Open Access
Add to BibSonomyAbstract
The horizontally scanning holographic display has increased viewing angle and display screen size as compared to conventional holographic displays. Elementary holograms, which are generated by a high-speed SLM and projected by an anamorphic imaging system, are aligned horizontally by a galvano mirror. When the frame rate of the SLM is high, the width of the elementary holograms becomes several times as large as their horizontal display pitch so that several sets of elementary holograms can be displayed. A laser is modulated to illuminate different elementary hologram sets by different laser powers. The grayscale representation of reconstructed images is improved by properly designing the elementary hologram sets and the illumination laser powers.
©2010 Optical Society of America
1. Introduction
The horizontally scanning holographic display [1, 2] was developed in order to increase both the viewing angle and the hologram size of holographic displays. In this technique, a series of elementary holograms generated by a high-speed spatial light modulator (SLM) are aligned horizontally by a mechanical scanner. In the present study, the grayscale representation of the horizontally scanning holographic display is improved.
Basic holographic display systems simply simulate the principle of optical holography, i.e., an interference pattern of a hologram is displayed on an SLM. Therefore, a very fine pixel pitch and an ultra-high resolution are required for an SLM. The pixel pitch has to be reduced in order to increase the viewing angle, and the resolution has to be increased in order to enlarge the hologram screen size. For instance, in order to obtain a viewing angle of 30° and a hologram screen size of 20 inches when the wavelength of light is 0.5 μm, the pixel pitch should be 0.97 μm and the resolution should be 421,000 × 316,000. Therefore, the techniques to overcome this problem have been developed in order to construct practical holographic displays. The techniques proposed thus far are categorized into spatial multiplexing techniques and time-multiplexing techniques. Spatial multiplexing techniques physically increase the number of pixels by using a number of SLMs, whereas time-multiplexing techniques virtually increase the number of pixels by using a high-speed SLM. In both of these techniques, the pixel pitch is reduced by a reduction imaging system. As spatial multiplexing techniques, the use of four high-resolution liquid crystal display (LCD) panels was reported [3, 4], and the use of 12 LCD panels in a curved array was also reported [5]. Time-multiplexing techniques include the combination of an acousto-optic modulator and a two-dimensional mechanical scanner [6, 7], the combination of a ferroelectric LCD (FLCD) panel and an optically addressable SLM [8, 9], and the above-described horizontally scanning holographic display, in which the combination of a digital micro-mirror device (DMD) and a one-dimensional mechanical scanner is used. Although spatial multiplexing can be implemented using normal-speed SLMs, a greater number of SLMs is required. In contrast, time-multiplexing requires fewer SLMs. However, high-speed SLMs are needed. Normal-speed SLMs can generally display continuous tone images or multiple grayscale images using, for example, a twisted nematic LCD panel. In contrast, high-speed SLMs tend to be able to display only low-bit resolution grayscale images or purely binary images, as is the case for an FLCD or a DMD. When an interference pattern of a hologram is displayed as a low-bit resolution grayscale or binary image, image degradation occurs in the reconstructed images, i.e., poor grayscale representation and image deformation arise.
Significant research has been performed in order to develop design methods for binary holograms. Early computer-generated holograms (CGHs) were binary holograms because a hologram pattern was rendered by a plotter or a printer and was then de-magnified by a photographic process. Several notable design methods were proposed, including the Lohmann hologram [10], the Lee hologram [11, 12], the binary synthetic hologram [13], and the pulse-density modulation hologram [14]. Advances in computers then enabled iterative search algorithms to be applied to binary hologram design. For example, the direct binary search method [15, 16] made optimal use of the SLM resolution.
In the present study, a time-multiplexing technique to produce grayscale reconstructed images is developed for the horizontally scanning holographic display.
2. Horizontally scanning holographic display
Before explaining the technique used to improve the grayscale representation of reconstructed images, the operating principle of the horizontally scanning holographic display [1] is briefly explained. The present study takes into account the occurrence of spatial overlap among elementary holograms.
