OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 7 — Mar. 1, 2013
  • pp: 1404–1412
« Show journal navigation

Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display

Jia Jia, Yongtian Wang, Juan Liu, Xin Li, Yijie Pan, Zhumei Sun, Bin Zhang, Qing Zhao, and Wei Jiang  »View Author Affiliations


Applied Optics, Vol. 52, Issue 7, pp. 1404-1412 (2013)
http://dx.doi.org/10.1364/AO.52.001404


View Full Text Article

Acrobat PDF (869 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A fast algorithm with low memory usage is proposed to generate the hologram for full-color 3D display based on a compressed look-up table (C-LUT). The C-LUT is described and built to reduce the memory usage and speed up the calculation of the computer-generated hologram (CGH). Numerical simulations and optical experiments are performed to confirm this method, and several other algorithms are compared. The results show that the memory usage of the C-LUT is kept low when number of depth layers of the 3D object is increased, and the time for building the C-LUT is independent of the number of depth layers of the 3D object. The algorithm based on C-LUT is an efficient method for saving memory usage and calculation time, and it is expected that it could be used for realizing real-time and full-color 3D holographic display in the future.

© 2013 Optical Society of America

1. Introduction

Holographic display is regarded as an attractive approach for true 3D display that can produce full depth cue without using any special glasses. In this approach, the computer-generated hologram (CGH) is calculated and used to reconstruct a 3D image. There are many different methods for generating a CGH pattern of a 3D object. The coherent ray trace (CRT) method [1

1. A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992). [CrossRef]

] is a simple and widely used technique that can achieve a 3D image with higher quality. However, because we assume that the 3D object decomposes into many self-luminous points of light and each point light source will propagate from the 3D object to all the hologram pixels, CRT has a heavy computational load.

For reducing the computation load of the CRT method, many approaches have been proposed in recent years [2

2. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587–6594 (2000). [CrossRef]

5

5. M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an approximate Fresnel integral,” J. Opt. 13, 075405 (2011). [CrossRef]

]. The look-up table (LUT) [6

6. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993). [CrossRef]

,7

7. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wave front-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509(2010). [CrossRef]

] method precomputes the possible CGH patterns of point sources and stores them during off-line computation. Then in in-line computation, CGH patterns for each point consisting of the 3D object can be generated just by reading out the corresponding ones from the table instead of computing again. Therefore, the LUT method calculates CGH patterns faster than those methods without using LUT, but it needs a huge memory to store the precomputed hologram patterns of object point sources. Kim and co-workers [8

8. S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008). [CrossRef]

11

11. S. C. Kim, J. H. Kim, and E. S. Kim, “Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram,” Appl. Opt. 50, 3375–3382 (2011). [CrossRef]

] developed a novel look-up table (N-LUT) method to reduce the memory usage of LUT. In this method the 3D object is divided into several sliced 2D image planes with different depths and only the CGH pattern of the center point on each sliced 2D image plane is precomputed; CGH patterns of the other points on each sliced 2D image plane can be generated by shifting this pattern. The number of precomputed CGH patterns equals the number of sliced 2D image planes divided from the 3D object. Pan et al. [12

12. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009). [CrossRef]

] implemented a split look-up table (S-LUT) method to improve the computational speed and reduce the memory usage simultaneously. In the S-LUT method, the object is composed of several sliced 2D image planes, and the holograms of point sources on each slice are generated by the horizontal and vertical light modulation factors. Both N-LUT and S-LUT methods need less memory than LUT, since they only compute and store one CGH pattern or the light modulation factors for each sliced 2D image plane of 3D object instead of all the CGH patterns of object points. However, because the 3D object is composed of a lot of sliced 2D image planes, we still need gigabytes (GBs) of memory for N-LUT and megabytes (MBs) of memory for S-LUT, and also they will take a lot of time to generate the table and read out the data, which is still a problem in real-time 3D display.

