Efficient two-step digit-set-restricted modified signed-digit algorithm based on optoelectronic shared content-addressable memory

A two-step digit-set-restricted modified signed-digit (MSD) adder based on symbolic substitution is presented. In the proposed addition algorithm, carry propagation is avoided by using reference digits to restrict the intermediate MSD carry and sum digits into {(1) over bar ,0} and {0, 1}, respectively. The algorithm requires only 12 minterms to generate the final results, and no complementarity operations for nonzero outputs are involved, which simplifies the system complexity significantly. An optoelectronic shared content-addressable memory based on an incoherent correlator is used for experimental demonstration. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

A reliable phase unwrapping algorithm based on the local fitting plane and quality map

A fast and reliable phase unwrapping (PhU) algorithm, based on the local quality-guided fitting plane, is presented. Its framework depends on the basic plane-approximated assumption for phase values of local pixels and on the phase derivative variance (PDV) quality map. Compared with other existing popular unwrapping algorithms, the proposed algorithm demonstrated improved robustness and immunity to strong noise and high phase variations, given that the plane assumption for local phase is reasonably satisfied. Its effectiveness is demonstrated by computer-simulated and experimental results.

Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools

As the feature size decreases, degradation of image quality caused by wavefront aberrations of projection optics in lithographic tools has become a serious problem in the low-k1 process. We propose a novel measurement technique for in situ characterizing aberrations of projection optics in lithographic tools. Considering the impact of the partial coherence illumination, we introduce a novel algorithm that accurately describes the pattern displacement and focus shift induced by aberrations. Employing the algorithm, the measurement condition is extended from three-beam interference to two-, three-, and hybrid-beam interferences. The experiments are performed to measure the aberrations of projection optics in an ArF scanner. (C) 2006 Optical Society of America.

Analysis of optical systems with extended depth of field using the Wigner distribution function

We describe the use of a Wigner distribution function approach for exploring the problem of extending the depth of field in a hybrid imaging system. The Wigner distribution function, in connection with the phase-space curve that formulates a joint phase-space description of an optical field, is employed as a tool to display and characterize the evolving behavior of the amplitude point spread function as a wave propagating along the optical axis. It provides a comprehensive exhibition of the characteristics for the hybrid imaging system in extending the depth of field from both wave optics and geometrical optics. We use it to analyze several well-known optical designs in extending the depth of field from a new viewpoint. The relationships between this approach and the earlier ambiguity function approach are also briefly investigated. (c) 2006 Optical Society of America.

Superresolution, extended focal depth or focal shift with electrically controllable radial birefringent filter

In this paper an electrically controllable radial birefringent pupil filter is proposed. It consists of two polarizers and an improved electrically controllable optical azimuth rotator which has two lambda/4 retarders, one electro-optical crystal and one radial birefringent crystal. The evolution and distribution of polarization states of this pupil filter are discussed. The most interesting and useful advantage of such a structure is that the characteristic of transverse superresolution and axial extended focal depth or focal shift can be obtained merely by controlling the applied voltage on the electro-optical crystal. The radial birefringent crystal azimuth angle cooperating with different electrical inductive phase differences will determine the transverse and axial intensity distribution. It is shown that for particular ranges of electrical inductive phase difference it is possible to obtain transverse superresolution along with extended focal depth or with a focal shift.

Optimized phase pupil masks for extended depths of field

By properly designing a phase pupil mask to modulate or encode the optical images and then digitally restoring them, one can greatly extend the depth of field and improve image quality. The original works done by Dowski and Cathey introduce the use of a cubic phase pupil mask to extend the depth of field. The theoretical and experimental researches all verified its effectiveness. In this paper, we suggest the use of an exponential phase pupil mask to extend the depth of field. This phase mask has two variable parameters for designing to control the shape of the mask so as to modulate the wave-front more flexible. We employ an optimization procedure based on the Fisher information metric to obtain the optimum values of the parameters for the exponential and the cubic masks, respectively. A series of performance comparisons between these two optimized phase masks in extending the depth of field are then done. The results show that the exponential phase mask provide slight advantage to the cubic one in several aspects. (c) 2006 Elsevier B.V. All rights reserved.

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources. (c) 2006 Elsevier GmbH. All rights reserved.

Discussions about FFT-based two-step phase-shifting algorithm

An FFT-based two-step phase-shifting (TPS) algorithm is described in detail and implemented by use of experimental interferograms. This algorithm has been proposed to solve the TPS problem with random phase shift except pi. By comparison with the visibility-function-based TPS algorithm, it proves that the FFT-based algorithm has obvious advantages in phase extracting. Meanwhile, we present a pi-phase-shift supplement to the TPS algorithm, which combines the two interferograms and demodulates the phase map by locating the extrema of the combined fringes after removing the respective backgrounds. So combining this method and FFT-based one, one could really implement the TPS with random phase shift. Whereafter, we systematically compare the TPS with single-interferogram analysis algorithm and conventional three-step phase-shifting one. The results demonstrate that the FFT-based TPS algorithm has a satisfactory accuracy. At last, based on the polarizing interferometry, a schematic setup of two-channel TPS interferometer with random phase shift is suggested to implement the simultaneous collection of interferograms. (c) 2007 Elsevier GrnbH. All rights reserved.

Algorithm of far-field centre estimation based on phase-only matched filter

Estimation of the far-field centre is carried out in beam auto-alignment. In this paper, the features of the far-field of a square beam are presented. Based on these features, a phase-only matched filter is designed, and the algorithm of centre estimation is developed. Using the simulated images with different kinds of noise and the 40 test images that are taken in sequence, the accuracy of this algorithm is estimated. Results show that the error is no more than one pixel for simulated noise images with a 99% probability, and the stability is restricted within one pixel for test images. Using the improved algorithm, the consumed time is reduced to 0.049 s.

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions. (c) 2006 Optical Society of America.

Extended effective medium model for refractive indices of thin films with oblique columnar structure

The refractive indices of thin films, containing dielectric and voids in an oblique columnar structure, are modeled by extended effective medium in the quasi-static limit. The dielectric function is shown to be strongly dependent on the angle of incidence and on the columnar orientation for p-polarized light. This model is applied to model ZrO2 thin films with oblique columnar structures and the computed results, with the Maxwell Garnett, the Bragg-Pippard, and the Bruggeman formalisms, have been given. (c) 2004 Elsevier B.V. All rights reserved.

Novel method for design of surface relief guided-mode resonant gratings at normal incidence

We demonstrate that the surface relief guided-mode resonant gratings with specified central wavelength and FWHM in the visible wavelength range can be designed by analyzing the complex poles of Reflectance and transmission coefficient matrix algorithm (RTCM), a variant of S-matrix propagation algorithm proposed for calculation of multilayer gratings. In addition, FWHM is computed with couple-mode (CM) theory of resonant gratings which is firstly extended by Norton et al. in calculation of waveguide grating. Furthermore, the side band reflections of the filter can be reduced to less than 5% in the visible wavelength with the antireflection (AR) design technique widely used in the thin-film field. (C) 2008 Elsevier B.V. All rights reserved.