A schematic diagram of the horizontally scanning holographic display system is shown in Fig. 1 . An image generated by a high-speed SLM is squeezed in the horizontal direction and enlarged in the vertical direction by an anamorphic imaging system. The anamorphic imaging system, consisting of two orthogonally aligned cylindrical lenses, has different magnifications in the horizontal and vertical directions. The generated vertically stretched image, which is an elementary hologram, is scanned horizontally by a mechanical scanner. The high-speed SLM displays a series of elementary images in synchronization with the horizontal scanning. The pixel pitch of the SLM is reduced in the horizontal direction so that the horizontal viewing angle increases. The image is enlarged in the vertical direction and is scanned in the horizontal direction so that the hologram size increases. Since the vertical pixel pitch increases, this system displays a horizontal parallax-only hologram. A screen lens redirects light to observers, and a vertical diffuser increases the vertical viewing zone.
The resolution of the high-speed SLM is denoted by X×Y, and the pixel pitch is denoted by p. The horizontal and vertical magnifications of the anamorphic imaging system are denoted by Mx and My, respectively. The number of elementary holograms displayed by a single scan is denoted by N, and the horizontal pitch of the displayed elementary holograms is denoted by q. The width and height of the elementary holograms are given by MxXp and MyYp, respectively. The horizontal viewing angle of the reconstructed images is given by 2 sin−1(λ/2Mxp), where λ is the wavelength of light. The width and the height of the hologram screen are given by (N−1)q + MxXp and MyYp, respectively.
The width of the elementary hologram must be equal to or larger than the horizontal pitch of the displayed elementary holograms, i.e., MxXp ≥ q. In the experimental systems developed in a previous study [1, 2], the width was more than five times greater than the pitch. Therefore, there is substantial overlap among the elementary holograms. Redundant hologram information was displayed in previous experimental systems.
3. Improvement of grayscale representation
When the width of the elementary holograms is several times larger than their pitch, multiple sets of elementary holograms can be displayed by using the time-multiplexing technique. In the present study, this capability combined with intensity modulation of the laser illuminating a high-speed SLM is used to improve the grayscale representation of reconstructed images.
3.1 Sets of elementary holograms
Here, we assume that the width of the elementary holograms is Q times larger than their pitch. As shown in Fig. 2, Q sets of elementary holograms can be displayed by a single scan. Since different elementary holograms can be displayed in the forward and backward scans, 2Q sets of elementary holograms can be displayed. In Fig. 2, the forward scan displays elementary holograms sequentially from left to right, and the backward scan displays elementary holograms sequentially from right to left. Those displayed by the forward scan are denoted by h 0, h 1, h 2, ···, hi, ···, and those displayed by the backward scan are denoted by h’0, h’1, h’2, ···, h’i, ···, in the display order. Hologram set #q displayed by the forward scan (0 ≤ q < Q) consists of the elementary holograms hq, hq+Q, hq+2Q, ···, hq+jQ, ···, and hologram set #q displayed by the backward scan (Q ≤ q < 2Q) consists of elementary holograms h’q−Q, h’q, h’q+Q, ···, h’q+(j− 1 )Q, ···. The power of the illumination laser is denoted by Iq when the SLM displays elementary holograms belonging to hologram set #q.
In the present study, methods of determining binary patterns of elementary holograms and illumination laser powers are developed.
3.2 Calculation of continuous tone elementary holograms
The continuous values of the intensity distributions of elementary holograms have to be calculated prior to the binary hologram generation.
The intensity distributions of elementary holograms are calculated based on the bipolar intensity technique [17]. The bipolar intensity is given by OR* + O*R, where O is an object wave and R is a reference wave. The bipolar intensity has both positive and negative real values, as shown in Fig. 3(a) . The bipolar intensity is converted to a non-negative real value by adding a bias component, as shown in Fig. 3(b). The bias component is, for example, the modulus of the lower envelope of the bipolar intensity distribution. The bias component generates a zero-order diffraction component in the hologram reconstruction. Since the spatial frequency of the bias component is much lower than that of the bipolar intensity, the bias component can be removed effectively by a spatial filter that is placed on the Fourier plane in the horizontally scanning hologram display system [1]. The decomposition of the non-negative hologram distribution into multiple binary patterns is achieved using multiple threshold levels. As shown in Fig. 3(b), the lengths of the on-state regions become shorter for a higher threshold level and longer for a lower threshold level. Experiments revealed that the lengths of the on-state regions affected the light intensity of the reconstructed images because the diffraction efficiency depends on the widths of the fringes in an interference pattern. Therefore, the lengths of the on-state regions should not depend on the threshold level. The bipolar intensity distribution is thus transformed into a rectangular wave, as shown in Fig. 3(c). Positive and negative peaks in the bipolar intensity distribution are replaced by rectangles with positive and negative heights, which have the same areas as the corresponding peaks. Then, a non-negative rectangular wave is generated, as shown in Fig. 3(d). The modulus of the average height of two negative rectangles existing at both sides of one positive rectangle is added to the height of this positive rectangle. Finally, all negative rectangles are removed. This calculation is performed in the vertical direction because the elimination of the zero-order diffraction light and the conjugate image is performed in the vertical direction [1]. Then, the generated non-negative rectangular wave is decomposed into multiple binary holograms using multiple threshold levels, as shown in Fig. 3(e).
