CN105466666A - Variable focusing optical path-based laser beam quality measurement device - Google Patents

Abstract

The invention discloses a variable focusing optical path-based laser beam quality measurement device and method. The variable focusing optical path-based laser beam quality measurement device is composed of a negative lens, a positive lens, an attenuation module and a photosensitive element which are located on the same optical axis, two linear guide rails used for driving the negative lens and the photosensitive element to move, and a data processing module used for controlling the movement of the linear guide rails and acquiring and analyzing the images of the photosensitive element; a variable focusing optical path is composed of the negative lens and the positive lens; the negative lens is installed on one of the linear guide rails and can move in the travel range of the linear guide rail; the positive lens is fixedly installed; the data processing module can control a distance between the positive lens and the negative lens precisely through the movement position of the linear guide rail so as to realize variable focusing; the attenuation module can realize attenuation of the power of an incident laser beam so that the power of laser irradiating on the photosensitive element can be proper assuredly; the photosensitive element is installed on the other linear guide rail and can move in the travel range of the linear guide rail so as to realize measurement of the size of the light spot of the laser beam at different positions. With the variable focusing optical path-based laser beam quality measurement device of the invention adopted, the application range of a laser beam quality measurement system can be greatly expanded, and measurement accuracy can be improved.

Description

A kind of apparatus for measuring quality of laser beam based on variable focus light path

Technical field

The invention belongs to laser beam quality field tests, more specifically, relate to a kind of apparatus for measuring quality of laser beam based on variable focus light path and method.

Background technology

Laser industry is the emerging strategic industries of 21st century, and along with the development of laser technology, it is more and more extensive in the application of industry, scientific research field.Particularly laser energy type application, as a kind of machining tool, Laser Processing equipment to China in recent years manufacturing transition and upgrade serve great facilitation.Energy type for laser is applied, and the beam quality of laser is a very important parameter, and it is the input parameter that in laser equipment, of light path design is very important, also determines laser to a great extent and equips final performance index.Therefore the importance of laser beam quality measuring technology highlights day by day, and having concurrently applied widely is that market is badly in need of with laser beam quality testing apparatus that is high measurement accuracy.

According to the hyperbolic curve transport property of Gaussian beam, the spot radius w of laser beam is expressed as the function of light path z, A, B, C are respectively equation coefficient:

w ²(z)＝A+Bz+Cz ²(1)

Existing laser beam quality tester focuses on laser beam to be measured with simple lens (focal distance f), remake with a tight waist after, utilize line slideway (stroke l) dynamic optical element near focal point (also namely remake with a tight waist near) at least 10 different light path place z after the lens _imeasure the spot radius size w of laser beam _i, then by these group data (z recorded _i, w _i) coefficient A, B, C of above-mentioned Hyperbolic Equation, then the beam quality M of testing laser bundle is gone out according to least square fitting ²waist radius w after Summing Factor focuses on _fprovided by following formula:

$M^2=\frac{\mathrm{\π}}{\mathrm{\λ}}\sqrt{AC-\frac{B^2}{4}}$

(2)

$w_f=\sqrt{A-\frac{B^2}{4C}}$

Wherein λ is the wavelength of testing laser bundle.

But, in order to ensure the accuracy measured, two conditions must be met: the minimum light spot that the beam waist diameter after (a) focusing must be greater than photo-sensitive cell measures diameter D ₀; B the stroke of () line slideway is at least greater than the Rayleigh distance of laser beam after the focusing of 5 times.Suppose that the initial waist radius of testing laser bundle is w ₀, then above-mentioned two conditions can represent with Mathematical inequalities below:

$2\frac{M^2\mathrm{\λ}}{{\mathrm{\πw}}_0}\·f\≥D_0$

(3)

$5\frac{M^2\mathrm{\λ}}{{\mathrm{\πw}}_0^2}\·f^2\≤l$

Obviously, diameter D is measured for given condenser lens focal distance f, line slideway stroke l and photo-sensitive cell minimum light spot ₀, only have (the M of certain limit ², w ₀) above-mentioned constraint inequality could be met, this means by a set of given laser beam quality testing apparatus of existing method, its testing laser bundle scope be suitable for will be restricted, or be difficult to the precision ensureing measurement.

