<title>Application of error diffusion in diffractive optics</title>

The error diffusion method can effectively reduce quality degradation by propagating thresholding errors to neighboring pixels in the conversion of a gray-scale hologram to a binary hologram. In previous works, the four weighting coefficients in error diffusion are mostly set as the Floyd-Steinberg coefficient, which was determined empirically and originally proposed for photograph processing. In this work, we point out that the Floyd-Steinberg coefficients can be suboptimal for hologram error diffusion binarization. Furthermore, the weighting coefficients are optimized for each different hologram adaptively. Compared with conventional coefficients, our optimized coefficients can better preserve the fidelity of a reconstructed image after a hologram is binarized.

Dot diffusion is an efficient approach which utilizes concepts of block-wise and parallel-oriented processing to generate halftones. However, the block-wise nature of processing reduces image quality much more significantly as compared to error diffusion. In this work, four types of filters with various sizes are employed in co-optimization procedures with class matrices of size 8 n 8 and 16 x 16 to improve the image quality. The optimal diffused weighting and area are determined through simulations. Many well-known halftoning methods, some of which includes direct binary search (DBS), error diffusion, ordered dithering, and prior dot diffusion methods, are also included for comparisons. Experimental results show that the proposed dot diffusion achieved quality close to some forms of error diffusion, and additionally, superior to the well-known Jarvis and Stucki error diffusion and Mese's dot diffusion. Moreover, the inherent parallel processing advantage of dot diffusion is preserved, allowing us to reap higher executing efficiency than both DBS and error diffusion.

Multiscale error diffusion is superior to conventional error diffusion methods in digital halftoning as it can eliminate directional hysteresis completely. However, there is a bias to favor a particular type of dots in the course of the halftoning process. A new multiscale error diffusion method is proposed to improve the diffusion performance by reducing the aforementioned bias. The proposed method can eliminate the pattern noise in flat regions and the boundary effect found in some other conventional multiscale error diffusion methods. At the same time, it can preserve the local features of the input image in the output. This is critical to quality, especially when the resolution of the output is limited by the physical constraints of the display unit.

The objective of this work is to reconstruct high quality gray-level images from halftone images, or the inverse halftoning process. We develop high performance halftone reconstruction methods for several commonly used halftone techniques. For better reconstruction quality, image classification based on halftone techniques is placed before the reconstruction process so that the halftone reconstruction process can be fine tuned for each halftone technique. The classification is based on enhanced 1D correlation of halftone images and processed with a three- layer back propagation neural network. This classification method reached 100 percent accuracy with a limited set of images processed by dispersed-dot ordered dithering, clustered-dot ordered dithering, constrained average, and error diffusion methods in our experiments. For image reconstruction, we apply the least-mean-square adaptive filtering algorithm which intends to discover the optimal filter weights and the mask shapes. As a result, it yields very good reconstruction image quality. The error diffusion yields the best reconstructed quality among the halftone methods. In addition, the LMS method generates optimal image masks which are significantly different for each halftone method. These optimal masks can also be applied to more sophisticated reconstruction methods as the default filter masks.

We developed a newhalftoning method, adaptive cell, which generates unstructured dots as by error diffusion method, but the produced binary image is less granular and more stable than that of error diffusion. The basic idea is covering the input image with cells which vary in size and shape depending on the input image data. Then appropriate number of pixels at the center of each cell are set on, to preserve the local average of the input image. The characteristics of the generated binary image shows that this method is suitable for high density electro photographic binary printers.

In the final optics assembly of Inertial Confinement Fusion (ICF) driver, Diffractive Optical Elements (DOEs) are applied to achieve some important functions, such as harmonic wave separation, beam sampling, beam smoothing and pulse compression etc. However, in order to optimize the system structure, decrease the energy loss and avoid the damage of laser induction or self-focusing effect, the number of elements used in the ICF system, especially in the final optics assembly, should be minimized. The multiple exposure method has been proposed, for this purpose, to fabricate BSG and CSG on one surface of a silica plate. But the multiple etch processes utilized in this method is complex and will introduce large alignment error. Error diffusion method that based on pulse-density modulation has been widely used in signal processing and computer generated hologram (CGH). In this paper, according to error diffusion method in CGH and partial coherent imaging theory, we present a new method to design coding mask of combine CSG-BSG element with error diffusion method. With the designed mask, only one exposure process is needed in fabricating combined element, which will greatly reduce the fabrication difficulty and avoid the alignment error introduced by multiple etch processes. We illustrate the designed coding mask for CSG-BSG element with this method and compare the intensity distribution of the spatial image in partial coherent imaging system with desired relief.

Several investigations has been conducted to determine the best way to improve the reconstruction of Kinoform images. Many of these investigations, however, forcused on the use of the iterative algorithm method, and little attention was paid to the use of the error-diffusion method. Most of the studies that have focused on the error-diffusion method examined its use in relation to binary-phase quantized holograms, not kinoform. Moreover, the relationship between an input object's position and the diffusion coefficients has not been reported. This is because the error-diffusion method reconstructed to separate the object as for the noise that originated in the quantization error. This paper discribes the application of a error-diffusion method that uses a complex number for the diffusion coefficient a kinoform. Results of Computer Simulation showd that the error diffusion method is superior to the iterative algorithm method for image reconstruction iterative algorithm because less processing. they also demonstrared that the restriction on the position of an object can be eased by changing the diffusion coefficient on the basis of that object's position.