Fig. 3 Calculation of the intensity distribution of elementary holograms: the hologram distribution is represented by (a) a bipolar intensity distribution, (b) a non-negative real value distribution, (c) a rectangular wave, (d) a non-negative rectangular wave, and (e) multiple binary distributions.
3.3 Decomposition methods
The non-negative intensity distributions of holograms are decomposed into multiple binary holograms. In the present study, four decomposition methods are examined.
(a) Bit-plane method
The bit-plane decomposition method is used to determine the binary hologram patterns. The non-negative intensity is quantized into 22Q gray levels, and the quantized hologram distribution is decomposed into 2Q bit planes, as shown in Fig. 4(a) . The weight of q-th bit-plane is Iq.
Fig. 4 Decomposition methods: (a) bit-plane method, (b) intensity threshold method, (c) amplitude threshold method, and (d) histogram method.
Hologram set #q is the collection of 2q-th bit-plane images for the forward scan (0 ≤ q < Q) and [2(q−Q) + 1]-th bit-plane images for the backward scan (Q ≤ q < 2Q). The illumination laser power is Iq = α 22 q for the forward scan and Iq = α 22( q−Q) +1 for the backward scan, where α is a constant coefficient. Using the above-described method, a lower bit plane and a higher bit plane are displayed at the same position by the forward and backward scans.
(b) Intensity threshold method
The non-negative intensity is quantized using multiple threshold levels. As shown in Fig. 4(b), intensities with a regular interval are used as multiple threshold levels. In this case, the illumination laser power Iq is constant because the differences between adjacent threshold levels are equal. If the non-negative intensity is simply quantized into 2Q levels, then the binary pattern corresponding to the highest threshold level becomes an almost totally black image. Therefore, as shown in Fig. 4(b), the maximum intensity value Imax is multiplied by the coefficient η (≤ 1), and the threshold levels are then determined as Jq = η Imax (q + 1)/2Q.
The threshold level for hologram set #q is J 2 q for the forward scan and J 2( q − Q ) + 1 for the backward scan.
(c) Amplitude threshold method
Amplitudes with a regular interval are used as multiple threshold levels, as shown in Fig. 4(c). The threshold level in intensity increases quadratically and is represented by Jq = η I max (q + 1)2/4Q 2.
For hologram set #q, for the forward scan, the threshold level is J 2 q, and the illumination laser power is the difference between the threshold levels, which is given as Iq = α [(2q + 1)2−(2q)2] = α (4q + 1), and, for the backward scan, the threshold level is J 2( q − Q ) + 1, and the laser power is Iq = α {[2(q − Q) + 2]2−[2(q − Q) +1]2} = α [4(q − Q) + 3].
(d) Histogram method
The threshold levels are determined so that the number of pixels having intensities between each pair of adjacent threshold levels becomes constant, as shown in Fig. 4(d). In this figure, two peaks exist between each pair of adjacent threshold levels. This method is similar to the histogram equalization technique used for the image quality improvement. As shown in the figure, the average value of the intensity distribution between threshold levels Jq −1 and Jq is represented by Pq.
For hologram set #q, for the forward scan, the threshold level is J 2 q, and the illumination laser power is the difference between the average intensities, which is given as Iq = α (P 2 q – P 2 q −1), and, for the backward scan, the threshold level is J 2( q −Q) + 1, and the laser power is Iq = α (P 2( q−Q) +1 – P 2( q−Q)).
4. Experimental system
The experimental system is basically that reported in Reference 2.
