CN105444889A - Spectrum restoration method suitable for Fourier transformation spectrograph - Google Patents

Abstract

The invention relates to a spectrum restoration method suitable for a Fourier transformation spectrograph. The spectrum restoration method includes the following steps that: interference signals acquired by the Fourier transformation spectrograph are arranged sequentially, so as to form a light intensity matrix; a transformation matrix is constructed according to the light intensity matrix; and the transformation matrix is multiplied by an interference light intensity matrix, so that spectrum intensity data can be obtained. With the spectrum restoration method suitable for the Fourier transformation spectrograph of the invention adopted, problems existing in spectrum restoration of an interference type spectrum measurement system under a sampling nonlinearity and dispersion nonlinearity conditions can be solved simultaneously.

Description

Spectrum restoration method suitable for Fourier transform spectrometer

Technical Field

The invention belongs to the field of Fourier transform spectrum signal processing, and particularly relates to a spectrum restoration method suitable for a Fourier transform spectrometer.

Background

The fourier transform spectroscopy technique recovers the spectral intensity information of a target by fourier transforming an interference signal using the physical relationship between the interference signal and the spectral signal. In general, the fast fourier transform process is performed on uniformly sampled data. Due to the imaging principle, system adjustment or system scanning acquisition and the like, the interferogram data obtained by the fourier transform spectrometer usually has the problem of non-linearity of sampling, and the dispersion characteristic of the optical element causes the optical path difference to be related to the wavelength, namely, the problem of non-linearity of dispersion exists at the same time. Therefore, fourier transforming the interference data needs to take into account the effects of non-uniform sampling and dispersion non-linearity. For the sampling nonlinearity, several nonlinear sampling error correction methods are disclosed in published documents, including interferogram subsampling, optical path difference substitution, and fast non-uniform fourier transform NUFFT. However, these methods cannot effectively solve spectrum restoration under the nonlinear sampling and dispersion conditions.

Disclosure of Invention

The invention aims to provide a spectrum recovery method suitable for a Fourier transform spectrometer, which can simultaneously solve the spectrum recovery problem of sampling nonlinearity and dispersion nonlinearity.

The technical solution for realizing the purpose of the invention is as follows: a spectrum recovery method suitable for a Fourier transform spectrometer is characterized by comprising the following steps:

step 1: sequentially arranging interference signals collected by a Fourier transform spectrometer to form a light intensity matrix I:

where N is a serial number of the interference data, and N is 0,1,2,3, N-1, where N is 512 or 1024.

Step 2: using the light intensity matrix I, a transformation matrix S is constructed:

wherein K is the number of wave number σ, K is 0,1,2,3, K-1, wherein

And step 3: multiplying the transformation matrix S by the light intensity matrix I to obtain data B of the restored spectrum:

B＝S·I(3)

wherein,

b (σ (k)) is a wave number σ (k)Spectral intensity, wave number σ (k) to σ_min+kσ，σ_minTo recover the minimum wavenumber, σ is the spectral resolution.

In step 2, the calculation method of the element S (k, n) in the transformation matrix S is as follows:

wherein N is a sampling position serial number, that is, a serial number of interference data of the light intensity matrix I, and N is 0,1,2,3., N-1;a partial derivative of the optical path difference function Δ (x, σ) with respect to the sampling position x; the sampling position x is a function of the sampling position number n;is a discrete optical path difference function related to the sampling position serial number n and the wave number sigma; a (n, σ) is a trigonometric apodization function;is a phase distortion compensation function.

Wherein Δ_maxThe maximum optical path difference scanned by the system;

compared with the prior art, the invention has the remarkable advantages that: (1) the spectrum recovery problem under the nonlinear sampling condition can be solved.

(2) Meanwhile, the spectrum recovery problem under the dispersion nonlinearity condition can be solved.

Drawings

FIG. 1 is a diagram of a spectral reconstruction method for interferogram data according to the invention.

Fig. 2 is an image collected by a fourier transform spectrometer in embodiment 1 of the present invention.

FIG. 3 is a graph of relative light intensity versus wavelength in example 1 of the present invention.

Detailed Description

The present invention is described in further detail below with reference to the attached drawing figures.

Referring to fig. 1, a spectrum recovery method for fourier transform spectrometer includes the following steps

Step 1: sequentially arranging interference signals collected by a Fourier transform spectrometer to form a light intensity matrix I:

where N is a serial number of the interference data, and N is 0,1,2,3, N-1, where N is 512 or 1024.

Step 2: using the light intensity matrix I, a transformation matrix S is constructed:

step 2-1: calculating the trigonometric apodization function A (n, sigma) and the phase distortion compensation function

Wherein N is a sampling position serial number, that is, a serial number of interference data of the light intensity matrix I, and N is 0,1,2,3., N-1; delta_maxThe maximum optical path difference scanned by the system;is a discrete optical path difference function related to the sampling position serial number n and the wave number sigma;

whereinA partial derivative of the optical path difference function Δ (x, σ) with respect to the sampling position x; the sample position x is a function of the sample position number n.

