Point diffraction interferometer (PDI) has become the most promising measurement tool since it is firstly proposed by Linnik and its key component used to generate the reference wave can be called as the reference wave source (RWS). A new RWS based on the silicon nitride (SiN) waveguide is now proposed, aimed at providing a spherical reference wave with high NA and high accuracy. Simulation results show that the PV and the RMS of the reference wave generated by the waveguide RWS are 2.86×10-4λ (λ=532nm) and 4.83×10-5λ respectively, and the maximum light transmittance of this RWS could reach 24%. In addition, the NA of the reference wave reaches up to 0.58.
It is necessary to fit the discrete sampling value of the optical element surface obtained by measuring equipment, because the results of fitting are useful for manufacturing and optical design. The commonly used fitting methods are X-Y polynomial approximation, Zernike polynomial approximation and radial basis function (RBF) approximation. Compared with others, radial basis function is more suitable to fit the complex optical surface. However, the further improvement of fitting accuracy and cost are limited by the fixed shape parameter of the classic RBF approximation. In this paper, we propose the sparse radial basis function approximation with spatially variable shape parameters to fit discretely sampled optical surfaces. Our main purpose is to improve fitting accuracy and to reduce computational cost. Then, we analyze the impact of the spatial distribution of RBF nodes on fitting. Finally, we compare the accuracy and cost between the classic RBF approximation and the sparse RBF approximation with spatially variable shape parameters by fitting various complex surface.
Point diffraction interferometer (PDI) uses the nearly ideal spherical wave front diffracted by the pinhole as the reference, thus its measurement accuracy depends mainly on the quality of the diffraction wave front. However, aberrations and numerical aperture (NA) of the microscope objective (micro-objective) used to illuminate the pinhole in PDI can affect the quality of the diffraction wave front and further reduce the measurement accuracy of PDI. It’s necessary to analyze the influence of the micro-objective on the quality of the diffraction wave front detailly. In this paper, numerical simulation of the propagation of the incident light through the pinhole is carried out with the method of the finite difference time domain (FDTD), vector diffraction integral and vector diffraction theory. Then energy transmittance, homogeneity and deformation are obtained, which are used to evaluate the influence of the micro-objective on the quality of the diffraction wave front. These simulation results will provide a reference for rational selection of the micro-objective parameters, contributing to establish PDI system with best measurement accuracy.
In order to achieve the precision of sub-nanometer and even higher of surface testing, this paper presents a highprecision point diffraction interferometric system for high-NA spherical surface testing. The point diffraction mask as a key component is designed and analyzed in detail. The circularly polarized light is used as the light source of interferometer system to calibrate the oblique-reflection wavefront aberration introduced by the point diffraction mask. Besides, the calibration of adjustment error is a critical issue in the test of high-numerical-aperture spherical surface, and it is hard to separate the high-order aberrations introduced by wavefront defocus from the mearsured data. We present a novel calibration method based on the Zernike aberration coefficients introduced by wavefront tilt and defocus. This novel method can be carried out without knowing the actual adjustment error amount and just needs the numerical aperture of testing wavefront to solve the high-order aberrations. With the proposed calibration method, the requirement for accuracy of the mechanism and experience of operator is lowered. Experiment shows the accuracy of calibrated system is better than 0.001λ rms, which can realize the high-precision testing.
As a high accurate measurement for wavefront metrology, the point diffraction interferometer(PDI) has been developed to overcome the accuracy limitation in traditional interferometers enabling the measurement precision in the order of a subnanometer. The PDI employs a nearly ideal spherical wavefront generated by pinhole diffraction as the reference wavefront, and is expected to be a powerful tool for high-precision optical testing. The diffraction reference wavefront is the key factor which determines the achievable precision in the measurement. In order to achieve high measurement accuracy precise characterization of the properties of diffraction wave is required. The structure of the pinhole functions as a cylinder waveguide and the fields in the pinhole are described as sums over waveguide modes whose behavior are determined by the interaction between the sidewall and the light. The pinhole functions as a cylindrical waveguide, in the way it determines the light field in the hole and the properties of the diffraction wave. In the paper, we make clear the physical mechanism of pinhole diffraction. The vector diffraction theory and the field equivalence principle are discussed. The field in the pinhole is analyzed according to the waveguide theory, and the waveguide effect on pinhole diffraction transmittance is discussed. Our results provide an important theoretical reference for design of the PDI system.
This paper discusses the pulse signal of a novel opto-mechanical zeroth-order grating transducer based on an anomalous diffraction phenomenon, Wood’s type anomaly and its corresponding tolerance analysis. In this device, tiny changes in the displacement of the nanostructured grating elements lead to a dramatic increase or decrease of the optical reflection amplitude. With this special feature, this structure is ideal to measure very small displacement. Unexpectedly, the original sinusoidal signal of the device develops into a new signal form, i.e. pulse signal with the decrease of the air gap between two layers of gratings. Thus the sensitivity of the structure is improved 8 times higher, as the slope of the pulse signal, namely 2.5%/nm, i.e. 0.65dB/nm, is 8 times higher than that of the original signal form, namely 0.3%/nm, i.e. 0.03dB/nm. However, this device is very sensitive to parameters including wavelength, period, duty ratio, air gap as well as thickness of the gratings. Thus, in this paper the performance of the structures with different parameter settings is analyzed and optimized through rigorous coupled wavelength analysis (RCWA) and 3-D finite difference time domain (FDTD) method. All the calculated data enables us to apply the structure into fields required for different sensitivities with different values of grating parameters and thus broadens the further usage of such novel structure. In addition, a synthetic tolerance analysis of the pulse signal is conducted and indicates the possibility of achieving an actual device with the highest slope superior to 0.5%/nm is close to 85% and the possibility that the highest slope of an actual device falls in the interval ranging from 1.0%/nm to 2.0%/nm is 64%. All the simulated data enables us to get a better understanding of the tolerance of the pulse signal and a guidance of successful realization of an actual device.
This paper discusses the analysis and optimization of a novel optomechanical structure based on a Wood’s type anomaly, in which tiny changes in the spacing of the nanostructured grating elements lead to a dramatic increase or decrease of the optical reflection amplitude. With this special feature, this structure is an ideal sensor component to observe very small amount of relative motion. This device is very sensitive to light source wavelength, the period and the width of the grating. Here, we analyze the performance of the structure with different parameters and incident light of different wavelengths through 3-D Finite Difference Time Domain method (FDTD). Simulation gives out the respective influence of those parameters and the optimized structure designs for different wavelengths which are most possible to fabricate with current surface micromachining processing similar to that used for the fabrication of polysilicon MEMS. The calculated data enables us to apply the structure into fields required for different sensitivities and dynamic ranges with different grating designs and thus broadens the further usage of such novel structure.
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