CN102519597B - Phase correction apodization method for Fourier transform spectrometer - Google Patents

Abstract

The invention relates to a phase correction apodization method for a Fourier transform spectrometer. In the method, by weighting a zero-crossing single-sided interferogram, the errors caused by utilizing data near a zero optical path difference point in the calculation process twice are reduced. The method has better weighting effects than an apodization method provided by Mertz, the accuracy of a recovery spectrum can be ensured, and the calculation complexity is effectively reduced simultaneously. After the zero-crossing single-sided interferogram is weighted by the apodization method provided by the invention, the sum of products of light intensity of two corresponding points with the same optical path difference in a short double side of the zero-crossing single-sided interferogram and respective corresponding twiddle factors is an average value of the sum of the products of the light intensity of the two corresponding points and respective corresponding twiddle factors before weighting. Thus the calculation errors brought by asymmetry of the interferogram are reduced, and a more precise recovery spectrum is obtained.

Description

A kind of phase correction apodization method for Fourier transform spectrometer

Technical field

The present invention relates to the phase correction field of spectrometer, relate in particular to a kind of phase correction apodization method for Fourier transform spectrometer.

Background technology

At present, Fourier transform spectrometer, is by detecting interference signal, then interferogram being carried out to the instrument that Fourier transform is measured spectrum.Ideally, interferogram is symmetrical about the zero optical path difference point, but owing to detecting, interference signal is difficult to from zero optical path difference, beam-splitting board exists absorption loss and unevenness, electronic circuit error etc., cause interferogram asymmetry and phase error to a certain degree to occur, reduce detection sensitivity, and cause line distortion.Therefore, the correction of phase error is the important step that the Fourier trasform spectroscopy analyser calculates.In the product method phase error correction, near the data zero optical path difference point of zero passage Single sided interferogram in field are calculated twice, produce certain error.

The error produced in order to reduce this phenomenon, a kind of feasible technical scheme is: the apodizing function and the zero passage Single sided interferogram that with Mertz, propose multiply each other, and 2 interference strength sums that make in short bilateral interferogram to have the same light path difference equal the amplitude of single-point.Apodizing function is as follows:

$y=\left\{\begin{array}{cc}0& x<-L\\ \frac{x+L}{2L}& \left|x\right|\&le;L\\ 1& x>L\end{array}\right.$

Wherein, x is optical path difference, and L is the maximum optical path difference of short bilateral interferogram.

Yet prior art has the deficiency of following several aspects:

In the product method phase error correction, when adopting the zero passage Single sided interferogram to carry out spectrum recovering, short bilateral interferogram data are reused twice, cause that the curve of spectrum becomes smoothly, resolution decline.In order to eliminate this phenomenon, the method for weighting that generally adopts Mertz to propose, be multiplied by different coefficients to short bilateral interferogram each point, and the interference light intensity sum of 2 that makes to have the same light path difference keeps the amplitude of single-point.

When interferogram, during about zero optical path difference point almost symmetry, this apodization can reach the weighted effect of expection.But, when phase error exceeds certain scope, the sin component is excessive, there is serious asymmetry in interferogram, now adopt this method of weighting not only can not offset the asymmetric error of calculation of bringing, can increase the weight of asymmetry on the contrary, do not reach the weighted effect of expection.This situation is along with the minimizing of zero crossing data volume becomes more obvious.

As can be seen here, the apodizing function that uses Mertz to propose has obvious shortcoming to the method for zero passage Single sided interferogram weighting: when the asymmetry of interferogram is more serious, this method of weighting not only can not be offset the asymmetric error of calculation of bringing, can increase the weight of asymmetry on the contrary, not reach the weighted effect of expection.And along with this phenomenon of the minimizing of zero crossing data volume becomes more obvious.

Therefore, adopt which kind of apodization, the more serious interferogram weighting to asymmetry, reduce the error of calculation that the asymmetry of interferogram is brought, and become problem demanding prompt solution.

Summary of the invention

The object of the invention is to overcome the defect of above-mentioned technical matters, a kind of phase correction apodization method for Fourier transform spectrometer is proposed, after with this apodization, the weighting of zero passage Single sided interferogram being processed, the sum of products of light intensity and each self-corresponding twiddle factor that makes to have in zero passage Single sided interferogram short bilateral two corresponding point of same light path difference is the weighting mean value of the sum of products of the light intensity of these two corresponding point and each self-corresponding twiddle factor before.Thereby the error of calculation that the asymmetry that reduces interferogram is brought, obtain more high-precision reduction spectrum.