In a traditional full-color holographic display system [13

13. Y. Z. Liu, J. W. Dong, Y. Y. Pu, H. X. He, B. C. Chen, H. Z. Wang, H. Zheng, and Y. Yu, “Fraunhofer computer-generated hologram for diffused 3D scene in Fresnel region,” Opt. Lett. 36, 2128–2130 (2011). [CrossRef]

,14

14. F. Yaras, H. Kang, and L. Onural, “Real-time phase-only color holographic video display system using LED illumination,” Appl. Opt. 48, H48–H53 (2009). [CrossRef]

], since the CGH is based on the interference of a single wavelength, three holograms corresponding to primary color of RGB need to be calculated and illumined by the red, green, and blue lasers, and then the reconstructed monochromatic images are combined into color images. On the one hand, three tables (LUT-red, LUT-green, and LUT-blue) should be used to store three kinds of holograms, respectively, and the memory usage of LUT will be increased three times. On the other hand, if the hologram generated by a single wavelength is illumined by different wavelength lasers, it will cause distortions to the 3D reconstructed images.

In this paper, a new method is proposed to reduce the LUT memory usage and to speed up the CGH computation by compressed LUT (C-LUT). The 3D object is divided into several sliced 2D image planes, and only the light modulation factors for one sliced 2D image plane are precomputed and stored as basic factors into LUT, so the size of LUT can be significantly reduced. The CGH patterns of other object points on different sliced 2D image planes can be generated by the longitudinal light modulation factors. Numerical simulation and an optical experiment based on the proposed method are performed. In addition, the speeds and the memory usages of the LUT, the S-LUT, and the C-LUT are compared, where the N-LUT method is not included since it still needs GBs of memory and more time than that of the S-LUT though it can reduce the memory usage to a certain extent. Finally, the 3D colorful image without distortion is experimentally produced by CGHs that are generated by one wavelength based on C-LUT.

2. Conventional CRT and LUT Algorithms

In the CRT method, a 3D object is considered to be decomposed of a large number of point sources as shown in Fig. 1. The complex amplitude of the point source of a 3D object arriving at the hologram plane is given by
H(xp,yq)=j=0N1Ajexp[i(krj+ϕj)],
(1)
where
rj=(xpxj)2+(yqyj)2+(dzj)2
is the distance between the jth point (xj,yj,zj) on the 3D object space and the (p,q) pixel (xp,yq,0) on the hologram plane as shown in Fig. 1. d is the distance between the coordinate system of the object space and the hologram plane. N and Aj stand for the number of the sampling point and the wave amplitude of the sampling point source of the 3D object. k=2π/λ is the wave number in free space and λ is the wavelength. ϕj is the initial phase, which is often randomized as a uniform deviation between 0 and 2π. In the CRT method, Eq. (1) runs N×p×q times to generate the CGH patterns, and each time has ×, , and exponential operations. These operations cause heavy computational load. Therefore, as the object points are increased, the computational time will be increased.

Fig. 1. Diagram of CGH for recording 3D object.

To solve this problem, Lucente [6

6. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993). [CrossRef]

] proposed the LUT method first in 1993. All possible CGH patterns are off-line precomputed, and stored in memory. When the CGH patterns are needed in in-line computation, they will be directly read out from the table. They also need N×p×q loops to generate the CGH patterns, but only one addition and one multiplication operation are performed at each time in in-line computation. Considering the memory usage of LUT, when the table is assumed to have the N CGH patterns with p×q pixels, and the memory size of one pixel is M, the total size of memory is N×p×q×M. The huge memory usage limits the application of this method, although it is faster than the traditional CRT.

Pan et al. [12

12. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009). [CrossRef]

] developed the S-LUT method to improve the computational speed and reduce the memory usage of LUT. In this method, the horizontal light modulation factors H(xpxj,zj)=exp{ik[(xpxj)2+(dzj)2]1/2} and the vertical light modulation factors V(yqyj,zj)=exp{ik[(yqyj)2+(dzj)2]1/2} of points falling on each sliced 2D image plane instead of the holograms are precomputed in off-line computational time and stored in the LUT. The light modulation factors of points falling on each sliced 2D image plane need a memory size of Nx×p×M for horizontal and Ny×q×M for vertical. Nx and Ny are the numbers of the horizontal and vertical sampling points of the object. While the number of depth layers is Nz, the total size of the memory usage is (Nx×p×M+Ny×q×M)×Nz. Normally, they are indexed as a 3D matrix. In in-line computation, the light modulation factors are read out from the table and used to generate the hologram by two equations as follows:
Vs(yq)=j=0Ny1AjV(yqyj,zj),
(2)
HNy(xp,yq)=Vs(yq)×H(xpxj,zj).
(3)

The hologram is the sum of all contributions from the object points falling on different vertical lines Nx and different depth layers Nz. Equation (2) runs Ny×q times and Eq. (3) runs p×q times. Therefore, the total in-line computational complexity is Nz×[Nx×(Ny×q+p×q)+p×q].

