Binary Encoding

In this paper we integrate two essential processes, discretization of continuous data and learning of a model that explains them, towards fully computational machine learning from continuous data. Discretization is fundamental for machine learning and data mining, since every continuous datum; e.g., a real-valued datum obtained by observation in the real world, must be discretized and converted from analog (continuous) to digital (discrete) form to store in databases. However, most machine learning methods do not pay attention to the situation; i.e., they use digital data in actual applications on a computer whereas assume analog data (usually vectors of real numbers) theoretically. To bridge the gap, we propose a novel measure of the difference between two sets of data, called the coding divergence, and unify two processes discretization and learning computationally. Discretization of continuous data is realized by a topological mapping (in the sense of mathematics) from the d-dimensional Euclidean space R d into the Cantor space Σ ω , and the simplest model is learned in the Cantor space, which corresponds to the minimum open set separating the given two sets of data. Furthermore, we construct a classifier using the divergence, and experimentally demonstrate robust performance of it. Our contribution is not only introducing a new measure from the computational point of view, but also triggering more interaction between experimental science and machine learning.

This paper presents a multi-representational computer-based environment, the Starting with Parallel Processing (SPAP) environment, designed for learning the concept of parallel processing to beginners through the possibility of their both performing and exploring serial and parallel sorting procedures. In designing this environment, social and constructivist learning theories have been taken into account. By interacting within SPAP, learners have opportunities to express their previous knowledge of serial and parallel sorting through a step-by -step procedure and receiving constructive feedback. Moreover, learners have the chance to actively exp lore stepby-step serial and parallel sorting automatically performed by the system. Students have the chance to observe these sorting procedures step -by -step in Multiple Representation Systems. SPAP was piloted with a class of 31 actual first grade students in secondary school. The analysis of the data shows that all these students recognized that sorting using parallel comparators is faster than when serial comparators are used.

This paper presents a multi-representational computer-based environment, the Starting with Parallel Processing (SPAP) environment, designed for learning the concept of parallel processing to beginners through the possibility of their both performing and exploring serial and parallel sorting procedures. In designing this environment, social and constructivist learning theories have been taken into account. By interacting within SPAP, learners have opportunities to express their previous knowledge of serial and parallel sorting through a step-by -step procedure and receiving constructive feedback. Moreover, learners have the chance to actively exp lore stepby-step serial and parallel sorting automatically performed by the system. Students have the chance to observe these sorting procedures step -by -step in Multiple Representation Systems. SPAP was piloted with a class of 31 actual first grade students in secondary school. The analysis of the data shows that all these students recognized that sorting using parallel comparators is faster than when serial comparators are used.

Since Extensible Markup Language abbreviated as XML, became an official World Wide Web Consortium recommendation in 1998, XML has emerged as the predominant mechanism for data storage and exchange, in particular over the World Web. Due to the flexibility and the easy use of XML, it is nowadays widely used in a vast number of application areas and new information is increasingly being encoded as XML documents. Because of the widespread use of XML and the large amounts of data that are represented in XML, it is therefore important to provide a repository for XML documents, which supports efficient management and storage of XML data. Since the logical structure of an XML document is an ordered tree consisting of tree nodes, establishing a relationship between nodes is essential for processing the structural part of the queries. Therefore, tree navigation is essential to answer XML queries. For this purpose, many proposals have been made, the most common ones are node labeling schemes. On the other hand, XML repeatedly uses tags to describe the data itself. This self-describing nature of XML makes it verbose with the result that the storage requirements of XML are often expanded and can be excessive. In addition, the increased size leads to increased costs for data manipulation. Therefore, it also seems natural to use compression techniques to increase the efficiency of storing and querying XML data. In our previous works, we aimed at combining the advantages of both areas (labeling and compaction technologies), Specially, we took advantage of XML structural peculiarities for attempting to reduce storage space requirements and to improve the efficiency of XML query processing using labeling schemes. In this paper, we continue our investigations on variations of binary string encoding forms to decrease the label size. Also We report the experimental results to examine the impact of binary string encoding on reducing the storage size needed to store the compacted XML documents.

