CN102980667A - Laser beam detection device and method based on ENZ theory - Google Patents

Abstract

A laser beam detection device and method based on an ENZ theory, and belongs to the technical field of laser. The laser beam detection device and method in the prior art has the defects of being cumbersome in operating steps, low in detection precision, hard to improve the resolution ratio, low in signal-to-noise ratio and high in cost. The device charge coupled device (CCD) detector is connected with a data processing computer. An imaging lens is arranged ahead of the CCD detector. The light-sensitive surface of the CCD detector and the focal plane c of the imaging lens are in parallel. The CCD detector is fixed on a slider. A guide slider mechanism is composed of the slider and a guide. The method takes the detected laser beam flare intensity image in the imaging lens focal plane c and the symmetrical front out-of focal plane a and the back out-of focal plane b and adopts an ENZ polynomial structure wave-front fitting coefficient to get an equation set. The multiple wave-front coefficient value correlation of the wave-front of the fitting pupil flat surface laser beam is obtained by solving the equation set, and then the high order error is eliminated by iterative algorithm and the accurate wave-front fitting coefficient value is got, thereby obtaining the phase position and the amplitude of the pupil flat surface laser beam. The characteristic value is calculated through moment method according to phase position and intensity information.

Description

Laser beam pick-up unit and method based on the ENZ theory

Technical field

The present invention relates to a kind of laser beam pick-up unit and method based on the ENZ theory, described laser beam pick-up unit belongs to before a kind of laser wave and the eigenwert pick-up unit, can finish the front high-acruracy survey of laser wave, described laser beam pick-up unit can also be as wavefront sniffer in the laser communication, described laser beam detection method can be finished the calculating of laser associated eigenvalue, belongs to laser technology field.

Background technology

Laser has been widely used in all trades and professions, and laser detection equipment also is various.Because all technical requirement to laser is more and more higher, and laser detection equipment has also just been proposed more and more higher requirement.Existing Wavefront detecting device is Hartmann wave front sensor, is used for laser measurement, laser communication and optical element detection etc.The front end of Hartmann wave front sensor need to cooperate and expands and the contracting beam system, and simultaneously, Hartman wavefront detector also need to be debug microlens array at the ccd detector front end.As seen adopt Hartmann wave front sensor detection laser light beam complex operation step; Debug microlens array at the ccd detector front end and can bring to whole system and debug error, affect the accuracy of detection of whole wavefront, microlens array also can restrict the detection dynamic range; The resolution of Hartmann wave front sensor is the number of arrays of front end microlens array, therefore, adopts Hartmann wave front sensor Wavefront detecting resolution to be difficult to improve; Be the existence owing to microlens array equally, the energy of the laser beam that detects also can reduce, thereby the signal to noise ratio (S/N ratio) of the image that detects is reduced; The employed ccd detector of Hartmann wave front sensor should have the test surface of large-size, and microlens array cost wherein is higher and resetting difficulty is large, must be equipped with to expand and contracting bundle parts, and these factors cause the Hartmann wave front sensor cost to raise.

Have based on the method for the calculating wavefront of described device and eigenwert several, yet as complete scheme, its deficiency from device still exists.

Summary of the invention

For in the laser beam testing process, simplify detecting step, improve the detection accuracy of whole wavefront, improve Wavefront detecting resolution, improve the signal to noise ratio (S/N ratio) of the image that detects, reduce the cost of pick-up unit, we have invented a kind of laser beam pick-up unit and method based on the ENZ theory.

In the present invention's the laser beam pick-up unit based on the ENZ theory, ccd detector 1 links to each other with data handling machine 2, as shown in Figure 1, it is characterized in that, imaging len 3 is positioned at ccd detector 1 the place ahead, and ccd detector light-sensitive surface 4 is parallel with imaging len 3 focal plane c; Ccd detector 1 is fixed on the slide block 5, and slide block 5 consists of guide rail slide block mechanism with guide rail 6.

