CN102519597A - 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 Fourier transform spectrometer, phase correction apodization

Technical field

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

Background technology

At present, Fourier transform spectrometer, is through detecting interference signal, then interferogram being carried out the instrument that Fourier transform is measured spectrum.Under the ideal situation; Interferogram is symmetrical about the zero optical path difference point; But since detect interference signal be difficult to from zero optical path difference begin, there is absorption loss in beam-splitting board and unevenness, electronic circuit error etc.; Cause interferogram to a certain degree asymmetry and phase error 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 product method phase error correction, near the data the zero optical path difference point of the monolateral interferogram of zero passage in the field are calculated twice, produce certain error.

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

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

Wherein, x is an 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 product method phase error correction, when adopting the monolateral interferogram of zero passage to carry out spectrum recovering, short bilateral interferogram data are repeated to use 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 promptly multiply by different coefficients to short bilateral interferogram each point, makes 2 interference light intensity sum with same light path difference keep the amplitude of single-point.

When interferogram was symmetrical basically about zero optical path difference point, this apodization can reach the weighted effect of expection.But when phase error exceeded certain scope, the sin component was excessive; There is serious asymmetry in interferogram; Adopt this method of weighting not only can not offset the asymmetric error of calculation of bringing this moment, 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.

This shows; Use apodizing function that Mertz proposes that the method for the monolateral interferogram weighting of zero passage is had significant disadvantages: when the asymmetry of interferogram is relatively 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 interferogram weighting more serious to asymmetry reduces the error of calculation that the asymmetry of interferogram is brought, and become problem demanding prompt solution.

Summary of the invention

The objective of the invention is to overcome the defective of above-mentioned technical matters; A kind of Fourier transform spectrometer, phase correction apodization is proposed; To after the monolateral interferogram weighted of zero passage, the sum of products of light intensity and each self-corresponding twiddle factor that makes the weak point of the monolateral interferogram of zero passage have two corresponding point of same light path difference in bilateral is the weighting mean value of the sum of products of light intensity and each self-corresponding twiddle factor of these two corresponding point before with this apodization.Thereby the error of calculation that the asymmetry that reduces interferogram is brought obtains more high-precision reduction spectrum.

According to the present invention, a kind of Fourier transform spectrometer, phase correction apodization is provided, it is characterized in that may further comprise the steps:

Step (one) obtains interferogram light distribution I (x) through 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 an optical path difference, L ₁, L ₂It is respectively the maximum optical path difference of monolateral interferogram of zero passage and short bilateral interferogram;

Step (three) is at optical path difference-L ₂～L ₁In the scope, interferogram is carried out the monolateral sampling of zero passage, the SI 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, adopts step apodizing function A then ₁(x) the monolateral sampled data of the zero passage after the zero padding is cut 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; Wherein cut after the toe, the sum of products of light intensity and each self-corresponding twiddle factor that makes the weak point of the monolateral interferogram of zero passage have two corresponding point of same light path difference in bilateral is the mean value of the sum of products of light intensity and each self-corresponding twiddle factor of these two corresponding point before the weighting.

According to a preferred embodiment of the invention, this method also further comprises: step (four) is at optical path difference-L ₂～L ₂In the scope, interferogram is lacked bilateral sampling, the SI is T, then to lacking 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 the 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, this method also further comprises: step (five) is according to the odd even symmetry of discrete Fourier transformation, light distribution sequence I ₁(x) and I ₂(x) respectively as the real part and the imaginary part of one group of imaginary number sequence, form one group of sequence of complex numbers f ₀(x), expression as follows

f ₀(x)＝I ₁(x)+i·I ₂(x) (4)

Adopt triangle apodizing function A then ₂(x) this sequence of complex numbers is cut toe, the sequence of complex numbers f (x) that cuts behind the toe is:

f(x)＝f ₀(x)·A ₂(x) (5)

Wherein, A ₂(x) be the triangle apodizing function, represent 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 is 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; This method also further comprises: step (six) is carried out Fast Fourier Transform (FFT) to sequence of complex numbers f (x); Obtain the sequence of complex numbers F (k) after the conversion; Character according to conjugation symmetry sequence of complex numbers is 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 real part and the imaginary part of C (k) mid point k respectively, 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 ₁Always counting (x) carried out phase correction to sequence of complex numbers F (k), just can obtain having put the light intensity of k behind the phase correction, and the light distribution of bearing calibration and correction back point k is following:

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

According to a preferred embodiment of the invention, this 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 normalization and handle, 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 the formula (11) k and wave number v, just can convert the distribution of light intensity to light distribution B (k) into about wave number v;

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

Wherein, T is the SI.