Since Extensible Markup Language abbreviated as XML, became an official World Wide Web Consortium recommendation in 1998, XML has emerged as the predominant mechanism for data storage and exchange, in particular over the World Web. Due to the flexibility and the easy use of XML, it is nowadays widely used in a vast number of application areas and new information is increasingly being encoded as XML documents. Because of the widespread use of XML and the large amounts of data that are represented in XML, it is therefore important to provide a repository for XML documents, which supports efficient management and storage of XML data. Since the logical structure of an XML document is an ordered tree consisting of tree nodes, establishing a relationship between nodes is essential for processing the structural part of the queries. Therefore, tree navigation is essential to answer XML queries. For this purpose, many proposals have been made, the most common ones are node labeling schemes. On the other hand, XML repeatedly uses tags to describe the data itself. This self-describing nature of XML makes it verbose with the result that the storage requirements of XML are often expanded and can be excessive. In addition, the increased size leads to increased costs for data manipulation. Therefore, it also seems natural to use compression techniques to increase the efficiency of storing and querying XML data. In our previous works, we aimed at combining the advantages of both areas (labeling and compaction technologies), Specially, we took advantage of XML structural peculiarities for attempting to reduce storage space requirements and to improve the efficiency of XML query processing using labeling schemes. In this paper, we continue our investigations on variations of binary string encoding forms to decrease the label size. Also We report the experimental results to examine the impact of binary string encoding on reducing the storage size needed to store the compacted XML documents.

The article discusses the use of computer-generated holograms (CGHs) for the application as one of the security features in the relief-phase protective holograms. An improved method of calculating CGHs is presented, based on ray-tracing approach in the case of interference of parallel rays. Software is developed for the calculation of multilevel phase CGHs and their integration in the application of security holograms. Topology of calculated computer-generated phase holograms was recorded on the photoresist by the optical greyscale lithography. Parameters of the recorded microstructures were investigated with the help of the atomic-force microscopy (AFM) and scanning electron microscopy (SEM) methods. The results of the research have shown highly protective properties of the security elements based on CGH microstructures. In our opinion, a wide use of CGHs is very promising in the structure of complex security holograms for increasing the level of protection against counterfeit.

Nowadays, wavefront sensors are widely used to control the shape of the wavefront and detect aberrations of the complex field amplitude in various fields of physics. However, almost all of the existing wavefront sensors work only with quasi-monochromatic radiation. Some of the methods and approaches applied to work with polychromatic radiation impose certain restrictions. However, the contemporary methods of computer and digital holography allow implementing a holographic wavefront sensor that operates with polychromatic radiation. This paper presents a study related to the analysis and evaluation of the error in the operation of holographic wavefront sensors with such radiation.

In this paper we consider the combinatorial optimization problem known as workflow scheduling. We compare three encoding schemes of varying density: one-hot, binary, and domain wall, and test their performance against two wellknown hybrid quantum-classical algorithms: Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). In an attempt to obtain the best results possible, we investigate various parameters of the algorithms and test out other state-of-the-art improvements, such as dedicated QAOA mixers. Ultimately, we prove that, despite its popularity, one-hot encoding is not always the best, and using a denser encoding scheme, such as binary or domain wall, can allow for solving larger instances of workflow scheduling. Additionally, combining the above-mentioned encodings with dedicated QAOA mixers reduces the number of infeasible solutions, leading to better results.

This paper presents a novel approach to optimizing the design of phase-only computer-generated holograms (CGH) for the creation of binary images in an optical Fourier transform system. Optimization begins by selecting an image pixel with a temporal change in amplitude. The modulated image function undergoes an inverse Fourier transform followed by the imposition of a CGH constraint and the Fourier transform to yield an image function associated with the change in amplitude of the selected pixel. In iterations where the quality of the image is improved, that image function is adopted as the input for the next iteration. In cases where the image quality is not improved, the image function before the pixel changed is used as the input. Thus, the proposed approach is referred to as the pixelwise hybrid input-output (PHIO) algorithm. The PHIO algorithm was shown to achieve image quality far exceeding that of the Gerchberg-Saxton (GS) algorithm. The benefits were particularly evident when the PHIO algorithm was equipped with a dynamic range of image intensities equivalent to the amplitude freedom of the image signal. The signal variation of images reconstructed from the GS algorithm was 1.0223, but only 0.2537 when using PHIO, i.e., a 75% improvement. Nonetheless, the proposed scheme resulted in a 10% degradation in diffraction efficiency and signal-to-noise ratio.