The present invention's the laser beam detection method based on the ENZ theory is characterized in that, as shown in Figure 1 and Figure 2, gets imaging len c place, 3 focal plane and symmetrical front out of focus face a place, the tested laser beam spot intensity image at rear out of focus face b place; The fit procedure of tested laser beam wavefront is as follows, at first adopt expansion Nijboer-Zernike polynomial construction wavefront fitting coefficient to ask for system of equations, find the solution the plural wavefront fitting coefficient value that this system of equations obtains match pupil plane laser beam wavefront, then pass through iterative algorithm, remove the high-order error of introducing, obtain accurate wavefront fitting coefficient value, thereby obtain phase place and the amplitude of pupil plane laser beam, at last, match obtains tested laser beam pupil plane wavefront; Tested laser beam eigenwert computation process is as follows, according to the phase information of the laser beam that is obtained by tested laser beam wavefront and the strength information in the tested laser beam spot intensity image, calculate tested laser beam eigenwert by moments method, comprise beamwidth value d, beam divergence angle θ _σ, quality factor M ², waist width d ₀, Rayleigh range z _R, beam waist position z ₀

Its technique effect of the present invention is, in the present invention's pick-up unit, not do not expand such as the existing essential front end of pick-up unit that adopts Hartmann wave front sensor and the parts such as contracting beam system, microlens array, therefore, adopt the present invention's device detection laser light beam simplified operational procedure.Equally do not exist because debuging the error of debuging that microlens array brings yet, avoid this error on the impact of accuracy of detection, broken away from microlens array to surveying the restriction of dynamic range.Because tested laser beam images on the ccd detector light-sensitive surface 4 through imaging len 3, the resolution of spot intensity image is not subjected to the restriction of the parameter of the parts as microlens array, therefore can access due raising, theoretically, actual wavefront detection resolution of the present invention is higher than the resolution of ccd detector 1, is higher than the resolution of Hartman wavefront detector simultaneously far away.Be that the tested laser beam energy that detects is higher owing to there is not the existence of microlens array equally, therefore the signal to noise ratio (S/N ratio) of the spot intensity image that detects is improved.Since the present invention only by an imaging len 3 with tested laser beam imaging, give up not only that prior art is employed to be expanded and contract bundle parts, microlens array, and can reduce the size of ccd detector light-sensitive surface 4, compare with the ccd detector in the existing Hartmann wave front sensor, ccd detector light-sensitive surface 4 in the pick-up unit of the present invention reduces 1/2nd and also can meet the demands, although set up the guide rail slide block mechanism that is consisted of by slide block 5 and guide rail 6, Comparatively speaking, the cost of pick-up unit still significantly reduces.

The present invention's detection method only need the width of cloth that detect according to the pick-up unit by the present invention in burnt, the tested laser beam spot intensity of the symmetrical out of focus of two width of cloth image strength information and the defocusing amount that reads from guide rail slide block mechanism, according to expansion Nijboer-Zernike theoretical (ENZ) and moments method algorithm, can obtain tested laser beam wavefront and eigenwert, when pick-up unit overcomes the prior art deficiency, realize the detection of laser beam.Have the advantages that pick-up unit is simple, testing process is simple and direct.

Description of drawings

Fig. 1 is the present invention's the laser beam pick-up unit general structure synoptic diagram based on the ENZ theory.Fig. 2 is each step block diagram of laser beam detection method based on the ENZ theory of the present invention, and this figure is simultaneously as Figure of abstract.

Embodiment

In the present invention's the laser beam pick-up unit based on the ENZ theory, ccd detector 1 links to each other by the USB connecting line with data handling machine 2, as shown in Figure 1.Imaging len 3 is positioned at ccd detector 1 the place ahead, and ccd detector light-sensitive surface 4 is parallel with imaging len 3 focal plane c; The light path that swashs light inlet side at imaging len 3 arranges laser intensity attenuation factor 7, attenuation factor 7 is combined by the different tested Excitation Filter with High 8 of some transmitances, such as 6, attenuation factor 7 can decay to the degree that ccd detector 1 can bear with the tested laser intensity from the different capacity of laser instrument 9, below 10W.Ccd detector 1 is fixed on the slide block 5, and slide block 5 consists of guide rail slide block mechanism with guide rail 6; One graticule on the slide block 5 cooperates with the scale that arranges along slide block 5 glide directions on guide rail 6, reads thus the displacement of slide block 5, and this distance is exactly the tested laser beam spot intensity of out of focus image defocusing amount f.

