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A horizontally scanning holographic display offers a wide viewing angle and a large hologram size. To obtain this display, a series of images generated by a high-speed spatial light modulator are imaged to vertically long images (elementary holograms) by an anamorphic imaging system and are aligned horizontally by a horizontal scanner. However, scan error and focusing error cause blurring in the reconstructed images. In this study, the scan error is corrected by measuring the positions and pixel pitches of the elementary holograms in advance. The focusing error is corrected by experimentally determining the focusing parameter that is used to calculate the elementary holograms.
©2010 Optical Society of America
1. Introduction
Holography is an ideal three-dimensional (3D) display technique. When a spatial light modulator (SLM) is used directly to display holograms, there are two major problems: limited viewing angle and small hologram size. A very fine pixel pitch is necessary for a wide viewing angle, and a huge pixel count is necessary for a large hologram size. Therefore, techniques have been explored to overcome these problems. In addition to several excellent techniques that have been proposed, we proposed horizontally scanning holography [1]. In this technique, a series of elementary holograms generated by a high-speed SLM are aligned horizontally by a mechanical scanner.
Some of the techniques prior to our work are explained. MIT proposed the hologram display system [2,3], in which the high-resolution one-dimensional hologram distribution generated by an acousto-optic modulator is scanned two-dimensionally by a mechanical scanner to reduce the pixel pitch and to increase the pixel count. The technique to double the viewing angle using time-multiplexing was also proposed [4,5]. The active tilting technique [6] was proposed, with which de-magnified images generated by a high-speed SLM are tiled onto an optically addressed SLM in a time-sequential manner. Several authors have proposed techniques using multiple SLMs [7,8]. Our research group has also reported the use of the resolution redistribution optical system [9,10]. In this technique, the horizontal resolution is increased several times by sacrificing the vertical resolution.
In the present study, a technique to reduce blurring in reconstructed images produced by the horizontally scanning holographic display is presented.
2. Horizontally scanning holographic display
Before explaining the reduction of image blurring in reconstructed images, the operating principle of horizontally scanning holography is briefly explained. We also describe the modification of the experimental system that was done after our previous report [1].
2.1 Operating principle
The horizontally scanning holographic display system is illustrated 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 long 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 in order to increase the horizontal viewing angle. Since the image is enlarged in the vertical direction and is scanned in the horizontal direction, the hologram size increases. Because the vertical pixel pitch increases, this system displays a horizontal parallax-only hologram. A screen lens redirects light to the observers, and a vertical diffuser is placed on the image plane to increase the vertical viewing zone.
2.2 Modification of the experimental system
As stated above, the experimental system was modified from the one constructed in our previous work [1]. The modified experimental system is illustrated in Fig. 2 . The modification is that a linear Fresnel lens was used as the screen lens. In the previous experimental system, a glass lens was used, and the screen size was limited by the available sizes of the glass lens. A large glass lens is not easily obtained. In contrast, a large linear Fresnel lens can be easily obtained because this type of lens is made of plastic. Thus, the screen size was increased to 88.6×52.5 mm2 (4.1 inches) from 73.1×52.5 mm2 (3.5 inches) of the previous system. The focal length of the linear Fresnel lens was 150.0 mm, and the groove pitch was 0.30 mm. The scan angle of the mechanical scanner increased to ±16°.
Fig. 2 Modified optical system for horizontally scanning holography: (a) horizontal cross section, and (b) vertical cross section. Unit of focal lengths and distances is millimeters.