Optically addressed spatial light modulators (OASLMs) provide an appropriate solution for large-area and wide-viewing angle holographic displays because of the possibility of uploading holograms on it through tiling and with sub-micron diffraction feature sizes. A prototype with a large-size OASLM of 100 mm × 100 mm was fabricated using a solution-based deposition process for ZnO nanoparticles (NPs). ZnO NP-based OASLM is suitable for hologram tiling because of the extended charge carrier lifetime as a result of trap states in the ZnO NP layer annealed at a low temperature of 180°C, of which the activation energy was determined firstly by low-temperature measurements. Operating the ZnO NP OASLM in a DC driving mode was subsequently proposed, to utilize the extended charge carrier lifetime in the photosensor layer for temporary information storage. Finally, techniques to tile computer generated holograms (CGHs) spatially on a single OASLM were explored and evaluated, including the demonstration of simultaneous image replay from sequentially tiled two separate phase-only CGHs.

quality. We validate our approach on a holographic display prototype and show that the method can fully compensate unknown aberrations and erroneous and non-linear SLM phase delays, without explicitly modeling them. As a result, the proposed method significantly outperforms existing stateof-the-art methods in simulation and experimentation-just by observing captured holographic images. CCS Concepts: • Computing methodologies → Computational photography.

A novel technique for the fabrication of binary-phase computer-generated reflection holograms is described. By use of integrated circuit technology, the holographic pattern is etched into a silicon wafer and then aluminum coated to make a reflection hologram. Because these holograms reflect virtually all the incident radiation, they may find application in machining with high-power lasers. A number of possible modifications of the hologram fabrication procedure are discussed.

This paper presents a multi-representational computer-based environment, the Starting with Parallel Processing (SPAP) environment, designed for learning the concept of parallel processing to beginners through the possibility of their both performing and exploring serial and parallel sorting procedures. In designing this environment, social and constructivist learning theories have been taken into account. By interacting within SPAP, learners have opportunities to express their previous knowledge of serial and parallel sorting through a step-by-step procedure and receiving constructive feedback. Moreover, learners have the chance to actively explore stepby-step serial and parallel sorting automatically performed by the system. Students have the chance to observe these sorting procedures step -by-step in Multiple Representation Systems. SPAP was piloted with a class of 31 actual first grade students in secondary school. The analysis of the data shows that all these students recognized...

A new hybrid optical device that is capable of splitting a monochromatic laser beam into an arbitrary number of lines over a wide angle is presented. It consists of a binary surface-relief computer-generated phase hologram and a continuous parabolic surface-relief grating. In this device the phase hologram serves to generate three small, parallel lines while the continuous parabolic surface-relief phase grating acts as an array of diverging parabolic lenses to widen these lines. The binary surface-relief was generated into one side of a quartz substrate through a plasma-etching process, and the parabolic profile was generated into a thick photoresist deposited on the other side of the quartz substrate. Calculations showed that a diverging parabolic lens with a f-number of 0.5 would deliver the desired optical pattern of multiple beams distributed over 90°. A surface-relief depth of 6.0 m was calculated with consideration of the phase distributions of such lens. The parabolic profiles were fabricated in a 10-m-thick photoresist, by use of a contact exposure through a mask with a space pattern of repetitive 4-and 6-m lines. He-Ne laser light was passed through a device that generated three parallel lines over a 90°a ngle. The resulting diffraction patterns were characterized, and a satisfying result was obtained. The resulting multiple-line pattern can be used in robot vision and other applications.

In the present research we have fabricated and investigated dot-matrix hologram in the photoresist. Using X-Y motorized translation stage we have covered the substrate with diffractive pixels. Dot-matrix pixels in the photoresist where formed by laser beam interference lithopgraphy (LIL) employing He-Cd (441.6 nm) laser. A simplified Diffractive Optically Variable Imaging Device (DOVID) allowing quantative image analysis was formed from the array of two different orientation difractive pixels. The orientation of the diffraction grating in the single pixel was changed using rotational motorized stage. The sample was analysed opticaly demonstrating its capabilities of suppression and addition of the "LT" image and the baground. Diffraction efficiency of single pixels estimated using diffraction stand and employing three different lasers: He-Ne 632.8 nm, DPSS 532 nm and He-Cd 441.6 nm was performed to demonstrate efficiency of the simplified dot matrix hologram. The original ...