According to another embodiment of the present invention, a kind of Fourier transform spectrometer, phase correction apodization is provided, it is characterized in that may further comprise the steps:

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

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

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

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

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

Result of study shows; The apodization that proposes with the present invention is to the monolateral interferogram weighting of zero passage; Reduced since in the computation process near the data of zero optical path difference point be utilized the error that causes for twice; The apodization that proposes than Mertz has better weighted effect, can guarantee to restore the accuracy of spectrum, effectively reduces computation complexity simultaneously.

Though will combine certain exemplary enforcement and method of application to describe the present invention hereinafter, and 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 that are included in defined spirit of the present invention of appending claims and the scope.

Other advantage of the present invention, purpose and characteristic will be set forth in instructions subsequently to a certain extent; And to a certain extent; Based on being conspicuous to those skilled in the art, perhaps can from practice of the present invention, obtain instruction to investigating of hereinafter.The object of the invention and other advantage can be passed through following instructions, claims, and the structure that is particularly pointed out in the accompanying drawing realizes and obtains.

Description of drawings

In order to make the object of the invention, technical scheme and advantage clearer, will combine accompanying drawing that the present invention is made further detailed description below, 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 the most advanced and sophisticated enlarged drawing of spectrogram part of step apodizing function and the inverting of Mertz apodizing function respectively.

Embodiment

Do further detailed description below in conjunction with the accompanying drawing specific embodiments of the invention.Fig. 1 shows technical scheme of the present invention: at first interferogram is carried out 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 handle (cutting toe promptly multiplies each other with it with apodizing function); To short bilateral sampled data zero padding, make zero passage monolateral with short bilateral sampled data count identical and symmetrical about zero optical path difference; The monolateral sampled data of zero passage after next processing and short bilateral sampled data are respectively as the 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 toe handle (triangle or cosine or Gauss cut toe and handle), carry out Fast Fourier Transform (FFT) again; According to the character of conjugation symmetry sequence of complex numbers, carry out spectrum phase and proofread and correct then, obtain spectral distribution accurately.

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

Next, will specify embodiment of the present invention with reference to accompanying drawing:

One, at first obtains interferogram light distribution I (x) through interferometer measurement;

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 an optical path difference, L ₁, L ₂It is respectively the maximum optical path difference of monolateral interferogram of zero passage and short bilateral interferogram.

Three, at optical path difference-L ₂～L ₁In the scope, interferogram is carried out the monolateral sampling of zero passage, the SI 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; The monolateral sampled data of zero passage after adopting the step apodizing function to zero padding is then cut toe, and the sum of products of light intensity and each self-corresponding twiddle factor that makes the weak point of the monolateral interferogram of zero passage have two corresponding point of same light path difference in bilateral is the mean value of the sum of products of light intensity and each self-corresponding twiddle factor of these two corresponding point before the weighting.For instance; Two corresponding point such as having the same light path difference are respectively A, B, the product of the twiddle factor that the light intensity that B is ordered after the product+weighting of the twiddle factor that the light intensity that A is ordered after the weighting so is corresponding with the A point and B point are corresponding=(product of the twiddle factor that the preceding B of product+weighting of the twiddle factor that the light intensity that A order before the weighting 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 behind the toe ₁(x) do

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

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

Four, at optical path difference-L ₂～L ₂In the scope, interferogram is lacked bilateral sampling, the SI is T, then to lacking 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 ₁(x) and I ₂(x) respectively as the real part and the imaginary part of one group of imaginary number sequence, form one group of sequence of complex numbers f ₀(x), expression as follows

f ₀(x)＝I ₁(x)+i·I ₂(x) (4)

Adopt triangle apodizing function (adopting other apodizing functions such as cosine function, Gaussian function also to be fine) that this sequence of complex numbers is cut toe then, the sequence of complex numbers f (x) that cuts behind the toe is:

f(x)＝f ₀(x)·A ₂(x) (5)

Wherein, A ₂(x) be the triangle apodizing function, represent 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 Fast Fourier Transform (FFT), obtain the sequence of complex numbers F (k) after the conversion, the character according to conjugation symmetry sequence of complex numbers is 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 real part and the imaginary part of C (k) mid point k respectively, a ₂(k), b ₂K) be respectively real part and the imaginary part of D (k) mid point k, N is light distribution I ₁Always counting (x) carried out phase correction to sequence of complex numbers F (k), just can obtain having put the light intensity of k behind the phase correction, and the light distribution of bearing calibration and correction back point k is following:

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

Seven, because the unit that adopts is different, need 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 normalization and handle, 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 the formula (11) k and wave number v, just can convert the distribution of light intensity to light distribution B (k) into about wave number v;

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

Wherein, T is the SI.

