconstruction at full frame rate. However, this approach has limited volume of full-color holographic reconstruction in both transverse (limited Field of View) and longitudinal (reconstructions far from the SLM plane are possible only) dimension. For the displays that use incoherent illumination the longitudinal restriction is the most critical, since this limits the resolution of an obtained reconstruction. The FPMR is a color hologram projection method that is based on the SLM having large range of phase modulation. In this approach the individual color 2π holograms are coded in the phase range that extends over several multiples of 2π. It was shown that the reconstruction of the combined color hologram provides individual color images with a crosstalk level below 5%. Similarly to the SDM the FPMR approach allows reconstructing color images that are far from the SLM panel.
The display approach of this work is free of above disadvantages. It uses full SLM bandwidth and has capability of full-color imaging with a full frame rate. The display design is based on a single SLM, which is illuminated by a single broad band white light LED (size of 960 µm diameter) from on-axis direction. We show that with such an experimental constrains it is possible to obtain full-color reconstructions of outstanding quality and resolution limited by parameters of the SLM. This is achieved through: (i) optimal use of source coherence volume, (ii) application of a single white light LED source, and (iii) improved diffraction efficiency. First feature is realized by complex coding scheme and centering volume of hologram reconstruction around image plane of the SLM, and it allows obtaining images of the highest resolution. Within the imaging area that is close to the image plane of the SLM, the resolution is determined solely by the SLM pixel, while for more distant planes by limited coherence of the illumination source. Second feature fulfills fundamental assumption of holography. Because the full aperture of the SLM is illuminated by a single source with all RGB components, obtained RGB holographic field is accurately reconstructed in the entire reconstruction volume. The last feature is realized by optimizing performance of the SLM. The display design of this work is based on the phase-only SLM because it provides higher diffraction efficiency and improved quality of reconstructed image. However, applied complex coding scheme at higher diffraction efficiencies becomes nonlinear. In this work we linearize it by utilizing a look-up table technique.
The design of color holographic display is based on a novel concept of color multiplexing technique, here referred as frequency division method (FDM). The core of experimental realization of the FDM is a RGB color filter mask that is placed in Fourier plane of the SLM. Each of the RGB filter of color mask occupies different spatial frequency region of Fourier space of the SLM. FDM is a multiplexing technique that encodes RGB component holograms to the distinct Fourier spaces of a single synthesized RGB complex hologram. Such a synthesized hologram addresses the SLM. Thus, when the SLM is illuminated by white light beam, the holographic display decodes RGB complex wavefields of full-color synthesized hologram. It has to be noted that the FDM uses full spatial spectrum of the SLM.
The laser color holographic projection method [21] is based on the SDM color multiplexing where similar color filter mask is used, however the mask is placed near the surface of the SLM. This SDM implementation employs phase while FDM complex wave modulation. Thus SDM has higher diffraction efficiency. The FDM technique complements the State of the Art of a holographic display color multiplexing techniques. Because none of the known techniques can provide full-color reconstruction in 3D area close to a display SLM, and support RGB source illumination from a single direction.
This work is organized as follows: Section 2 introduces the holographic display system. Section 3 presents a Frequency Division Method that supports the color holographic imaging of the display system. The holographic imaging quality is evaluated in Section 4 by presenting experimental reconstructions for three different objects: flat gray 2D photo, flat color image and 3D color computer graphics model. The conclusions are finally presented in Section 5.
2. Display setup
Figure 1(a) presents the developed in this work holographic display system, which uses incoherent source of wide white light spectrum (Doric Lenses LED W55, fiber core 960 µm, NA 0.5). The source is located in back focal plane of a collimator lens (F = 400 mm). After collimation statistically stationary white light beam illuminates the phase only SLM (Holoeye 1080P, 1920 x 1080 pixels, pixel pitch 8 µm). The modulator screen is placed at back focal plane of a lens L1. Lenses L1 and L2 (both with F = 200 mm, NA = 0.19, and diameter = 75 mm) create 4F imaging system, which conjugates the SLM with imaging volume of reconstructed hologram. In Fourier plane of the SLM there is a specially designed mask with horizontal RGB color filters and vertical-absorbing cut-off filter. The mask with color filters splits the white light beam into three RGB components of color holographic image. The light shaping method based on generalized phase contrast [31] improves imaging performance by using color filter in Fourier plane as well. However, the used filter is a phase one, and a single color imaging is considered.