According to the present invention, a kind of phase correction apodization method for Fourier transform spectrometer is provided, it is characterized in that comprising the following steps:

Step (one) obtains interferogram light distribution I (x) by interferometer measurement;

Step (two) proposes step apodizing function A ₁(x):

$A_1\left(x\right)=\left\{\begin{array}{cc}0& -{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\&le;x<-L_2\\ 0.5& -L_2\&le;x\&le;L_2\\ 1& L_2<x\&le;L_1\end{array}\right.---\left(1\right)$

Wherein, x is optical path difference, L ₁, L ₂it is respectively the maximum optical path difference of zero passage Single sided interferogram and short bilateral interferogram;

Step (three) is at optical path difference-L ₂～L ₁in scope, interferogram is carried out to the monolateral sampling of zero passage, sampling interval is T, at optical path difference-L ₁～-L ₂between to the monolateral sampled data zero padding of zero passage, zero padding is spaced apart T, then adopts step apodizing function A ₁(x) the monolateral sampled data of the zero passage after zero padding is cut to toe, cutting toe light distribution afterwards is I ₁(x):

$I_1\left(x\right)=\left\{\begin{array}{cc}0& x<{-L}_2\\ I_s\left(x\right)\&CenterDot;A_1\left(x\right)& -L_2\&le;x\&le;L_1\end{array}\right.---\left(2\right)$

Wherein, I _s(x) be the light distribution of the monolateral sampling of zero passage.

According to a preferred embodiment of the invention, after wherein cutting toe, the mean value of the light intensity that the sum of products that makes to have in zero passage Single sided interferogram short bilateral the light intensity of two corresponding point of same light path difference and each self-corresponding twiddle factor is these two corresponding point before weighting and the sum of products of each self-corresponding twiddle factor.

According to a preferred embodiment of the invention, the method also further comprises: step (four) is at optical path difference-L ₂～L ₂in scope, interferogram is carried out to short bilateral sampling, sampling interval is T, then to short bilateral sampled data at optical path difference-L ₁～-L ₂and L ₂～L ₁between carry out zero padding, zero padding is spaced apart T, obtains new light distribution I after zero padding ₂(x) be:

$I_2\left(x\right)=\left\{\begin{array}{cc}0& -{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\&le;x<-L_2\\ I_d\left(x\right)& -L_2\&le;x\&le;L_2\\ 0& L_2<x\&le;L_1\end{array}\right.---\left(3\right)$

Wherein, I _d(x) be the light distribution of short bilateral sampling.

According to a preferred embodiment of the invention, the method also further comprises: step (five) is according to the odd-even symmetry of discrete Fourier transformation, light distribution sequence I ₁and I (x) ₂(x) respectively as real part and the imaginary part of one group of imaginary number sequence, form one group of sequence of complex numbers f ₀(x), be expressed as follows

f ₀(x)＝I ₁(x)+i·I ₂(x) (4)

Then adopt triangle apodizing function A ₂(x) this sequence of complex numbers is cut to toe, the sequence of complex numbers f (x) cut after toe is:

f(x)＝f ₀(x)·A ₂(x) (5)

Wherein, A ₂(x) be the triangle apodizing function, be expressed as follows:

$A_2\left(x\right)=\left\{\begin{array}{cc}\frac{x+L_1}{L_1}& -{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\&le;x\&le;0\\ \frac{L_1-x}{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}& 0<x\&le;L_1\end{array}\right.---\left(6\right)$

According to a preferred embodiment of the invention, the apodizing function that wherein adopted, can adopt cosine apodizing function or Gauss's apodizing function to substitute the triangle apodizing function.

According to a preferred embodiment of the invention, the method also further comprises: step (six) is carried out Fast Fourier Transform (FFT) to sequence of complex numbers f (x), sequence of complex numbers F (k) after being converted, character according to the symmetrical sequence of complex numbers of conjugation, sequence of complex numbers F (k) is divided into to sequence of complex numbers C (k) and D (k) two parts, wherein

$C\left(k\right)=\frac{F\left(k\right)+F^{*}(-k)}{2}=a_1\left(k\right)+{\mathrm{ib}}_1\left(k\right),k=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;N---\left(7\right)$

$D\left(k\right)=\frac{F\left(k\right)-F^{*}(-k)}{2i}=a_2\left(k\right)+{\mathrm{ib}}_2\left(k\right),k=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;N---\left(8\right)$