The present invention's the laser beam detection method embodiment based on the ENZ theory is as follows, as shown in Figure 1 and Figure 2, gets imaging len c place, 3 focal plane and symmetrical front out of focus face a place, the tested laser beam spot intensity image at rear out of focus face b place.

The fit procedure of tested laser beam wavefront is as follows, at first adopts expansion Nijboer-Zernike polynomial construction wavefront fitting coefficient

Ask for system of equations (1), find the solution the plural wavefront fitting coefficient that this system of equations obtains match pupil plane laser beam wavefront by data handling machine 2

:

$\begin{array}{c}\left\{\begin{array}{c}\frac{1}{2}{\left({\mathrm{\β}}_0^0\right)}^2({\mathrm{\χ}}_0^0,{\mathrm{\χ}}_{n^{\′}}^0)+{\underset{n}{\mathrm{\Σ}}}^{\′}{\mathrm{\β}}_0^0\mathrm{Re}\left({\mathrm{\β}}_n^0\right)({\mathrm{\χ}}_n^0,{\mathrm{\χ}}_{n^{\′}}^0)\≈(I_d^0,{\mathrm{\χ}}_{n^{\′}}^0)\\ {\underset{n}{\mathrm{\Σ}}}^{\′}{\mathrm{\β}}_0^0\mathrm{Im}\left({\mathrm{\β}}_n^0\right)({\mathrm{\Ψ}}_n^0,{\mathrm{\Ψ}}_{n^{\′}}^0)\≈(I_d^0,{\mathrm{\Ψ}}_{n^{\′}}^0)\end{array}\right.m=\mathrm{1,2,3}...;n,n^{\′}=m,m+2,...\\ \left\{\begin{array}{c}{\underset{n}{\mathrm{\Σ}}}^{\′}{\mathrm{\β}}_0^0\mathrm{Re}\left({\mathrm{\β}}_n^m\right)({\mathrm{\χ}}_n^m,{\mathrm{\χ}}_{n^{\′}}^m)\≈(I_d^m,I_{n^{\′}}^m)\\ {\underset{n}{\mathrm{\Σ}}}^{\′}{\mathrm{\β}}_0^0\mathrm{Im}\left({\mathrm{\β}}_n^m\right)(I_d^m,{\mathrm{\Ψ}}_{n^{\′}}^m)\end{array}\right.m=\mathrm{1,2,3}...;n,n^{\′}=m,m+2,...\end{array}---\left(1\right)$

Wherein, m, n are integer,

The m rank cosine transform of the light intensity that expression detects,

, Be respectively

Real part and imaginary part,

,

Be respectively

Real part and imaginary part,

,

Be respectively

Real part and imaginary part." ' " represents n=m=0, and item is deleted.

Wherein

,

Calculated by formula (2) respectively:

$\left\{\begin{array}{c}{\mathrm{\χ}}_n^m=8{\mathrm{\ϵ}}_m\mathrm{Re}\left[i^m{V}_n^m(r,f)V_0^{0*}(r,f)\right]\\ {\mathrm{\ψ}}_n^m=-8{\mathrm{\ϵ}}_m\mathrm{Im}\left[i^m{V}_n^m(r,f)V_0^{0*}(r,f)\right]\end{array}\right.---\left(2\right)$

Wherein, when m=0, ε _m=1(ε _m=1), when m ≠ 0, ε _m=0.5(ε _m=0.5).