Holographic techniques offer a route to the generation of 3-D images having all the depth cues used by the human vision system. Reconfigurable computer generated holograms allow interactive display of computer held data and synthetic objects. The available number of pixels within the computer generated hologram (CGH) constrains the image size and field of view of such holograms and up to 1012 pixels are required to generate full parallax images having widths of-5OO mm and a field of view of This has significant implications on both the computation and electro-optic replay of CGH images. To fmd practical applications, such CGH display systems require electro-optic modulators which deliver a spatial band width product (SBWP) significantly higher than currently available electro-optic modulator or display solutions. A new electro-optic modulator system has been developed by the authors to replay dynamic holographic images. This Active TilingTM system offers a route to replay giga-pixel CGH images with video refresh rates. High speed, medium complexity electrically addressed spatial light modulators are combined with a high resolution optically addressed spatial light modulator to provide ultra-high complexity, video frame rate holographic data suitable for coherent readout.

A global iterative coding method for computer-generated holo National Optics Institute/lnstitut national grams (CGH) is introduced. The method is based on the iterative cor d'optique rection of a CGH using standard lee coding. The correction, i.e., the 369 Franquet difference between the desired and the obtained reconstruction, is coded Sainte-Foy, Quebec and added to the current CGH. The coding and weighting factors are Canada, G1 P 4N8 introduced to control the speed of convergence and the SNR. Advan and tages lie in low computing time and improvement of the object SNR, the Universite laval neighborhood SNR, and the background SNR. Reducing the standard COPl deviation of the phase of the reconstructed object also results. A slight Sainte-Foy, Quebec improvement of the diffraction efficiency is also observed. The compar Canada, G1 K 7P4 ison is realized using the lee interferogram method as a reference. This method is tested on binary and complex gray-level objects, Simulation Henri H. Arsenault, FELLOW SPIE results and optical reconstruction are also presented.

Rigorous diffraction theory is applied for the first time to the analysis of periodic, binary computer-generated holographic optical fan-out elements, often called Dammann gratings. The effects of the length of the grating period on the reconstruction noise and the diffraction efficiency are analyzed and discussed. Novel schemes are proposed for producing compact and highly efficient space-invariant optical interconnects that operate in the resonance domain.

A new hybrid optical device that is capable of splitting a monochromatic laser beam into an arbitrary number of lines over a wide angle is presented. It consists of a binary surface-relief computer-generated phase hologram and a continuous parabolic surface-relief grating. In this device the phase hologram serves to generate three small, parallel lines while the continuous parabolic surface-relief phase grating acts as an array of diverging parabolic lenses to widen these lines. The binary surface-relief was generated into one side of a quartz substrate through a plasma-etching process, and the parabolic profile was generated into a thick photoresist deposited on the other side of the quartz substrate. Calculations showed that a diverging parabolic lens with a f-number of 0.5 would deliver the desired optical pattern of multiple beams distributed over 90°. A surface-relief depth of 6.0 m was calculated with consideration of the phase distributions of such lens. The parabolic profiles were fabricated in a 10-m-thick photoresist, by use of a contact exposure through a mask with a space pattern of repetitive 4-and 6-m lines. He-Ne laser light was passed through a device that generated three parallel lines over a 90°a ngle. The resulting diffraction patterns were characterized, and a satisfying result was obtained. The resulting multiple-line pattern can be used in robot vision and other applications.

A new hybrid optical device that is capable of splitting a monochromatic laser beam into an arbitrary number of lines over a wide angle is presented. It consists of a binary surface-relief computer-generated phase hologram and a continuous parabolic surface-relief grating. In this device the phase hologram serves to generate three small, parallel lines while the continuous parabolic surface-relief phase grating acts as an array of diverging parabolic lenses to widen these lines. The binary surface-relief was generated into one side of a quartz substrate through a plasma-etching process, and the parabolic profile was generated into a thick photoresist deposited on the other side of the quartz substrate. Calculations showed that a diverging parabolic lens with a f-number of 0.5 would deliver the desired optical pattern of multiple beams distributed over 90°. A surface-relief depth of 6.0 m was calculated with consideration of the phase distributions of such lens. The parabolic profiles were fabricated in a 10-m-thick photoresist, by use of a contact exposure through a mask with a space pattern of repetitive 4-and 6-m lines. He-Ne laser light was passed through a device that generated three parallel lines over a 90°a ngle. The resulting diffraction patterns were characterized, and a satisfying result was obtained. The resulting multiple-line pattern can be used in robot vision and other applications.