Summary of the invention

The defect of contradiction between broad applicability and measuring accuracy cannot be taken into account for prior art, the object of the present invention is to provide a kind of apparatus for measuring quality of laser beam based on variable focus light path and method, for different testing laser bundles, remake out the beam waist diameter and Rayleigh distance that meet constraint condition requirement by variable focus light path; The scope of application of laser beam quality measuring system can be expanded greatly, improve measuring accuracy.

The invention provides a kind of apparatus for measuring quality of laser beam based on variable focus light path, comprising: variable focus module, photo-sensitive cell, for driving the first line slideway and the data processing module of described photo-sensitive cell movement; The testing laser light beam that variable focus module is used for accepting carries out variable focus process, makes the position of focusing adjustable; Photo-sensitive cell, its input end is used for the laser after collectiong focusing, and output facula view data; Data processing module, its input end is connected to the output terminal of photo-sensitive cell, and the first output terminal is connected to the control end of the first line slideway, and the second output terminal is connected to the control end of variable focus module; Moving for controlling the first line slideway dynamic optical element, controlling the second line slideway and driving negative lens to move, gathering the light spot image data of photo-sensitive cell at diverse location, and rear quality for outputting laser beam M is processed to light spot image data ²the factor.

Further, described variable focus module comprises the negative lens and positive lens that arrange with optical axis successively, and for driving described negative lens along the second line slideway of optical axis direction movement; Drive negative lens to move along optical axis direction by line slideway, change the spacing between negative lens and positive lens, realize variable focus process.

Further, the surface of described negative lens and described positive lens is coated with the anti-reflection deielectric-coating matched with optical maser wavelength.

Further, described apparatus for measuring quality of laser beam also comprises attenuation module, is arranged between described variable focus module and described photo-sensitive cell, for decaying to the laser after focusing.

Further, described data processing module comprises: control module, controls the first line slideway dynamic optical element and moves, and controls the second line slideway and drives negative lens to move; Collecting unit, for gathering the light spot image data of photo-sensitive cell at diverse location; And processing unit, for processing rear quality for outputting laser beam M to light spot image data ²the factor.

Further, described photo-sensitive cell can be CCD or CMOS.

Present invention also offers a kind of method laser beam quality measured based on above-mentioned apparatus for measuring quality of laser beam, comprise the steps:

(1) control the first line slideway dynamic optical element to move along optical axis, at least 10 different light path place z in guide rail stroke range _imeasure the light spot image data after variable focus module focuses on, and rear acquisition laser beam radius w is processed to light spot image data _i,

According to described light path z _iwith laser beam radius w _icalculate the beam quality M of testing laser bundle ²waist radius w after Summing Factor focuses on _f;

According to the beam quality M of testing laser bundle ²with the waist radius w after focusing _fobtain the waist radius w that incoming laser beam is initial ₀, and by beam quality M ²with waist radius w ₀the first class value (M of testing laser light beams mass parameter is obtained after combination ², w ₀) ₁;

(2) according to the first class value (M ², w ₀) ₁calculate spacing d ' between negative lens and positive lens, control the second line slideway by data processing module and drive negative lens to move to target range d ' place;

(3) the second class value (M that step (1) obtains testing laser light beams mass parameter is repeated ², w ₀) ₂;

(4) the second class value (M is calculated ², w ₀) ₂with the first class value (M ², w ₀) ₁relative error, and compared with control errors factor ε; If then obtain the Beam quality parameter (M of testing laser bundle ², w ₀) ₂; If then according to incoming laser beam beam quality second group of parameter (M ², w ₀) ₂, repeat step (2) to step (4).

Further, the initial waist radius w of incoming laser beam is obtained according to following formulae discovery ₀:

$q_0=d_0+i\frac{{\mathrm{\πw}}_0^2}{M^2\mathrm{\λ}};q_1=\frac{t_{11}\·q_0+t_{12}}{t_{21}\·q_0+t_{22}};\begin{array}{c}{Z}_{Rf}=\mathrm{Im}\left(q_1\right)\\ w_f=\sqrt{\frac{\mathrm{Im}\left(q_1\right)\·M^2\mathrm{\λ}}{\mathrm{\π}}}\end{array};$