Step 2-2: based on the trigonometric apodization function A (n, sigma) and the phase distortion compensation functionDetermining transformation matrix elements S (k, n), and calculating according to the following method:

wherein K is the number of the wave number sigma, K is 0,1,2,3, K-1, and K is not less than 0; wave number sigma (k) sigma_min+kσ，σ_minTo recover the minimum wavenumber, σ is the spectral resolution.

Step 2-3: obtaining a transformation matrix S according to transformation matrix elements S (k, n):

and step 3: multiplying the transformation matrix S by the light intensity matrix I to obtain data B of the restored spectrum:

B＝S·I(3)

wherein,

b (σ (k)) is the spectral intensity of the wave number σ (k).

Example 1

Taking a fourier transform spectrometer based on birefringence polarization interference as an example:

a spectrum recovery method suitable for a Fourier transform spectrometer comprises the following steps:

detecting two incident lasers by using a Fourier transform spectrometer based on birefringence polarization interference, acquiring an image, and sequentially arranging interference signals of the image acquired by the Fourier transform spectrometer to form a light intensity matrix I as shown in figure 2:

step 1: sequentially arranging interference signals collected by a Fourier transform spectrometer to form a light intensity matrix I:

where N is a serial number of the interference data, and N is 0,1,2,3, N-1, where N is 1024.

Step 2: using the light intensity matrix I, a transformation matrix S is constructed:

step 2-1: calculating apodization function A (n, sigma) and phase distortion compensation function

Wherein N is a sampling position serial number, that is, a serial number of interference data of the light intensity matrix I, and N is 0,1,2,3., N-1; delta_maxThe maximum optical path difference scanned by the system;is a discrete optical path difference function related to the sampling position serial number n and the wave number sigma;

whereinA partial derivative of the optical path difference function Δ (x, σ) with respect to the sampling position x; the sampling position x is a function of the sampling position number n;

step 2-2: according to apodization function A (n, sigma) and phase distortion compensation functionDetermining transformation matrix elements S (k, n), and calculating according to the following method:

wherein K is the number of the wave number sigma, K is 0,1,2,3, K-1, and K is not less than 0; wave number sigma (k) sigma_min+kσ，σ_minTo recover the minimum wavenumber, σ is spectral resolutionAnd (4) rate.

Step 2-3: obtaining a transformation matrix S according to transformation matrix elements S (k, n):

and step 3: multiplying the transformation matrix S by the light intensity matrix I to obtain data B of the restored spectrum, as shown in fig. 3:

B＝S·I(3)

wherein,

b (σ (k)) is the spectral intensity of the wave number σ (k).

With reference to fig. 2 and fig. 3, the spectrum recovery method for the fourier transform spectrometer according to the present invention can effectively solve the spectrum recovery problem under the nonlinear sampling condition, and can also solve the spectrum recovery problem under the nonlinear dispersion condition.

Claims (2)

1. A spectrum recovery method suitable for a Fourier transform spectrometer is characterized by comprising the following steps:

step 1: sequentially arranging interference signals collected by a Fourier transform spectrometer to form a light intensity matrix I:

$I=\left(I_{n1}\right)=\left[\begin{array}{c}I\left(0\right)\\ I\left(1\right)\\ \·\\ \·\\ \·\\ I(N-1)\end{array}\right]---\left(1\right)$

wherein N is a serial number of the interference data, and N is 0,1,2,3, N-1, wherein N is 512 or 1024;

step 2: using the light intensity matrix I, a transformation matrix S is constructed:

wherein K is the number of wave number σ, K is 0,1,2,3, K-1, wherein

And step 3: multiplying the transformation matrix S by the light intensity matrix I to obtain data B of the restored spectrum:

B＝S·I(3)

wherein,

$B=\left[\begin{array}{c}B\left(\mathrm{\σ}\right(0))\\ B\left(\mathrm{\σ}\right(1))\\ \·\\ \·\\ \·\\ B\left(\mathrm{\σ}\right(K-1))\end{array}\right]---\left(4\right)$

b (σ (k)) is the spectral intensity of the wave number σ (k), where σ (k) is σ_min+kσ，σ_minTo recover the minimum wavenumber, σ is the spectral resolution.

2. The method for spectrum recovery for a fourier transform spectrometer as recited in claim 1, wherein: in step 2, the element S (k, n) in the transformation matrix S is calculated as follows:

wherein N is a sampling position serial number, that is, a serial number of interference data of the light intensity matrix I, and N is 0,1,2,3., N-1;a partial derivative of the optical path difference function Δ (x, σ) with respect to the sampling position x; the sampling position x is a function of the sampling position number n;is a discrete optical path difference function related to the sampling position serial number n and the wave number sigma; a (n, σ) is a trigonometric apodization function;is a phase distortion compensation function;

$A(n,\mathrm{\σ})=\left\{\begin{array}{cc}1-|\widetilde{\mathrm{\Δ}}(n,\mathrm{\σ})/{\mathrm{\Δ}}_{max}& for|\widetilde{\mathrm{\Δ}}(n,\mathrm{\σ})\≤{\mathrm{\Δ}}_{max}\\ 0& for|\widetilde{\mathrm{\Δ}}(n,\mathrm{\σ})>{\mathrm{\Δ}}_{max}\end{array}\right.,n=0,1,2,3,...N-1---\left(6\right)$

wherein Δ_maxThe maximum optical path difference scanned by the system;