Phase-searching look-up table method for computer-generated holograms

Evaluation of satellite-based algorithms to estimate photosynthetically available radiation (PAR) reaching the ocean surface at high northern latitudes

An experiment was conducted in a grid generated, nominally homogeneous, isotropic turbulent flow, in a wind tunnel of 0.33 m*0.33 m cross-sectional area, in order to evaluate the performance of an explicit non-real time data analysis algorithm for a crossed wire anemometer in highly turbulent flow. The 7000 data values acquired at various downstream locations with different turbulence intensities were analysed by the explicit non-real time method which assumes a constant yaw factor KT in the fixed angle calibration procedure, and by the 'look-up table' method which requires calibration at several yaw angles. It was found that the simple explicit non-real time method is adequate in computing the Reynolds stresses up a turbulence intensity of 40% when compared with the tedious look-up table method. The discrepancies are less than +or-6% for Reynolds normal stresses and less than +or-15% for Reynolds shear stress. A theoretical model based on the Gaussian probability density function was also developed to predict the probability distribution of the yaw angle of flow at various turbulence intensities in order to refine the explicit non-real time and look-up table methods of data analysis.

Digital noise signal synthesis methods have good scalability and flexibility, and can be divided into table look-up and transform methods depending on the implementation method. The accuracy of noise distribution synthesized by the look-up table method is limited by the storage depth, on the other hand, the maximum synthesis speed of the transform method is limited by the hardware computation speed. In this paper, we propose a new implementation method for digital noise signal synthesis, which divides the noise output into high probability intervals and low probability intervals by probability. The high probability interval noise generation is based on the look-up table method, and the low probability interval noise generation is based on the transformation method for real-time computation. The method is validated experimentally in terms of distribution accuracy, storage space occupation and output speed. The results show that the method has higher output accuracy than the look-up table method and faster output speed compared to the transformation method.

In the C-band high-speed long-reach optical intensity modulation direct detection (IM/DD) communication system, severe signal distortion, including chromatic dispersion and device bandwidth limitations, making the size of lookup tables (LUTs) required by equalizers too large to be operated. In this paper, we propose a cluster-assisting lookup table (CLUT) approach to reduce the table size significantly. In addition, we also propose multiplication-free CLUT-based decision-feedback equalizer (CLUT-DFE) and CLUT-based log-maximum a posteriori estimation with a fixed number of surviving states (CLUT-FS-MAP) to effectively compensate for channel distortions. Using the k-means clustering algorithm, the proposed CLUT significantly shortens the table size by reducing the number of independent variable values input. The table size of traditional LUTs increases exponentially with the filter tap number, making it impossible for LUTs to replace filters with tap numbers greater than 20. The CLUT breaks this limitation. The proposed schemes are experimentally performed in a C-band 61-Gb/s IM/DD optical on-off keying (OOK) system featuring a 3.65-GHz 3-dB bandwidth over a 100-km standard single mode fiber (SSMF). Compared to traditional LUT, CLUT reduces table size by about 10 orders of magnitude with the same performance. To the best of our knowledge, this study represents the first deployment of ultrasmall-size CLUT in equalization.

Abstract. We present a new aerosol extinction profile retrieval algorithm for multi-axis differential optical absorption spectrometer (MAX-DOAS) measurements at high-altitude sites. The algorithm is based on the lookup table method. It is applied to retrieve aerosol extinction profiles from the long-term MAX-DOAS measurements (February 2012 to February 2016) at the Environmental Research Station Schneefernerhaus (UFS), Germany (47.417∘ N, 10.980∘ E), which is located near the summit of Zugspitze at an altitude of 2650 m. The lookup table consists of simulated O4 differential slant column densities (DSCDs) corresponding to numerous possible aerosol extinction profiles. The sensitivities of O4 absorption to several parameters were investigated for the design and parameterization of the lookup table. In the retrieval, simulated O4 DSCDs for each possible profile are derived by interpolating the lookup table to the observation geometries. The cost functions are calculated for each aerosol profile in the lookup table based on the simulated O4 DSCDs, the O4 DSCD observations, and the measurement uncertainties. Valid profiles are selected from all the possible profiles according to the cost function, and the optimal solution is defined as the weighted mean of all the valid profiles. A comprehensive error analysis is performed to better estimate the total uncertainty. Based on the assumption that the lookup table covers all possible profiles under clear-sky conditions, we determined a set of O4 DSCD scaling factors for different elevation angles and wavelengths. The profiles retrieved from synthetic measurement data can reproduce the synthetic profile. The results also show that the retrieval is insensitive to measurement noise, indicating the retrieval is robust and stable. The aerosol optical depths (AODs) retrieved from the long-term measurements were compared to coinciding and co-located sun photometer observations. High correlation coefficients (R) of 0.733 and 0.798 are found for measurements at 360 and 477 nm, respectively. However, especially in summer, the sun photometer AODs are systematically higher than the MAX-DOAS retrievals by a factor of ∼2. The discrepancy might be related to the limited measurement range of the MAX-DOAS and is probably also related to the decreased sensitivity of the MAX-DOAS measurements at higher altitudes. The MAX-DOAS measurements indicate the aerosol extinction decreases with increasing altitude during all seasons, which agrees with the co-located ceilometer measurements. Our results also show maximum AOD and maximum Ångström exponent in summer, which is consistent with observations at an AERONET station located ∼43 km from the UFS.