$\begin{array}{c}{T}_1=\left(\begin{array}{cc}1& 0\\ -\frac{1}{f_1}& 1\end{array}\right)\\ T_2=\left(\begin{array}{cc}1& d\\ 0& 1\end{array}\right);T=T_3\·T_2\·T_1=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& t_{22}\end{array}\right)=\left(\begin{array}{cc}1-\frac{d}{f_1}& d\\ -\frac{1}{f_2}+\frac{d}{f_1{f}_2}-\frac{1}{f_1}& 1-\frac{d}{f_2}\end{array}\right)\\ T_3=\left(\begin{array}{cc}1& 0\\ -\frac{1}{f_2}& 1\end{array}\right)\end{array}.$

Further, according to above-mentioned formula and $\begin{array}{c}5\mathrm{Im}\left(q_1\right)\≤l_2\\ 2\sqrt{\frac{Im\left(q_1\right)\·M^2\mathrm{\λ}}{\mathrm{\π}}}\≥D_0\end{array}$ Obtain spacing d ' between negative lens and positive lens.

Namely the present invention is by introducing variable focus light path, the first line slideway is utilized to drive negative lens motion, the spacing d changed between negative lens and positive lens realizes above-mentioned purpose, to ensure extensive adaptability and the high measurement accuracy of laser beam quality proving installation simultaneously.

Accompanying drawing explanation

Fig. 1 is the structural representation of the apparatus for measuring quality of laser beam based on variable focus light path that the embodiment of the present invention provides;

Fig. 2 is the realization flow figure of the apparatus for measuring quality of laser beam measuring method based on variable focus light path that the embodiment of the present invention provides;

1 is negative lens, and 2 is positive lens, and 3 is attenuation module, and 4 is photo-sensitive cell, and 5 is the second line slideway, and 6 is the first line slideway, and 7 is data processing module.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

A kind of apparatus for measuring quality of laser beam based on variable focus light path provided by the invention, comprise the negative lens of same optical axis successively, positive lens, attenuation module and photo-sensitive cell, for the data processing module driving the first line slideway of negative lens movement, the second line slideway of dynamic optical element movement and analyze for Systematical control.Negative lens, positive lens, attenuation module, photo-sensitive cell are on same optical axis; The data line of described photo-sensitive cell, the control line of the first line slideway are connected with data processing module respectively with the control line of the second described line slideway.Data processing module has Image Data Acquisition Card, control card and calculating laser beam quality M ²the data processor of the factor, realize controlling the motion of two line slideways, and then accurately control the locus of negative lens and photo-sensitive cell, to realize photo-sensitive cell become the collection analysis of laser beam spot view data, obtain laser beam spot size, realize laser beam beam quality M ²the calculating of the factor.

In embodiments of the present invention, the second line slideway moves along optical axis direction for driving negative lens, and accurately locates the position of negative lens.Attenuation module can decay to incident laser power, and the attenuator of appropriate attenuation multiplying power can be selected to change according to the size of incident laser power.First line slideway is used for dynamic optical element and moves along optical axis direction, and accurately locates the position of photo-sensitive cell.Photo-sensitive cell can carry out analytical calculation to the spot size of incoming laser beam; Line slideway can move along optical axis direction with photo-sensitive cell, and the position of accurate location photo-sensitive cell, thus realizes measuring laser beam spot size at least 10 different light path places.Data processing module has Image Data Acquisition Card, control card and calculating laser beam quality M ²the data processor of the factor, be connected with photo-sensitive cell by data line, be connected with the second line slideway by control line, be connected with line slideway (6) by control line, realize controlling the motion of the second line slideway and the first line slideway, and then accurately control the position of negative lens and photo-sensitive cell, realize the collection analysis to the light spot image data that photo-sensitive cell obtains, obtain laser beam spot size, realize laser beam beam quality M ²the calculating of the factor.

In embodiments of the present invention, f ₁for the focal length of negative lens; f ₂for the focal length of positive lens; D is the spacing between negative lens and positive lens; l ₁it is the stroke of the first line slideway; l ₂it is the stroke of the second line slideway.Theoretical according to the q Parametric Representation of Gaussian laser beam, by the q parameter q of testing laser bundle at the incident front surface place of negative lens ₀be expressed as following formula:

$q_0=d_0+i\frac{{\mathrm{\πw}}_0^2}{M^2\mathrm{\λ}}---\left(4\right)$

Wherein d ₀for laser emitting mouth is to the distance of negative lens, λ is the wavelength of testing laser bundle, w ₀for the initial waist radius of testing laser bundle, M ²for the beam quality factor of testing laser bundle.

