CN1333231C - Method for measuring light-beam central position by array CCD - Google Patents

Abstract

The invention relates to a method for measuring the central position of a light beam with a linear array CCD, relating to a photoelectric measurement method for measuring the central position of a light beam incident on the surface of the linear array CCD and a specific method for measuring displacement and angular displacement by using the method. The invention makes the radiation power density of the light spot on the CCD surface be Gaussian distribution or quasi-Gaussian distribution; determine the error limit of the digital signal output and select the truncation threshold by the CCD, relevant circuit characteristics, etc.; the effective digital signal of the truncated quasi-Gaussian distribution The weighted regression method is used to calculate the estimated beam center position; the Monte Carlo method is used to numerically simulate the error distribution to determine the beam width range. The method of the present invention can reduce the effective resolution and precision of the central position of the line array CCD light beam from about 1W to below 0.03W (W is the pixel pitch), so as to realize submicron precision displacement and 1 second effective resolution angle It can be used to measure the rotation angle of the shock galvanometer mirror, the wavelength of the linear spectrum and other related quantities.

Description

A Method of Measuring the Center Position of Beam with Linear Array CCD

technical field

The invention relates to a new photoelectric measurement method for measuring the central position of a light beam incident on the surface of a linear array CCD, and a specific method for measuring linear displacement, length, angular displacement, angle, etc. by using this method, which belongs to the geometric quantity measurement method and The technical field of the instrument; it can also be applied to other types of measured measurements that can be converted into displacements and angles, such as measuring the magnetic flux density through the deflection angle of the shock galvanometer rotating mirror, passing the measured spectral line on the spectral surface Position measurement spectral line wavelength, etc.

Background technique

In the previous measurement technology using linear array CCD, most of the effective resolution corresponds to 1 pixel interval W, and the report of individual sub-pixel resolution technology can only reduce the effective resolution value to about 0.5W. For example, in some literatures, two columns of CCDs with staggered 0.5W are used to realize sub-pixel measurement. Although there are individual literature reports with a resolution below 0.1 pixel, there is no description of indicators such as nonlinear standard deviation or uncertainty in such literature, so it cannot be regarded as the same as the standard deviation of measurement within a certain measurement range. The effective resolution of the connection.

In the prior art, the width of the beam on the surface of the CCD is usually required to be below 5W, preferably as narrow as 2W to 3W; the beam distribution is usually required to be as uniform as possible, and the "center of gravity" judgment method or the least squares regression method under the assumption of equal weight is generally used. Regression theory can be used to prove that when the dependent variables of equal weight regression have the same error eigenvalue, the influence of the error of the edge data with a small value on the result is significantly greater than the influence of the error of the middle data; The weight factor of the variable y _j =lnV _Dj is proportional to the square of the magnitude V _Dj , and the error characteristic value of the linear edge dependent variable is large and the weight is small. Existing technologies also need to fully retain the acquired effective information, and take a cautious attitude towards data elimination.

Among the existing technologies, grating technology and laser interferometry are mainly used to measure displacement with a range of about 35mm and a resolution of submicron. However, the measurement nonlinear error of grating technology is limited to the order of microns. In the prior art, the devices whose angle measurement resolution and accuracy are worse than 0.5' mainly include photoelectric encoders, etc., and the angle measurement resolution and accuracy are better than 2 "with circular grating technology. The angle measurement accuracy is between 3 and 6". 、The effective resolution of 1" digital automatic measuring device has a wide range of application requirements, and it is difficult to realize it with methods other than circular grating technology.

Most of the CCD spectrometers in the prior art use the pixel interval W as the basis for determining the wavelength resolution, and the stability and repeatability of the optical mechanical system to ensure the accuracy of wavelength measurement.

Contents of the invention

The purpose of the present invention is to provide a method for measuring the central position of the beam with a linear array CCD for improving the effective resolution and precision of the existing linear array CCD for measuring the central position of the beam, so that it can reach below 0.03W (W is the pixel pitch ), in order to realize the measurement method of displacement or length with submicron precision, the measurement method of angular displacement or angle with an effective resolution of 1", and make it applicable to the measurement fields of other related physical quantities.

Technical scheme of the present invention is as follows:

A method for measuring the central position of a light beam with a linear array CCD, characterized in that:

1) Make the radiation power line density of the light spot on the surface of the CCD detector along the line array direction be Gaussian distribution or quasi-Gaussian distribution;

2) Calculate the truncation threshold: set the effective digital signal output of the pixel whose jth center coordinate of the CCD detector is _xj to be V _Dj , and the V _Dj is an integer multiple of LSB; according to the characteristics of the CCD detector and related circuits , output bit number N and noise amplitude, express the error limit of V _Dj with formula ±U _Vj =±(a+c%V _j ), a is a normal number in the formula, and c% is a proportional coefficient; With (a+c %×2 ^N ) to a certain integer between 2 ^N /20 as the truncation threshold V _th , so that the effective digital output signal V _Dj of the pixel not less than the threshold V _th after truncation is a truncation quasi-Gaussian distribution;