Calculated by formula (3):

$V_m^n(r,f)={\∫}_0^1\exp \left(\mathrm{if}{\mathrm{\ρ}}^2\right)\mathrm{\ρ}{R}_n^m\left(\mathrm{\ρ}\right)J_m\left(2\mathrm{\π\ρr}\right)\mathrm{d\ρ}---\left(3\right)$

In the formula

Expand by the Nijboer-Zernike polynomial theory, use the formal expansion of progression to become:

$\begin{array}{c}{V}_n^m(r,f)\exp \left(\mathrm{if}\right)\underset{l=1}{\overset{\∞}{\mathrm{\Σ}}}{(-2\mathrm{if})}^{l-1}\underset{j=0}{\overset{p}{\mathrm{\Σ}}}{\mathrm{\υ}}_{\mathrm{lj}}\frac{J_{m+l+2j}\left(\mathrm{\υ}\right)}{{\mathrm{l\υ}}^l}\\ {\mathrm{\υ}}_{\mathrm{lj}}={(-1)}^p(m+l+2j)\left(\begin{array}{c}m+j+l-1\\ l-1\end{array}\right)\left(\begin{array}{c}j+l-1\\ l-1\end{array}\right)\left(\begin{array}{c}l-1\\ p-j\end{array}\right)/\left(\begin{array}{c}q+l+j\\ l\end{array}\right)\end{array}$

Wherein, i is imaginary unit, i ²=-1; F is defocusing amount; υ=2 π r, r are tested laser beam spot radius;

,

Then by iterative algorithm, remove the high-order error of introducing, namely by the Predictor-Corrector iterative algorithm, the high-order error of introducing in the correcting algorithm obtains the wavefront fitting coefficient of high accuracy approximation

At last, match obtains tested laser beam pupil plane wavefront, namely carries out pupil function P (u, v) match by formula (4):

$P(u,v)=\mathrm{\Σ}{\mathrm{\β}}_n^m{Z}_n^m(u,v)=\mathrm{\Σ}{\mathrm{\β}}_n^m{R}_n^m\left(\mathrm{\ρ}\right)\cos \left(\mathrm{m\θ}\right)---\left(4\right)$

Following formula is that pupil function P (u, v) is launched into the polynomial linear combination of Zernike, and u, v are coordinate figure in the formula, and θ is the phasing degree.

Calculate point spread function U (r, θ) through formula (5):

$U(r,\mathrm{\θ})=\mathrm{\Σ}{\mathrm{\β}}_n^{m}2i^m{V}_n^m(r,f)\cos \left(\mathrm{m\θ}\right)---\left(5\right)$

In the formula:

Be the wavefront fitting coefficient,

Provided by formula (3), m, n are integer, and i is imaginary unit, i ²=-1, f is defocusing amount, and r is tested laser beam spot radius, and θ is the phasing degree.

Thereby calculate high-precision wavefront and the phase information of tested laser beam, finish laser beam wavefront high-acruracy survey.

Tested laser beam eigenwert computation process is as follows, according to the phase information of the laser beam that is obtained by tested laser beam wavefront and the strength information in the tested laser beam spot intensity image, calculate tested laser beam eigenwert by moments method, comprise beamwidth value d, beam divergence angle θ _σ, quality factor M ², waist width d ₀, Rayleigh range z _R, beam waist position z ₀

The concrete detection scheme of relevant tested laser beam eigenwert is as follows.After the phase information and the strength information in the tested laser beam spot intensity image of the pupil plane laser beam that in the detection of tested laser beam wavefront, obtains, calculate tested laser beam eigenwert by moments method.At first, the strength information by pupil plane calculates facula mass center first moment＜x on the one hand 〉,＜y 〉, and then calculate facula mass center second moment＜x ²,＜y ².Phase information by pupil plane calculates wavefront gradients first moment＜u on the other hand 〉,＜v 〉, and then calculate wavefront gradients second moment＜u ²,＜v ².Then, calculate again mixed moment＜xu 〉,＜yv 〉.At last, calculate tested laser beam beamwidth value d, beam divergence angle θ according to following formula (6) ~ (11) _σ, quality factor M ², waist width d ₀, Rayleigh range z _R, beam waist position z ₀

Obtain tested laser beam beamwidth value d by formula (6), comprise d _x, d _y:

$\left\{\begin{array}{c}{d}_x=4\sqrt{<x^2>}\\ d_y=4\sqrt{<y^2>}\end{array}\right.---\left(6\right)$

In the formula＜x ²,＜y ²It is the facula mass center second moment.