Fig. 1 a) Color holographic display system based on the FDM with white light and large size incoherent LED source; b) Normalized output power spectrum of each of the RGB channels.
We have measured the output power spectrums separately for each of the RGB component of our display. The measurement results as normalized power spectrum of each RGB channel is presented in the Fig. 1(b). The central wavelengths of these RGB components are given as: λB = 450 nm, λG = 530 nm, and λR = 625 nm.
3. Frequency division method (FDM)
3.1 General approach of RGB FDM coding scheme
In our display system, the SLM is addressed with a white light hologram, which is synthesized from three RGB color component holograms. The component holograms share the same spatial domain of the SLM, but they occupy different spatial frequency ranges. The segments of the RGB color filter mask cover spatial locations in Fourier plane, which are corresponding to the spatial frequency ranges of the RGB component holograms. That property of the experimental system enables implementation of the FDM and RGB hologram synthesis, which allows reconstructing all three RGB complex holographic images from a single phase hologram.
The Y dimensions of the RGB mask are selected to obtain equal resolutions of all RGB holographic components. X directional negative absorbing cut-off filter provides capability of a complex imaging. The blue (B) image component is the most focused in Fourier plane of the 4F system. Thus only Y sequence of color filters with the blue mask in the center enables spatial separation of the RGB components. Otherwise addressing the full frequency space of the SLM would not be possible. In our solution we choose sequence where the R component occupies positive frequency in Y direction while G negative. In the FDM approach each of the RGB image component is band limited to addresses equal bandwidth (Bf) of the SLM in X and Y directions, i.e.:and where Δ is a pixel pitch of the SLM. What is interesting to notice the utilized Y frequency sequence of filters gives spatial gaps in Fourier plane between B-G and B-R spectrums of component holograms as:
This presents practical advantage over spatial realization of 3D holographic display with the color masking approach, where the filter mask is placed close to the SLM surface [21].Let now develop the FDM hologram coding technique, which codes three RGB color component holograms into single white light hologram that addresses the SLM. The component holograms are referred as uBL,p where p = R, G, B. The subscript BL means that each of the RGB component is band limited to the equal frequency range:
This element of the FDM coding is visualized in left part of the diagram that is presented in the Fig. 2. In the FDM approach RGB component holograms are coded in a single real signal as:where dash denotes complex conjugation; fm,p are corresponding modulation frequency vectors: fm,G = [(4Δ)−1,-(3Δ)−1], fm,B = [(4Δ)−1, 0], and fm,R = [(4Δ)−1,(3Δ)−1]. In our display the SLM is addressed with the color hologram ureal. The parameter βp enables control over intensity ratio in three RGB hologram channels, which is necessary due to the different output powers of corresponding illumination components [Fig. 1(b)].Fig. 2 Diagram of the FDM coding of RGB component holograms into white light hologram; Left column ‘Real domain’ represents RGB input holographic images; Column ‘Frequency domain’ illustrates generation of a real hologram; Right column ‘Real domain’ represents post processing part of the FDM coding: nonlinear correction, phase conversion.
The real signal ureal can be used for reconstruction of color images in holographic display with amplitude SLM. However, diffraction efficiency of this approach is limited to 6.2%. Higher diffraction efficiency can be achieved by using complex modulation scheme when employing phase SLM [18]. In our work we use phase modulation, thus the real signal ureal given by Eq. (3) generates optical field as:
For the phase modulation case, the optical field u can be decomposed into a set of diffraction orders as:In our system the diffraction orders for q≤0 are removed by absorbing cut-off filter [Fig. 1(a)], while for q>1 are neglected due to the lower diffraction efficiencies. Then, the reconstructed color holographic image ur is received for q = 1:3.2 Reduction of nonlinear amplitude distortion
The holographic image ur has distribution with nonlinearly distorted amplitude. The distortion is linear for small βp and becomes nonlinear for larger values. In fact, for small βp, where only linear part of Bessel function is used, the images of low diffraction efficiency are received and the advantage of phase modulation is not fully employed. The modulation using nonlinear part of Bessel function – large βp – potentially can provide holographic images with higher diffraction efficiencies.