Except for the screen lens, the remaining parts of the experimental system were the same as those in the previous work. A digital micromirror device (DMD) was used as the high-speed SLM. The resolution was 1,024×768, and the pixel pitch was 13.68 μm. A fiber coupled laser diode module with a wavelength of 635 nm (FCLM635, Oplink Communications Inc.) was used as the light source. A spherical wave emitted from the single mode fiber of the laser module was collimated by a spherical lens to illuminate the DMD. A galvano scanner was used as the mechanical scanner. Elementary holograms were displayed in both the forward scan and the backward scan. The scan rate was 60 scans/sec and the frame rate of the DMD was 13.333 kHz. The anamorphic imaging system consisted of one spherical lens and three cylindrical lenses with their axes aligned horizontally, instead of two orthogonally aligned cylindrical lenses. The cylindrical lens 1 in Fig. 1 must be large in order to reduce the horizontal pixel size several times to obtain a small pixel pitch. Unfortunately, such a large cylindrical lens was not available. Therefore, instead of a cylindrical lens, a large spherical lens was used for the horizontal magnification. In the vertical direction, two 4f imaging systems were constructed by adding three cylindrical lenses to the spherical lens [1]. 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, and so the horizontal viewing angle was 14.6°. A lenticular sheet was used as a vertical diffuser.
3. Correction of scanning error
A nonlinear relationship exists between the scan position and the drive voltage in the galvano mirror scanning system. The magnification of the anamorphic imaging system slightly changes depending on the scan angle of the galvano mirror, and so the pixel pitches of the elementary holograms are not constant. The position error and the pixel pitch error of the elementary holograms degrade the sharpness of the reconstructed images. In the ideal condition, depicted in Fig. 3(a) , lights diffracted from several elementary holograms converge at one object point. The reconstructed image consists of numerous object points. When a scanning error exists, the lights do not converge at one point, as depicted in Fig. 3(b). The position error disturbs the position of the elementary hologram, and the pixel pitch error disturbs the light diffraction direction.
Fig. 3 Blurring of object point: (a) without scanning error and focusing error, (b) with scanning error, and (c) with focusing error.
To reduce the image degradation caused by the scanning errors, the positions and the pixel pitches of the elementary holograms are measured in advance. Then, the hologram patterns of the elementary holograms are calculated, taking the measured data into account.
A triangular drive voltage for the galvano mirror was generated from the synchronization signal outputted from the DMD device. The scan angle changes 2.0° per one volt change. Because it is difficult to perform the measurements for all the elementary holograms, the measurements were done for 34 elementary holograms that corresponded to the drive voltages with an interval of one volt. In each measurement, only one elementary hologram was displayed to measure its position on the scan plane. The horizontal pixel pitch was calculated from the measured width of the elementary hologram. The measured positions are shown in Fig. 4(a) . There are two plots for each drive voltage. These plots correspond to the forward scan and the backward scan. A hysteresis behavior appears in the scanning position. The measured pixel pitches are shown in Fig. 4(b). The pixel pitch is larger when the position of the elementary hologram is farther from the center of the scan plane. The positions and the pixel pitches of non measured elementary holograms are interpolated from those of the measured elementary holograms.
Figure 5(a) shows the photograph of a reconstructed image without using the measured results. It is assumed that the position is proportional to the drive voltage and the pixel pitch is constant. Each object point was split into two blurred dots. Figure 5(b) shows the reconstructed image when the measured pixel pitches were used to calculate the elementary holograms. The dots are sharper. Figure 5(c) shows the result when both the measured positions and the pixel pitches were used for the calculation. Each object point is now one dot.
Fig. 5 Reconstructed images improved with correction of scanning error: (a) without correction, (b) with correction of pixel pitch error, and (c) with correction of position error and pixel pitch error.
4. Correction of the focusing error
As illustrated in Fig. 6 , light converges horizontally on the focal plane of the cylindrical lens (1 in Fig. 1) or the focal plane of the spherical lens (Fig. 2). Therefore, the distribution of the elementary holograms on the scan plane is the multiplication of the magnified distribution displayed by the DMD, the phase distribution of the cylindrical wave diverged from the focal plane, and the phase distribution of the screen lens (linear Fresnel lens). Because the focal point of the screen lens coincides with the rotation center of the galvano mirror, the cylindrical wave after passing through the screen lens proceeds in the direction perpendicular to the scan plane and also proceeds as if it diverges from the diverging plane, as indicated by the dashed lines in Fig. 6. In the calculation of the elementary holograms, the phase distribution of the cylindrical wave must be canceled. Therefore, the optical length between the scan plane and the focal plane, denoted by t in Fig. 6, must be known. In this study, this optical length is assumed to be constant, although it actually changes slightly depending on the scan angle. It is not easy to measure this optical length directly in the experimental system because of the thickness of the optical components. If t is incorrect, light diffracted by the elementary holograms converges at a wrong distance so that a focusing error occurs; that is, the converging position does not coincide with the position where the lights from several elementary holograms intersect, as shown in Fig. 3(c).
