Multiplexed computer-generated hologram with polygonal apertures.

We present a novel approach for securing valuable documents using a complementary approach based on the encryption of computer-generated holograms (CGHs). The proposed approach utilizes the well-known iterative Fourier transform algorithm (IFTA) to generate a phase-only CGH for valuable digital and/or physical documents. The generated CGH is then secured by binary phase randomization, which is implemented using the symmetric encryption technique, exclusive OR (XOR). The reconstruction process for the calculated secured CGHs varied slightly depending on whether the documents were digital or physical. For digital documents, reconstruction was performed using a symmetric decryption key followed by an inverse Fourier transform (IFFT). On the other hand, the reconstruction of the physical document involved two additional processes: printing and scanning. To evaluate the quality of the digital reconstruction, the speckle signal-to-noise ratio (SSNR) was estimated for both printed grayscale and binary CGHs. The security analysis of the XOR-encrypted CGH was quantitatively evaluated to ensure the level of protection against various cryptographic attacks such as plaintext and brute-force attacks. The results revealed that the combination of phase CGHs and the XOR encryption/decryption provides robust cryptographic protection for valuable documents, benefiting document security and anti-counterfeiting.

The diffraction efficiency, defined as the ratio of diffracted power to incident power, is one of the key working indicators for a computer-generated hologram (CGH). The CGH with high diffraction efficiency could suppress stray light and eliminate ghost images, thus improving interferometric performance in aspherical testing of low-reflectivity or large off-axis distance surfaces. However, the high-efficiency CGH is hard to precisely fabricate by traditional reactive ion etching and focusing ion beam, because it requires high etching depth with a high uniformity and sub-nanometric roughness in the glass, especially in the fabrication of a large CGH with an aperture of up to 300 mm. In this study, fabrication of the above-mentioned CGH was demonstrated via what we believe to be a new method called scanning homogenization etching (SHE), in which the ion source with a Gaussian energy distribution accurately scans the glass surface to realize homogenization etching. Different from controlling dwell time at each etching point, this paper proposes to control the scanning rate to achieve not only uniform but also quantitative depth removal in a single scan. Moreover, the depth errors in deep etching across the whole glass surface can be remarkably reduced due to homogenization effects introduced by multiple scanning etching. Finally, the target etching depth of 692.3 nm with an etching uniformity of 2.2% in the etching of a 300 mm CGH was achieved. The roughness of the etched and unetched area both have Ra values of 0.3 nm. The diffraction efficiency of working order is 39.998%, achieving 98.6% of the theoretical diffraction efficiency. In addition, the SHE is not limited by the aperture of the ion source, so it can achieve even larger diffractive optical elements with high diffraction efficiency and high accuracy.

Scanning ion beam etching: A method for the fabrication of computer-generated hologram with nanometric accuracy for aspherical testing

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.

We report the generation of a real-time large computer generated hologram (CGH) using the wavefront recording plane (WRP) method with the aid of a graphics processing unit (GPU). The WRP method consists of two steps: the first step calculates a complex amplitude on a WRP that is placed between a 3D object and a CGH, from a three-dimensional (3D) object. The second step obtains a CGH by calculating diffraction from the WRP to the CGH. The disadvantages of the previous WRP method include the inability to record a large three-dimensional object that exceeds the size of the CGH, and the difficulty in implementing to all the steps on a GPU. We improved the WRP method using Shifted-Fresnel diffraction to solve the former problem, and all the steps could be implemented on a GPU. We show optical reconstructions from a 1,980 × 1,080 phase only CGH generated by about 3 × 10(4) object points over 90 frames per second. In other words, the improved method obtained a large CGH with about 6 mega pixels (1,980 × 1,080 × 3) from the object points at the video rate.

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.

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.

Computer-generated holograms (CGH’s) synthesized by the iterative direct-binary-search (DBS) algorithm yield lower reconstruction error and higher diffraction efficiency than do CGH’s designed by conventional methods, but the DBS algorithm is computationally intensive. A fast algorithm for DBS is developed that recursively computes the error measure to be minimized. For complex amplitude-based error, the required computation for an L-point CGH is reduced by a factor of (L/log2L)1/2. The fast intensity-based algorithm is substantially more complicated, and modifications are considered in order to make the algorithm more efficient. An acceleration technique that attempts to increase the rate of convergence of the DBS algorithm is also investigated.