The nonlinear distortion can be removed when the SLM is modulated with distribution, which generates color images uBL,p of corrected amplitude:
where the subscript c denotes correcting amplitude distribution. The CF is a correcting function with property:which provides amplitude distribution that is required for correcting the nonlinear modulation error of a holographic image. The CF is implemented using interpolation method. The values of are evaluated by employing numerical lookup table approach where the sampling points (ξ) are amplitude responses while the corresponding values [f(ξ)] are amplitude modulations.Equation (7) is the final formula of FDM coding scheme showing that the synthetized hologram is a sum of three independent RGB hologram components. However, as presented in Fig. 2, the process of assembling RGB components into white light hologram is implemented as a phase summation. Such an implementation results in formation of crosstalk images. Nevertheless, by analyzing the coefficients of crosstalk images it can be shown that they have very small diffraction efficiency. Thus, similarly as higher order terms, they are neglected.
The performance and accuracy of the proposed method of nonlinear error correction is demonstrated here by simulation of coding and decoding process for the exemplary case of an object, which has linearly increasing distribution of amplitude from 0 to 0.58. The value of 0.58 was selected because it corresponds to the maximum diffraction efficiency 0.34 that can be achieved in the phase modulation case. The object amplitude is plotted in the Fig. 3 with black dashed line. Solid lines plot reconstructed amplitudes with applied correction – red line – and without correction – green line. The simulation verifies that the correction method effectively minimizes the nonlinear errors of amplitude modulation. For values of amplitude modulation close to 0.58 the method gives noticeable errors. However for these values of modulation higher diffraction orders cannot be neglected and the image quality will be decreased.
3.3 Conversion of individual phase component holograms to bit levels
In our display system the SLM provides holographic images with maximum amplitude of 0.55. This is achieved by modulating phase of the SLM in range of ± 1.45 rad. Thus each of the RGB hologram component is generated by phase modulation in the range of 0 to 2.9 rad. The RGB holograms are generated according to the different phase response lines, which are illustrated in Fig. 4(a). These lines enable phase modulation of ± 1.45 rad with zero phase offset of 1.45 rad for each component. For example the zero phase (1.45 rad) for red hologram component is achieved for value of phase level 52.2, while phase modulation of ± 1.45 corresponds to a level range from 0 to 104.5. The phase levels for different components are presented in Fig. 4(a). The phase line responses were designed to meet following condition: the sum of phase levels for maximum modulations of each component is 255, i.e. 68.5 + 82 + 104.5 = 255. This element of the FDM coding is illustrated in right part of the Fig. 2.
Fig. 4 a) Phase line responses used for corresponding RGB component holograms; b) Measured phase responses of calibrated SLM wavelengths: 445, 532, 660 [nm].
The phase line responses were calculated using laser based calibration procedure. In this procedure we have calibrated the SLM at laser wavelength 532 nm. Then, to find dispersion characteristics, we have measured the phase responses for different laser wavelengths: 445 nm and 660 nm. The measurement results are shown in the Fig. 4(b). Using interpolation methods we have found linear phase response curves of each of the RGB component. The display SLM has loaded characteristic of R component that gives the phase modulation of 0 to 2.9 rad for phase level range from 0 to 104.5.
4. Experimental evaluation
4.1 Experimental results
The 3D holographic imaging quality of our holographic system is evaluated here by presenting three different experiments. The purpose of the first one is to obtain reconstruction of the gray color object. The second one presents reconstructions of well-known and colorful 2D images. They are presented for different reconstruction depth, which illustrates the loss of resolution that depends on reconstruction distance. The final experiment proves the possibility of color reconstruction of 3D object.