3. New Method Based on C-LUT

In order to reduce the memory requirement of LUT, we propose a new method using a set of basic light modulation factors. Because Frahnhofer CGH can reconstruct a similar 3D intensity distribution to that of Fresnel CGH [15

15. H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. 49, 5993–5996 (2010). [CrossRef]

] in an appropriate observation distance, the hologram can be described in Fraunhofer approximation as
HFH(xp,yq)=j=0N1Ajexp[ik(xp2+yq22(dzj)xpxj+yqyjdzj)],
(4)
where k(xp2+yq2)/2 is the quadratic phase factor in the hologram plane. When the size of the reconstructed image is much smaller than the distance between the object and the hologram (zjd), Eq. (4) can be approximately written as
HFH(xp,yq)=j=0N1Ajexp[ikxp2+yq22(dzj)]×exp(ikxpxj+yqyjd)=j=0N1Ajexp[ikxp2+yq22(dzj)]×exp(ikxpxjd)exp(ikyqyjd),
(5)

Here the horizontal light modulation factor is defined as H(xp,xj)=exp(ikxpxj/d), the vertical light modulation factor is defined as V(yq,yj)=exp(ikyqyj/d), and the longitudinal light modulation factor is defined as L(z,zj)=exp[ik(xp2+yq2)/2(dzj)]; then Eq. (5) can be simply rewritten as
HFH(xp,yq)=j=0N1AjH(xp,xj)V(yq,yj)L(z,zj).
(6)

The 3D object can be approximately considered as a set of sliced 2D image planes with different depths and each sliced 2D image plane is composed of several self-luminous point sources as shown in Fig. 2(a). Since Nxy object points falling on the same sliced 2D image plane have the same longitudinal light modulation factor, Eq. (6) can be rewritten as
HFH(xp,yq)=jz=0Nz1[jxy=0Nxy1AjxyH(xp,xjxy)V(yq,yjxy)]×L(z,zjz),
(7)
where jz (jz=0,,Nz1) is the number of sliced 2D image planes of the 3D object, and jxy (jxy=0Nxy1) is the number of points in each sliced 2D image plane. For each sliced 2D image plane, there are Ny points falling on the same vertical line; that is, their horizontal light modulation factors H(xp,xj) are the same. The hologram is the sum of all contributions from the object points on different vertical lines Nx and different depth layers Nz, and it can be calculated by
HFH(xp,yq)=jz=0Nz1{jx=0Nx1[jy=0Ny1AjyV(yq,yjy)]×H(xp,xjx)}L(z,zjz),
(8)
where jx (jx=0Nx1) is the number of points on the horizontal line and jy (jy=0Ny1) is the number of points on the vertical line in each 2D sliced image plane. Since the points falling on different sliced 2D image planes with the same distribution have the same X and Y coordinates (xs1=xsn, ys1=ysn) as shown in Fig. 2(b), they have the same horizontal and vertical light modulation factors but different longitudinal light modulation factors. Therefore, only the horizontal and the vertical light modulation factors of the points falling on one sliced 2D image plane need to be precomputed as the basic light modulation factors, and the points distributed in other sliced 2D image planes can be described by these basic factors multiplying by different longitudinal light modulation factors. Because we only pre-compute and store the basic light modulation factors in LUT during off-line computation, the size of memory usage is compressed, which is named as compressed-LUT (C-LUT) and its data are indexed by 2D matrix.

Fig. 2. Model of 3D object: (a) set of sliced 2D image planes with different depths and (b) points falling on different sliced 2D image planes.

Therefore, the proposed method includes two steps, and the block diagram is shown in Fig. 3. The first step is to build a LUT that is composed of the horizontal and the vertical light modulation factors corresponding to the 3D object point contributions in one sliced 2D image plane of the cubic points array during off-line computation, and then to generate the hologram of the target 3D object by reading out the data from this table during in-line computation. The program of the off-line computation can be listed as in Table 1.

