The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the refle...The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.展开更多
This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to c...This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).展开更多
If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show tha...If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.展开更多
In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the p...This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the phase retrieval problem can be transformed into the low rank matrix recovery problem and then be solved by convex programming known as PhaseLift.Thus,stable guarantees for such problem have been gradually established for measurements sampled from sufficiently random distribution,for instance,the standard normal distribution.Further,exact recovery results have also been set up for masked Fourier measurements which are closely related to practical applications.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11604115the Educational Commission of Jiangsu Province of China under Grant No 17KJA460004the Huaian Science and Technology Funds under Grant No HAC201701
文摘The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.
文摘This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).
基金This research is supported by a grant of NSF of P.R.China.
文摘If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.
文摘In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
基金Supported by the National Natural Science Foundation of China(11531013,U1630116)the fundamental research funds for the central universities.
文摘This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the phase retrieval problem can be transformed into the low rank matrix recovery problem and then be solved by convex programming known as PhaseLift.Thus,stable guarantees for such problem have been gradually established for measurements sampled from sufficiently random distribution,for instance,the standard normal distribution.Further,exact recovery results have also been set up for masked Fourier measurements which are closely related to practical applications.