A DMD was used as a high-speed SLM. The resolution was 1,024×768, and the pixel pitch was 13.68 μm. The horizontal and vertical magnifications of the anamorphic imaging system were 0.183 and 5.00, respectively. The size of the elementary hologram was 2.56×52.5 mm2. The horizontal pixel pitch was reduced to 2.50 μm. A laser diode with a wavelength of 635 nm was used as a light source. The horizontal viewing angle was 14.6°. The frame rate of the DMD was 13.333 kHz. The horizontal scan rate was 60 scans/s. The horizontal pitch of the elementary holograms was 0.51 mm. Whereas the DMD can display 222 images during each scan time, 186 elementary holograms were displayed for each of the forward and backward scans, while avoiding the nonlinear scan regions. The hologram size was 96.9×52.5 mm2 (4.3 inches).
The width of the elementary holograms is approximately five times as large as the horizontal pitch of the elementary holograms, i.e., Q = 5. Therefore, 10 sets of elementary holograms can be displayed using the forward and backward scans. For the bit-plane method, 5 sets of elementary holograms were displayed, because the power modulation of the illumination laser is limited to 128 levels, as described in the following paragraph. The laser intensity has to be modulated by 512 levels in order to display 10 sets of elementary holograms using the bit-plane method. For the other three decomposition methods, 10 sets of elementary holograms were displayed.
The modulation of the illumination laser power was achieved by pulse width modulation. The frame time of the image update of the DMD was 75.0 μs. In order to avoid light illumination during the mirror transition state of the DMD, the maximum pulse width was set to 51.2 μs. An H8 microcomputer running at 2.5 MHz was used to control the pulse width. The microcomputer receives the image update signals from a DMD driver and generates pulses to modulate the laser diode. The maximum pulse width corresponded to 128 clock cycles. The time-averaged optical power of the pulse-modulated light was measured by an optical power meter and found linear according to the number of clock cycles. The pulse widths corresponding to the illumination laser power Iq are {8, 16, 32, 64, 128} for the bit-plane method, {128, 128, 128, 128, …, 128} for the intensity threshold method, and {7, 20, 34, 47, 61, 74, 88, 101, 115, 128} for the amplitude threshold method. The pulse widths for the histogram method depend on the reconstructed images.
5. Experimental results and discussion
5.1 Test image reconstruction
A test image was displayed in order to compare the four decomposition methods.
The test image consisted of eight filled rectangles having different gray levels, and was displayed at a distance of 50 mm in front of the screen. The elementary holograms were generated by setting the coefficient to be constant at η = 0.6 for the intensity threshold method and the amplitude threshold method. The calculated pulse widths for the laser modulation used for the histogram method were {1, 6, 13, 19, 26, 34, 44, 59, 84, 128}.
Photographs of the reconstructed images captured by a cooled CCD camera are shown in Fig. 5 . The average light intensities in the filled rectangles were measured, and the measurement results are shown in Fig. 6 .
Fig. 5 Reconstructed images of a test pattern generated by (a) the bit-plane method, (b) the intensity threshold method, (c) the amplitude threshold method, and (d) the histogram method.
Fig. 6 Measured average light intensities in eight filled rectangles of the reconstructed images generated by the four decomposition methods.
As shown in Fig. 6, the linearity of the grayscale representation of the bit-plane method was poor because the bit-plane patterns were very different from the original non-negative intensity distributions. Lower bit patterns tended to be noisy, and high bit patterns tended to be sparse. The other methods appeared to be able to more accurately represent the gray levels, even though the linearity was not very high. The brightness of the reconstructed image was the highest for the histogram method because the numbers of white pixels in the elementary holograms were larger for the histogram method, as compared to the other methods.
The reason for the non-linearity of the grayscale representation shown in Fig. 6 is now considered. The proposed methods represent a continuous tone image as a sum of weighted binary patterns. However, the diffraction of the continuous tone image is not generally identical to the sum of the diffraction components of the weighted binary patterns. This is because the binary patterns are displayed in a time-multiplexing manner, so that the intensity distributions of the diffraction, rather than the complex amplitude distributions of the diffraction, are added.
The reconstructed images shown in Fig. 5 reveal the leakage of light between the rectangles. The light leaked only in the horizontal direction because the system scans the elementary holograms in the horizontal direction and the elementary holograms are horizontal-parallax-only holograms. This increases the background level of a reconstructed image in the case of reconstructing a complex image. Therefore, the contrast of reconstructed images might not be increased.
