Optical intrinsically fuzzy mathematical morphology for gray-scale image processing

Intrinsically fuzzy morphological erosion and dilation are extended to a total of eight operations that have been formulated in terms of a single morphological operation--biased dilation. Based on the spatial coding of a fuzzy variable, a bidirectional projection concept is proposed. Thus, fuzzy logic operations, arithmetic operations, gray-scale dilation, and erosion for the extended intrinsically fuzzy morphological operations can be included in a unified algorithm with only biased dilation and fuzzy logic operations. To execute this image algebra approach we present a cellular two-layer processing architecture that consists of a biased dilation processor and a fuzzy logic processor. (C) 1996 Optical Society of America

Morphological ordered gray-scale erosion for optical image processing

An ordered gray-scale erosion is suggested according to the definition of hit-miss transform. Instead of using three operations, two images, and two structuring elements, the developed operation requires only one operation and one structuring element, but with three gray-scale levels. Therefore, a union of the ordered gray-scale erosions with different structuring elements can constitute a simple image algebra to program any combined image processing function. An optical parallel ordered gray-scale erosion processor is developed based on the incoherent correlation in a single channel. Experimental results are also given for an edge detection and a pattern recognition. (C) 1998 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(98)00306-7].

Coma measurement using a PSM and transmission image sensor

As feature size decreases, especially with the use of resolution enhancement technique, requirements for the coma aberrations in the projection lenses of the lithographic tools have become extremely severe. So, fast and accurate in situ measurement of coma is necessary. In the present paper, we present a new method for characterizing the coma aberrations in the projection lens using a phase-shifting mask and a transmission image sensor. By measuring the image positions at multiple NA and partial coherence settings, we are able to extract the coma aberration. The simulation results show that the accuracy of coma measurement increases approximately 20% compared to the previous straightforward measurement technique. (c) 2005 Elsevier GmbH. All rights reserved.

Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings

In this paper, we propose a novel method for measuring the coma aberrations of lithographic projection optics based on relative image displacements at multiple illumination settings. The measurement accuracy of coma can be improved because the phase-shifting gratings are more sensitive to the aberrations than the binary gratings used in the TAMIS technique, and the impact of distortion on displacements of aerial image can be eliminated when the relative image displacements are measured. The PROLITH simulation results show that, the measurement accuracy of coma increases by more than 25% under conventional illumination, and the measurement accuracy of primary coma increases by more than 20% under annular illumination, compared with the TAMIS technique. (c) 2007 Optical Society of America.

A high accuracy image sensor for sinusoidal phase-modulating interferometry

We proposed a high accuracy image sensor technique for sinusoidal phase-modulating interferometer in the field of the surface profile measurements. It solved the problem of the CCD's pixel offset of the same column under two adjacent rows, eliminated the spectral leakage, and reduced the influence of external interference to the measurement accuracy. We measured the surface profile of a glass plate, and its repeatability precision was less than 8 nm and its relative error was 1.15 %. The results show that it can be used to measure surface profile with high accuracy and strong anti-interference ability. (C) 2007 Elsevier GmbH. All rights reserved.

A high-speed image sensing technique with adjustable frame rate based on an ordinary CCD

In the sinusoidal phase modulating interferometer technique, the high-speed CCD is necessary to detect the interference signals. The reason of ordinary CCD's low frame rate was analyzed, and a novel high-speed image sensing technique with adjustable frame rate based on ail ordinary CCD was proposed. And the principle of the image sensor was analyzed. When the maximum frequency and channel bandwidth were constant, a custom high-speed sensor was designed by using the ordinary CCD under the control of the special driving circuit. The frame rate of the ordinary CCD has been enhanced by controlling the number of pixels of every frame; therefore, the ordinary of CCD can be used as the high frame rate image sensor with small amount of pixels. The multi-output high-speed image sensor has the deficiencies of low accuracy, and high cost, while the high-speed image senor with small number of pixels by using this technique can overcome theses faults. The light intensity varying with time was measured by using the image sensor. The frame rate was LIP to 1600 frame per second (f/s), and the size of every frame and the frame rate were adjustable. The correlation coefficient between the measurement result and the standard values were higher than 0.98026, and the relative error was lower than 0.53%. The experimental results show that this sensor is fit to the measurements of sinusoidal phase modulating interferometer technique. (c) 2007 Elsevier GmbH. All rights reserved.