A Complementary Approach for Securing and Anti-Counterfeiting of Valuable Documents Based on Encryption of Computer-Generated Hologram.

A novel type of multiplexed computer-generated hologram (CGH) is designed with more than one billion of pixels per period. It consists of elementary cells divided into arbitrary-shaped polygonal apertures, the division being identical in all cells. The cells are further digitized into pixel arrays to exploit the huge space-bandwidth product of electron-beam lithography. The polygonal apertures in the same location inside the cells constitute a subhologram. With the Abbe transform that has never, to our knowledge, been used in other CGH designs, the subhologram images (subimages) are obtained with fast Fourier transforms. It is therefore possible to design a multiplexed CGH that has a size thousands of times larger than the manageable size of a conventional CGH designed with the iterative Fourier transform algorithm (IFTA). A much larger object window than that of the conventional CGH can also be achieved with the multiplexed polygonal-aperture CGH, owing to its extremely large dimensions. The multiplexed polygonal-aperture CGH is designed with the novel iterative subhologram design algorithm, which considers the coherent summation of the subimages and applies constraints on the total image, subimages, and subholograms. As a result, the noise appearing in the preceding multiplexed-CGH designs is avoided. The multiplexed polygonal-aperture CGH has a much higher diffraction efficiency than that resulting from either the preceding multiplexed-CGH designs or the conventional CGH designed by the IFTA.

The binary computer-generated hologram (BCGH) has attracted much attention recently because it can address the high-speed binary spatial light modulator (SLM), such as a digital micromirror device (DMD) SLM. In this paper, our concern is the development of an algorithm to produce high-quality BCGHs. In particular, simulated annealing (SA) is an efficient algorithm used to produce a phase-only computer-generated hologram. In the study of SA for the production of a BCGH, we found some inherent shortcomings of SA, and the quality of the produced BCGHs is limited. Accordingly, we have modified SA and propose the simulated-annealing binary search (SABS) algorithm. We have also proposed a method to quickly determine the parameters for SABS. In the comparison with SA, the mean square error of the SABS BCGHs decreases by 32% on average. Therefore, the SABS is a promising technique for a high-quality holographic display by DMD.

The accuracy of digital and optical Hough transform (HT) processors is analyzed. New correction techniques to achieve improved accuracy are addressed. A new output format optical HT system using computer generated holograms (CGHs) is described and analyzed and its accuracy is found to be superior to that of digital HT processors. Its speed is much faster; the CGH space bandwidth product (SBWP) requirements are much less than for other methods; CGH error sources are addressed; and simple multiple binary exposure CGH fabrication is found to be sufficient.

Binary computer-generated holograms are similar to interferograms with fringe patterns hardclipped by a photographic process. Therefore the fringe locations in the binary hologram can be determined by solving a grating equation. However, there are two difficulties in using this approach to make binary Fourier transform holograms. First the discrete Fourier transform provides only data at discrete sampling locations. Second, the phase angles thus calculated are given in terms of the residues of the original phase angles after multiples of 2pi rad are removed. In this paper an accurate numerical method which circumvents these two difficulties is described. Also discussed are three different techniques for storing amplitude information in the binary computer-generated holograms. The different solution methods discussed in this paper are further illustrated by a number of computer-generated holograms and their reconstructed images.

A new approach for designing the binary computer-generated hologram (CGH) of a very large number of pixels is proposed. Diffraction of the CGH apertures is computed by the analytical Abbe transform and by considering the aperture edges as the basic diffracting elements. The computation cost is independent of the CGH size. The arbitrary-shaped polygonal apertures in the CGH consist of quadrilateral apertures, which are designed by assigning the binary phases using the parallel genetic algorithm with a local search, followed by optimizing the locations of the co-vertices with a direct search. The design results in high performance with low image reconstruction error.

A new approach for designing the binary phase-only hologram with arbitrary-shaped polygonal apertures is proposed. The diffraction of the aperture was computed with the analytical Abbe transform. To explore the very high number of degrees of freedom available in the computer-generated hologram (CGH) of very large pixel count, a two-step optimization including the genetic algorithm with local search for encoding binary phases of apertures followed by the direct search for floating covertices of the elementary triangular apertures was developed for high performance and low image-reconstruction error of the binary CGH.

We propose a simple gradation representation method for a reconstructed three-dimensional (3-D) image without controlling the brightness of the reference light. In the proposed method, we use multiple bit planes comprised of binary-weighted computer-generated holograms (CGHs) with various light transmittances. Binary-weighted CGH is generated by changing the white in the conventional binary CGH to gray. The light transmittance of a binary-weighted CGH is less than that of a conventional binary CGH. The object points of a 3-D object are assigned to multiple bit planes according to the gray level of the object points. The multiple bit planes are displayed sequentially in a time-division multiplex manner. Consequently, the proposed method realizes a gradation representation of a reconstructed 3-D object.

