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

A kind of spectrum recovering method being applicable to Fourier transform spectrometer

Technical field

The invention belongs to FT-NIR spectra signal transacting field, be specifically related to a kind of spectrum recovering method being applicable to Fourier transform spectrometer.

Background technology

FT-NIR spectra technology utilizes the physical relation between interference signal and spectral signal, by carrying out Fourier transform to interference signal, gets final product the spectral intensity information of rejuvenation target.Under normal circumstances, the object of fast fourier transform process is the data of uniform sampling.Because image-forming principle, system are debug or the reason such as system scan collection, usually there is the nonlinear problem of sampling in the interferogram data that Fourier transform spectrometer obtains, and the dispersion characteristics of optical element make optical path difference relevant with wavelength, namely there is the problem of dispersion non-linearity simultaneously.Therefore, the impact that Fourier transform needs to consider nonuniform sampling and dispersion non-linearity is carried out on interference data.For sampling nonlinear situation, disclose the method for several nonlinear sampling error correction in the document delivered, comprise interferogram double sampling method, optical path difference Shift Method and Fast Inhomogeneous Fourier transform NUFFT method etc.But it is non-linear with the spectrum recovering in dispersion non-linearity situation that these methods effectively can not solve sampling.

Summary of the invention

The object of the present invention is to provide a kind of spectrum recovering method being applicable to Fourier transform spectrometer, spectrum recovering problem that is non-linear and dispersion non-linearity of sampling can be solved simultaneously.

The technical solution realizing the object of the invention is: a kind of spectrum recovering method being applicable to Fourier transform spectrometer, and it is characterized in that, step is as follows:

Step 1: the interference signal collected by Fourier transform spectrometer is arranged in order, forms light intensity matrix I:

Wherein, n is the sequence number of interference data, n=0,1,2,3..., N-1, and wherein N is 512 or 1024.

Step 2: utilize light intensity matrix I, tectonic transition matrix S:

Wherein, k is the sequence number of wave number σ, k=0,1,2,3..., K-1, wherein

Step 3: be multiplied with light intensity matrix I by transformation matrix S, obtains the data B restoring spectrum:

B＝S·I(3)

Wherein,

The spectral intensity that B (σ (k)) is wave number σ (k), wave number σ (k)=σ _min+ k δ σ, σ _minfor the smallest wavenumber of restoring, δ σ is spectral resolution.

In described step 2, the element S (k, n) in described transformation matrix S, computing method are as follows:

Wherein, n is sampling location sequence number, i.e. the sequence number of the interference data of light intensity matrix I, n=0,1,2,3..., N-1; for optical path difference function Δ (x, σ) is to the partial derivative of sampling location x; Sampling location x is the function about sampling location sequence number n; for the discrete light path difference function about sampling location sequence number n and wave number σ; A (n, σ) is triangle apodizing function; for phase distortion penalty function.

Wherein Δ _maxfor the maximum optical path difference of system scan;

Compared with prior art, its remarkable advantage is in the present invention: (1) can solve the spectrum recovering problem under sampling nonlinear situation.

(2) also can solve the spectrum recovering problem in dispersion non-linearity situation simultaneously.

Accompanying drawing explanation

Fig. 1 is interferogram data spectrum recovering method of the present invention.

Fig. 2 is the image that in the embodiment of the present invention 1, Fourier transform spectrometer collects.

Fig. 3 is relative light intensity and wavelength curve figure in embodiments of the invention 1.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Composition graphs 1, a kind of spectrum recovering method being applicable to Fourier transform spectrometer, step is as follows

Step 1: the interference signal collected by Fourier transform spectrometer is arranged in order, forms light intensity matrix I:

Wherein, n is the sequence number of interference data, n=0,1,2,3..., N-1, and wherein N is 512 or 1024.

Step 2: utilize light intensity matrix I, tectonic transition matrix S:

Step 2-1: calculate triangle apodizing function A (n, σ) and phase distortion penalty function

Wherein, n is sampling location sequence number, i.e. the sequence number of the interference data of light intensity matrix I, n=0,1,2,3..., N-1; Δ _maxfor the maximum optical path difference of system scan; for the discrete light path difference function about sampling location sequence number n and wave number σ;

Wherein for optical path difference function Δ (x, σ) is to the partial derivative of sampling location x; Sampling location x is the function about sampling location sequence number n.

