Sensitivity Analysis of Grating Parameter Estimation (original) (raw)
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Spectrophotometric method for measuring the groove depth of calibration reflection gratings
2012
A method for measuring the groove depth of calibration gratings is proposed which is based on measuring the spectral dependence of the the zero-order reflection diffraction efficiency. The errors of the method are determined by three main factors: the shift of the maxima of the spectrum due to the wall slope of the grating grooves, the error in setting the wavelength of the spectrophotometer, and the divergence of the light beam in the setup. It is shown theoretically that the measurement error is in the range of 0.25-1%, depending on the fabrication technology of the grating and measuring equipment. The method was tested experimentally using commercial calibration gratings. The range of applicability of the method is discussed in terms of the geometrical parameters of the microstructure of reflection gratings and the characteristics of the spectrophotometer used.
Advanced optimization algorithms for grating based sensors: A comparative analysis
Optik, 2018
This study explores the use of advanced optimization algorithms for determining optimum parameters for grating based sensors. Shift in wavelength in the resonance bands is always accompanied by reduction in loss of the attenuation peaks due to changing coupling coefficients in long period grating sensors. Maximization of strength of the rejection bands is considered as the objective function to enhance the range of detection for both amplitude and wavelength based demodulation schemes. Effect of grating period, length of the grating and peak induced index change, on core cladding mode resonances has been analyzed in detail. Transmission loss in resonance bands and shift in the resonance band are strong functions of the grating period, length of grating, peak induced-index change, order of the cladding mode and fiber parameters. The results of effect of optimization algorithms on the convergence and fitness values of the objective functions are reported. Transmission spectra obtained by analytical model has been verified with the experimental results. Maximum transmission loss of ≈76 dB has been achieved with optimized grating parameters. Effect of variation of the optimized parameters by 10% on the strength of rejection band has been analyzed.
Enhanced resolution light scattering analyzer for curved gratings – ELSA/CG-S
International Conference on Space Optics — ICSO 2022
The knowledge of the bi-directional scattering distribution function (BSDF) of an optical component is an import requirement for the design and assessment of high-performance optical instruments. However, precise BSDF measurement with high resolution close to the specular beam can be very challenging and require sophisticated instrumentation. In this paper, we present a newly developed scatterometer, the "Enhanced Resolution Light Scattering Analyzer for Curved Gratings (single detector axis)"-ELSA/CG-S which is designed specifically to measure the BSDF of curved optical components with a very high resolution not only close to the specular direction, but throughout the whole angular measurement range with an instrument signature that can compete with the top of the class of current commercially available instruments. The distinguishing feature of the instrument is the use of a high-resolution silicon sCMOS imaging detector which enables fast acquisition times and provides access to a two-dimensional section of the BSDF around the main detection plane of the instrument with an out-of-plane FoV of about ±0.6°. In the following, we will describe the general design of the instrument and explain the measures that have been taken to enable a very low stray light signature with the chosen detection scheme. After this, we will assess the instruments capabilities and present measurements of the instrument signature and BRDF measurements of plane and curved diffraction gratings with high groove densities. These measurements will also demonstrate the additional value that is provided by using an imaging detector. All measurements will be compared to results obtained with ESTEC's commercial CASI scatterometer from The Scatter Works, that represent the current state of the art.
Cornell University - arXiv, 2017
This technical note aims at presenting both theoretical and practical aspects of the diffraction grating ONELAB models 1. The model grating2D.pro applies to so-called mono-dimensional grating, i.e. structures having one direction of invariance as shown in Fig. 0.1(a). Various geometries and materials can be handled or easily added. The two classical polarization cases, denoted here E (also denoted TE in the literature) and H (or TM), are addressed. These are scalar problems where a scalar Helmholtz equation is solved. The model grating3D.pro applies to possibly skewed crossed gratings, which are 3D structures with two directions of periodicity as shown in Fig. 0.1(b). The output of both models consist in a full energy balance of the problem computed from the field maps. This is a vector problem where a vector Helmholtz equation is solved. Finally, the conical incidence (2D geometry, 3D incidence, see Fig. 0.1(c)) is treated thanks to a mixed formulation. These models are based on free the open source pieces of software Gmsh [Geu+09], GetDP [Dul+98] and their interface ONELAB. For more technical insights and a more complete bibliography, the reader is invited to refer to [Dem+07; Dem+09; Dem+10]. Figure 0.1: Scalar diffraction by a mono-dimensional grating (2D). (b) Vector diffraction by a crossed grating (3D). (c) Vector diffraction by a mono-dimensional grating (2.5D).
Optik, 1990
A close examination is carried out of the amplitude and phases of the light diffracted from two types of dielectric square-wave surface relief grating, for TE polarized incident light. Results are calculated using the rigorous modal method, the convergence of which is described. The variations of the results with the angle of incidence of the input beam for several periods and thicknesses, are discussed. An attempt is made to indicate general trends for the variation of these parameters. A sampling rule of thumb, for angular incidence, is suggested.
Metrology, Inspection, and Process Control for Microlithography XXXIV, 2020
The paper represents a comparison of simulated light scattering of the near and far fields of subwavelength grating at various wavelengths. By quantifying and comparing the scattered near and far fields of multiple grating parameters to the nominal parameter based scattered field, the sensitivity to the change of grating parameters is determined. The wavelength influence on the near field is analyzed by applying a plane wave at certain angle of incidence and the far field diffraction patterns are simulated by applying coherent focused light (conical incidence). The paper analyses how each wavelength affects the sensitivity to the change of the height and the sidewall angle of a subwavelength grating.
A Onelab model for the parametric study of mono-dimensional diffraction gratings
2017
This document aims at presenting both theoretical and practical aspects of the grating_2D Onelab model (available at http://onelab.info/wiki/Diffraction\_grating). This model applies to so-called mono-dimensional grating, i.e. structures having one direction of invariance. Various geometries and materials can be handled or easily added. The two classical polarization cases, denoted here E// and H//, are addressed. The output consists in a full energy balance of the problem computed from the field maps. This model is based on free the GNU softwares Gmsh, GetDP and their interface Onelab.
Photopolarimeter based on planar grating diffraction
Journal of The Optical Society of America A-optics Image Science and Vision, 1993
A division-of-amplitude photopolarimeter (DOAP) is described that employs a diffraction grating in the conventional spectrometer orientation with the grating grooves normal to the plane of incidence. Four coplanar diffracted orders are used for polarimetric analysis to determine all four Stokes parameters of incident light simultaneously and virtually instantaneously (with the speed being determined solely by the photodetectors and their associated electronics); a fifth order is used for alignment by autocollimation or by use of a positionsensing quadrant detector. To sensitize the instrument for the +45° and -45° azimuths of incident linearly polarized light and for the handedness of incident circular polarization (i.e., for the third and fourth Stokes parameters), we insert two linear polarizers in two diffracted orders with their transmission axes inclined at appropriate angles with respect to the plane of incidence. The calibration and testing of an instrument of this type that uses an Al-coated 600-groove/mm holographic grating at 632.8-nm wavelength are reported as an example.