Obtain tested laser beam beam divergence angle θ by formula (7) _σ, comprise

,

:

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_x}=4\sqrt{<u^2>}\\ {\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_y}=4\sqrt{<v^2>}\end{array}\right.---\left(7\right)$

In the formula＜u ²,＜v ²It is the wavefront gradients second moment.

Obtain tested Laser Beam Quality Factor M by formula (8) ², comprise

,

:

$\left\{\begin{array}{c}{M}_x^2=\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{<x^2><u^2>-{<\mathrm{xu}>}^2}\\ M_y^2=\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{<y^2><v^2>-{<\mathrm{yv}>}^2}\end{array}\right.---\left(8\right)$

In the formula＜x ²,＜y ²Be the facula mass center second moment,＜u ²,＜v ²Be the wavefront gradients second moment,＜xu 〉,＜yv〉be mixed moment, the tested optical maser wavelength of λ.

Obtain tested laser beam waist width d by formula (9) ₀, comprise d _0x, d _0y:

$\left\{\begin{array}{c}{d}_{0x}=\frac{4M_x^2\mathrm{\&lambda;}}{\mathrm{\&pi;}{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_x}}\\ d_{0y}=\frac{4M_y^2\mathrm{\&lambda;}}{{\mathrm{\&pi;\&theta;}}_{{\mathrm{\&sigma;}}_y}}\end{array}\right.---\left(9\right)$

In the formula

,

Be tested Laser Beam Quality Factor, ,

Be tested laser beam beam divergence angle, the tested optical maser wavelength of λ.

Obtain tested laser beam Rayleigh range z by formula (10) _R, comprise z _Rx, z _Ry:

$\left\{\begin{array}{c}{z}_{\mathrm{Rx}}=\frac{d_{0x}}{{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_x}}\\ z_{\mathrm{Ry}}=\frac{d_{0y}}{{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_y}}\end{array}\right.---\left(10\right)$

D in the formula _0x, d _0yBe tested laser beam waist width,

,

Be tested laser beam beam divergence angle.

Obtain tested laser beam beam waist position z by formula (11) ₀, comprise z _0x, z _0y:

$\left\{\begin{array}{c}{z}_{0x}=\frac{<\mathrm{xu}>z_{\mathrm{Rx}}}{|<\mathrm{xu}>|}\sqrt{{\left(\frac{d_x}{d_{0x}}\right)}^2-1}\\ z_{0y}=\frac{<\mathrm{yv}>z_{\mathrm{Ry}}}{|<\mathrm{yv}>|}\sqrt{{\left(\frac{d_y}{d_{0y}}\right)}^2-1}\end{array}\right.---\left(11\right)$

In the formula＜xu 〉,＜yv〉be mixed moment, z _Rx, z _RyBe tested laser beam Rayleigh range, d _x, d _yBe tested laser beam beamwidth value, d _0x, d _0yBe tested laser beam waist width.

Claims (6)

1. laser beam pick-up unit based on the ENZ theory, ccd detector (1) links to each other with data handling machine (2), it is characterized in that imaging len (3) is positioned at ccd detector (1) the place ahead, ccd detector light-sensitive surface (4) is parallel with imaging len (3) focal plane c; Ccd detector (1) is fixed on the slide block (5), and slide block (5) consists of guide rail slide block mechanism with guide rail (6).

2. the laser beam pick-up unit based on the ENZ theory according to claim 1, it is characterized in that, the light path that swashs light inlet side at imaging len (3) arranges laser intensity attenuation factor (7), attenuation factor (7) is combined by the different tested Excitation Filter with High (8) of some transmitances, and attenuation factor (7) can decay to the degree that ccd detector (1) can bear with the tested laser intensity from the different capacity of laser instrument (9).