For the performance test with the flat gray object we have used a gray projection photo of Gargoyle statue. To obtain the RGB component holograms we have assumed that the pure amplitude object is in-focus at the distance of 10 mm from the SLM plane. The in-focus object has equal powers and distributions for each of the RGB component. These in-focus object distributions were propagated to the SLM plane using Angular Spectrum method. Obtained component holograms were coded using the FDM. Figure 5(a) presents images captured for color reconstruction of the gray object. To equalize powers of the RGB components in the experimental setup we have applied βR = 0.42, βG = 1, and βB = 0.82. The values were used through entire paper experiment, and correspond to the maximum amplitudes of each of the RGB reconstructed component: 0.23, 0.55 and 0.45. The optimal values of βp were found experimentally by displaying hologram of rectangular test pattern object with constant and equal intensity of each RGB image component. The optimal set of coefficients give reconstruction in white color. For illustrative purposes Figs. 5(b) to 5(d) additionally present images taken for reconstructions that were obtained separately for each of the RGB channel. The photos were captured using color camera.
Fig. 5 a) Captured images of white light reconstruction of hologram generated for gray Gargoyle projection photo. Photos of reconstructions of corresponding RGB components b) R, c) G, and d) B.
In our system the LED source provides limited spatial and temporal coherence of the illumination beam. The limitation decreases resolution of the reconstructed images, and the decrease is spatially variant [32–34]. Our display is built in the configuration of image holography. Thus at the image central plane, which is the image plane of the SLM, the coherence is not affecting resolution of a hologram reconstruction. However, when the display attempts to reconstruct holographic images in the plane, which is axially distant from the image plane of the SLM the resolution decreases. In our display the dominant effect is given by spatial coherence of the illumination source that acts as a low pass filter with exemplary cutoff frequencies 42 and 8.3 [mm−1] for zrec = 10, 50 [mm], respectively.
The paper second experiment is presented in the Fig. 6. The experiment illustrates colorful reconstructions, which were obtained for different reconstruction distances. The holograms were generated with the same procedure as the one used for preparations of Fig. 5. In the case of the Fig. 6 we use well known colorful planar objects: photo of baboon and photo of Rubik’s cube. We have designed holograms for reconstruction distances in range ± 5 cm. Figure 6 shows reconstructions obtained for both objects designed and captured for distances: −5, −3, −1, 0, 1, 3, 5 [cm]. The presented experimental results confirm that our white LED based display is able to provide color holographic reconstructions with high imaging quality.
Fig. 6 White light reconstructions of baboon and Rubik’s cube projection photos designed and captured for different reconstruction distances; a) and b) presents the images captured for holograms designed for reconstruction distance zrec = 0 mm. The images have dimensions 7.2 × 7.2 [mm].
The final experiment proves the possibility of color reconstruction of 3D objects. The object that was selected for this experiment is a computer graphics model in the representation of 3D cloud of points. It represents a blue dog with white nose, eyes and tail, red tongue, two green patches on its head, yellow locket on its neck, and two red patches on the body. For generation of the RGB component holograms the point based method of reference [35] was used. The obtained three component holograms were coded into single white light hologram using the FDM. In the Fig. 7 we present white light reconstructions of two holograms of the same 3D dog object, however, designed for two different reconstruction distances. Figures 7(a)-7(e) show images that were captured when reconstructing the hologram of dog located close to the SLM plane. In this case the longitudinal center of 16 mm deep object is put at the distance of 10 mm from the SLM. To illustrate the possibility of 3D reconstruction we show images that were captured for five different camera in-focus positions. The positions were selected to obtain sharp focus on the different parts of the dog object: nose, right eye, neck with locket, bottom, and tail. The experiment verifies the quality of 3D color holographic imaging feature of the display. The bottom row of the Fig. 7 presents the set of corresponding in-focus captures for hologram design for the same dog object but now with the center at the axial distance of 50 mm from the SLM. Again, as in the case of experiment presented in the Fig. 6, the resolution drop is observable. Nevertheless the 3D distribution of color and geometry of reconstructed dog object is still well distinguishable. Attached visualizations in Fig. 7 illustrate rotation and walk of the dog object.
