CN101776489A - Femtosecond laser plasma channel interference pattern phase and electron density extraction method - Google Patents

Abstract

A femtosecond laser plasma channel interference pattern phase and electron density extraction method comprises the following steps: shooting a background interference light intensity image of probe light without plasma and a plasma channel interference light intensity image of the probe light with the plasma by a CCD camera; filtering and denoising the interferogram; searching the positions of light and dark stripes; calculating to obtain the plasma channel phase difference spatial distribution P (i, j) and the background phase difference spatial distribution P_bg(i, j); obtaining a phase difference space distribution map P after deducting the background₀(i, j); the phase difference space distribution map P after deducting the background₀(i, j) denoising; the phase difference distribution of the smooth phase difference space distribution diagram is symmetrical to obtain a symmetrical phase difference distribution diagram P_s(i, j); subjecting said symmetrical phase difference profile P to Abel transform_s(i, j) processing to obtain a plasma channel electron density distribution diagram.

Description

Femtosecond laser plasma channel interferogram phase place and electron density extracting method

Technical field

The invention belongs to the optical measurement field, particularly a kind of femtosecond laser plasma channel interferogram phase place and electron density extracting method.

Background technology

Femtosecond light laser and matter interaction are one of focus forward positions of current scientific research.In recent years,, on the desk-top laser system of miniaturization, realized that time width has only the ultra-short pulse laser of several femtoseconds at present, can focus on power density and reach 10 along with the fast development of ultrashort ultra-intense laser technology ²¹W/cm ²Even high-magnitude more.So high laser intensity be applied to solid and the interactional experiment of gas target in, comprise that laser particle quickens the generation of sigmatron and nuclear fusion neutron etc.In the research of these high-intensity ultrafast lasers and matter interaction, the electron density distribution of plasma channel is an indispensable important parameter.As a kind of common optical measurement means, interferometric method is applied in the ultrafast optical detection of article on plasma body parameter.By analyzing the phase information relevant of carrying in the interferogram, can realize the measurement of article on plasma body channel electron Density Distribution and other parameters with the plasma channel electron density.Fast and effeciently extract phase information and electron density distribution in the femtosecond laser interferogram, significant to the research of the diagnosis of femtosecond laser plasma channel characteristic and high-intensity ultrafast laser and matter interaction.

In the prior art " information handling system of phase-shift interference image and disposal route thereof " (patent publication No. CN1975321) of extracting the interferogram phase information, need to absorb continuously the interference image of multiframe, from the multiframe interferogram, recover the original phase information on corrugated with the CCD camera.But in ultrafast laser is measured, because the interference region of laser pulse in the space only is μ m magnitude, some uncertain factors of detection system, can make interference fringe bigger improper shake occur such as temperature, air-flow, laser direction subtle change and laser energy fluctuating etc., can not satisfy the requirement of the continuous photographing process of multiframe.Therefore the extractive technique at continuous light interferogram phase information commonly used is difficult for realizing in the interferometry of ultrafast laser pulse laser.

People such as M.Takeda are once at article " Fourier-transform method of fringe-pattern analysis forcomputer-based topography and interferometry " (J.Opt.Soc.Am., Vol.72, No.1,1982, p156-160) propose a kind of means in and extract interference fringe phase information method based on the Fourier transform denoising, and be used to afterwards to [" Characterization of laser plasmas for interaction studies:Progress in time-resolved densitymapping " (Phys.Rev.E in the extractive technique of ultrafast interferometry phase information and plasma electron density distribution, Vol.54, No.6,1996, p6769-6773)].This kind method does not need to take continuously the interferogram of multiframe, but with being compared by phase information modulation and not modulated interference light intensity in the interferogram of single frames, extracts phase information by Fourier transform method.Yet, be subject to its algorithm itself, the phase value that extracts be limited in (π, π) interval in and be discontinuously arranged, need by further judging and phase compensation, the phase value of step is stitched together to obtain continuous PHASE DISTRIBUTION.This phase place splicing will increase the unnecessary error of calculation and restricting data processing speed, and the terseness of its calculating and efficient remain further to be improved.

Summary of the invention

The objective of the invention is at above-mentioned the deficiencies in the prior art, consider the actual conditions of ultrafast laser interferometry, a kind of femtosecond laser plasma channel interferogram phase place and electron density extracting method are provided, to extract directly perceived and continuous space phase distribution value quickly and accurately, increase work efficiency greatly.