Table 1. Pseudo Code of Off-Line Computational Program

table-icon
View This Table
| View All Tables
Fig. 3. Diagram of the proposed method to generate the CGH using C-LUT.

The table size of horizontal modulation factors is Nx×p×M, and that of vertical modulation factors is Ny×q×M. As a result, the total size of C-LUT is Nx×p×M+Ny×q×M. The number of the loop to compute the horizontal and the vertical light modulation factors is Nx×p+Ny×q, and each loop includes one exp and four multiplications.

The second step is to read out the light modulation factors from C-LUT and then generate the hologram in in-line computation. The program of the in-line computation can be described as in Table 2.

Table 2. Pseudo Code of In-Line Computational Program

table-icon
View This Table
| View All Tables

The total complexity of the in-line computation is Nz×[Nx×(Ny×q+p×q)+p×q] for Nz sliced image planes and each loop includes one addition and one multiplication operation. In loop ⑤, the longitudinal light modulation factors need to be calculated, which includes one exp, four multiplications, and one addition further. Actually, the off-line and the in-line computation can be performed in parallel, and they will speed up the table building and CGH computation individually.

The comparison of the computational complexity, the operation, and the memory usage for the CRT, the LUT, the S-LUT, and the new algorithm is listed in Table 3. There are Nx and Ny sample points in horizontal and vertical directions, and Nz sliced 2D image planes. It is assumed that the memory usage of one pixel of the CGH pattern is M.

Table 3. Complexity, Operation, and Memory Usage Comparison Among Algorithms

table-icon
View This Table
| View All Tables

From Table 3, the computational complexity is defined as the number of the loop for computing a hologram. It is clear that the computational complexity usages of the S-LUT and the new algorithm are less than those of CRT and LUT in in-line computation, which is the key reason that the S-LUT and the new algorithm run faster than CRT and LUT algorithms. The operations in in-line computation of the new algorithm are a little bit more than those of the S-LUT. However, the operations in off-line computation of the new algorithm are reduced and the memory usage of the new method is less than the S-LUT method because it is independent of the depth layers of the 3D object.

4. Errors of the New Method and Corresponding Correction

For a 3D object with fine structure, distortion of the 3D reconstructed image could be introduced by Eq. (5) and incident different wavelengths. To correct the distortion, we now analyze the probably distortion error and present the possible solution. Comparing Eq. (4) with Eq. (5), the light modulation errors of the horizontal H(xp,xj) and the vertical V(yq,yj) light modulation caused by the approximation are determined by
εH=φHφH=k(xpxjdxpxjdzj)=k(zjd(dzj)xpxj)εV=φVφV=k(yqyjdyqyjdzj)=k(zjd(dzj)yqyj)},
(9)
where φ represents the desired phase distributions and φ represents the phase distributions with error. The reconstructed images could have different sizes in different sliced 2D image planes because of the error of the light modulation. The distortions in X and Y directions in each sliced 2D image plane are defined by
δxj=xjxj=dzjdxjxj=zjdxjδyj=yjyj=dzjdyjyj=zjdyj},
(10)
which only depend on the depth zj and the distance between the object and the hologram plane d. (xj,yj,zj) denotes the coordinate of the distortion image. If the imaging distance is fixed, it has the maximum value at the xmax. Considering the acuity of the human visual system, it is well known that, when zjd, the distortion is so small that it is imperceptible from the specified viewing distance, and the error could be ignored. Otherwise, it needs the error correction or the precompensation.

Here two ways are provided for the error correction. One way is that the correction phase factor is precalculated and then added into the hologram. The correction phase factor is determined by
ΔφH=ΔφV=ddzj.
(11)

Then the light modulation factor in X direction is
H(xp)ΔφH=[exp(ikxpxjd)]ddzj=exp(ikxpxjd×ddzj)=exp(ikxpxjdzj),
(12)

The processing of the light modulation factor in the Y direction is the same as in the X direction. It is seen that the light modulation factor is corrected, and the distortion of the image is controlled, but the computational load of correction should not be ignored.