In amplitude-modulation-type electroholography, the binary-weighted computer-generated hologram (BW-CGH) facilitates the gradation-expressible reconstruction of three-dimensional (3D) objects. To realize real-time gradation-expressible electroholography, we propose an efficient and high-speed method for calculating bit planes consisting of BW-CGHs. The proposed method is implemented on a multiple graphics processing unit (GPU) cluster system comprising 13 GPUs. The proposed BW-CGH method realizes eight-gradation-expressible electroholography at approximately the same calculation speed as that of conventional electroholography based on binary computer-generated holograms. Consequently, we were able to successfully reconstruct a real-time electroholographic 3D video comprising approximately 180,000 points expressed in eight gradations at 30 frames per second.

This paper describes a computer generated hologram (CGH) on a curved surface for laser machining. The CGH fabricated on a parabolic copper mirror converts a 14mm diameter Gaussian beam of a CO 2 laser into a shaped beam whose intensity distribution is uniform (4mm) in x direction and gaussian (1mm) in y direction. The binary CGH pattern was drawn by a laser direct writing machine with a focus servo mechanism. To obtain an accurate step height of CGH pattern, a palladium thin film was placed between the copper mirror and a plated copper layer 3.75μm thick. While the plated layer was etched by a ferric chloride solution, the palladium film prevented the substrate mirror from being etched. The beam shaping by the fabricated CGH was demonstrated experimentally with a low power CO 2 laser and an infrared-camera.

Holographic display has been considered as a promising display technology. Currently, low-speed generation of holograms with big holographic data is one of crucial bottlenecks for three dimensional (3D) dynamic holographic display. To solve this problem, the acceleration method computation platform is presented based on look-up table point source method. The computer generated holograms (CGHs) acquisition is sped up by offline file loading and inline calculation optimization, where a pure phase CGH with gigabyte data is encoded to record an object with 10 MB sampling data. Both numerical simulation and optical experiment demonstrate that the CGHs with 1920×1080 resolution by the proposed method can be applied to the 3D objects reconstruction with high quality successfully. It is believed that the CGHs with huge data can be generated by the proposed method with high speed for 3D dynamic holographic display in near future.

When applying phase-only computer-generated hologram (CGH) as a standard model of optical measurement in computer-generated holography for aspheric surface testing, it has the advantage of simplifying optical path configuration and improving the diffraction efficiency of the incoming light. However, errors always exists during the encoding process of fabricating multiphase level CGHs and this kind of errors will be amplified level by level in the measurement. According to the analysis of the encoding error, the error of CGH increases linearly when its quantified period increases. For example, if the quantified period is 32, the maximum of encoding error is 16.46 which can lead wave-front aberration 0.085λ of a secondary parabolic surface with 512×512 sampling pixels. In this article, an optimization method based on deviation of minimum boundary value has been used to eliminate the encoding error of CGH. In the experiment, we use a liquid crystal spatial light modulator to generate CGHs and measure residuals of reconstructed wave-front of a secondary parabolic surface. The measurement results show that average decrease of the RMS values of the residuals is 0.07 when their periods range from 3 to 6, which indicates the optimization method is effective.

A region based random multi-pixel search algorithm to improve the binary hologram reconstruction quality

A computer generated hologram (CGH) has been developed for laser transformation hardening with a fiber-coupled high-power diode laser (HPDL). The laser beam shaped with the CGH is purposely non-uniform in order to obtain uniform depth of the hardened profile. The optimum intensity distribution of laser beam has been determined with the numerical simulation of dynamic thermal analysis based on the finite element method. A binary phase CGH of silica glass was designed and fabricated to realize the optimized intensity distribution of laser beam. When a steel plate surface was hardened by the 330W laser beam with the fabricated CGH, the cross-sectional hardened profile had a uniform depth, compared with experimental results for a defocused Gaussian beam and a flat-top shaped beam.

Optical encryption of information using Computer Generated Holograms (CGH) is a well-known discipline based on the modification of the phase pattern obtained from the calculation of the hologram from a scene. This paper presents an evolution of this technique adding random pixel permutation. The complete workflow is described starting from the synthesis of a 3D scene by Computer Graphics, its storage in a CGH, the encryption and decryption process, showing results obtained in the laboratory and by simulation. Special emphasis is given to the proposals related to the encryption phase, allowing the use, if desired, of a single key in the pixel permutation and phase modification processes to generate the encrypted CGH. The similarity between different encryption levels is used as a metric to evaluate the results obtained.

Secured lightweight authentication for 6LoWPANs in machine-to-machine communications