Watermarking in halftone images with parity-matched error diffusion

Error diffusion (ED) and pseudorandom encoding (PRE) methods of designing Fourier transform holograms are compared in terms of their properties and the optical performance of the resulting far-field diffraction patterns. Although both methods produce a diffuse noise pattern due to the error between the desired fully complex pattern and the encoded modulation, the PRE errors reconstruct uniformly over the nonredundant band-width of the discrete-pixel spatial light modulator, while the ED errors reconstruct outside the window of the designed diffraction pattern. Combining the two encoding methods produces higher-fidelity diffraction patterns than either method produces individually. For some designs the fidelity of the ED-PRE algorithm is even higher over the entire nonredundant bandwidth than for the previously reported [J. Opt. Soc. Am. A 16, 2425 (1999)] minimum-distance-PRE algorithm.

A digital micromirror device (DMD) provides 2D- and 3D-scene reconstruction by displaying diffractive and holographic optical elements. The highest frame rates (tens of thousands of Hz) can be achieved if the displayed optical elements are binarized. Except for DMD applications, hologram binarization is useful for display creation, image encryption, information compression and storage, fast 3D printing, etc. Error diffusion is one of the most qualitative implementations of hologram binarization. In this paper, three group's weighting matrices of error diffusion are analyzed: 16 standard, eight dot and six diagonal matrices. Thus, 30 error diffusion methods were used for optically recorded off-axis digital hologram binarization. The quality of the image reconstruction from the binarized holograms was compared. Direct applications of error diffusion with large weighting matrices and dot diffusion provide the highest reconstruction quality. Seven metrics were used as the error diffusion threshold. Twelve bypass directions of error diffusion were analyzed. In addition, the joint application of Otsu threshold and complex bypass directions allows us to improve the quality of hologram binarization by 15%.

This paper proposes an adaptive error diffusion algorithm for text enhancement followed by an efficient text segmentation that uses the maximum gradient difference (MGD). The gradients are calculated along with scan lines, then the MGD values are filled within a local window to merge text segments. If the value is above a threshold, the pixel is considered as potential text. Isolated segments are then eliminated in a non-text region filtering process. After the text segmentation, a conventional error diffusion method is applied to the background, while edge enhancement error diffusion is used for the text. Since it is inevitable that visually objectionable artifacts are generated when using two different halftoning algorithms, gradual dilation is proposed to minimize the boundary artifacts in the segmented text blocks before halftoning. Sharpening based on the gradually dilated text region (GDTR) then prevents the printing of successive dots around the text region boundaries. The method is extended to halftone color images to sharpen the text regions. The proposed adaptive error diffusion algorithm involves color halftoning that controls the amount of edge enhancement using a general error filter. However, edge enhancement unfortunately produces color distortion, as edge enhancement and color difference are trade-offs. The multiplicative edge enhancement parameters are selected based on the amount of edge sharpening and color difference. Plus, an additional error factor is introduced to reduce the dot elimination artifact generated by the edge enhancement error diffusion. In experiments, the text of a scanned image was sharper when using the proposed algorithm than with conventional error diffusion without changing the background.

In this paper, we propose a method of embedding images into a speech signal. An image is embedded in the high frequency band above 16 kHz of the speech signal to be difficult to perceive for humans. In the proposed method, the image is embedded after being binarized by the error diffusion method. When the image is embedded, we apply an iterative phase restoration method to avoid noise generation. We also investigate a compensation method for an extracted image whose quality degrades due to transmission channel characteristics. Simulation and real‐environmental experiments showed that the proposed method significantly improved the quality of the extracted image on the receiver side.

The error diffusion method and the ordered dither matrix method are the most frequently used techniques for displaying shaded graphics on bi-level devices. The error diffusion method generates images with a smooth intensity variation appearance while the ordered dither matrix method generates images composed of constant intensity areas. This paper is concerned with the use of the two methods together. It is found that the resulting images have a greater contrast than that of the input image.

Flat-panel displays based on liquid crystal technology are becoming widely used in the medical imaging arena. Despite the impressive capabilities of presently-existing panels, some medical images push their boundaries. We are working with mammograms that contain up to 4800 x 6400 14-bit pixels. Stated differently, these images contain 30 mega-pixels each. In the standard environment, for film viewing, the mammograms are hung four-up, i.e. four images are located side by side. Because many of the LCD panels used for monochrome display of medical images are based on color models, the pixels of the panels are divided into sub-pixels. These sub-pixels vary in their numbers and in the degrees of independence. Manufacturers have used both spatial and temporal modulation of these sub-pixels to improve the quality of images presented by the monitors. In this presentation we show how the sub-pixel structure of some present and future displays can be used to attain higher spatial resolution than the full-pixel resolution specification would suggest while also providing increased contrast resolution. The error diffusion methods we discuss provide a natural way of controlling sub-pixels and implementing trade-offs. In smooth regions of the image contrast resolution can maximized. In rapidly-varying regions of the image spatial resolution can be favored.

We have previously developed a two-dimensional monochromatic halftoning with error diffusion neural networks (EDNs). We showed that EDNs find local minima of frequency-weighted error between a binary halftone output and corresponding smoothly varying input, an ideal framework for solving halftone problems. The advantage of the neural algorithm is that all pixel quantization decisions are computed in parallel and therefore the error diffusion process becomes un-directional and symmetric. Thus eliminates the artifacts caused by the traditional error diffusion method. This paper casts color halftoning as four related sub-problems: the first three are to compute good binary halftones for each primary color and the fourth is to simultaneously minimize frequency-weighted error in the luminosity of the composite result. We show that an EDN with a three-dimensional interconnect scheme can solve all four problems in parallel with user-adjustable emphasis on the relative importance of weighted error in luminosity. Our results show that the three-dimensional EDN matrix not only shapes the error to frequencies that human visual system (HVS) is least sensitive but also shapes the error in colors to which the HVS is least sensitive - namely it satisfies the minimum brightness variation criterion.