Fig. 7 White light reconstructions of 3D object designed for two different depths; (a) – (e) center of the object is 10 mm from the SLM, while for (f) – (j) 50 mm. The images were captured with CCD for different in-focus positions: (a) and (f) – nose, (b) and (g) right eye, (c) and (h) neck with locket, (d) and (i) bottom, (e) and (j) tail. The images have dimensions 7.2 × 7.2 [mm]. See Visualization 1 and Visualization 2 illustrating rotating and walking dog, respectively. For both visualizations the camera is placed at zrec = 15 mm.
4.2 Evaluation of the display light efficiency and color crosstalk
The display system uses LCoS SLM that can modulate the light with diffraction efficiency close to 100%. Our display uses complex modulation scheme, which is based on filtering of diffraction orders that lowers light efficiency. Thus we have experimentally evaluated diffraction efficiency of FDM coding scheme, the filtering effect of used optical elements was disregarded (lenses, prism). The evaluation procedure is based on the measurement of intensity of diffraction orders with power sensor (Photodiode Power Sensor S121C) placed in the focal plane of the lens L1 (color filter mask is removed). In the first step we have measured powers of RGB components, separately. This was done by measuring power in zero diffraction order for SLM working as a mirror. During the measurement the RGB color filters were sequentially placed in front of the source. The obtained reference values were: I0R = 20.28 µW, I0G = 3.5 µW, and I0B = 7.9 µW. Then we have displayed the test hologram. The test hologram was designed to produce, at distance zrec = 0 mm, three holographic images of constant amplitude distribution 0.45 for each of the colors. We have measured powers of diffraction orders corresponding to each image, the measured values are I1R = 14.8 µW, I1G = 0.4 µW and I1B = 1.2 µW. The diffraction efficiency of coding scheme of our display is evaluated as . Please note that the measured value is lowered by higher diffraction orders of SLM. In simulation the diffraction efficiency was few times larger.
The evaluation procedure of color crosstalk was based on displaying three holograms, each having only one color component. For each reconstructed hologram we have captured three color images and compared obtained intensities. The obtained value of color crosstalk was below 1%.
5. Conclusions
A novel holographic display design based on white light on-axis LED illumination is reported. This novel display has capability of full-color holographic imaging of outstanding quality with full use of SLM bandwidth and full frame rate from single phase only SLM. The design is based on a novel FDM color multiplexing technique. The core of experimental realization of the FDM is the RGB color filter mask, which is placed in Fourier plane of the SLM. The display uses complex coding scheme with linearized, in this work, amplitude response. The method has several advantages: (i) the single SLM color imaging; (ii) full frame rate; (iii) imaging with maximum resolution; and (iv) optimal use of source coherence volume. Within experimental part we present holographic reconstructions for three different objects: 2D gray image, 2D color image and 3D color computer graphics model. These objects were selected to verify possibility of 3D reconstruction for both gray and full-color objects. In the display setup LED source of large diameter is used. This decreases resolution of reconstructed images for planes of an object, which are far from the plane of the SLM. Therefore the depths of object reconstructions were selected to cover longitudinal depth of approx. 10 cm.
In comparison to the State of the Art the proposed here FDM color coding scheme has several shortcomings. The employed complex coding scheme lowers light efficiency. Both, masking and complex coding introduces small level of background noise: color crosstalk, higher diffraction orders, and diffraction orders crosstalk images.
Acknowledgments
This work is supported by National Science Center Poland (MAESTRO 2011/02/A/ST7/00365); The Cross-Ministry Giga KOREA Project Ministry of Science ICT and Future Planning, Korea (GigaKOREA GK14D0100); and statutory founds of Warsaw University of Technology.
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