Birefringent filter synthesis by use of a digital filter design algorithm

We present an efficient method for designing birefringent filters comprising a number of birefringent sections with equal length and arbitrary orientation between two polarizers and for producing a specified spectral response in transmission. The method uses a digital filter design algorithm (i.e., the Remez algorithm) to determine an optimal polynomial approximation to obtain a specified finite impulse response, and a layer-peeling algorithm to calculate the filter structure parameters. The design procedure is demonstrated for a 14-section bandpass filter with sidelobes below -40 dB. The influence of errors in length and orientation of the birefringent sections on the filter's spectral response is also discussed.     

Multispectrum,spatially addressable polarization interference filter

We review current synthesis techniques for generating and improving birefringent filters. The relationship between wave-plate orientation and the resulting spectral output is shown to be that of a simple Fourier transform. By using this relationship and starting from the fan Solc configuration, we easily generated plate orientations providing lower sidelobe levels and improved finesse. We outline a method by which filters can be constructed to provide from 0 to 100% of the desired passband in a continuous fashion. Such a filter can be stacked to allow rapid control of any number of passbands and is shown, as an example in a novel design employing super-twisted nematic liquid crystal elements, to control a maximum of three color bands.     

Sidelobe cancellation technique for achieving high rejection in SAW filters

A new technique called sidelobe cancellation technique (SCT) to achieve high stopband rejection in SAW filters is described, for varying requirements of shape factor and sidelobe levels, by using an eigenfunction approach. Cosine series functions with improved sidelobe levels are employed. Each design is characterized by the order of the cosine series and the number of functions used to obtain a particular shape factor and rejection. Limited trimming of shape factor also can be achieved in each design. The filters described here are compared with the Kaiser window filter and are found to be efficient. Measured response of a prototype SAW filter using the approach given in this paper is plotted, and it is in good agreement with the simulated response     

Design of adjustable superresolving filters based on birefringent crystals

A two-mode adjustable superresolving filter based on a birefringent filter is proposed. This kind of filter has superresolution in two modes of adjustment. One is rotation of the binary pupil filter on the optical axis of the system and the other is the tilt of the filter away from the pupil plane on axis parallel or perpendicular to the optical axis of the crystal. The filters act as complex amplitude filters in the former mode, and as pure phase filters in the latter. By analyzing two superresolving parameters, we obtain the optimal design parameters that ensure a large field of view, a large superresolving range, and a high setting accuracy. This kind of filter can provide more flexibility in practical applications.     

Code optimization for direct sequence spread spectrum and SAW-matched filter implementation

This paper introduces a new optimization algorithm for the minimization of the time sidelobes of the correlation function of a pseudonoise (PN) sequence by applying dynamic weighting to the sequence. The resulting optimized time sidelobe level sequences are to be used in direct sequence spread spectrum (DS-SS) systems with digital modulations such as BPSK, DPSK, QPSK, etc. The new optimization algorithm starts with a PN sequence. It first optimizes the correlation time sidelobes for the case where the consecutive data bits are identical (11 or 00). It then optimizes the correlation time sidelobes for the case of alternating consecutive data bits (10 or 01). The suppressed time sidelobe level sequences are derived by iterating these algorithms alternately starting from the initial PN sequence. The derived suppressed time sidelobe sequences show excellent correlation characteristics when compared to conventional PN sequences such as maximal length sequences, Gold sequences and Barker codes. Surface acoustic wave (SAW) devices were used to implement the optimized time sidelobe level sequences in a matched filter pair. The design of the apodized SAW-matched filters and their predicted second order effects are presented. The experimental results for the SAW-matched filters for the optimized time sidelobe level sequences derived from a Barker code were found to be in good agreement with the theoretical predictions from this new algorithm.     

Comparison of antireflection surfaces based on two-dimensional binary gratings and thin-film coatings

A comparison of antireflection surfaces based on the two-dimensional binary gratings and thin-film coatings is presented. First, a two-dimensional hybrid binary grating is proposed and analyzed by use of a vector-based implementation of the rigorous coupled-wave analysis method. The optimum parameters of the structure are determined and the effects that changing them have on spectral characteristics of the structure are studied. Then this structure is compared with multilayer thin-film antireflection filters. These filters are designed by genetic algorithm and needle methods, which are powerful methods for multilayer filter design. The comparison results show that the sensitivity of the grating to changes in the incident wavelength is high. However, a reflectance of the order of 10(-3)% at the design wavelength can be achieved. The sensitivity of designed antireflection thin-film filters to wavelength changes is lower, however, and the minimum achievable reflectance is higher.     

Design of binary long-period fiber grating filters by the inverse-scattering method with genetic algorithm optimization

An approach is presented to the design of binary long-period fiber grating (LPFG) filters based on the Gel'fand-Levitan-Marchenko (GLM) inverse-scattering method and genetic algorithm optimization. The nonuniform coupling strength of the binary grating can be realized by varying the local duty ratio. A coupled-mode theory combined with the Poisson sum formula for treating the binary index perturbation is developed for the application of the GLM synthesis method. Since the coupled-mode theory, which smears out the discrete coupling nature, can be regarded only as an approximation to the modeling of a binary LPFG, we use instead the transfer-matrix model to analyze the coupling behavior of a nonuniform binary LPFG. Based on the synthesized grating patterns from the GLM method, a real-coded genetic algorithm with the transfer-matrix model is used to compensate for the discrepancies resulting from use of the coupled-mode theory and to optimize the design. We exemplify the above procedure by designing a flatband LPFG filter and a high-visibility all-fiber Mach-Zehnder filter.     

Implementation of broadband low-sidelobe beamforming in time domain

In modern active and passive sonar systems, broadband beamforming for acoustic arrays is widely used to suppress unwanted interference and to detect target signals of interest. A broadband low sidelobe beamforming scheme in time domain is proposed in this paper. The first step of this scheme is to delay the outputs of each element in the acoustic array by a tapped-delay-line (TDL) to accomplish the integer part of the time delay need to form a beam. Then, finite impulse response (FIR) digital filters are used to implement the fractional part of the time delay. The weighting coefficients for all array elements at different frequencies to realize the low sidelobe beams are also implemented with the FIR digital filters. Finally, the outputs of the digital filters are summed up to yield the time domain beam output. The design of low sidelobe beam pattern and that of the FIR digital filters are two crucial technical issues in this beamforming procedure. The low sidelobe beams of each sub-band are designed using the optimized beam synthesis approach based on the principle of MVDR beamforming. An improved adaptive approach are used for the design of FIR digital filters, and the design requirements of these filters were specified by the weights of low sidelobe beams of each sub-band over the broad frequency band. Results of computer simulation for a twelve-element arc array show that the beamforming scheme is very effective in forming low sidelobe broadband beam.     

斜变滤波器频域加窗对图像重建的影响

斜变滤波器的性能对图像重建有重要的影响,频域加窗设计法是其主要的设计方法。设计了4种经典的加窗滤波器：RL滤波器、SL滤波器、Hamming窗滤波器和指数窗滤波器。从单位冲激响应和频率响应2个方面分析了这4种滤波器的特性;从频率响应和旁瓣衰减速度2个方面比较了这4种滤波器。理论分析与仿真结果表明：指数窗滤波器的震荡噪声最小;SL滤波器整体最优。     

Nearly-off-axis transmissivity of Solc birefringent filters

The characteristics of light propagating near the axis of a birefringent filter are studied. A generalized formulation to describe the nearly-off-axis transmissivity of a Solc birefringent filter is derived. On this basis, the polarization conoscopic figures of Solc filters with different numbers of birefringent plates are simulated. Furthermore the variation of spectral transmission with angle of incidence is analyzed, and the field-of-view transmissivity and the spectral transmissivity averaged with respect to the spread of incident light are given. Primary experiments for verification are also demonstrated.     

Continuous radial superresolution filters with large focal depth

A new set of continuous superresolution filters is proposed which exhibits a radial superresolution performance with an extended depth of focus in an optical system by properly choosing the design parameters. Numerical simulation results of the performance parameters of the superresolution gain, the radial central core size, the Strehl ratio, the side-lobe factor and the depth of focus with different design parameters for the optimized patterns are displayed. We also give a design example for this kind of filter characterized by a birefringent element inserted between two parallel polarizers. This kind of filter would be useful in fields such as optical data storage systems.     

Design techniques for SAW filters using slanted finger interdigital transducers

This paper describes useful design techniques for wide-band linear phase SAW filters using slanted finger interdigital transducers (SFITs): to increase stop band attenuation, to flatten the pass band response, and to draw SFIT patterns for photo-masks. In order to increase stop band attenuation, a withdrawal-weighted SFIT is employed. A combination of a withdrawal-weighted SFIT and an unweighted SFIT provides good stop band responses, even though the number of finger pairs is small. In order to achieve a desired amplitude response in the pass band, an aperture-weighting technique for divided channels of SFITs is presented. A design method for drawing SFIT patterns for photo-masks is also described. A linear-phase SAW filter using SFITs with a 50% fractional bandwidth is designed and fabricated on 128 degrees y-x LiNbO(3). A sidelobe suppression of 40 dB and a 3 dB to 40 dB shape factor of 1.12 were realized. Good agreement between theoretical and experimental results is obtained.     

The use of linear programming for the design of SAW filters andfilterbanks

A linear programming algorithm is proposed for designing surface acoustic wave (SAW) filters or filterbanks with arbitrary amplitude and phase responses. A modified sampling theorem representation is employed for the transducer frequency responses which allows the number of independent variables to be minimized without degrading the filter characteristics. The method can also be used as part of an iterative procedure to generate optimal corrections for second order effects such as diffraction and circuit loading. A simplified algorithm for this procedure is given, and the method is illustrated with theoretical and experimental data from a three channel contiguous SAW filterbank design. Although the method given in this paper is formulated primarily for SAW filters, it is equally applicable to FIR digital filter design     

Unconstrained correlation filters

A mathematical analysis of the distortion tolerance in correlation filters is presented. A good measure for distortion performance is shown to be a generalization of the minimum average correlation energy criterion. To optimize the filter's performance, we remove the usual hard constraints on the outputs in the synthetic discriminant function formulation. The resulting filters exhibit superior distortion tolerance while retaining the attractive features of their predecessors such as the minimum average correlation energy filter and the minimum variance synthetic discriminant function filter. The proposed theory also unifies several existing approaches and examines the relationship between different formulations. The proposed filter design algorithm requires only simple statistical parameters and the inversion of diagonal matrices, which makes it attractive from a computational standpoint. Several properties of these filters are discussed with illustrative examples.     

Modelling high-order filters in a transient microwave circuit simulator

Transient simulation of narrowband bandpass filters used in microwave circuits is challenging because of matrix ill-conditioning. Here, such filters are modelled as the equivalent discrete-time form developed using a bilinear z-transform. The technique has been implemented in a general purpose transient circuit simulator and validated using a 1.7 GHz 5-section coaxial filter with a 0.9% bandwidth.     

模式识别相关滤波器设计的峰值锐化技术

提出一种锐化相关峰的滤波器设计方法，把初始滤波函数乘上一个因子，实现相关输出的拉普拉斯运算，从而得到更税利的相关峰和更好的识别效果。     

Representation of birefringent filters by directly composed 4 × 4 matrices

The interaction of an obliquely incident plane wave with an arbitrary birefringent plane structure can be described exactly by a so-called 4 × 4 layer matrix. However, its formation is rather complex, and therefore a simplified method to set up this matrix is proposed. It is deduced from the boundary conditions for the tangential components of the E and the H fields at the interfaces of the birefringent layer and the phase shifts of the four waves within the layer between both interfaces. The refractive indices and the directions of polarization of the four waves are calculated from the well-known dispersion relation in the principal coordinate system and a coordinate transformation. Transmission curves of Lyot filters made of uniaxial and biaxial materials are calculated in the cases of plane waves of finite or infinite lateral extension that are incident under Brewster's angle upon the filter positioned outside or within a laser resonator. The special examples given for a quartz filter and a YAlO(3) filter are characterized by a high selectivity within a broad bandwidth if Fabry-Perot effects can be neglected. Transmission curves of a quartz filter were verified by measurements.     

Nonpolarizing and polarizing filter design

We describe a nonpolarizing filter design at oblique incidence and a polarizing filter design at normal incidence that use a uniaxially anisotropic layer. The phase thicknesses and the optical admittances of the layers are compensated for by the birefringent properties of a thin film at oblique incidence. This concept can be applied to the design of nonpolarizing bandpass and edge filters at oblique incidence and of polarizing beam splitters at normal incidence. Besides, the dependence of narrow-bandpass filters on normal incidence is discussed.     

A Solid-State Reference Waveform Standard

A solid-state reference waveform filter has been developed which uses the Maxwell-Wagner capacitor effect. This filter is realized in a stripline configuration with a lossy dielectric consisting of a thick (5-?m) layer of SiO2 on Si. The equivalent circuit of this filter is equivalent to that for previously developed filters which used a lossy liquid dielectric. A preliminary design has been completed and a filter fabricated for which the design characteristic impedance, 38 ?, and transition duration (rise time), 300 ps, agree with measured values to within 2 and 17 percent, respectively. The temperature dependence of the filter transition duration has been estimated from the temperature dependence of the filter conductance to be about 1 percent/° C.     

Filter for biomedical imaging and image processing

Image filtering techniques have numerous potential applications in biomedical imaging and image processing. The design of filters largely depends on the a priori, knowledge about the type of noise corrupting the image. This makes the standard filters application specific. Widely used filters such as average, Gaussian, and Wiener reduce noisy artifacts by smoothing. However, this operation normally results in smoothing of the edges as well. On the other hand, sharpening filters enhance the high-frequency details, making the image nonsmooth. An integrated general approach to design a finite impulse response filter based on Hebbian learning is proposed for optimal image filtering. This algorithm exploits the interpixel correlation by updating the filter coefficients using Hebbian learning. The algorithm is made iterative for achieving efficient learning from the neighborhood pixels. This algorithm performs optimal smoothing of the noisy image by preserving high-frequency as well as low-frequency features. Evaluation results show that the proposed finite impulse response filter is robust under various noise distributions such as Gaussian noise, salt-and-pepper noise, and speckle noise. Furthermore, the proposed approach does not require any a priori knowledge about the type of noise. The number of unknown parameters is few, and most of these parameters are adaptively obtained from the processed image. The proposed filter is successfully applied for image reconstruction in a positron emission tomography imaging modality. The images reconstructed by the proposed algorithm are found to be superior in quality compared with those reconstructed by existing PET image reconstruction methodologies.