3. the laser beam pick-up unit based on the ENZ theory according to claim 1, it is characterized in that, one graticule on the slide block (5) cooperates with the scale that arranges along slide block (5) glide direction on guide rail (6), read thus the displacement of slide block (5), this distance is exactly the tested laser beam spot intensity of out of focus image defocusing amount f.

4. the laser beam detection method based on the ENZ theory is characterized in that, gets c place, imaging len (3) focal plane and symmetrical front out of focus face a place, the tested laser beam spot intensity image at rear out of focus face b place; The fit procedure of tested laser beam wavefront is as follows, at first adopt expansion Nijboer-Zernike polynomial construction wavefront fitting coefficient to ask for system of equations, find the solution the plural wavefront fitting coefficient value that this system of equations obtains match pupil plane laser beam wavefront, then pass through iterative algorithm, remove the high-order error of introducing, obtain accurate wavefront fitting coefficient value, thereby obtain phase place and the amplitude of pupil plane laser beam, at last, match obtains tested laser beam pupil plane wavefront; Tested laser beam eigenwert computation process is as follows, according to the phase information of the laser beam that is obtained by tested laser beam wavefront and the strength information in the tested laser beam spot intensity image, calculate tested laser beam eigenwert by moments method, comprise beamwidth value d, beam divergence angle θ _σ, quality factor M ², waist width d ₀, Rayleigh range z _R, beam waist position z ₀

5. the laser beam detection method based on the ENZ theory according to claim 4 is characterized in that, the concrete fit procedure of tested laser beam wavefront is as follows, at first adopts expansion Nijboer-Zernike polynomial construction wavefront fitting coefficient

Ask for system of equations (1), find the solution the plural wavefront fitting coefficient that this system of equations obtains match pupil plane laser beam wavefront by data handling machine (2)

:

$\begin{array}{c}\left\{\begin{array}{c}\frac{1}{2}{\left({\mathrm{\&beta;}}_0^0\right)}^2({\mathrm{\&chi;}}_0^0,{\mathrm{\&chi;}}_{n^{\&prime;}}^0)+{\underset{n}{\mathrm{\&Sigma;}}}^{\&prime;}{\mathrm{\&beta;}}_0^0\mathrm{Re}\left({\mathrm{\&beta;}}_n^0\right)({\mathrm{\&chi;}}_n^0,{\mathrm{\&chi;}}_{n^{\&prime;}}^0)\&ap;(I_d^0,{\mathrm{\&chi;}}_{n^{\&prime;}}^0)\\ {\underset{n}{\mathrm{\&Sigma;}}}^{\&prime;}{\mathrm{\&beta;}}_0^0\mathrm{Im}\left({\mathrm{\&beta;}}_n^0\right)({\mathrm{\&Psi;}}_n^0,{\mathrm{\&Psi;}}_{n^{\&prime;}}^0)\&ap;(I_d^0,{\mathrm{\&Psi;}}_{n^{\&prime;}}^0)\end{array}\right.m=\mathrm{1,2,3}...;n,n^{\&prime;}=m,m+2,...\\ \left\{\begin{array}{c}{\underset{n}{\mathrm{\&Sigma;}}}^{\&prime;}{\mathrm{\&beta;}}_0^0\mathrm{Re}\left({\mathrm{\&beta;}}_n^m\right)({\mathrm{\&chi;}}_n^m,{\mathrm{\&chi;}}_{n^{\&prime;}}^m)\&ap;(I_d^m,I_{n^{\&prime;}}^m)\\ {\underset{n}{\mathrm{\&Sigma;}}}^{\&prime;}{\mathrm{\&beta;}}_0^0\mathrm{Im}\left({\mathrm{\&beta;}}_n^m\right)(I_d^m,{\mathrm{\&Psi;}}_{n^{\&prime;}}^m)\end{array}\right.m=\mathrm{1,2,3}...;n,n^{\&prime;}=m,m+2,...\end{array}---\left(1\right)$ ，