Technical solution of the present invention is as follows:

A kind of femtosecond laser plasma channel interferogram phase place and electron density extracting method, its characteristics are that this method comprises the following steps:

The background interference plot of light intensity I of probe light when 1. taking no plasma with the CCD camera _Bg(i, and the plasma channel interference light intensity figure I of probe light j) and when plasma is arranged (i, j);

2. interferogram filtering and noise reduction:

Described plasma channel interference light intensity figure is carried out Fast Fourier Transform (FFT) obtain the plasma channel frequency domain information, filter the high-frequency signal in the frequency spectrum, reduce the noise of system, the plasma channel interference light intensity figure I after the acquisition denoising _f(i, j);

3. to described denoising post plasma passage interference light intensity figure I _f(i, j) seek and get the light and shade fringe position:

Seek crest and the trough among the plasma channel interference light intensity figure that removes after making an uproar line by line and write down its position obtain plasma channel light and shade fringe position figure A (i, j);

4. from described plasma channel light and shade fringe position figure A (i, j) calculate plasma channel phase differential space distribution P (i, j):

5. with the 2. extremely 4. same method of above-mentioned steps, to described background interference plot of light intensity I _Bg(i j) handles, the background phase difference space distribution P when obtaining not having plasma _Bg(i, j);

6. with the 4. space distribution P (i, j) the 5. background phase difference space distribution P in step of deduction the of plasma channel phase differential _Bg(i, j), the phase differential spatial distribution map P after the acquisition background correction ₀(i, j);

7. with the phase differential spatial distribution map P after the described background correction ₀(i, j) denoising:

The phase differential spatial distribution map P of the method that reuses Fast Fourier Transform (FFT) after to described background correction ₀(i, j) filtering and noise reduction obtain level and smooth phase differential spatial distribution map P _0f(i, j);

8. with the phase differential distribution symmetrization of described level and smooth phase differential spatial distribution map, obtain the phase difference Butut P of symmetry _s(i, j);

9. use the phase difference Butut P of Abel transformation method to described symmetry _s(i j) handles, and obtains plasma channel electron density distribution figure.

The concrete grammar of described interferogram filtering and noise reduction is:

1. the CCD camera is captured plasma channel interference light intensity figure with two-dimensional matrix I (i, j) statement, i=1 wherein, 2 ..., M; J=1,2 ..., N, store, the corresponding CCD pixel of this row matrix value i and train value j position, M, N respectively corresponding CCD camera capable to row to the pixel number, wherein (i j) is the interference field coordinate, and this I (i, matrix element value j) is to interference light intensity value that should pixel;

2. (i j) through two-dimensional fast fourier transform, obtains spectral matrix I with described interference light intensity two-dimensional matrix I _ω(i, j), this spectral matrix I _ω(i comprises high frequency noise composition and low frequency interference light intensity composition in j), uses second order Butterworth LPF elimination high frequency noise composition wherein, and the magnification G of this second order Butterworth LPF and frequencies omega relation are as follows:

$G\left(\mathrm{\ω}\right)=\frac{1}{\sqrt{1+{(\mathrm{\ω}/{\mathrm{\ω}}_c)}^4}},$

In the formula: ω _cBe cutoff frequency, unit is radian per second (rad/s), by ω is set _cSize, remove frequency greater than ω _cHigh frequency noise, only keep needed interference light intensity and change low-frequency information, obtain filtered spectral matrix I _{ω f}(i, j);

3. to described filtered spectral matrix I _{ω f}(i j) carries out inverse Fourier transform, and reduction obtains the plasma channel interference light intensity distribution matrix I after the denoising _f(i, j).

Interferogram is sought the concrete grammar of getting the light and shade fringe position and is after the described denoising:

1. to the interferogram light intensity matrix I after the described denoising _f(i j) lines by line scan, and seeks the crest location and the wave trough position of getting every row, to I _f(a, j) element is along column direction, wherein a get 1,2 successively ... M, the direction that increases along j scans, when satisfying I _f(a, j-1)＜=I _f(a, j)＞=I _f(a, in the time of j+1), the corresponding crest location of j; When satisfying I _f(a, j-1)＞=I _f(a, j)＜=I _f(a, in the time of j+1), the corresponding wave trough position of j;

2. set up one and I _f(i, j) (i j), will seek the I that gets to the full null matrix A of identical size _f(i, crest j) and wave trough position (i, j) pairing A (i, j) matrix dot unit assignment is 1 in the matrix, promptly (i j) writes down described I with the A after the assignment _f(i, j) position of middle interference fringe crest and trough, i.e. interferogram light and shade fringe position after the denoising.