Step 2-2: according to triangle apodizing function A (n, σ) and phase distortion penalty function determine transformation matrix element S (k, n), computing method are as follows:

Wherein, k is the sequence number of wave number σ, k=0,1,2,3..., K-1, wherein K>=0; Wave number σ (k)=σ _min+ k δ σ, σ _minfor the smallest wavenumber of restoring, δ σ is spectral resolution.

Step 2-3: according to transformation matrix element S (k, n), obtains transformation matrix S:

Step 3: be multiplied with light intensity matrix I by transformation matrix S, obtains the data B restoring spectrum:

B＝S·I(3)

Wherein,

The spectral intensity that B (σ (k)) is wave number σ (k).

Embodiment 1

Fourier transform spectrometer to interfere based on birefringent polarizing:

Be applicable to a spectrum recovering method for Fourier transform spectrometer, step is as follows:

Utilize the Fourier transform spectrometer of interfering based on birefringent polarizing to detect two incident lasers, gather piece image, as shown in Figure 2, the interference signal of the image collected by Fourier transform spectrometer is arranged in order, and forms light intensity matrix I:

Step 1: the interference signal collected by Fourier transform spectrometer is arranged in order, forms light intensity matrix I:

Wherein, n is the sequence number of interference data, n=0,1,2,3..., N-1, and wherein N is 1024.

Step 2: utilize light intensity matrix I, tectonic transition matrix S:

Step 2-1: calculate apodizing function A (n, σ) and phase distortion penalty function

Wherein, n is sampling location sequence number, i.e. the sequence number of the interference data of light intensity matrix I, n=0,1,2,3..., N-1; Δ _maxfor the maximum optical path difference of system scan; for the discrete light path difference function about sampling location sequence number n and wave number σ;

Wherein for optical path difference function Δ (x, σ) is to the partial derivative of sampling location x; Sampling location x is the function about sampling location sequence number n;

Step 2-2: according to apodizing function A (n, σ) and phase distortion penalty function determine transformation matrix element S (k, n), computing method are as follows:

Wherein, k is the sequence number of wave number σ, k=0,1,2,3..., K-1, wherein K>=0; Wave number σ (k)=σ _min+ k δ σ, σ _minfor the smallest wavenumber of restoring, δ σ is spectral resolution.

Step 2-3: according to transformation matrix element S (k, n), obtains transformation matrix S:

Step 3: be multiplied with light intensity matrix I by transformation matrix S, obtains the data B restoring spectrum, as shown in Figure 3:

B＝S·I(3)

Wherein,

The spectral intensity that B (σ (k)) is wave number σ (k).

Composition graphs 2 and Fig. 3, adopt the spectrum recovering method being applicable to Fourier transform spectrometer of the present invention, both effectively can solve the spectrum recovering problem under sampling nonlinear situation, also can solve the spectrum recovering problem in dispersion non-linearity situation simultaneously.

Claims (2)

1. be applicable to a spectrum recovering method for Fourier transform spectrometer, it is characterized in that, step is as follows:

Step 1: the interference signal collected by Fourier transform spectrometer is arranged in order, forms 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 the sequence number of interference data, n=0,1,2,3..., N-1, and wherein N is 512 or 1024;

Step 2: utilize light intensity matrix I, tectonic transition matrix S:

Wherein, k is the sequence number of wave number σ, k=0,1,2,3..., K-1, wherein

Step 3: be multiplied with light intensity matrix I by transformation matrix S, obtains the data B restoring spectrum:

B＝S·I(3)

Wherein,

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

The spectral intensity that B (σ (k)) is wave number σ (k), wave number σ (k)=σ _min+ k δ σ, σ _minfor the smallest wavenumber of restoring, δ σ is spectral resolution.

2. the spectrum recovering method being applicable to Fourier transform spectrometer according to claim 1, is characterized in that: in step 2, the element S (k, n) in described transformation matrix S, and computing method are as follows:

Wherein, n is sampling location sequence number, i.e. the sequence number of the interference data of light intensity matrix I, n=0,1,2,3..., N-1; for optical path difference function Δ (x, σ) is to the partial derivative of sampling location x; Sampling location x is the function about sampling location sequence number n; for the discrete light path difference function about sampling location sequence number n and wave number σ; A (n, σ) is triangle apodizing function; for phase distortion penalty 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 _maxfor the maximum optical path difference of system scan;