Wherein, m, n are integer,

The m rank cosine transform of the light intensity that expression detects, ,

Be respectively

Real part and imaginary part,

, Be respectively

Real part and imaginary part,

,

Be respectively

Real part and imaginary part." ' " represents n=m=0, and item is deleted;

Wherein

,

Calculated by formula (2) respectively:

$\left\{\begin{array}{c}{\mathrm{\&chi;}}_n^m=8{\mathrm{\&epsiv;}}_m\mathrm{Re}\left[i^m{V}_n^m(r,f)V_0^{0*}(r,f)\right]\\ {\mathrm{\&psi;}}_n^m=-8{\mathrm{\&epsiv;}}_m\mathrm{Im}\left[i^m{V}_n^m(r,f)V_0^{0*}(r,f)\right]\end{array}\right.---\left(2\right),$

Wherein, when m=0, ε _m=1(ε _m=1), when m ≠ 0, ε _m=0.5(ε _m=0.5);

Calculated by formula (3):

$V_m^n(r,f)={\&Integral;}_0^1\exp \left(\mathrm{if}{\mathrm{\&rho;}}^2\right)\mathrm{\&rho;}{R}_n^m\left(\mathrm{\&rho;}\right)J_m\left(2\mathrm{\&pi;\&rho;r}\right)\mathrm{d\&rho;}---\left(3\right),$

In the formula Expand by the Nijboer-Zernike polynomial theory, use the formal expansion of progression to become:

$\begin{array}{c}{V}_n^m(r,f)\exp \left(\mathrm{if}\right)\underset{l=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{(-2\mathrm{if})}^{l-1}\underset{j=0}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&upsi;}}_{\mathrm{lj}}\frac{J_{m+l+2j}\left(\mathrm{\&upsi;}\right)}{{\mathrm{l\&upsi;}}^l}\\ {\mathrm{\&upsi;}}_{\mathrm{lj}}={(-1)}^p(m+l+2j)\left(\begin{array}{c}m+j+l-1\\ l-1\end{array}\right)\left(\begin{array}{c}j+l-1\\ l-1\end{array}\right)\left(\begin{array}{c}l-1\\ p-j\end{array}\right)/\left(\begin{array}{c}q+l+j\\ l\end{array}\right)\end{array}$

Wherein, i is imaginary unit, i ²=-1; F is defocusing amount; υ=2 π r, r are tested laser beam spot radius;

,

Then by iterative algorithm, remove the high-order error of introducing, namely by the Predictor-Corrector iterative algorithm, the high-order error of introducing in the correcting algorithm obtains the wavefront fitting coefficient of high accuracy approximation

At last, match obtains tested laser beam pupil plane wavefront, namely carries out pupil function P (u, v) match by formula (4):

$P(u,v)=\mathrm{\&Sigma;}{\mathrm{\&beta;}}_n^m{Z}_n^m(u,v)=\mathrm{\&Sigma;}{\mathrm{\&beta;}}_n^m{R}_n^m\left(\mathrm{\&rho;}\right)\cos \left(\mathrm{m\&theta;}\right)---\left(4\right),$

Following formula is that pupil function P (u, v) is launched into the polynomial linear combination of Zernike, and u, v are coordinate figure in the formula, and θ is the phasing degree;

Calculate point spread function U (r, θ) through formula (5):

$U(r,\mathrm{\&theta;})=\mathrm{\&Sigma;}{\mathrm{\&beta;}}_n^{m}2i^m{V}_n^m(r,f)\cos \left(\mathrm{m\&theta;}\right)---\left(5\right),$

In the formula:

Be the wavefront fitting coefficient,

Provided by formula (3), m, n are integer, and i is imaginary unit, i ²=-1, f is defocusing amount, and r is tested laser beam spot radius, and θ is the phasing degree;

Thereby calculate high-precision wavefront and the phase information of tested laser beam, finish laser beam wavefront high-acruracy survey.