The method discussed above can also be used to correct the distortion caused by different wavelengths in full-color holographic display. The errors are determined by
Δφλ=φλφλ=krkr=(λλλλ)2πrδxj=xjxj=λλxjxj=(λλ1)xjδyj=yjyj=λλyjyj=(λλ1)yjδzj=zjzj=λλzjzj=(λλ1)zj},
(13)
where λ is the wavelength for generating the hologram, λ is the wavelength of illumination light, and φλ and φλ are the phase distributions of the recording and the illumination lights. With the correction of distortion, only one table needs to be built, which concludes the holograms with single wavelength. Other holograms with different wavelengths can be obtained by reading out the holograms from the table and adding the compensatory phase.

5. Implementations and Results

To compare the computational speed and the memory usage for generating the CGH by use of these four techniques, we now perform numerical simulations and the optical experiments. Our program is run by a personal computer with a CPU core of a 2.6 GHz clock frequency under Matlab 2010. The hologram is numerically generated by the four methods and then loaded in a phase-only SLM (Boulder Nonlinear Systems, Lafayette, Colorado, USA), with pixel sampling of 512×512 and pixel size of δx=δy=15μm, and with each pixel having 256 gray-scale levels. The full-color holographic display system based the space-division method is set up as shown in Fig. 4. Three lasers with wavelengths of 671, 533, and 471 nm are collimated, and they illuminate the SLMs. They will construct a color 3D image by combining monochromatic images using a beam splitter. The concave reflecting mirror is used to adjust the image size. Lumenera camera INFINITY 4-11C is used to record the experimental results.

Fig. 4. Setup of full-color holographic display system.

Some parameters used in CGH computation are listed in Table 4.

Table 4. CGH and Table Parameters

table-icon
View This Table
| View All Tables

The LUT is built first in off-line computation. The comparisons of memory usage among these three algorithms are shown in Table 5. If the resolution of the hologram is 512×512 and every pixel occupies 1 byte of memory, to build the LUT that includes all hologram patters for an image volume of 133×133×100 points, the memory size of 512×512×1bytes×133×133×100=432GB should be used in the LUT method and that of (512×1bytes×133+512×1bytes×133)×100=13MB in the S-LUT method. From Table 5, the memory sizes are increased linearly as the numbers of the depth layers are increased for the LUT and the S-LUT methods. The new method uses only a small amount of memory—that is, 512×1bytes×133+512×1bytes×133=0.13MB—and the memory usage does not increase as the number of depth layers in the table is increased.

Table 5. Memory Usage Comparition Among Algorithms

table-icon
View This Table
| View All Tables

The calculation times for building the LUTs for different methods are compared and shown in Fig. 5. It can be seen that the times needed for the off-line calculation are proportional to the numbers of object points in the sliced 2D image planes and the number of depth layers in the LUT and S-LUT methods. With the increase in the number of depth layers, the calculation time is 0.106 s and it keeps unchanged for the new method, which will boost the calculation speed effectively. The new method is about 2182 times faster than the S-LUT and 1.2×108 times faster than the LUT to build the table, which includes 200×200×1000 points, and the time for building the LUT only depends on the number of object points on one sliced 2D image plane.

Fig. 5. Comparisons of the off-line calculation time for building an LUT among the LUT, the S-LUT, and the new algorithm (C-LUT).

The comparisons of the in-line computational speed among these methods are shown in Fig. 6. It is assumed that the object points are distributed randomly in 3D object space with 10 depth layers. The results show that the new method is faster than other methods. However, the new method is a little more complex than the S-LUT; the speed of the new method is even about 1.5 times faster than the S-LUT. This is because the S-LUT spends more time in data reading from the memory than the C-LUT. On the one hand, the data reading from indexing the 3D matrix used in the S-LUT method costs much more time than that of the 2D matrix in the C-LUT method by computer. On the other hand, as we know, every computer has two types of data storage, which are its disk and its random access memory (RAM). Since data reading from the disk is much slower than reading the same data from the RAM, prereading all the useful data of the LUT from the disk into the RAM once in off-line time and then performing further processing can save more time than reading data from the disk in in-line time. Because the data size of the S-LUT is proportional to the layers of the 3D object, it cannot read all the useful data one time when layers of the 3D object are increased so that the data size of the table overflows the memory bandwidth. In this case, the data should be read from the disk many times, which will cost much time. As for the new method, it will not overflow the memory bandwidth because the data is less and independent of the layers of the 3D object. Therefore, the data of the C-LUT can be read into RAM one time, which will reduce the total computational time.