Wherein, a ₁(k), b ₁(k) be respectively real part and the imaginary part of C (k) mid point k, a ₂(k), b ₂(k) be respectively real part and the imaginary part of D (k) mid point k, N is light distribution I ₁(x) always count, carry out phase correction to sequence of complex numbers F (k), just can obtain having put the light intensity of k after phase correction, and after bearing calibration and correction, the light distribution of some k is as follows:

$B_0\left(k\right)=\frac{a_1\left(k\right)\&CenterDot;a_2\left(k\right)+b_1\left(k\right)\&CenterDot;b_2\left(k\right)}{\sqrt{a_2^2\left(k\right)+b_2^2\left(k\right)}}---\left(9\right)$

According to a preferred embodiment of the invention, the method also further comprises: step (seven) is carried out normalization to light intensity.

According to a preferred embodiment of the invention, wherein normalization specifically comprises:

Suppose light distribution B ₀(k) maximal value is a, and minimum value is b, to B ₀(k) adopt following method to carry out normalized, just can obtain normalized light distribution B (k):

$B\left(k\right)=\frac{B_0\left(k\right)-b}{a-b}---\left(10\right)$

According to the relation of count in formula (11) k and wave number v, just can be converted to the distribution of light intensity about wave number v to light distribution B (k);

$v=\frac{2\&CenterDot;k}{T\&CenterDot;N}---\left(11\right)$

Wherein, T is sampling interval.

According to another embodiment of the present invention, provide a kind of phase correction apodization method for Fourier transform spectrometer, it is characterized in that comprising the following steps:

Interferogram is carried out to the monolateral sampling of zero passage and short bilateral sampling;

The monolateral sampled data zero padding of zero passage and step are cut to toe and process, to short bilateral sampled data zero padding, make counting of the monolateral and short bilateral sampled data of zero passage identical and about the zero optical path difference symmetry;

The monolateral sampled data of zero passage after above-mentioned processing and short bilateral sampled data, respectively as real part and the imaginary part of imaginary number, are formed to one group of sequence of complex numbers, this sequence of complex numbers is carried out to triangle and cut toe and process, then carry out Fast Fourier Transform (FFT);

According to the character of the symmetrical sequence of complex numbers of conjugation, carry out phase correction, obtain spectral distribution accurately.

According to a preferred embodiment of the invention, wherein said triangle is cut toe and is processed and can cut that toe is processed or Gauss cuts toe and processes to substitute with cosine.

Result of study shows, the apodization proposed with the present invention is to the weighting of zero passage Single sided interferogram, reduced because near data zero optical path difference point in computation process are utilized the error caused for twice, the apodization proposed than Mertz has better weighted effect, can guarantee to restore the accuracy of spectrum, effectively reduce computation complexity simultaneously.

Although describe the present invention in connection with some exemplary enforcements and using method hereinafter, it will be appreciated by those skilled in the art that and be not intended to the present invention is limited to these embodiment.Otherwise, be intended to cover all substitutes, correction and the equivalent be included in the defined spirit of the present invention of appending claims and scope.

Other advantage of the present invention, purpose and feature will be set forth to a certain extent in the following description, and to a certain extent, based on will be apparent to those skilled in the art to investigating hereinafter, or can be instructed from the practice of the present invention.Purpose of the present invention and other advantage can be passed through following instructions, claims, and in accompanying drawing, the specifically noted structure realizes and obtains.

The accompanying drawing explanation

In order to make the purpose, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing, the present invention is described in further detail, wherein:

Fig. 1 is apodization and inverting spectrum process flow diagram;

The short bilateral sampling interferogram of Fig. 2;

Fig. 3 is the spectrogram that adopts the inverting of step apodizing function;

Fig. 4 is for adopting respectively the most advanced and sophisticated enlarged drawing of spectrogram part of step apodizing function and the inverting of Mertz apodizing function.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.Fig. 1 shows technical scheme of the present invention: at first interferogram is carried out to the monolateral sampling of zero passage and short bilateral sampling, to the monolateral sampled data zero padding of zero passage and utilize the present invention to carry out step and cut toe and process (cutting toe multiplies each other with it with apodizing function), to short bilateral sampled data zero padding, make counting of the monolateral and short bilateral sampled data of zero passage identical and about the zero optical path difference symmetry; The monolateral sampled data of zero passage after next processing and short bilateral sampled data are respectively as real part and the imaginary part of imaginary number, be combined into one group of sequence of complex numbers, this sequence of complex numbers is cut to toe and processed (triangle or cosine or Gauss cut toe and process), then carried out Fast Fourier Transform (FFT); Then according to the character of the symmetrical sequence of complex numbers of conjugation, carry out the spectrum phase correction, obtain spectral distribution accurately.