Adaptive predistortion is one of the most promising methods to linearize RF power amplifiers. The size of gain look-up table is a performance limiting factor and so are various error sources existing in the system. In this paper, we study the table size effects in combination with system imperfections. It is shown that errors introduced in the adaptation path can cause an inverse relationship between the table size and the output adjacent channel power ratio. Thus, this implies that there exists an optimal table size in practice and a further increase of the table size beyond that value can even result in linearity degradation instead of improvement. The reason behind this unexpected result is discussed. This study indicates that the table size shall be properly chosen based on a good understanding of various error sources located in the system.

A memory and speed efficient CAVLC (context adaptive variable length coding) decoder for H.264/AVC baseline profile is proposed. Because the CAVLC consists of a kind of bit-level operations, general processor (like RISC or MIPS) and DSP incorporating multiple parallel arithmetic units (like SIMD or VLIW) are ineffective to decode it. Though the dedicated hardwires are very effective to decode the CAVLC, they are expensive and not programmable. Also, the size of the CAVLC lookup table is more than 400 bytes. Demand for highly flexible and fast implementations and lower memory size for CAVLC decoding is rising nowadays. The four instructions--ShowBits, GetBits, FlushBits and LeadingBits, are designed after the exploiting of the functions coverage. In order to reduce the codewords matching miss and the lookup table size, a new grouping, remainder generation method and a merged lookup table (LUT) are used; and the specific group decoding instruction GroupDecoding is also presented. In summary, a based instruction set level acceleration with the codewords group partition hardware architecture is proposed to speed up the CAVLC decoding. Based on those instructions and the hardware platform, the CAVLC decoding can be significantly accelerated compared with the method in H.264 reference software. Simulation results show that the architecture is sufficient for the CAVLC decoding of 30 frames HDTV (1902 x 1080 pixels) per second.

Higher logic density is a key goal pursued by Field Programmable Gate Arrays (FPGA). The higher the logic density is, the lower the cost of the circuit spends, and the shorter the line length of the circuit is, the less power is required. Technology mapping is used to map technology-independent logic gates into a lookup table (LUT) netlist. A big problem with the 6-input LUT used in the FPAG at the present stage is that the utilization rate of the lookup table is insufficient. Modern FPGA architectures have good support for dual-output LUTs. We can merge two small LUTs into a new dual-output LUT, if the total number of inputs of the two small LUTs is not greater than the input limit specified by the LUT, thereby reducing the area, that is, reducing the number of LUTs. In this paper, the dual-output LUTs are merged in the technology mapping stage, and a new method of merging single-output LUTs into dual-output LUTs is proposed. The experimental results show that the algorithm used in this paper has an average reduction of 10.21 % in the number of LUTs without worsening delay.

While the development of the optic interferometric sensors achieves great progress, one fact that restricts this development is the demodulation technique. An applicable demodulation method for interferometric sensors is called "The Phase Generated Carrier (PGC) demodulation". Yet this demodulation fails to content the large-scale sensors application for the limitations of the electronic devices. Another arctangent approach based on digital demodulator proves more advantages than the traditional Differentiate and Cross Multiply (DCM) approach which is used in PGC demodulation. In this paper, the arctangent approach based on PGC demodulation is discussed and simulated. Lookup table is used in the arctangent approach. Values equal to the existent data in the lookup table are chosen from the table, and values between two different data in the table are modulated to the linear approximate values. Two primary objects are aimed to demonstrate the advantages of the arctangent approach: (1). the noise analysis of this demodulation, considered two aspects: a. the relativity of the noise amplitude and the size of lookup table. Simulation result indicates that when double the lookup size, the noise amplitude decreases about 6dB; b. the influence to the noise generation which is leaded in by the rank of the polynomial approximate coefficients, the higher this rank is, the better the result comes. An approximate function is proposed about this relationship. (2). the measurement range, operation complexity, quality of operation, and applicability of the arctangent approach are discussed for an effective digital realization.

Transcendental functions cannot be expressed algebraically, which brings a big challenge to efficient and accurate approximation. Lookup table (LUT) and piecewise fitting are common traditional methods. However, they either trade approximate accuracy for computation and storage or require unaffordable resources when the expected accuracy is high. In this paper, we have developed a high-precision approximation method, which is error-controllable and resource-efficient. The method originally divides a transcendental function into two parts based on their slope. The steep slope part is approximated by the method of LUT with the interpolation, while the gentle slope part is approximated by the range-addressable lookup table (RALUT) algorithm. The boundary of two parts can be adjusted adaptively according to the expected accuracy. Moreover, we analyzed the error source of our method in detail, and proposed an optimal selection method for table resolution and data bit-width. The proposed algorithm is verified on an actual FPGA board and the results show that the proposed method’s error can achieve arbitrarily low. Compared to other methods, the proposed algorithm has a more stable increase in resource consumption as the required accuracy grows, which consumes fewer hardware resources especially at the middle accuracy, with at least 30% LUT slices saved.