The method of described calculating plasma phase difference between channels space distribution is:

1. choose A (i, j) the capable interference fringe of preceding X does not have the knee and lines by line scan, the equispaced number of pixels n and the full figure that calculate adjacent light and shade interference fringe are interfered light and shade striped sum T;

2. obtain every average column position of interfering the light and shade striped not have the knee, be every corresponding A (i of interference fringe institute, j) the capable value of X is the average column position of 1 matrix element before in, be placed in delegation's Matrix C (k), k is the interference fringe sequence number, and the length of C is T, for example, when k=b, the value of C (b) is the b bar interference fringe capable average column position that does not have each pixel in knee of X of going forward;

3. capable since X+1, to A (i j) lines by line scan, when scan A (i, when j)=1 being crest or wave trough position, calculate this position does not have bending position with respect to this interference fringe phase difference value:

When scanning i=c when capable, wherein the value of c be followed successively by X+1, X+2 ... M, to A (c, j) increase direction by column scan along j, when A (c, j)=1 o'clock, record interference fringe sequence number this moment k, and calculate (c, j) locate corresponding phase differential and be: [j-C (k)] * π/n, wherein n is the equispaced number of pixels between the adjacent light and shade interference fringe;

In like manner calculate A (i, j) in the phase difference value of all Wave crest and wave trough place correspondences, result of calculation is put into a size and A (i, j) identical matrix B (i, j) correspondence position in;

4. to described B (i, j) in the matrix each the row neutral element according to following approach based on linear interpolation assignment, with obtain complete phase differential space distribution P (i, j):

The capable B of i=d (d, j) neutral element assignment, wherein d get 1,2 successively ... M, B (d, j) the nonzero element value is the capable crest of i=d that calculated or the phase difference value at trough place in, to the neutral element assignment between adjacent x and x+1 the nonzero element, by following formula calculating assignment also:

X is jx1 and jx2 with the row coordinate of x+1 nonzero element, then the B in row coordinate j belongs to (jx1:jx2) interval (d, j) value is:

$B(d,j)=B(d,\mathrm{jx}1)+j\·\frac{B(d,\mathrm{jx}2)-B(d,\mathrm{jx}1)}{\mathrm{jx}2-\mathrm{jx}1},j\∈(\mathrm{jx}1,\mathrm{jx}2);$

Consider that interference fringe self tilts, hot spot unevenness and survey the influence of disturbing factors such as minute surface flatness in the light path system, should from P (i, j) in background phase difference cloth during the no plasma channel of deduction.Therefore, with same step from described background interference plot of light intensity I _Bg(i j) calculates background phase difference space distribution P _Bg(i, j), from P (i, j) middle deduction P _Bg(i j) obtains removing phase differential distribution matrix P after the background ₀(i, j).

Reuse the method for Fast Fourier Transform (FFT) filtering and noise reduction, cutoff frequency ω is set _c, with P ₀(i, j) the high frequency noise composition that causes because of computation processes such as interpolation and background corrections in removes, and keeps the phase information of low frequency, obtains level and smooth reasonably PHASE DISTRIBUTION matrix P _0f(i, j).

Describedly be with the distribute concrete grammar of symmetrization of phase differential:

1. seek the middle shaft position of getting plasma channel: at first seek and get P _0f(i, j) line position at every row phase differential maximal value place.Set up the row matrix AX that a length is N (N).To P _0f(i, j) element is along column direction, i.e. and the direction of j increase scans.When scanning the j=e row, seek and get P _0f(i, c) phase differential maximal value place line position ie is placed on corresponding position among the AX (N) in, i.e. AX (e)=ie calculates the mean value Axis of all elements among the AX (N) again, consider the higher symmetry of plasma channel, with the axis line position of Axis as plasma channel;