Fig. 6. Comparison of the in-line computational time among different algorithms.

The error caused by Eq. (5) could be corrected by adding the phase compensation factor in the in-line computation. Consider the acuity of normal human vision; in distance of 200 mm, the acuity of the human visual system is 0.06 mm. Assume that the reconstructed distance is 1000 mm; the error0.06mm can be ignored while 10mmzj10mm and xmax=±6mm. In other words, the basic modulation light factors will not cause the error in the range of each 20 mm depth layer. We can increase the basic modulation light factors to obtain the corrected image. For z=40mm, the modulation light factors should be computed in zj=0, zj=10mm, and zj=10mm. The memory usage is increased three times, but it is still small.

The numerical reconstructed images with distortion in zj=10mm and zj=20mm are shown in Figs. 7(b) and 7(c). The distortion in zj=10mm is even smaller, and in zj=20mm, the error is increased to be 0.12 mm. It is larger than the original image as shown in Fig. 7(a). After correction, the image has the correct size as shown in Fig. 7(d).

Fig. 7. Numerical reconstructed image: (a) original image, (b) distortion image in zj=10mm, (c) distortion image in zj=20mm, and (d) image without distortion.

For better demonstrating the feasibility of the proposed new algorithm, a CGH of a teapot and a cup (5200 points) is computed. The reconstructed image is projected by the SLM, and recorded by the camera. The experimental results are shown in Fig. 8. The CGH calculation costs 46 s including all the in-line and the off-line computation times. The zero-order beam elimination method [17

17. H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009). [CrossRef]

] is adopted to improve the quality of the 3D reconstructed image.

Fig. 8. Reconstructed 3D image: (a) perspective image of 3D object, (b) numerical simulation results of focusing on the teapot reconstructed in 1010 mm, (c) focusing on the cup reconstructed in 980 mm, (d) optical experimental results of focusing on the teapot reconstructed in 1010 mm, and (e) focusing on the cup reconstructed in 980 mm.

It is worthwhile to note that not all the sampling points are in focus. This is because the sampling points are distributed in 3D space, and the CCD can record only a 2D image. Therefore, the 2D image planes are focused on the teapot reconstructed in 1010 mm as shown in Figs. 8(b) and 8(d), and focused on the cup reconstructed in 980 mm as shown in Figs. 8(c) and 8(e). The results show that the new method keeps the depth cue well.

To exhibit the advantage of C-LUT for calculating the hologram in full-color display, we compute the CGH of a red teapot, a green cup, and a white ground. The memory usage remains unchanged. The color reconstructed image is projected by the SLM, and recorded by the camera. A short animated movie for a colorful dynamic holographic project is also performed, and the experimental results are shown in Fig. 9. It is clearly seen that the colorful 3D images are achieved successfully.

Fig. 9. Reconstructed colorful 3D images. (a) Perspective object and (b) reconstructed image (Media 1).

6. Conclusions

This work was supported by the National Basic Research Program of China (973 Program, Grant No. 2013CB328801), the National Natural Science Foundation of China (61235002 and 61077007), and the National High Technology Research and Development Program of China (863 Program, Grant No. 2009AA01Z309).

References

1.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992). [CrossRef]

2.

K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587–6594 (2000). [CrossRef]

3.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007). [CrossRef]

4.

H. Kang, T. Yamaguchi, and A. H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44–D54 (2008). [CrossRef]

5.

M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an approximate Fresnel integral,” J. Opt. 13, 075405 (2011). [CrossRef]

6.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993). [CrossRef]

7.

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wave front-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509(2010). [CrossRef]

8.

S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008). [CrossRef]

9.

S. C. Kim, J. H. Yoon, and E. S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986–5995 (2008). [CrossRef]

10.

S. C. Kim and E. S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48, 1030–1041 (2009). [CrossRef]

11.

S. C. Kim, J. H. Kim, and E. S. Kim, “Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram,” Appl. Opt. 50, 3375–3382 (2011). [CrossRef]

12.

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009). [CrossRef]

13.

Y. Z. Liu, J. W. Dong, Y. Y. Pu, H. X. He, B. C. Chen, H. Z. Wang, H. Zheng, and Y. Yu, “Fraunhofer computer-generated hologram for diffused 3D scene in Fresnel region,” Opt. Lett. 36, 2128–2130 (2011). [CrossRef]

14.