It should be noted that embodiment according to phase correction apodization method for Fourier transform spectrometer of the present invention is as just example, but the invention is not restricted to this embodiment.

Next, describe with reference to the accompanying drawings the specific embodiment of the present invention in detail:

One, at first by interferometer measurement, obtain interferogram light distribution I (x);

Two, step apodizing function A is proposed ₁(x):

$A_1\left(x\right)=\left\{\begin{array}{cc}0& -{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\&le;x<-L_2\\ 0.5& -L_2\&le;x\&le;L_2\\ 1& L_2<x\&le;L_1\end{array}\right.---\left(1\right)$

Wherein, x is optical path difference, L ₁, L ₂it is respectively the maximum optical path difference of zero passage Single sided interferogram and short bilateral interferogram.

Three, at optical path difference-L ₂～L ₁in scope, interferogram is carried out to the monolateral sampling of zero passage, sampling interval is T, at optical path difference-L ₁～-L ₂between to the monolateral sampled data zero padding of zero passage, zero padding is spaced apart T, then the monolateral sampled data of zero passage after adopting the step apodizing function to zero padding is cut toe, the mean value of the light intensity that the sum of products that makes to have in zero passage Single sided interferogram short bilateral the light intensity of two corresponding point of same light path difference and each self-corresponding twiddle factor is these two corresponding point before weighting and the sum of products of each self-corresponding twiddle factor.For instance, such as two corresponding point with same light path difference are respectively A, B, the product of the twiddle factor that the light intensity that after the product+weighting of the twiddle factor that the light intensity that after weighting, A is ordered so is corresponding with the A point, B is ordered and B point are corresponding=(product of the twiddle factor that the front B of product+weighting of the twiddle factor that the light intensity that before weighting, A order and A point the are corresponding light intensity of ordering and B point are corresponding)/2.Wherein, the twiddle factor that difference is corresponding is different.Cut the light distribution I after toe ₁(x) be

$I_1\left(x\right)=\left\{\begin{array}{cc}0& x<{-L}_2\\ I_s\left(x\right)\&CenterDot;A_1\left(x\right)& -L_2\&le;x\&le;L_1\end{array}\right.---\left(2\right)$

Wherein, I _s(x) be the light distribution of the monolateral sampling of zero passage.

Four, at optical path difference-L ₂～L ₂in scope, interferogram is carried out to short bilateral sampling, sampling interval is T, then to short bilateral sampled data at optical path difference-L ₁～-L ₂and L ₂～L ₁between carry out zero padding, zero padding is spaced apart T, obtains new light distribution I ₂(x) be:

$I_2\left(x\right)=\left\{\begin{array}{cc}0& -{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\&le;x<-L_2\\ I_d\left(x\right)& -L_2\&le;x\&le;L_2\\ 0& L_2<x\&le;L_1\end{array}\right.---\left(3\right)$

Wherein, I _d(x) be the light distribution of short bilateral sampling.

Five, according to the odd-even symmetry of discrete Fourier transformation, light distribution sequence I ₁and I (x) ₂(x) respectively as real part and the imaginary part of one group of imaginary number sequence, form one group of sequence of complex numbers f ₀(x), be expressed as follows

f ₀(x)＝I ₁(x)+i·I ₂(x) (4)

Then adopt triangle apodizing function (adopting other apodizing functions such as cosine function, Gaussian function also to be fine) to be cut toe to this sequence of complex numbers, the sequence of complex numbers f (x) cut after toe is:

f(x)＝f ₀(x)·A ₂(x) (5)

Wherein, A ₂(x) be the triangle apodizing function, be expressed as follows:

$A_2\left(x\right)=\left\{\begin{array}{cc}\frac{x+L_1}{L_1}& -{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\&le;x\&le;0\\ \frac{L_1-\mathrm{<figure-callout\; id="1"\; label="x\; L"\; filenames="HSA00000635731500041.png"\; state="\{\{state\}\}">x</figure-callout>}}{L_{}}& 0<x\&le;L_1\end{array}\right.---\left(6\right)$

Six, sequence of complex numbers f (x) is carried out to Fast Fourier Transform (FFT), sequence of complex numbers F (k) after being converted, character according to the symmetrical sequence of complex numbers of conjugation, be divided into sequence of complex numbers C (k) and D (k) two parts to sequence of complex numbers F (k), wherein