2. be axis of symmetry with Axis, the phase difference value of axle both sides is done average treatment, set up a full null matrix P _0f1 (i, j), its size is M ₁* N, wherein M ₁=M-Axis is with matrix P _0f(i, j) part of middle Axis upside, i.e. P _0f(Axis:Axis+M ₁, j) matrix is put into P _0f1 (i, j) in, other sets up a full null matrix P _0f2 (i, j), its size is M ₂* N, wherein M ₂=Axis is with matrix P _0f(i, j) part of middle Axis downside, i.e. P _0f(1:Axis, j) matrix is put into P _0f2 (i, j) in;

3. set up a full null matrix P _s(i, j), its size is M _s* N, wherein M _sBe M ₁With M ₂Smaller value, to P _s(i, every row j) carry out assignment, make its value be P _0f1 (i, j) and P _0f2 (i, j) average, i.e. P _s(i, j)=[P _0f1 (i, j)+P _0f2 (i, j)]/2, P _s(i j) is symmetrical treatment phase differential later and distributes.

The concrete grammar that described use Abel transformation method is calculated electron density distribution is:

The known phase difference is distributed as P _s(i, j), plasma channel electron density n then _eFor:

$n_e(r,j)=-n_c\frac{{\mathrm{\λ}}_0}{{\mathrm{\π}}^2}\underset{M_s}{\overset{\∞}{\∫}}\frac{1}{\sqrt{i^2-r^2}}\frac{\∂\left[P_s(i,j)\right]}{\∂i}\·\mathrm{di},r\∈[0,M_s]$

Wherein, λ ₀For surveying optical wavelength, n _cBe the plasma critical density, r is the plasma channel radial coordinate, with matrix P _s(i j) carries out integral and calculating according to following formula, can obtain electron density distribution n _e(r, j).

The invention has the beneficial effects as follows:

Owing to only need to gather the single frames interferogram, can avoid the influence that thrashing was brought when the multiframe interferogram was gathered in the interferometry of ultrafast laser pulse laser, and improve conventional efficient.Can extract phase information and electron density distribution in the femtosecond laser plasma channel interferogram exactly, more quickly.Compare with existing interferogram phase information extractive technique, the present invention need not the phase value that be interrupted to jump is judged and is connected, by directly relatively interference fringe bending and the not displacement in knee, can extract directly perceived and continuous space phase distribution value quickly and accurately, improve efficient greatly.

Description of drawings

Fig. 1 is distributed in the comparison diagram of Fast Fourier Transform (FFT) filtering front and back for interference light intensity of the present invention.

The light and shade position of interference fringe figure that Fig. 2 extracts for the present invention.

The phase differential spatial distribution map of Fig. 3 for extracting from Fig. 2, phase differential unit is a radian.

Fig. 4 is the location drawing of light and shade striped among the background interference figure that extracts of the present invention.

The background interference figure phase differential spatial distribution map of Fig. 5 for extracting from Fig. 4, phase differential unit is a radian.

Fig. 6 is the final phase differential spatial distribution map behind background correction phase differential of the present invention and the filtering and noise reduction, and phase differential unit is a radian.

Fig. 7 is the phase difference Butut behind the symmetrization of the present invention, and phase differential unit is a radian.

Fig. 8 is plasma channel electron density distribution figure of the present invention, and electron density unit is cm ^-3

Embodiment

The invention will be further described below in conjunction with drawings and Examples, but should not limit protection scope of the present invention with this.

Femtosecond laser plasma channel interferogram phase place of the present invention and electron density extracting method, this method comprises the following steps:

The background interference plot of light intensity I of probe light when 1. taking no plasma with the CCD camera _Bg(i, and the plasma channel interference light intensity figure I of probe light j) and when plasma is arranged (i, j);

2. interferogram filtering and noise reduction:

(i, j) (promptly matrix size is 200 * 800 for M=200, N=800) gets its spectral matrix I through two-dimensional fast fourier transform to the two-dimentional interference light intensity matrix I of the CCD camera photographs when plasma is arranged probe light _ω(i, j).The cutoff frequency ω of second order Butterworth LPF is set _cBe 50rad/s, filter spectral matrix I _ω(i, j) noise information of the HFS ω ∈ [50rad/s ,+∞] in obtains filtered spectral matrix I _{ω f}(i, j).With I _{ω f}(i, j) inverse Fourier transform reduction obtains removing the interference light intensity distribution I behind the high frequency noise _f(i, j).Figure 1 shows that the capable comparison of the capable and filtered interference light intensity i=100 of interference light intensity i=100 before the filtering, promptly I (100, j) and I _f(100, comparison j).As seen from the figure, noise was obvious during original interference light intensity distributed, and was difficult to judge with simple algorithm the position of its Wave crest and wave trough; After Fast Fourier Transform (FFT) filtering, filter the high-frequency signal in the frequency spectrum, reduce the noise of system, the plasma channel interference light intensity figure I after the acquisition denoising _f(i, j); Interference light intensity distributes and becomes level and smooth, can satisfy the requirement that the Wave crest and wave trough position is accurately extracted fully; Interference light intensity distribution I after the denoising lines by line scan _f(i j), seeks the position light and shade striped of interference image (respectively corresponding with) of every capable crest and trough, and (i, j) order of the point of correspondence position is 1 in (matrix size is 200 * 800) with the full null matrix A of same size.Be the interferogram light and shade fringe position that extracts shown in Fig. 2.The light and shade striped distributes alternately and represents that by solid line each pixel on the solid line is corresponding to matrix A (i, pixel place j)=1 among the figure.

3. to described denoising post plasma passage interference light intensity figure I _f(i, j) seek and get the light and shade fringe position:

By A (i j) calculates among Fig. 2 and to interfere light and shade striped total number, promptly A (i, j) every capable intermediate value is 1 the total number of matrix element, is T=101; Calculate to interfere the light and shade striped not have the average headway in knee, promptly A (i, j) preceding X=20 capable (X=20 is determined by Fig. 2) value be 1 matrix element between average row be spaced apart n=7.85 pixel; Obtain the average column position of interfering the light and shade striped not have the knee, promptly (i, j) the capable value of preceding X=20 is the average column position of 1 matrix element to A, is placed on (C length is T=101) in delegation's Matrix C (k).For example, the average column position of going as if k=25 striped preceding 20 is j=195.22, then C (25)=195.22.With obtain plasma channel light and shade fringe position figure A (i, j);

4. from described plasma channel light and shade fringe position figure A (i, j) calculate plasma channel phase differential space distribution P (i, j):

(i, j) the 21st (X+1=21) row begins to line by line scan from A.The phase difference value that calculates is put into full null matrix B (i, j) correspondence position in of same size.For example, when scan A (i, the 21st when row j), to A (21, j) direction that increases along j is by column scan, when scan A (21, j)=1 o'clock, then note the striped ordinal number k of this moment, and the phase difference value that calculates this place correspondence put into B (i, j) in.For example, when scan for the k=25 time A (21, j)=1 o'clock, promptly scan Fig. 2 the 21st row from a left side several the 25th striped the time, calculate this position (21, phase difference value B j) (21, j) be:

B(21，j)＝[j-C(25)]×π/7.85

Calculate A (i, j) in the phase difference value of all pixel place, Wave crest and wave trough place correspondences, with the result of calculation correspondence put into matrix B (i, j) in order to next step calculating.To B (i, j) carry out the linear interpolation match: with the capable B of i=100 (100, j) describe for example.B (100, j) in the nonzero element value be the capable crest of i=100 that calculated or the phase difference value at trough place, now to carry out interpolation to the neutral element between adjacent peaks and the trough.For example, the 1st the row coordinate with the 2nd nonzero value is j=9 and j=16, then row coordinate j belong to (9:16) B in interval (100, j) value is:

$B(100,j)=B\left(\mathrm{100,9}\right)+j\·\frac{B\left(\mathrm{100,16}\right)-B\left(\mathrm{100,9}\right)}{16-9},j\∈\left(\mathrm{9,16}\right)$

With B (i, j) in the matrix each the row neutral element according to this approach based on linear interpolation assignment, promptly obtain complete phase differential space distribution P (i, j), as shown in Figure 3.

5. with the 2. extremely 4. same method of above-mentioned steps, to described background interference plot of light intensity I _Bg(i j) handles, the background phase difference space distribution P when obtaining not having plasma _Bg(i, j); Figure 4 shows that the background interference figure Wave crest and wave trough position distribution that extracts, the peak valley position is represented by solid line.The background phase difference space distribution P that calculates according to Fig. 4 that is shown in Figure 5 _Bg(i, j).