Theoretical according to the Transfer-matrix of Gaussian beam, negative lens, the air layer between negative lens and positive lens, positive lens three can be expressed in matrix as following formula:

$\begin{array}{c}{T}_1=\left(\begin{array}{cc}1& 0\\ -\frac{1}{f_1}& 1\end{array}\right)\\ T_2=\left(\begin{array}{cc}1& d\\ 0& 1\end{array}\right)\\ T_3=\left(\begin{array}{cc}1& 0\\ -\frac{1}{f_2}& 1\end{array}\right)\end{array}---\left(5\right)$

The transmission matrix that then three is total can be expressed as following formula:

$T=T_3\·T_2\·T_1=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& t_{22}\end{array}\right)=\left(\begin{array}{cc}1-\frac{d}{f_1}& d\\ -\frac{1}{f_2}+\frac{d}{f_1{f}_2}-\frac{1}{f_1}& 1-\frac{d}{f_2}\end{array}\right)---\left(6\right)$

Then after lens transformation at the laser beam q parameter q at positive lens outgoing rear surface place ₁be expressed as following formula:

$q_1=\frac{t_{11}\·q_0+t_{12}}{t_{21}\·q_0+t_{22}}---\left(7\right)$

Then after variable focus lens group focuses on, the Rayleigh Distance geometry waist radius of laser beam is:

$\begin{array}{c}{Z}_{Rf}=\mathrm{Im}\left(q_1\right)\\ w_f=\sqrt{\frac{\mathrm{Im}\left(q_1\right)\·M^2\mathrm{\λ}}{\mathrm{\π}}}\end{array}---\left(8\right)$

Now, aforesaid constraint condition can be expressed as:

$\begin{array}{c}5\mathrm{Im}\left(q_1\right)\≤l_2\\ 2\sqrt{\frac{\mathrm{Im}\left(q_1\right)\·M^2\mathrm{\λ}}{\mathrm{\π}}}\≥D_0\end{array}---\left(9\right)$

For given testing laser bundle parameter (M ², w ₀), and the f determined ₁and f ₂, above-mentioned constraint inequality can be met by the value changing d, guarantee measuring accuracy.

Fig. 1 shows the structural representation of the apparatus for measuring quality of laser beam based on variable focus light path that the embodiment of the present invention provides, and for convenience of explanation, illustrate only the part relevant to the embodiment of the present invention, details are as follows:

It forms the negative lens 1, positive lens 2, attenuation module 3 and the photo-sensitive cell 4 that comprise same optical axis successively, for the data processing module 7 driving the line slideway 5 of negative lens 1 movement, the line slideway 6 of dynamic optical element 4 movement and analyze for Systematical control.Described negative lens 1, positive lens 2, attenuation module 3, photo-sensitive cell 4 are on same optical axis; The data line 8 of described photo-sensitive cell 4, the control line 10 of described line slideway 5 are connected with described data processing module 7 respectively with the control line 9 of described line slideway 6.Described data processing module has Image Data Acquisition Card, control card and calculating laser beam quality M ²the data processor of the factor, realize controlling the motion of two line slideways, and then accurately control the locus of negative lens and photo-sensitive cell, to realize photo-sensitive cell become the collection analysis of laser beam spot view data, obtain laser beam spot size, realize laser beam beam quality M ²the calculating of the factor.

Fig. 2 shows the workflow sketch of the apparatus for measuring quality of laser beam measuring method based on variable focus light path that the embodiment of the present invention provides, and concrete steps are as follows:

The first step: do not move the second line slideway 5, allows negative lens 1 be in initial value with the spacing of positive lens 2, controls mobile first line slideway 6, photo-sensitive cell 4 is moved along optical axis, at least 10 different light path place z in guide rail stroke range by data processing module 7 _imeasure the laser beam radius w after the focusing of line focus mirror group _i, then by these group data (z recorded _i, w _i) coefficient A, B, C of (1) formula Hyperbolic Equation is gone out according to least square fitting, the beam quality M of testing laser bundle is calculated according to (2) formula ²waist radius w after Summing Factor focuses on _f, then calculate the initial waist radius w of incoming laser beam according to (4) ~ (8) formula ₀, obtain the first class value (M of testing laser light beams mass parameter thus ², w ₀) ₁.