This Letter presents an in-line digital holographic system that can provide full amplitude and phase reconstruction without any reference wave, with a single recorded hologram. This major capability is obtained by using a coherent mixing between several object waves generated by a pure spatial phase modulation. A scaling parameter permits us to reconstruct the phase without any unwrapping. The capability of the method to provide quantitative phase contrast measurement and numerical refocusing is demonstrated through experimental results.

Since Extensible Markup Language abbreviated as XML, became an official World Wide Web Consortium recommendation in 1998, XML has emerged as the predominant mechanism for data storage and exchange, in particular over the World Web. Due to the flexibility and the easy use of XML, it is nowadays widely used in a vast number of application areas and new information is increasingly being encoded as XML documents. Because of the widespread use of XML and the large amounts of data that are represented in XML, it is therefore important to provide a repository for XML documents, which supports efficient management and storage of XML data. Since the logical structure of an XML document is an ordered tree consisting of tree nodes, establishing a relationship between nodes is essential for processing the structural part of the queries. Therefore, tree navigation is essential to answer XML queries. For this purpose, many proposals have been made, the most common ones are node labeling schemes. On the other hand, XML repeatedly uses tags to describe the data itself. This self-describing nature of XML makes it verbose with the result that the storage requirements of XML are often expanded and can be excessive. In addition, the increased size leads to increased costs for data manipulation. Therefore, it also seems natural to use compression techniques to increase the efficiency of storing and querying XML data. In our previous works, we aimed at combining the advantages of both areas (labeling and compaction technologies), Specially, we took advantage of XML structural peculiarities for attempting to reduce storage space requirements and to improve the efficiency of XML query processing using labeling schemes. In this paper, we continue our investigations on variations of binary string encoding forms to decrease the label size. Also We report the experimental results to examine the impact of binary string encoding on reducing the storage size needed to store the compacted XML documents.

Point-oriented phase computer-generated holograms that encode complex scalar fields are proposed and discussed. These holograms allow the reconstruction of the encoded fields with high signal to noise ratio, even if they are implemented with a pixelated spatial light modulator. The good performance of these holograms is enabled by a significant reduction in the relative intensity of the high order diffraction field contributions that share the spatial frequency domain of the encoded field.

This paper describes recent research and development related to data processing and imaging performance for a dynamic quantitative phase imaging microscope. This microscope provides instantaneous measurements of dynamic motions within and among live cells without labels or contrast agents. It utilizes a pixelated wire grid polarizer mask in front of the camera sensor that enables simultaneous measurement of multiple interference patterns. Optical path difference (OPD) and optical thickness (OT) data are obtained from phase images. Simulated DIC (gradient) and simulated dark field (gradient magnitude) images can be directly obtained from the phase enabling simultaneous capture of brightfield, phase contrast, quantitative phase, DIC and dark field. The OT is further processed to remove background shapes, and enhance topography. This paper presents a number of different processing routines to remove background surface shape enabling quantification of changes in cell position and volume over time. Data from a number of different moving biological organisms and cell cultures are presented.

This investigation presents a novel type of DOEs fabricated by the conventional CMOS process. A simple post-CMOS process is applied to form the relief pattern, which can be used directly for its optical properties or serve as a mold for the subsequent replication. By using the CMOS process, in addition to reducing the depth, alignment, dimension, and shape errors of the pattern, the scale is minimized by the advancing microfabrication as well.

The fabrication and replication of binary spot array generators using 4 and 16 levels gratings is investigated. The elements are designed using iterative Fourier transform algorithm and fabricated by electron-beam lithography. Finally elements are copied by fabricating nickel shims and using hot embossing technique. In each step the optical signals are measured and signals are characterized using bit error rate as a measure of quality. The results show that although 16 level element gives theoretically superior performance, the bit error rate is much lower (0.2%) for replicated 4 level elements than for their 16 level counterparts (9%).