Diffractive optical elements (DOE) are used for various purposes, such as a beam shaper, beam splitter and so on. In order to design DOEs, iterative Fourier transform algorithm (IFTA) is widely used. IFTA is fast and effective optimization method and can handle large size data. In the IFTA, propagation in the far field and near field is described by Fourier transform and Fresnel transform, respectively. Iterative angular spectrum approach (IASA) is one of iterative methods based on angular spectrum technique. IASA adopt angular spectrum technique as expression of propagation in near field instead of Fresnel transform. Angular spectrum technique is based on scalar diffraction theory and satisfies Helmholtz equation; therefore angular spectrum technique is the accurate method for the calculation of diffraction. We designed a DOE by using IASA and evaluated its diffraction characteristics based on vector diffraction theory. In this paper, we report on the outcome.

We present a simple and fast calculation algorithm for a computer-generated hologram (CGH) by use of wavefront recording plane. The wavefront recording plane is placed between the object data and a CGH. When the wavefront recording plane is placed close to the object, the object light passes through a small region on the wave recording plane. The computational complexity for the object light is very small. We can obtain a CGH to execute diffraction calculation from the wavefront recording plane to the CGH. The computational complexity is constant. The total computational complexity is dramatically reduced in comparison with conventional CGH calculations.

Generally, uniformity can be improved at the cost of a low diffraction efficiency in the design of diffractive optical elements by the conventional iterative Fourier transform algorithm. This trade-off is a fundamental limitation of the conventional iterative Fourier transform algorithm. However in this letter, a novel iterative Fourier transform algorithm with adaptive regularization parameter distribution for alleviating the trade-off between uniformity and diffraction efficiency and for improving uniformity is devised on the basis of the theoretical analysis of the trade-off property in the conventional iterative Fourier transform algorithm scheme. The validity of the proposed algorithm is proved by numerical experiments.

All of the existing holographic wavefront sensors are either bulky or have low accuracy of measuring wavefront aberrations. In this paper, we present an improvement of the holographic method of measuring wavefront aberrations using computer-generated Fourier holograms. The novelty of this work lies in the proposed approach to the synthesis of Fourier holograms, which are implemented using phase-only SLM. The main advantages of this method are the increased diffraction efficiency compared to the previously known methods, and the more compact implementation scheme due to the elimination of the conventional Fourier-lens. The efficiency of the proposed method was confirmed by numerical simulation and optical experiments.

In this paper, we present the design and fabrication of an on-axis Fresnel Computer Generated Hologram (CGH) which on illuminating with the laser diode projects the virtual image of a reticle pattern. This can find application in an aiming sight where the reticle pattern is projected onto a distant target. An iterative optimization algorithm has been used to design the CGH. The CGH of about 20 mm size with 5 microns pixel size is fabricated using a maskless lithography system.

Iterative Fourier transform algorithm (IFTA) has been widely applied to achieve holograms in diffractive optical elements, however it is insufficient for designing holograms uploaded on liquid crystal on silicon (LCOS) to steer multi-beams in a wavelength selective switch (WSS). In this paper, a three-step hybrid algorithm including IFTA, Symmetrical IFTA with both phase and amplitude freedoms (SIFTA-2) and Genetic algorithm (GA) is developed to optimize the multi-casting hologram and experimentally demonstrated the multi-casting function of WSS. The reconstructed output field not only has max 128 fan-out patterns with flexible power ratio, but also can be adjusted to balance multi-indicators like reconstructed root mean square error (RMSE), diffraction efficiency and crosstalk power by setting flexible weightings of fitness functions in GA.

State-of-the-art diffractive optical elements (DOEs) and computer generated holograms (CGHs) are fabricated using e-beam lithography and dry etching techniques to achieve multi-level phase elements with very high diffraction efficiencies. Electron beam lithography allows DOEs/CGHs with smaller feature sizes (e.g. for off-axis diffractive lenses with small f-number) to be fabricated. Dry etching techniques, especially chemically assisted reactive ion beam, allows DOEs/CGHs be fabricated in a variety of materials. Multi-level phase DOEs/CGHs, especially those of sixteen or more phase levels, mean their surface profiles are fabricated with high accuracy / quality. It is not only the e-beam system which dictates the feature size limitations, but also the alignment systems (mask aligner) and the materials (e-beam or photo resists). In order to allow DOEs/CGHs to be used in new optoelectronic systems, it is necessary also to fabricate the elements in different materials economically. Since the cost of a multi-level phase DOE/CGH is determined by the e-beam writing time, the number of etching steps for fabricating the master, and the technology for replication, we need to decrease the writing time and etching steps for the master and to develop a low cost replication technology for mass production without affecting the quality of the DOEs/CGHs. In this Chapter, we will review three DOE/CGH fabrication techniques and CAD development required, considering the overall design and fabrication time for multi-level phase DOEs.