Second step: the input laser beam parameters obtained according to the first step, calculates spacing value d ' between rational negative lens and positive lens according to (4) ~ (9) formula, to meet constraint condition (9) formula.Then mobile second line slideway 5 is controlled to target range d ' place by data processing module 7.

3rd step: control mobile first line slideway 6 by data processing module 7, photo-sensitive cell 4 is moved along optical axis, again at least 10 different light path place z in guide rail stroke range _imeasure the laser beam radius w after the focusing of line focus mirror group _i, then by these group data (z recorded _i, w _i) coefficient A, B, C of (1) formula Hyperbolic Equation is gone out according to least square fitting, the beam quality M of testing laser bundle is calculated according to (2) formula ²waist radius w after Summing Factor focuses on _f, then calculate the initial waist radius w of incoming laser beam according to (4) ~ (8) formula ₀, obtain the second class value (M of testing laser light beams mass parameter thus ², w ₀) ₂.

4th step: calculate incoming laser beam Beam quality parameter second class value (M ², w ₀) ₂with the first class value (M ², w ₀) ₁relative error, and compared with control errors factor ε.If then complete measurement, the Beam quality parameter providing testing laser bundle is (M ², w ₀) ₂.If then according to incoming laser beam beam quality second group of parameter (M ², w ₀) ₂, repeat second step to the 4th step, until complete measurement.Wherein, control errors factor ε is the measurement relative error of apparatus for measuring quality of laser beam; Particularly, for a set of measurement mechanism product, measure relative error and determined in the design phase by measurement mechanism, such as 10%, 5%, 1% etc., be finally labeled as the measuring accuracy index of product.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (9)

1. the apparatus for measuring quality of laser beam based on variable focus light path, it is characterized in that, comprise: variable focus module, photo-sensitive cell (4), for driving the first line slideway (6) and the data processing module (7) of described photo-sensitive cell (4) movement;

The testing laser light beam that variable focus module is used for accepting carries out variable focus process, makes the position of focusing adjustable;

Photo-sensitive cell (4), its input end is used for the laser after collectiong focusing, and output facula view data;

Data processing module (7), its input end is connected to the output terminal of photo-sensitive cell (4), and the first output terminal is connected to the control end of the first line slideway (6), and the second output terminal is connected to the control end of variable focus module; Mobile for controlling the first line slideway (6) dynamic optical element (4), controlling the second line slideway (5) drives negative lens (1) mobile, gather the light spot image data of photo-sensitive cell (4) at diverse location, and rear quality for outputting laser beam M is processed to light spot image data ²the factor.

2. apparatus for measuring quality of laser beam as claimed in claim 1, it is characterized in that, described variable focus module comprises the negative lens (1) and positive lens (2) that arrange with optical axis successively, and for driving described negative lens (1) along second line slideway (5) of optical axis direction movement;

Drive negative lens (1) to move along optical axis direction by line slideway (5), change the spacing between negative lens (1) and positive lens (2), realize variable focus process.

3. apparatus for measuring quality of laser beam as claimed in claim 1 or 2, it is characterized in that, the surface of described negative lens (1) and described positive lens (2) is coated with the anti-reflection deielectric-coating matched with optical maser wavelength.

4. the apparatus for measuring quality of laser beam as described in any one of claim 1-3, it is characterized in that, described apparatus for measuring quality of laser beam also comprises attenuation module (3), be arranged between described variable focus module and described photo-sensitive cell (4), for decaying to the laser after focusing.

5. the apparatus for measuring quality of laser beam as described in any one of claim 1-4, is characterized in that, described data processing module (7) comprising:

Control module, controls the first line slideway (6) dynamic optical element (4) mobile, controls the second line slideway (5) and drives negative lens (1) mobile;

Collecting unit, for gathering the light spot image data of photo-sensitive cell (4) at diverse location; And

Processing unit, for processing rear quality for outputting laser beam M to light spot image data ²the factor.