6. with the 4. space distribution P of the plasma channel phase differential in step (i, j) the 5. background phase difference space distribution P in step of deduction the _Bg(i, j), the phase differential spatial distribution map P after the acquisition background correction ₀(i, j);

7. with the phase differential spatial distribution map P after the described background correction ₀(i, j) denoising:

From P (i, j) middle deduction P _Bg(i j) obtains removing the phase differential distribution P of background ₀(i, j)=P (i, j)-P _Bg(i, j).Reuse the method for Fast Fourier Transform (FFT) filtering and noise reduction, cutoff frequency ω is set _c=50rad/s is with P ₀(i, j) the high frequency noise composition because of bringing in the computation processes such as interpolation and background correction in removes, and obtains level and smooth PHASE DISTRIBUTION P _0f(i, j) as shown in Figure 6.

8. with the phase differential distribution symmetrization of described level and smooth phase differential spatial distribution map, obtain the phase difference Butut P of symmetry _s(i, j);

Seek the middle shaft position of getting plasma channel.At first seek and get P _0f(i, j) line position at every row phase differential maximal value place.Set up the row matrix AX that a length is N=800 (800).To P _0f(i, j) element is along column direction, i.e. and the direction of j increase scans.For example, when scanning the j=300 row, seek and get P _0fPhase differential maximal value place line position i=115 is placed on the corresponding position among the AX (800), i.e. AX (300)=115 in (i, 300).In like manner, calculate the value of each element among the whole row matrix AX (800).

Calculate the mean value Axis=121 of all elements among the AX (N).Owing to consider the higher symmetry of plasma channel, we are with the middle shaft position of the 121st row as plasma channel.

(9) phase differential is distributed symmetrization.With Axis=121 behavior axis of symmetry, the phase difference value of axle both sides is done average treatment.Set up a full null matrix P _0f1 (i, j), its size is (200-121) * 800, with matrix P _0f(i, j) part of middle Axis upside, i.e. P _0f(121:200, j) matrix is put into P _0f1 (i, j) in; In like manner, set up a full null matrix P _0f2 (i, j), its size is 121 * 800, with matrix P _0f(i, j) part of middle Axis downside, i.e. P _0f(1:121, j) matrix is put into P _0f2 (i, j) in.

Other sets up a full null matrix P _s(i, j), its size is M _s* 800, M wherein _sBe M ₁=79 and M ₂=121 smaller value, i.e. P _s(i, j) size is 79 * 800.To P _s(i, every column element j) carries out assignment, and making its corresponding element value is P _0f1 (i, j) and P _0f2 (i, j) average, i.e. P _s(i, j)=[P _0f1 (i, j)+P _0f2 (i, j)]/2.P _s(i j) is symmetrical treatment phase differential later and distributes, as shown in Figure 7.

9. use the phase difference Butut P of Abel transformation method to described symmetry _s(i j) handles, and obtains plasma channel electron density distribution figure:

The known phase difference is distributed as P _s(i, j), plasma channel electron density n _eCan be expressed as the form of formula, survey light wavelength lambda in this example ₀Be 800nm, plasma critical density n _c=1.75 * 10 ²¹Cm ^-3, then electron density distribution is:

$n_e(r,j)=-1.75\×{10}^{21}{\mathrm{cm}}^{-3}\frac{800\mathrm{nm}}{{\mathrm{\π}}^2}\underset{M_s}{\overset{\∞}{\∫}}\frac{1}{\sqrt{i^2-r^2}}\frac{\∂\left[P_s(i,j)\right]}{\∂i}\·\mathrm{di},r\∈[0,79]$

To matrix P _s(i j) carries out integral and calculating according to following formula, promptly obtains electron density distribution n _e(r, j) as shown in Figure 8, the electron density unit of mark is cm among the figure ^-3

Claims (6)

1. femtosecond laser plasma channel interferogram phase place and electron density extracting method is characterized in that this method comprises the following steps:

The background interference plot of light intensity I of probe light when 1. taking no plasma with the CCD camera _Bg(i, and the plasma channel interference light intensity figure I of probe light j) and when plasma is arranged (i, j);

2. interferogram filtering and noise reduction:

Described plasma channel interference light intensity figure is carried out Fast Fourier Transform (FFT) obtain the plasma channel frequency domain information, filter the high-frequency signal in the frequency spectrum, reduce the noise of system, the plasma channel interference light intensity figure I after the acquisition denoising _f(i, j);

3. to described denoising post plasma passage interference light intensity figure I _f(i, j) seek and get the light and shade fringe position:

Seek crest and the trough among the plasma channel interference light intensity figure that removes after making an uproar line by line and write down its position obtain plasma channel light and shade fringe position figure A (i, j);