When the asymmetry of interferogram is relatively more serious,, can obtain the more high-precision reduction spectrum of phase correction apodization that proposes than Mertz through above measure.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, SI T=632.8 * 10 ^-7Cm, Fig. 2 are the bilateral samplings of the weak point of interferogram, and 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 such as Fig. 3 and shown in 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 step apodizing function and the inverting of Mertz apodizing function respectively.As can be seen from Figure 3, adopt the spectrum of the inventive method inverting to overlap basically, thereby proof the method is feasible with former spectrum; 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 above is merely the preferred embodiments of the present invention, is not limited to the present invention, and 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, belong within the scope of claim of the present invention and equivalent technologies thereof if of the present invention these are revised with modification, then the present invention also is intended to comprise these changes and modification interior.

Claims (10)

1. Fourier transform spectrometer, phase correction apodization is characterized in that may further comprise the steps:

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

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

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

Wherein, x is an optical path difference, L ₁, L ₂It is respectively the maximum optical path difference of monolateral interferogram of zero passage and short bilateral interferogram;

Step (three) is at optical path difference-L ₂～L ₁In the scope, interferogram is carried out the monolateral sampling of zero passage, the SI 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, adopts step apodizing function A then ₁(x) the monolateral sampled data of the zero passage after the zero padding is cut 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.

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

Cut after the toe, the sum of products of light intensity and each self-corresponding twiddle factor that makes the weak point of the monolateral interferogram of zero passage have two corresponding point of same light path difference in bilateral is the mean value of the sum of products of light intensity and each self-corresponding twiddle factor of these two corresponding point before the weighting.

3. according to the apodization of claim 2, further comprise:

Step (four) is at optical path difference-L ₂～L ₂In the scope, interferogram is lacked bilateral sampling, the SI is T, then to lacking 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 the zero padding ₂(x) be:

$I_2\left(x\right)=\left\{\begin{array}{cc}0& -L_1\&le;x<-L_2\\ I_d\left(x\right)& -L_2\&le;x\&le;L_2\\ 0& L_2<x\&le;L_1\end{array}\right.---\left(3\right)$

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

4. according to the apodization of claim 3, further comprise:

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

f ₀(x)＝I ₁(x)+i·I ₂(x) (4)

Adopt triangle apodizing function A then ₂(x) this sequence of complex numbers is cut toe, the sequence of complex numbers f (x) that cuts behind the toe is:

f(x)＝f ₀(x)·A ₂(x) (5)

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

$A_2\left(x\right)=\left\{\begin{array}{cc}\frac{x+L_1}{L_1}& -L_1\&le;x\&le;0\\ \frac{L_1-x}{L_1}& 0<x\&le;L_1\end{array}\right.---\left(6\right)$

5. according to the apodization of claim 4, the apodizing function that is wherein adopted can adopt cosine apodizing function or Gauss's apodizing function to substitute the triangle apodizing function.

6. according to the apodization of claim 5, further comprise:

Step (six) is carried out Fast Fourier Transform (FFT) to sequence of complex numbers f (x), obtains the sequence of complex numbers F (k) after the conversion, and the character according to conjugation symmetry sequence of complex numbers is 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 real part and the imaginary part of C (k) mid point k respectively, 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 ₁Always counting (x) carried out phase correction to sequence of complex numbers F (k), just can obtain having put the light intensity of k behind the phase correction, and the light distribution of bearing calibration and correction back point k is following:

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

7. according to the apodization of claim 6, further comprise:

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

8. according to the apodization of claim 7, 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 normalization and handle, 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 the formula (11) k and wave number v, just can convert the distribution of light intensity to light distribution B (k) into about wave number v;

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

Wherein, T is the SI.

9. Fourier transform spectrometer, phase correction apodization is characterized in that may further comprise the steps:

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

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

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

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

10. according to the apodization of claim 9, wherein said triangle is cut toe and is handled and can cut that toe is handled or Gauss cuts toe and handles to substitute with cosine.

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