$C\left(k\right)=\frac{F\left(k\right)+F^{*}(-k)}{2}=a_1\left(k\right)+{\mathrm{ib}}_1\left(k\right),k=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;N---\left(7\right)$

$D\left(k\right)=\frac{F\left(k\right)-F^{*}(-k)}{2i}=a_2\left(k\right)+{\mathrm{ib}}_2\left(k\right),k=\mathrm{1,2,3}\&CenterDot;\&CenterDot;\&CenterDot;N---\left(8\right)$

Wherein, a ₁(k), b ₁(k) be respectively real part and the imaginary part of C (k) mid point k, a ₂(k), b ₂k) be respectively real part and the imaginary part of D (k) mid point k, N is light distribution I ₁(x) always count, carry out phase correction to sequence of complex numbers F (k), just can obtain having put the light intensity of k after phase correction, and after bearing calibration and correction, the light distribution of some k is as follows:

$B_0\left(k\right)=\frac{a_1\left(k\right)\&CenterDot;a_2\left(k\right)+b_1\left(k\right)\&CenterDot;b_2\left(k\right)}{\sqrt{a_2^2\left(k\right)+b_2^2\left(k\right)}}---\left(9\right)$

Seven, due to the unit difference adopted, need to carry out normalization to light intensity.Suppose light distribution B ₀(k) maximal value is a, and minimum value is b, to B ₀(k) adopt following method to carry out normalized, just can obtain normalized light distribution B (k):

$B\left(k\right)=\frac{B_0\left(k\right)-b}{a-b}---\left(10\right)$

According to the relation of count in formula (11) k and wave number v, just can be converted to the distribution of light intensity about wave number v to light distribution B (k);

$v=\frac{2\&CenterDot;k}{T\&CenterDot;N}---\left(11\right)$

Wherein, T is sampling interval.

When the asymmetry of interferogram is more serious, by above measure, can obtain the more high-precision reduction spectrum of phase correction apodization proposed than Mertz.In l-G simulation test, the maximum optical path difference L of the monolateral sampling of zero passage ₁=0.4502cm, the maximum optical path difference L of short bilateral sampling ₂=0.0136cm, sampling interval T=632.8 * 10 ^-7cm, Fig. 2 is the short bilateral sampling of interferogram, as can be seen from the figure, interferogram has more serious asymmetry.Adopt the inventive method, under these conditions, the inverting spectral results of acquisition as shown in Figure 3 and Figure 4.Fig. 3 is the spectrogram that adopts the inverting of step apodizing function, and Fig. 4 is the most advanced and sophisticated enlarged drawing of spectrogram part that adopts respectively step apodizing function and the inverting of Mertz apodizing function.As can be seen from Figure 3, adopt the spectrum of the inventive method inverting substantially to overlap with former spectrum, thereby proof the method is feasible; As can be seen from Figure 4, the weighted effect of the inventive method is better, and especially, in the tip location of spectrum, the resolution that obtains reduction spectrum than Mertz apodization is higher.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, obviously, those skilled in the art can carry out various changes and modification and not break away from the spirit and scope of the present invention the present invention.Like this, if within of the present invention these are revised and modification belongs to the scope of the claims in the present invention and equivalent technologies thereof, the present invention also is intended to comprise these changes and modification interior.

Claims (5)

1. a phase correction apodization method for Fourier transform spectrometer is characterized in that comprising the following steps:

Step (one) obtains interferogram light distribution I (x) by interferometer measurement;

Step (two) proposes step apodizing function A ₁(x):

$A_1\left(x\right)=\left\{\begin{array}{cc}0& -L_1\&le;x<-L_2\\ 0.5& -L_2\&le;x\&le;L_2\\ 1& L_2<x\&le;L_1\end{array}\right.$

(1)

Wherein, x is optical path difference, L ₁, L ₂it is respectively the maximum optical path difference of zero passage Single sided interferogram and short bilateral interferogram;

Step (three) is at optical path difference-L ₂～L ₁in scope, interferogram is carried out to the monolateral sampling of zero passage, sampling interval is T, at optical path difference-L ₁～-L ₂between to the monolateral sampled data zero padding of zero passage, zero padding is spaced apart T, then adopts step apodizing function A ₁(x) the monolateral sampled data of the zero passage after zero padding is cut to toe, cutting toe light distribution afterwards is I ₁(x):