In this study, parameter t was determined experimentally in order to correct the focusing error. This correction was performed after the correction of the scanning error, described in the previous section. To determine parameter t, three vertical lines were displayed at 50 mm, 70 mm, and 100 mm in front of the scan plane, as shown in Fig. 7 . The elementary holograms were calculated by changing parameter t, and then the depth where the line width became minimum was searched for each vertical line. Thin paper was placed in front of the scan plane and moved in the depth direction to measure the line width. At first, all of the elementary holograms were displayed. In this case, the three depths did not depend on parameter t. The three depths were 48.1 mm, 69.3 mm, and 96.5 mm. At these depths, lights from several elementary holograms intersected. Next, only the central elementary hologram was displayed. The three depths changed depending on parameter t, as shown in Fig. 8 . The light from the central elementary hologram converged at three depths. From the results, parameter t was determined to be 44 mm because the differences of the depths for the two cases were the smallest. The design value for t of the experimental system was 45.7 mm.
Figure 9(a) shows a photograph of the reconstructed image before correction of the focusing error (t = 45.7 mm). Figure 9(b) shows the result when t = 44 mm. A thin paper is placed around the front side of the 3D image to evaluate the spot sizes of the object points. The magnified images are shown in Figs. 9(c) and 9(d). The spot sizes became smaller after correction of the focusing error.
Fig. 9 Improvement of reconstruction image with correction of scanning and focusing errors when thin paper is placed around the front side of 3D image: (a) with correction of scanning error, and (b) with correction of scanning error and focusing error.
5. Discussion
In the modified experimental system described in Sec. 2.2, the linear Fresnel lens replaced the glass lens as the screen lens. We were concerned that speckles would appear on the reconstructed images, because the linear Fresnel lens has a saw-tooth surface structure. Fortunately, no speckles were observed, as shown in Fig. 5 and Fig. 8. However, the reconstructed images looked clearer when using the glass lens. Speckles were not observable because the reconstructed image consisted of a number of reconstructed images produced by the elementary holograms. Because the elementary holograms are displayed at different times, the intensity distributions of the reconstructed images generated by the elementary holograms are added to reduce the speckles by the time-averaging effect.
The horizontal width of the object points of the reconstructed image after correction of the scanning error and the focusing error was measured from the image projected on thin paper, shown in Fig. 9(d). The average width was approximately 0.5 mm. Because the DMD was illuminated by a pulse light to reduce the horizontal blurring caused by horizontal scanning as described in Ref [1], the width of the object points stretched by 0.23 mm in the modified experimental system. The width also stretched due to the light diffraction caused by the limited width of the elementary holograms. The object points in Fig. 9(d) were located at approximately 50 mm in front of the scan plane, and so the diffraction increased the width by 12 μm. The evaluation of the width of the object points shows that there remains room for further improvement to reduce image blurring.
6. Conclusion
The horizontally scanning holographic display can solve the problems of a small viewing angle and a small screen size. In this paper, the image degradation caused by the scanning error and the focusing error was reduced. The scan error was corrected by calculating elementary holograms using measured parameters. The focusing error was corrected by experimentally determining the optical parameter used for the calculation of elementary holograms.
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. P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” SPIE 1212, 174 (1990). [CrossRef]
3. 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]
4. T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38(17), 3703–3713 (1999). [CrossRef]
5. T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41(8), 1489–1499 (2002). [CrossRef] [PubMed]
6. 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]
7. K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” SPIE 2652, 15 (1996).
8. 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]
9. Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt. 47(19), D6–D11 (2008). [CrossRef] [PubMed]
10. Y. Takaki and Y. Hayashi, “Elimination of conjugate image for holograms using a resolution redistribution optical system,” Appl. Opt. 47(24), 4302–4308 (2008). [CrossRef] [PubMed]