A new hybrid optical device that is capable of splitting a monochromatic laser beam into an arbitrary number of lines over a wide angle is presented. It consists of a binary surface-relief computer-generated phase hologram and a continuous parabolic surface-relief grating. In this device the phase hologram serves to generate three small, parallel lines while the continuous parabolic surface-relief phase grating acts as an array of diverging parabolic lenses to widen these lines. The binary surface-relief was generated into one side of a quartz substrate through a plasma-etching process, and the parabolic profile was generated into a thick photoresist deposited on the other side of the quartz substrate. Calculations showed that a diverging parabolic lens with a f-number of 0.5 would deliver the desired optical pattern of multiple beams distributed over 90°. A surface-relief depth of 6.0 m was calculated with consideration of the phase distributions of such lens. The parabolic profiles were fabricated in a 10-m-thick photoresist, by use of a contact exposure through a mask with a space pattern of repetitive 4-and 6-m lines. He-Ne laser light was passed through a device that generated three parallel lines over a 90°a ngle. The resulting diffraction patterns were characterized, and a satisfying result was obtained. The resulting multiple-line pattern can be used in robot vision and other applications.

We suggest a method for coding high resolution computer-generated volume holograms. It involves splitting the computer-generated hologram into multiple holograms, each individually recorded as a volume hologram utilizing the maximal resolution available from the spatial light modulator.

An algorithm is reported for the design of a phase-only diffractive optical element (DOE) that reshapes a beam focused using a high numerical aperture (NA) lens. The vector diffraction integrals are used to relate the field distributions in the DOE plane and focal plane. The integrals are evaluated using the chirp-z transform and computed iteratively within the Method of Generalized Projections (MGP) to identify a solution that simultaneously satisfies the beam shaping and DOE constraints. The algorithm is applied to design a DOE that transforms a circularly apodized flat-top beam of wavelength λ to a square irradiance pattern when focused using a 1.4-NA objective. A DOE profile is identified that generates a 50λ × 50λ square irradiance pattern having 7% uniformity error and 74.5% diffraction efficiency (fraction of focused power).

An ultra-fast exact electromagnetic modeling approach based on the generalized source method (GSM) achieving O(NlogN) calculation time and memory resort is applied to the simulation of the diffraction of a relatively large section of a 2D pixelated DOE in the form of square pillars of identical cross-section. The size of the considered area is several wavelengths across, enough to achieve a reasonable separation of the central region from the influence of neighbouring areas, enabling the use of a stitching method for the simulation of very large elements that could so far only be modeled by scalar approximations. A time and memory resort comparison is made between a standard scalar method and the rigorous GSM-based simulation of the spectra of the element.

The arrangement of binary subwavelength structures is a promising alternative to the conventional multiheight level technique to generate computer generated holograms (CGHs). However, the current heuristic design approach leads to a slight mismatch between the target signal and experimental data. To evaluate this deviation, a diffractive beam splitter design is investigated rigorously using a finite-difference time-domain (FDTD) method. Since the use of a rigorous Maxwell-equation solver like FDTD requires a massive computational effort, an alternative scalar approach, a fast Fourier transform beam propagation method (FFT-BPM), is investigated with a substantial higher computing speed, showing still a good agreement with the FDTD simulation and experimental data. Therefore, an implementation of this scalar approach into the CGH design process offers the possibility to significantly increase the accuracy.

Computer generated holograms (CGH) offer the possibility of influencing phase and amplitude of a coherent wave in various ways. In the case of Fourier holograms, this can be used for the realization of image projection systems that exhibit some unique properties, e.g. an extremely large depth of focus. The authors presents the design, fabrication and measurement of a stacked CGH, capable of creating a multicolor image from an RGB-laser beam.

This paper focuses on the design of a microworld for the learning of binary representation by primary level education pupils. The proposed microworld has been constructed within the theoretical framework of modern social and constructivist perspectives of knowledge construction. In the context of the constructed microworld, pupils have opportunities to construct the concept of coding a piece of information represented in systems used in the real world, such as visual drawing information, in binary representation systems used by a computer. Pupils also have the opportunity to construct the concept of decoding a piece of information presented in a binary form to information represented in a system used in the real world. In the context of the proposed microworld, pupils are helped to construct these concepts by exploiting the following opportunities: a) to draw a picture by coloring in each cell of a grid, b) to use 0s and 1s to represent the picture in focus, c) to experiment in order to discover by themselves the encoding system implied by the system in their pictures, d) to use different coding systems to represent a picture, e) to observe the automatically-created binary representation corresponding to a picture they have constructed and f) to draw a picture by using a binary code and to observe its representation automatically created by the system.