6. the apparatus for measuring quality of laser beam as described in any one of claim 1-5, is characterized in that, described photo-sensitive cell (4) is CCD or CMOS.

7. based on the method that apparatus for measuring quality of laser beam according to claim 1 is measured laser beam quality, it is characterized in that, comprise the steps:

(1) control the first line slideway dynamic optical element to move along optical axis, at least 10 different light path place z in guide rail stroke range _imeasure the light spot image data after variable focus module focuses on, and rear acquisition laser beam radius w is processed to light spot image data _i,

According to described light path z _iwith laser beam radius w _icalculate the beam quality M of testing laser bundle ²waist radius w after Summing Factor focuses on _f;

According to the beam quality M of testing laser bundle ²with the waist radius w after focusing _fobtain the waist radius w that incoming laser beam is initial ₀, and by beam quality M ²with waist radius w ₀the first class value (M of testing laser light beams mass parameter is obtained after combination ², w ₀) ₁;

(2) according to the first class value (M ², w ₀) ₁calculate spacing d ' between negative lens and positive lens, control the second line slideway by data processing module and drive negative lens to move to target range d ' place;

(3) the second class value (M that step (1) obtains testing laser light beams mass parameter is repeated ², w ₀) ₂;

(4) the second class value (M is calculated ², w ₀) ₂with the first class value (M ², w ₀) ₁relative error, and compared with control errors factor ε; If then obtain the Beam quality parameter (M of testing laser bundle ², w ₀) ₂; If then according to incoming laser beam beam quality second group of parameter (M ², w ₀) ₂, repeat step (2) to step (4).

8. method as claimed in claim 7, is characterized in that, obtain the initial waist radius w of incoming laser beam according to following formulae discovery ₀:

$q_0=d_0+i\frac{{\mathrm{\πw}}_0^2}{M^2\mathrm{\λ}};q_1=\frac{t_{11}\·q_0+t_{12}}{t_{21}\·q_0+t_{22}};\begin{array}{c}{Z}_{Rf}=\mathrm{Im}\left(q_1\right)\\ w_f=\sqrt{\frac{\mathrm{Im}\left(q_1\right)\·M^2\mathrm{\λ}}{\mathrm{\π}}}\end{array};$

$\begin{array}{c}{T}_1=\left(\begin{array}{cc}1& 0\\ -\frac{1}{f_1}& 1\end{array}\right)\\ T_2=\left(\begin{array}{cc}1& d\\ 0& 1\end{array}\right)\\ T_3=\left(\begin{array}{cc}1& 0\\ -\frac{1}{f_2}& 1\end{array}\right)\end{array};$ $T=T_3\·T_2\·T_1=\left(\begin{array}{cc}{t}_{11}& t_{12}\\ t_{21}& t_{22}\end{array}\right)=\left(\begin{array}{cc}1-\frac{d}{f_1}& d\\ -\frac{1}{f_2}+\frac{d}{f_1{f}_2}-\frac{1}{f_1}& 1-\frac{d}{f_2}\end{array}\right);$

Wherein, q ₀for laser beam is in the q parameter at the incident front surface place of negative lens, q ₁for laser beam is in the laser beam q parameter at positive lens outgoing rear surface place, Im (q ₁) refer to q ₁imaginary part, d ₀for testing laser exit portal is to the distance of negative lens, d is the spacing between negative lens and positive lens, w ₀for the initial waist radius of testing laser bundle, M ²for the beam quality factor of testing laser bundle, λ is the wavelength of testing laser bundle, Z _rffor focusing on the Rayleigh distance of rear laser beam, w _ffor focusing on the waist radius of rear laser beam, f ₁for the focal length of negative lens; f ₂for the focal length of positive lens, l ₁it is the stroke of the first line slideway; l ₂be the stroke of the second line slideway, T ₁, T ₂, T ₃be respectively the transmission matrix of negative lens, air layer between negative lens and positive lens, positive lens three, T is the total transmission matrix of variable focus module, t ₁₁, t ₁₂, t ₂₁, t ₂₂be respectively four matrix elements of the total transmission matrix of variable focus module.

9. method as claimed in claim 8, is characterized in that, according to above-mentioned formula and obtain spacing d ' between negative lens and positive lens, wherein, D ₀for the minimum light spot of photo-sensitive cell measures diameter.