6. the laser beam detection method based on the ENZ theory according to claim 4, it is characterized in that, the concrete computation process of tested laser beam eigenwert is as follows, at first, strength information by pupil plane calculates facula mass center first moment＜x on the one hand 〉,＜y 〉, and then calculate facula mass center second moment＜x ²,＜y ²; Phase information by pupil plane calculates wavefront gradients first moment＜u on the other hand 〉,＜v 〉, and then calculate wavefront gradients second moment＜u ²,＜v ²; Then, calculate again mixed moment＜xu 〉,＜yv 〉; At last, calculate tested laser beam beamwidth value d, beam divergence angle θ according to following formula (6) ~ (11) _σ, quality factor M ², waist width d ₀, Rayleigh range z _R, beam waist position z ₀

Obtain tested laser beam beamwidth value d by formula (6), comprise d _x, d _y:

$\left\{\begin{array}{c}{d}_x=4\sqrt{<x^2>}\\ d_y=4\sqrt{<y^2>}\end{array}\right.---\left(6\right),$

In the formula＜x ²,＜y ²It is the facula mass center second moment;

Obtain tested laser beam beam divergence angle θ by formula (7) _σ, comprise

, :

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_x}=4\sqrt{<u^2>}\\ {\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_y}=4\sqrt{<v^2>}\end{array}\right.---\left(7\right),$

In the formula＜u ²,＜v ²It is the wavefront gradients second moment;

Obtain tested Laser Beam Quality Factor M by formula (8) ², comprise

,

:

$\left\{\begin{array}{c}{M}_x^2=\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{<x^2><u^2>-{<\mathrm{xu}>}^2}\\ M_y^2=\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{<y^2><v^2>-{<\mathrm{yv}>}^2}\end{array}\right.---\left(8\right),$

In the formula＜x ²,＜y ²Be the facula mass center second moment,＜u ²,＜v ²Be the wavefront gradients second moment,＜xu 〉,＜yv〉be mixed moment, the tested optical maser wavelength of λ;

Obtain tested laser beam waist width d by formula (9) ₀, comprise d _0x, d _0y:

$\left\{\begin{array}{c}{d}_{0x}=\frac{4M_x^2\mathrm{\&lambda;}}{\mathrm{\&pi;}{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_x}}\\ d_{0y}=\frac{4M_y^2\mathrm{\&lambda;}}{{\mathrm{\&pi;\&theta;}}_{{\mathrm{\&sigma;}}_y}}\end{array}\right.---\left(9\right),$

In the formula

,

Be tested Laser Beam Quality Factor,

, Be tested laser beam beam divergence angle, the tested optical maser wavelength of λ;

Obtain tested laser beam Rayleigh range z by formula (10) _R, comprise z _Rx, z _Ry:

$\left\{\begin{array}{c}{z}_{\mathrm{Rx}}=\frac{d_{0x}}{{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_x}}\\ z_{\mathrm{Ry}}=\frac{d_{0y}}{{\mathrm{\&theta;}}_{{\mathrm{\&sigma;}}_y}}\end{array}\right.---\left(10\right),$

D in the formula _0x, d _0yBe tested laser beam waist width,

,

Be tested laser beam beam divergence angle;

Obtain tested laser beam beam waist position by formula (11), comprise z _0x, z _0y:

$\left\{\begin{array}{c}{z}_{0x}=\frac{<\mathrm{xu}>z_{\mathrm{Rx}}}{|<\mathrm{xu}>|}\sqrt{{\left(\frac{d_x}{d_{0x}}\right)}^2-1}\\ z_{0y}=\frac{<\mathrm{yv}>z_{\mathrm{Ry}}}{|<\mathrm{yv}>|}\sqrt{{\left(\frac{d_y}{d_{0y}}\right)}^2-1}\end{array}\right.---\left(11\right),$

In the formula＜xu 〉,＜yv〉be mixed moment, z _Rx, z _RyBe tested laser beam Rayleigh range, d _x, d _yBe tested laser beam beamwidth value, d _0x, d _0yBe tested laser beam waist width.

Images