We show that computer generated holograms, implemented with amplitude-only liquid crystal spatial light modulators, allow the synthesis of fully complex fields with high accuracy. Our main discussion considers modified amplitude holograms whose transmittance is obtained by adding an appropriate bias function to the real cosine computer hologram of the encoded signal. We first propose a bias function, given by a soft envelope of the signal modulus, which is appropriate for perfect amplitude modulators. We also consider a second bias term, given by a constant function, which results appropriate for modulators whose amplitude transmittance is coupled with a linear phase modulation. The influence of the finite pixel size of the spatial light modulator is compensated by digital pre-filtering of the encoded complex signal. The performance of the discussed amplitude CGHs is illustrated by means of numerical simulations and the experimental synthesis of high order Bessel beams.

We suggest a method for coding high resolution computer-generated volume holograms. It involves splitting the computer-generated hologram into multiple holograms, each individually recorded as a volume hologram utilizing the maximal resolution available from the spatial light modulator. Our method enables their simultaneous subsequent reconstruction. We demonstrate the recording and the reconstruction of a computer-generated volume hologram with a space bandwidth product much higher than the maximal one of the spatial light modulator used as an interface. Finally, we analyze the scheduling procedure of the multiple holographic recording process in photorefractive medium in this specific application.

We have constructed a new type of modal wavefront sensor that uses a multiplexed hologram and position-sensing detectors to measure the amplitudes of a preselected set of eight Zernike modes in an input beam. The measurement is all optical, with the calculations made in encoding the holograms themselves. The result is a sensor with no computational overhead or postprocessing that has the potential to operate at megahertz speeds without the need for computer calculations. We have built and tested a prototype device, demonstrating its operation both as a stand-alone wavefront sensor and in a closed-loop adaptive optics control system.

It has been shown that high precision diffractive objectives are an alternative to their refractive counterparts for application in interferometers. A design for an all-diffractive, double-sided objective that fulfills the Abbe sine condition has been proposed. It allows eliminating aberrations due to a finite field angle. Ray tracing simulations show that field angles up to 0. 1 °cause aberrations less than X/20 PV in single pass.

Genetic Algorithm (GA) are randomized searching and optimization techniques guided by the principles of evolution and natural genetic. They are efficient, adaptive and robust search processes. Genetic Algorithm handles a population of possible solutions represented by a chromosome and a chromosome is a sequence of genes. The main issue is how to represent the genes in a chromosome. Choosing the right scheme of encoding the genes is a crucial task. Encoding mainly depends on the type of problem. This paper studies different encoding schemes the problems in which they are used.

We discuss a computer generated hologram whose transmittance is defined in terms of the Jacobi-Anger identity. If the hologram is implemented with a continuous phase spatial light modulator it generates integer-order non-diffracting Bessel beams, with a common asymptotic radial frequency, at separated propagation axes. On the other hand, when the hologram is implemented with a low-resolution pixelated phase modulator, it is possible to generate multiple Bessel beams with a common propagation axis. We employ this superposition of multiple Bessel beams to generate non-diffracting periodic and quasi-periodic wave fields.

A novel method of obtaining precision measurement using two binary phase diffractive optical elements, termed the hologram and phasemask, is presented. By encoding multiple views into the hologram, each of which corresponds to a horizontal or vertical relative displacement of the phasemask, the system is able to provide a visual feedback of the measurement without the use of electronics. A probabilistic method for detection of the resultant images, matched to the statistical properties of holographic replay, shows promise for enabling a fully-automated measurement system.

A method of encoding computer-generated holograms, which
is matched to the recently developed one-step phase retrieval
OSPR) algorithm, is described. Continuous amplitude and binary phase modulators are coupled to enable the encoding of the entire Fourier plane real axis, and an implementation using commonly available reflective and transmissive devices is described. It is shown that, if a binary phase
spatial light modulator (SLM), employing high switching angle liquid crystal (LC) material, is deployed in such a coupled modulator arrangement, the resultant reconstructed images exhibit signal-to-noise ratios some 3.5 and 15 times greater than those currently achievable with continuous and binary phase modulation, respectively.