$I_1\left(x\right)=\left\{\begin{array}{cc}0& x<-L_2\\ I_s\left(x\right)\&CenterDot;A_1\left(x\right)& -L_2\&le;x\&le;L_1\end{array}\right.$

(2)

Wherein, I _s(x) be the light distribution of the monolateral sampling of zero passage;

Step (four) is at optical path difference-L ₂～L ₂in scope, interferogram is carried out to short bilateral sampling, sampling interval is T, then to short bilateral sampled data at optical path difference-L ₁～-L ₂and L ₂～L ₁between carry out zero padding, zero padding is spaced apart T, obtains new light distribution I after zero padding ₂(x) be:

$I_2\left(x\right)=\left\{\begin{array}{cc}0& -L_1\&le;x<-L_2\\ I_d\left(x\right)& -L_2\&le;x\&le;L_2\\ 0& L_2<x\&le;L_1\end{array}\right.$

(3)

Wherein, I _d(x) be the light distribution of short bilateral sampling;

Step (five) is according to the odd-even symmetry of discrete Fourier transformation, light distribution sequence I ₁and I (x) ₂(x) respectively as real part and the imaginary part of one group of imaginary number sequence, form one group of sequence of complex numbers f ₀(x), be expressed as follows

f ₀(x)＝I ₁(x)+i·I ₂(x)

(4)

Then adopt triangle apodizing function A ₂(x) this sequence of complex numbers is cut to toe, the sequence of complex numbers f (x) cut after toe is:

f(x)=f ₀(x)·A ₂(x)

(5)

Wherein, A ₂(x) be the triangle apodizing function, be expressed as follows:

$A_2\left(x\right)=\left\{\begin{array}{cc}\frac{x+L_1}{L_1}& -L_1\&le;x\&le;0\\ \frac{L_1-x}{L_1}& 0<x\&le;L_1\end{array}\right.;$

Step (six) is carried out Fast Fourier Transform (FFT) to sequence of complex numbers f (x), sequence of complex numbers F (k) after being converted, character according to the symmetrical sequence of complex numbers of conjugation, be divided into sequence of complex numbers C (k) and D (k) two parts to sequence of complex numbers F (k), wherein

$\begin{array}{cc}C\left(k\right)=\frac{F\left(k\right)+F^{*}(-k)}{2}=a_1\left(k\right)+i{b}_i\left(k\right)& k=\mathrm{1,2,3}...N\end{array}$

(7) $\begin{array}{cc}D\left(k\right)=\frac{F\left(k\right)-F^{*}(-k)}{2i}=a_2\left(k\right)+{\mathrm{ib}}_2\left(k\right)& k=\mathrm{1,2,3}...N\end{array}$

(8)

Wherein, a ₁(k), b ₁(k) be respectively real part and the imaginary part of C (k) mid point k, a ₂(k), b ₂(k) be respectively real part and the imaginary part of D (k) mid point k, N is light distribution I ₁(x) always count, carry out phase correction to sequence of complex numbers F (k), just can obtain having put the light intensity of k after phase correction, and after bearing calibration and correction, the light distribution of some k is as follows:

$B_0\left(k\right)=\frac{a_1\left(k\right)\&CenterDot;a_2\left(k\right)+b_1\left(k\right)\&CenterDot;b_2\left(k\right)}{\sqrt{a_2^2\left(k\right)+b_2^2\left(k\right)}}$

(9)

2. according to the apodization of claim 1, it is characterized in that:

After cutting toe, the mean value of the light intensity that the sum of products that makes to have in zero passage Single sided interferogram short bilateral the light intensity of two corresponding point of same light path difference and each self-corresponding twiddle factor is these two corresponding point before weighting and the sum of products of each self-corresponding twiddle factor.

3. according to the apodization of claim 1, the apodizing function that wherein adopted, can adopt cosine apodizing function or Gauss's apodizing function to substitute the triangle apodizing function.

4. according to the apodization of claim 1, further comprise:

Step (seven) is carried out normalization to light intensity.

5. according to the apodization of claim 4, wherein normalization specifically comprises:

Suppose light distribution B ₀(k) maximal value is a, and minimum value is b, to B ₀(k) adopt following method to carry out normalized, just can obtain normalized light distribution B (k):

$B\left(k\right)=\frac{B_0\left(k\right)-b}{a-b}$

(10) according to the relation of count in formula (11) k and wave number v, just can be converted to light to light distribution B (k)

The strong distribution about wave number v;

$v=\frac{2\&CenterDot;k}{T\&CenterDot;N}$

(11)

Wherein, T is sampling interval.

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