This report presents results on the development of an adaptive predistorter for a generic TDMA transmitter A heterodyne architecture was used with the quadrature modulator and demodulator implemented as digital circuits. Previously reported results have indicated that increasing the look-up table (LUT) size improves the ACPR. Our results showed an opposite trend. Typical adjacent channel power rejection (ACPR) values of -57 dB were achieved using a 16 point LUT. The small LUT size may be attributed to memory effects inherent in a heterodyne system.

The computation capacity of conventional FPGAs is directly proportional to the size and expressive power of Look Up Table (LUT) resources. Individual LUT performance is limited by transistor switching time and power dissipation, defined by the CMOS fabrication process. In this paper we propose OLUT, an optical core implementation of LUT, which has the potential for low latency and low power computation. In addition, the use of Wavelength Division Multiplexing (WDM) allows parallel computation, which can further increase computation capacity. Preliminary experimental results demonstrate the potential for optically assisted on-chip computation.

This paper discusses the advantages of spatial light modulators (SLM) for the application of digital holography and dynamic pattern generation. Implementation demands are discussed on the example of designing an optical system for diffractive element synthesis based on LCOS SLM that is applicable not only for fringe pattern fabric structures but as well to allow for more complex patterns including polarization grating formation in polarization-sensitive liquid-crystalline polymers. We report a new method for the synthesis of digital holograms made by using the interference of laser beams that are diffracted on two amplitude and phase SLM's. Combining the original image-matrix technology with an interferometric image formed by two LCOS SLM's allows for obtaining new visual effects for hologram or diffractive elements synthesis. The proposed method for computer-generated holograms (CGH) enables one to synthesize CGH's and to simulate digital image processing techniques for 3D image reconstruction. The extension of the proposed technique of modeling diffraction on amplitude-phase masks and the possibilities of its practical application such as computer modeling of diffraction on a SLM, which consists of rectangular cells, for wavefront reconstruction are considered. Conclusions regarding the possibilities of the representation of the arbitrary fields by using the discrete matrix of elementary diffractive aperture cells for an enhancement of the iteration algorithm of hologram synthesis and phase retrieval are obtained. The results obtained by numerical and experimental means are presented together with a discussion of the limitations and further possibilities of this method.

A hologram display technique that provides speckle-free, shaded reconstructed images is proposed. A three-dimensional object consists of object points; these object points are divided into plural object point groups that are generated in a time-sequential manner. Each object point group consists of a two-dimensional (2D) array of object points that are separated so as to prevent interference among them. Each object point group is generated by displaying a 2D array of zone plates on a high-speed spatial light modulator (SLM). The amplitude distribution of the zone plates is modulated two-dimensionally based on Phong shading to shade the reconstructed images. The 2D amplitude distribution of the zone plates is decomposed into multiple binary patterns that are displayed by the SLM in a time-sequential manner. The proposed method is experimentally verified.

To evaluate the quality of microlithography result, massive aerial images are often generated for careful inspection using applications such as OPC LCC (Lithography Compaliance Check). The number of the pixels used in a 2D aerial image is in the order of 0(n * n), where n is the image resolution, which means the runtime scales in a n 2 fashion. However, most of the quality indexes such as CDs or EPE (Edge Placement Error) can be readily observed using contours only and the number of pixels in a specific contour is around O(n) in general. Therefore, there is a huge waste (at least O(n)) of both computation time and memory in most microlithography aerial image simulation tools. The question is: how to compute an image contour without explicitly generate images?. In this paper, we show that it is indeed feasible to know the image contour with an explicit image formation. The concept is to represent the image in an implicit way. In our algorithm, we utilize hierarchical region-wise function such as 2D polynomials to fit the aerial image kernels instead of using a bitmap type fit. Therefore, any LUT (Look-up-table) operation can be transformed into a polynomial look up and mathematical operations. Since there are only additive and subtractive operations during aerial image generation, we only need to apply same operations to the polynomial coefficients. Once the LUT operation is done, we have analytical forms of the light intensity in each region. To know the contour at each region, we only need to solve a local 2D polynomial equation. With these simple forms, the equation solution can be performed with great efficiency. Furthermore, due to the hierarchical structure, we can reduce the search time from O(m*m) to O(m logm), where m is the number of regions. Further speed up is achieved this way. Finally, our algorithm also does not suffer from increased feature count caused by the feature size reduction between process nodes because once the regional polynomial representation is complete, no future LUT search is necessary. Therefore, the runtime of our algorithm is significantly faster than the traditional image LUT method. The initial experiment demonstrates over hundreds of times speed up over the traditional LUT methods.