F. Yaras, H. Kang, and L. Onural, “Real-time phase-only color holographic video display system using LED illumination,” Appl. Opt. 48, H48–H53 (2009). [CrossRef]

15.

H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. 49, 5993–5996 (2010). [CrossRef]

16.

J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011). [CrossRef]

17.

H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009). [CrossRef]

18.

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14, 603–608 (2006). [CrossRef]

19.

A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector,” Opt. Express 17, 16038–16045 (2009). [CrossRef]

20.

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated-hologram on AMD HD5000 series GPU and OpenCL,” Opt. Express 18, 9955–9960(2010). [CrossRef]

21.

P. Tsang, W. K. Cheung, T. C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19, 15205–15211 (2011). [CrossRef]

OCIS Codes
(090.1760) Holography : Computer holography
(090.2870) Holography : Holographic display
(090.1705) Holography : Color holography
(090.5694) Holography : Real-time holography

ToC Category:
Holography

History
Original Manuscript: December 17, 2012
Revised Manuscript: January 16, 2013
Manuscript Accepted: January 16, 2013
Published: February 22, 2013

Citation
Jia Jia, Yongtian Wang, Juan Liu, Xin Li, Yijie Pan, Zhumei Sun, Bin Zhang, Qing Zhao, and Wei Jiang, "Reducing the memory usage for effectivecomputer-generated hologram calculation using compressed look-up table in full-color holographic display," Appl. Opt. 52, 1404-1412 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-7-1404


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992). [CrossRef]
  2. K. Matsushima and M. Takai, “Recurrence formulas for fast creation of synthetic three-dimensional holograms,” Appl. Opt. 39, 6587–6594 (2000). [CrossRef]
  3. H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007). [CrossRef]
  4. H. Kang, T. Yamaguchi, and A. H. Yoshikawa, “Accurate phase-added stereogram to improve the coherent stereogram,” Appl. Opt. 47, D44–D54 (2008). [CrossRef]
  5. M. Oikawa, T. Shimobaba, N. Masuda, and T. Ito, “Computer-generated hologram using an approximate Fresnel integral,” J. Opt. 13, 075405 (2011). [CrossRef]
  6. M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993). [CrossRef]
  7. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wave front-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509(2010). [CrossRef]
  8. S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008). [CrossRef]
  9. S. C. Kim, J. H. Yoon, and E. S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986–5995 (2008). [CrossRef]
  10. S. C. Kim and E. S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48, 1030–1041 (2009). [CrossRef]
  11. S. C. Kim, J. H. Kim, and E. S. Kim, “Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram,” Appl. Opt. 50, 3375–3382 (2011). [CrossRef]
  12. Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17, 18543–18555 (2009). [CrossRef]
  13. Y. Z. Liu, J. W. Dong, Y. Y. Pu, H. X. He, B. C. Chen, H. Z. Wang, H. Zheng, and Y. Yu, “Fraunhofer computer-generated hologram for diffused 3D scene in Fresnel region,” Opt. Lett. 36, 2128–2130 (2011). [CrossRef]
  14. F. Yaras, H. Kang, and L. Onural, “Real-time phase-only color holographic video display system using LED illumination,” Appl. Opt. 48, H48–H53 (2009). [CrossRef]
  15. H. Nakayama, N. Takada, Y. Ichihashi, S. Awazu, T. Shimobaba, N. Masuda, and T. Ito, “Real-time color electroholography using multiple graphics processing units and multiple high-definition liquid-crystal display panels,” Appl. Opt. 49, 5993–5996 (2010). [CrossRef]
  16. J. Jia, Y. Wang, J. Liu, X. Li, and J. Xie, “Magnification of three-dimensional optical image without distortion in dynamic holographic projection,” Opt. Eng. 50, 115801 (2011). [CrossRef]
  17. H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009). [CrossRef]
  18. N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14, 603–608 (2006). [CrossRef]
  19. A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector,” Opt. Express 17, 16038–16045 (2009). [CrossRef]
  20. T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated-hologram on AMD HD5000 series GPU and OpenCL,” Opt. Express 18, 9955–9960(2010). [CrossRef]
  21. P. Tsang, W. K. Cheung, T. C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19, 15205–15211 (2011). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: MOV (1490 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited