Variable narrowband transmission filters with a wide rejection band for spectrometry

Variable narrowband transmission filters are useful for the development of compact spectrometers. For this purpose the filter should be directly coupled to the detector and the wavelength of the transmission peak should move in one surface direction over a length of a few millimeters. To obtain both a wide measurement spectrum and high accuracy, the ratio of extreme operating wavelengths is required to be greater than 2:1 and the width of the transmission band narrower than 10 nm. A metal-dielectric variable transmission filter, with an operating range of 400-1000 nm, is proposed. The method for obtaining variable transmission filters, with dimensions of a few millimeters, is described.     

表面粗糙度测量中的高斯滤波快速算法

应用高斯函数的逼近法和冲激响应不变法,设计出用于表面粗糙度测量的高斯数字滤波器,并给出了其零相移的递归滤波算法,算法简洁,易于实现。递归计算方法的计算量小,计算效率高。适当增加滤波器节数,在不增加很多计算量的情况下,可以达到很高的精度。文中给出的滤波器例子,传输偏差大约为2％和1％,处理一次表面测量轮廓数据,在当今最普通的计算机上,滤波时间小于1s。     

Wavefront control of SiO2-based ultraviolet narrow-bandpass filters prepared by plasma ion-assisted deposition

Metal oxide layers produced by plasma ion-assisted deposition are extensively used for complex optical coatings due to the availability of materials, the high packing density of films, and the smooth surfaces. Stringent optical surface figure specifications necessary for both laser optics and precision optics require film stress to be well-controlled and surface deformation to be corrected or compensated. SiO(2)- based single-cavity UV narrow-bandpass filters were prepared by plasma ion-assisted deposition. The correlation between film stress, refractive index, deposition parameters, and postdeposition annealing was established. The film stress was calculated based on interferometric surface deformation. The refractive index and film thickness were determined by means of variable angle spectroscopic ellipsometry. The center wavelength of the filters was obtained through spectral transmission measurement. The results suggest that the wavefront distortion of the multilayer coatings is dominated by the compressive stress of the SiO(2) layers and can be controlled and corrected by the amount of plasma ion momentum transfer, substrate temperature, postdeposition annealing, and stress compensation via backside SiO(2) coating. Based on the understanding of the mechanical and optical properties, the wavefront correction technique enables us to satisfy stringent surface figure specifications.     

The effect of oblique functional gradation to transient thermal stresses in the functionally graded infinite strip

Transient thermal stresses in the strip with boundaries oblique to the functionally graded direction are studied theoretically. The transient temperature and the transient thermal stresses are derived by the use of the variable separation and the stress function method. The material properties are assumed to be exponential functions of the position along the functionally graded direction. The prescribed surface heat flux is given for temperature condition, and the initial temperature is assumed to be zero over the strip. The strip is free of surface traction for mechanical boundary condition. The numerical calculations are carried out for ZrO₂ /Ti-6Al-4V functionally graded materials. The numerical results of temperature and thermal stresses are illustrated with the lapse of time for certain oblique angles.     

Stepwise graded refractive-index profiles for design of a narrow-bandpass filter

A combination of stepwise graded refractive-index profiles and a cavity structure is used for designing narrow-bandpass filters of TiO(2)/SiO(2) multilayer films upon BK7 glass substrates. Symmetrical profiles of stepwise graded refractive indices result in high transmittance of passbands for the designed filters. The bandwidth of the narrow-bandpass filter is controlled by adjustment of parameters such as the thickness and the number of layers in the multilayer stack. This design is proposed as a new and simple method for coating synthesis of optical filters.     

An analysis of surface acoustic wave propagation in functionally graded plates with homotopy analysis method

Wave propagation in solids of functionally graded materials is difficult to analyze due to the resulting differential equations of variable coefficients associated with the spatial variation of the material properties. In this study, the homotopy analysis method is applied to obtain the solution of surface acoustic waves in a plate of functionally graded material. The variation of material properties as a polynomial of the thickness coordinate is studied along with the convergence of the solution. It is found that the homotopy analysis method is effective in solving wave propagation problems arising from functionally graded materials with differential equations of variable coefficients in particular.     

Schlieren systems with coherent illumination for quantitative measurements

Schlieren systems with a coherent light source were investigated by the Fourier optics technique. The imaging properties of the systems with various cutoff filters were studied. Systems with a graded piecewise linear filter and a Gaussian step function convolution (graded) filter are considered, demonstrating that the image can be approximated by the geometrical-optics theory of conventional schlieren systems. A nonlinear phase contribution was estimated, allowing for the measurement of strong phase objects. Within the framework of linear approximation the results are described by the phase derivative point-spread function, introduced in this paper as the schlieren point-spread function. In addition, modification of the Lopez cutoff filter is proposed, demonstrating its superiority over the piecewise linear and the Gaussian step convolution filters. Simulations of coherent schlieren imaging as well as phase derivative measurements were performed. Finally, the imaging properties of the schlieren systems with the different filters are compared.     

Love waves in a smart functionally graded piezoelectric composite structure

The propagation of Love waves in a smart functionally graded piezoelectric structure is analyzed by applying elastic wave theory. There is an additional functionally graded layer between the piezoelectric layer and the substrate in this smart structure. When the piezoelectric and dielectric constants vary individually in a functionally graded layer, the asymptotic solutions of Love waves are obtained by applying the WKB method and solving the fourth order differential equation with variable coefficients. The effects of gradient variation on the phase velocity and the coupled electromechanical factor are discussed in detail. The analysis shows that the number of vibration modes is greater than that in the non-graded layer structure, and the coupled electromechanical factor increases with the increase of piezoelectric constant graded variation. Presented results are useful for the improvement of properties of surface acoustic wave (SAW) devices.     

Axial and Extra-axial Responses in Aberrated Optical Systems with Apodizers. Optimization of the Strehl Ratio

Abstract

The effect of non-uniform transmission filters on the axial and extra-axial responses of aberrated optical systems is studied. The axial Strehl ratio (SR) is increased by varying the filter transmission function and the extra-axial SR by shifting the filter position along the axis of the optical system. It is shown that a filter which optimizes the axial SR can also improve the extra-axial SR. There are some positions of the filter for which the total results are improved. These positions are explained from the lack of radial symmetry of the wave aberration. The filters which improve the SR are also studied in terms of energy transmission.     

Design of a microwave multisine source using allpass functionsestimated in the Richards domain

In this paper a low-crest-factor microwave multisine source is developed. This is a broadband, periodic signal with a low crest factor (peak factor to effective value ratio). The design method consists of generating a pulse with a broad spectrum, amplitude filtering to get the desired power spectrum, and phase filtering for lowering the crest factor. A new technique to realize microwave phase filters is described. First, the properties of a rational allpass function in the Richards variable are examined. This enables us to estimate the coefficients using a nonlinear optimization technique, The function is realized with coupled transmission line filters. Using this general technique, a microwave multisine consisting of 20 components in the band [100 MHz, 2 GHz] is realized with a crest factor of 2     

Reflection and transmission properties of holographic mirrors and holographic Fabry-Perot filters. Ill. Holographic Fabry-Perot filters

The reflection and transmission coefficients of holographic Fabry-Perot filters (HFPF's) are derived. Angular selectivities and wavelength sensitivities of the HFPF's on transmitted light are investigated. The effects of transmission by a HFPF on the spectrum and on the coherence properties of a partially coherent incident light are also analyzed. Numerical examples are presented for the case in which the incident light is generated by a Gaussian Schell-model source.     

Energy-based effective length of the impulse response of arecursive filter

A measure for the effective length of the impulse response of a stable recursive digital filter based on accumulated energy is proposed. The new measure finds applications in several fields of digital signal processing, including estimation of the extent of attack transients for filters with dynamically varying inputs, elimination of transients in variable recursive filters, and design and implementation of linear-phase IIR systems. A general definition and a simple algorithm to evaluate it are introduced, and closed-form expressions are derived for first and second-order all-pole filters. The effect of zeros on the effective length is analyzed. An upper bound for the effective length of higher-order filters is derived using results for low-order filters, which is illustrated for classical digital lowpass filters. The use of the measure is demonstrated with examples of implementation of linear-phase IIR systems and estimation of transients in variable IIR filters     

Reliable deposition of induced transmission filters with a single metal layer

The sensitivity of an induced transmission filter (ITF) design to deposition errors is analyzed for the case of a single metal layer ITF. Theoretical knowledge of the least and most sensitive layers within the ITF design improves deposition reliability when using broadband optical monitoring of only the dielectric part of such metal-dielectric filters. Linearly variable ITFs have been successfully fabricated using this developed approach for error compensation.     

Application of optical broadband monitoring to quasi-rugate filters by ion-beam sputtering

Methods for the manufacture of rugate filters by the ion-beam-sputtering process are presented. The first approach gives an example of a digitized version of a continuous-layer notch filter. This method allows the comparison of the basic theory of interference coatings containing thin layers with practical results. For the other methods, a movable zone target is employed to fabricate graded and gradual rugate filters. The examples demonstrate the potential of broadband optical monitoring in conjunction with the ion-beam-sputtering process. First-characterization results indicate that these types of filter may exhibit higher laser-induced damage-threshold values than those of classical filters.     

Analysis of two-dimensional functionally graded rotating thick disks with variable thickness

Elasticity solutions of two-dimensional functionally graded rotating annular and solid disks with variable thickness are presented. Material properties vary through both the radial and axial directions continuously. Axisymmetric conditions are assumed for the two-dimensional functionally graded disk. The graded finite element method (GFEM) has been applied to solve the equations. The distributions of displacements and stresses in radial and axial directions for four different thickness profiles (constant, linear, concave and convex) and various power law exponents have been investigated. The achieved results show that by the use of functionally graded materials and variable thicknesses, the stresses are reduced, so a higher capability of angular velocity can be obtained. Also, using two-dimensional functionally graded materials leads to a more flexible design in comparison with conventional one-dimensional functionally graded materials. The GFEM solution of a functionally graded thin rotating annular disk has been compared with the published literature and it shows good agreement.     

Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness

A thermo elastic analysis is presented for axisymmetric rotating disks made of functionally graded material (FGM) with variable thickness. Material properties are assumed to be temperature-dependent and graded in the radial direction according to a grading index power law distribution. The temperature field considered is assumed to be uniformly distributed over the disk surface and varied in the radial direction. Semi-analytical solutions for the displacement field are given for solid disk and annular disk under free-free and fixed-free boundary conditions. The effects of the thermal field, the material grading index and the geometry of the disk on the displacement and stress fields are investigated. Results of this study emphasize on the crucial role of the temperature-dependent properties in a high temperature environment. A comparison of these results with the reported ones in the literature that is temperature-dependent versus temperature-independent suggests that a functionally graded rotating disk with concave thickness profile can work more efficiently than the one with uniform thickness irrespective of whether the material properties are assumed to be temperature-dependent or temperature-independent.     

A generic passive matching network for multiplexers

A systematic approach to matching an arbitrary number of bulk acoustic wave or surface acoustic wave filters is proposed. The filters can be modeled as capacitor networks at frequencies above and below their passbands. The generic matching network consists of a single shunt inductor (or a transmission line) and series capacitors in front of each filter.     

Reflection and transmission properties of holographic mirrors and holographic Fabry-Perot filters. I. Holographic mirrors with monochromatic light

The reflection and transmission coefficients of holographic mirrors (HM's) and holographic Fabry-Perot filters (HFPF's) are studied. The diffraction efficiencies, the angular selectivities, and the wavelength sensitivities of HM's and HFPF's and their effects on the spectrum and on the coherence properties of the incident light are investigated. The results show that holographic techniques can indeed be used to construct high-quality reflecting mirrors and Fabry-Perot filters. HM's illuminated by a monochromatic plane wave are investigated in detail. The reflection and transmission coefficients are first studied as functions of frequency (wavelength) of the incident light and also as functions of the angle of incidence. It is shown that HM's can be used as highly reflecting mirrors around their Bragg angle of incidences. Their reflectivity curves have fairly wide angular- and frequency-selectivity ranges.     

Plasmonic Color Filters for CMOS Image Sensor Applications

We report on the optical properties of plasmonic hole arrays as they apply to requirements for plasmonic color filters designed for state-of-the-art Si CMOS image sensors. The hole arrays are composed of hexagonally packed subwavelength sized holes on a 150 nm Al film designed to operate at the primary colors of red, green, and blue. Hole array plasmonic filters show peak transmission in the 40-50% range for large (>5 × 5 μm(2)) size filters and maintain their filtering function for pixel sizes as small as ～1 × 1 μm(2), albeit at a cost in transmission efficiency. Hole array filters are found to robust with respect to spatial crosstalk between pixel within our detection limit and preserve their filtering function in arrays containing random defects. Analysis of hole array filter transmittance and crosstalk suggests that nearest neighbor hole-hole interactions rather than long-range interactions play the dominant role in the transmission properties of plasmonic hole array filters. We verify this via a simple nearest neighbor model that correctly predicts the hole array transmission efficiency as a function of the number of holes.     

连续激光辐照窄带滤光片软损伤研究

利用YAG激光对ZnSe/MgF2窄带滤光片进行连续辐照研究,发现滤光片的通带发生了漂移, 严重时通带完全飘离使用波长,使其光学性能完全失效,即滤光片出现软损伤。根据实验结果和温度场分布,模拟了滤光片在连续激光辐照下的温度响应和光学性能失效过程,结果表明ZnSe材料的折射率温度梯度是引起软损伤的主要因素。