4. from described plasma channel light and shade fringe position figure A (i, j) calculate plasma channel phase differential space distribution P (i, j):

5. with the 2. extremely 4. same method of above-mentioned steps, to described background interference plot of light intensity I _Bg(i j) handles, the background phase difference space distribution P when obtaining not having plasma _Bg(i, j);

6. with the 4. space distribution P (i, j) the 5. background phase difference space distribution P in step of deduction the of plasma channel phase differential _Bg(i, j), the phase differential spatial distribution map P after the acquisition background correction ₀(i, j);

7. with the phase differential spatial distribution map P after the described background correction ₀(i, j) denoising:

The phase differential spatial distribution map P of the method that reuses Fast Fourier Transform (FFT) after to described background correction ₀(i, j) filtering and noise reduction obtain level and smooth phase differential spatial distribution map P _0f(i, j);

8. with the phase differential distribution symmetrization of described level and smooth phase differential spatial distribution map, obtain the phase difference Butut P of symmetry _s(i, j);

9. use the phase difference Butut P of Abel transformation method to described symmetry _s(i j) handles, and obtains plasma channel electron density distribution figure.

2. femtosecond laser plasma channel interferogram phase place according to claim 1 and electron density extracting method is characterized in that the concrete grammar of described interferogram filtering and noise reduction is:

1. the CCD camera is captured plasma channel interference light intensity figure with two-dimensional matrix I (i, j) statement, i=1 wherein, 2 ..., M; J=1,2 ..., N, store, the corresponding CCD pixel of this row matrix value i and train value j position, M, N respectively corresponding CCD camera capable to row to the pixel number, wherein (i j) is the interference field coordinate, and this I (i, matrix element value j) is to interference light intensity value that should pixel;

2. (i j) through two-dimensional fast fourier transform, obtains spectral matrix I with described interference light intensity two-dimensional matrix I _ω(i, j), this spectral matrix I _ω(i comprises high frequency noise composition and low frequency interference light intensity composition in j), uses second order Butterworth LPF elimination high frequency noise composition wherein, and the magnification G of this second order Butterworth LPF and frequencies omega relation are as follows:

$G\left(\mathrm{\ω}\right)=\frac{1}{\sqrt{1+{(\mathrm{\ω}/{\mathrm{\ω}}_c)}^4}},$

In the formula: ω _cBe cutoff frequency, unit is radian per second (rad/s), by ω is set _cSize, remove frequency greater than ω _cHigh frequency noise, only keep needed interference light intensity and change low-frequency information, obtain filtered spectral matrix I _{ω f}(i, j);

3. to described filtered spectral matrix I _{ω f}(i j) carries out inverse Fourier transform, and reduction obtains the plasma channel interference light intensity distribution matrix I after the denoising _f(i, j).

3. femtosecond laser plasma channel interferogram phase place according to claim 1 and electron density extracting method is characterized in that interferogram is sought the concrete grammar of getting the light and shade fringe position after the described denoising and are:

1. to the interferogram light intensity matrix I after the described denoising _f(i j) lines by line scan, and seeks the crest location and the wave trough position of getting every row, to I _f(a, j) element is along column direction, wherein a get 1,2 successively ... M, the direction that increases along j scans, when satisfying I _f(a, j-1)＜=I _f(a, j)＞=I _f(a, in the time of j+1), the corresponding crest location of j; When satisfying I _f(a, j-1)＞=I _f(a, j)＜=I _f(a, in the time of j+1), the corresponding wave trough position of j;

2. set up one and I _f(i, j) (i j), will seek the I that gets to the full null matrix A of identical size _f(i, crest j) and wave trough position (i, j) pairing A (i, j) matrix dot unit assignment is 1 in the matrix, promptly (i j) writes down described I with the A after the assignment _f(i, j) position of middle interference fringe crest and trough, i.e. interferogram light and shade fringe position after the denoising.