As described above, the grayscale representation is nonlinear. In particular, from Fig. 6, the light intensity of the reconstructed images was saturated for the higher intensity. This nonlinear response could be corrected using the correction table, which is prepared in advance by referring to the measured nonlinearity. The grayscale of the reconstructed image is modified using the correction table before performing the hologram calculation described in Sec. 3.2.
5.2 Three-dimensional image reconstruction
The histogram method was used to reconstruct a three-dimensional (3D) grayscale image. Figure 7 shows the texture data and depth data of the 3D image. Both the texture and depth were represented by 256 gray levels. The calculated pulse widths for the laser modulation were {4, 12, 16, 19, 25, 31, 39, 58, 82, 128}.
Photographs of the reconstructed images are shown in Fig. 8 . These photographs were captured from different horizontal viewpoints by a digital camera. A movie is also provided. The grayscale could be represented in the reconstructed images.
Fig. 8 Reconstructed 3D image captured from (a) the left, (b) the center, and (c) the right. (Media 1)
The intensity threshold and amplitude threshold methods were also used to reconstruct the 3D image, and the grayscale was also confirmed to be represented. There is no significant difference between the reconstructed images generated by the three methods, regardless of the light intensity of the reconstructed images.
6. Conclusion
The grayscale representation of the horizontally scanning holographic display was improved. Multiple sets of elementary holograms having binary amplitudes were displayed by the time-multiplexing technique. The power of the illumination laser was modulated. Four types of hologram generation methods were examined, namely, the bit-plane method, the intensity threshold method, the amplitude threshold method, and the histogram method. The histogram method provided 3D images having good linearity in the grayscale representation and the highest brightness.
References and links
1. Y. Takaki and N. Okada, “Hologram generation by horizontal scanning of a high-speed spatial light modulator,” Appl. Opt. 48(17), 3255–3260 (2009)). [CrossRef] [PubMed]
2. Y. Takaki and N. Okada, “Reduction of image blurring of horizontally scanning holographic display,” Opt. Express 18(11), 11327–11334 (2010). [CrossRef] [PubMed]
3. N. Fukaya, K. Maeno, O. Nishikawa, K. Matumoto, K. Sato, and T. Honda, “Expansion of the image size and viewing zone in holographic display using liquid crystal devices,” Proc. SPIE 2406, 283–289 (1995).
4. K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15 (1996). [CrossRef]
5. J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16(16), 12372–12386 (2008). [CrossRef] [PubMed]
6. P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” Proc. SPIE 1212, 174 (1990). [CrossRef]
7. P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992). [CrossRef]
8. M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” SPIE 5005, 247 (2003). [CrossRef]
9. C. W. Slinger, C. D. Cameron, S. D. Coomber, R. J. Miller, D. A. Payne, A. P. Smith, M. G. Smith, M. Stanley, and P. J. Watson, “Recent developments in computer-generated holography: toward a practical electroholography system for interactive 3D visualization,” Proc. SPIE 5290, 27–41 (2004). [CrossRef]
10. A. W. Lohmann and D. P. Paris, “Binary fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967). [CrossRef] [PubMed]
11. W. H. Lee, “Sampled fourier transform hologram generated by computer,” Appl. Opt. 9(3), 639–643 (1970). [CrossRef] [PubMed]
12. C. B. Burckhardt; “A simplification of Lee’s method of generating holograms by computer,” Appl. Opt. 9(8), 1949 (1970). [PubMed]
13. W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13(7), 1677–1682 (1974). [CrossRef] [PubMed]
14. R. Hauck and O. Bryngdahl, “Computer-generated holograms with pulse-density modulation,” J. Opt. Soc. Am. A 1(1), 5–10 (1984). [CrossRef]
15. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26(14), 2788–2798 (1987). [CrossRef] [PubMed]
16. M. Clark, “Two-dimensional, three-dimensional, and gray-scale images reconstructed from computer-generated holograms designed by use of a direct-search method,” Appl. Opt. 38(25), 5331–5337 (1999). [CrossRef]
17. M. Lucent, “Optimization of hologram computation for real-time display,” Proc. SPIE 1667, 32–43 (1992). [CrossRef]