4. femtosecond laser plasma channel interferogram phase place according to claim 1 and electron density extracting method is characterized in that the method for described calculating plasma phase difference between channels space distribution is:

1. choose A (i, j) the capable interference fringe of preceding X does not have the knee and lines by line scan, the equispaced number of pixels n and the full figure that calculate adjacent light and shade interference fringe are interfered light and shade striped sum T;

2. obtain every average column position of interfering the light and shade striped not have the knee, be every corresponding A (i of interference fringe institute, j) the capable value of X is the average column position of 1 matrix element before in, be placed in delegation's Matrix C (k), k is the interference fringe sequence number, and the length of C is T, for example, when k=b, the value of C (b) is the b bar interference fringe capable average column position that does not have each pixel in knee of X of going forward;

3. capable since X+1, to A (i j) lines by line scan, when scan A (i, when j)=1 being crest or wave trough position, calculate this position does not have bending position with respect to this interference fringe phase difference value:

When scanning i=c when capable, wherein the value of c be followed successively by X+1, X+2 ... M, to A (c, j) increase direction by column scan along j, when A (c, j)=1 o'clock, record interference fringe sequence number this moment k, and calculate (c, j) locate corresponding phase differential and be: [j-C (k)] * π/n, wherein n is the equispaced number of pixels between the adjacent light and shade interference fringe;

In like manner calculate A (i, j) in the phase difference value of all Wave crest and wave trough place correspondences, result of calculation is put into a size and A (i, j) identical matrix B (i, j) correspondence position in;

4. to described B (i, j) in the matrix each the row neutral element according to following approach based on linear interpolation assignment, with obtain complete phase differential space distribution P (i, j):

The capable B of i=d (d, j) neutral element assignment, wherein d get 1,2 successively ... M, B (d, j) the nonzero element value is the capable crest of i=d that calculated or the phase difference value at trough place in, to the neutral element assignment between adjacent x and x+1 the nonzero element, by following formula calculating assignment also:

X is jx1 and jx2 with the row coordinate of x+1 nonzero element, then the B in row coordinate j belongs to (jx1:jx2) interval (d, j) value is:

J ∈ (jx1, jx2).

5. femtosecond laser plasma channel interferogram phase place according to claim 1 and electron density extracting method is characterized in that describedly with the distribute concrete grammar of symmetrization of phase differential being:

1. seek the middle shaft position of getting plasma channel: at first seek and get P _0f(i, j) line position at every row phase differential maximal value place.Set up the row matrix AX that a length is N (N).To P _0f(i, j) element is along column direction, i.e. and the direction of j increase scans.When scanning the j=e row, seek and get P _0f(i, c) phase differential maximal value place line position ie is placed on corresponding position among the AX (N) in, i.e. AX (e)=ie calculates the mean value Axis of all elements among the AX (N) again, consider the higher symmetry of plasma channel, with the axis line position of Axis as plasma channel;

2. be axis of symmetry with Axis, the phase difference value of axle both sides is done average treatment, set up a full null matrix P _0f1 (i, j), its size is M ₁* N, wherein M ₁=M-Axis is with matrix P _0f(i, j) part of middle Axis upside, i.e. P _0f(Axis:Axis+M ₁, j) matrix is put into P _0f1 (i, j) in, other sets up a full null matrix P _0f2 (i, j), its size is M ₂* N, wherein M ₂=Axis is with matrix P _0f(i, j) part of middle Axis downside, i.e. P _0f(1:Axis, j) matrix is put into P _0f2 (i, j) in;

3. set up a full null matrix P _s(i, j), its size is M _s* N, wherein M _sBe M ₁With M ₂Smaller value, to P _s(i, every row j) carry out assignment, make its value be P _0f1 (i, j) and P _0f2 (i, j) average, i.e. P _s(i, j)=[P _0f1 (i, j)+P _0f2 (i, j)]/2, P _s(i j) is symmetrical treatment phase differential later and distributes.

6. femtosecond laser plasma channel interferogram phase place according to claim 1 and electron density extracting method is characterized in that the concrete grammar of described use Abel transformation method calculating electron density distribution is:

The known phase difference is distributed as P _s(i, j), plasma channel electron density n then _eFor:

$n_e(r,j)=-n_c\frac{{\mathrm{\λ}}_0}{{\mathrm{\π}}^2}\underset{M_s}{\overset{\∞}{\∫}}\frac{1}{\sqrt{i^2-r^2}}\frac{\∂\left[P_s(i,j)\right]}{\∂i}\·\mathrm{di},$ r∈[0，M _s]

Wherein, λ ₀For surveying optical wavelength, n _cBe the plasma critical density, r is the plasma channel radial coordinate, with matrix P _s(i j) carries out integral and calculating according to following formula, can obtain electron density distribution n _e(r, j).

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