3) For the output signal V _Dj of the truncated quasi-Gaussian distribution of the pixel whose center coordinate is x _j , the regression equation model is used ${\mathrm{the\; y}}_j=b_0+b_1{x}_j+b_2{x}_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">j</figure-callout>}}^2,$ Taking x _j and x _j ² as independent variables and y _j =ln(V _Dj ) as dependent variables respectively, the weighting factor is $w_{{\mathrm{the\; y}}_j}={(V_{\mathrm{Dj}}/u_{V_j})}^2$ Calculate the weighted regression of b1 _and b ₂ , and then calculate the estimated position of the center of the beam ${\hat{x}}_c=-b_1/\left({2b}_2\right);$

4) Determine the beam width range by numerically simulating the error distribution with the Monte Carlo method, and the specific steps are:

A). When the pixel spacing W is known, for the beam center position x _c , according to the Gaussian distribution of the radiation power line density E _l (x _c , x)=E _lm exp(-(xx _c ) ² /(2σ ² )), under the value of a certain distribution standard deviation σ, integrate the fixed sampling time interval and the position variable x in the pixel to calculate the analog signal V _j = V _j of the jth pixel whose center coordinate is x _j (x _j , x _c ), as the initial value of the photoelectric measurement signal before analog-to-digital conversion; V _j is a relative value, and a proportional constant is selected during integration so that the peak value of V _j is 0.8×2 ^N ;

B). According to the error limit is $\&PlusMinus;u_{V_j}=\&PlusMinus;(a+c\%V_j)$ Numerical simulation of a set of random error distributions ${\mathrm{\&epsiv;}}_{V_j}=r_{\mathrm{aj}}+r_{\mathrm{cj}}\%V_j,$ Here r _aj and r _cj are uniformly distributed random numbers whose error limits are ±a and ±c respectively; take the integer part of (V _j +ε _Vj ) as the digital signal output V _Dj after analog-to-digital conversion;

C). Intercept the effective digital signal of V _Dj ≥ V _th ;

D). pair equation ${\mathrm{the\; y}}_j=\ln \left(V_{\mathrm{Dj}}\right)=b_0+b_1{x}_j+b_2{x}_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">j</figure-callout>}}^2$ Authorization factor is $w_{{\mathrm{the\; y}}_j}={(V_{\mathrm{Dj}}/u_{V_j})}^2$ The weighted regression of ${\hat{x}}_c=-b_1/\left({2b}_2\right),$ and calculate the error ${\mathrm{\&epsiv;}}_{\mathrm{xc}}={\hat{x}}_c-x_c$ Come;

E). Calculate the error ε _xc of each group for multiple groups of simulation error distributions with the same law, and then calculate the standard deviation s _xc of the error, which is the measurement standard deviation of the beam center position x _c corresponding to the beam distribution standard deviation σ ;

F). Repeat the steps from A to E above to calculate the corresponding standard deviation s _xc for different σ values, and obtain the relationship curve between s _xc /W and σ/W, and then find out that s _xc /W is not greater than 0.08 The value range of the beam distribution parameter σ/W.

In the above method, it is characterized in that the number of effective digital output signals V _Dj of pixels not smaller than the threshold V _th after truncation, that is, the number of effective pixels within the beam width, is between 5 and 50.

The present invention provides the method utilizing above-mentioned method to measure the rotating mirror angle, it is characterized in that the method comprises the steps:

1) Use the first convex lens with a focal length of 10mm≤F ₁ ′≤50mm to make the slit illuminated by the light source form a bright slit real image with reduced equivalent width and convenient width adjustment. After mirror reflection, the beam width is formed on the surface of the CCD detector through the second convex lens with a focal length of 50mm≤f ₂ ′≤300mm; the number of effective output signals V _Dj of the pixel after truncating, that is, the number of beams within the beam width The effective number of pixels is between 5 and 50;

2) Utilize the CCD detector and the computer of signal acquisition and processing, according to the above-mentioned method of measuring the beam center position x _e with the linear array CCD detector, find the truncation threshold, and output V _Dj to the effective digital signal of the truncated quasi-Gaussian distribution Weighted regression, giving the beam center position in real time;

3) Using the first-order approximate relationship between the deflection angle α of the rotating mirror and the offset (x _c -x _c0 ) of the beam center position x _c on the surface of the CCD detector: (x _c -x _c0 )=(k ₂ d) sin(2α), the first-order estimate of the rotation angle α of the rotating mirror can be obtained, where k ₂ is the lateral magnification of the second lens, d is the distance from the slit real image Q ₁ to the rotating axis O of the rotating mirror, x _c0 is the coordinate of the beam center at the intersection of the CCD detector surface and the optical axis of the second lens when the rotating mirror angle α=0; after the installation and adjustment of the measuring device, the deflection angle α and the beam center position x _c on the CCD detector surface are obtained through calibration Quantitative measured data of the relationship between them, and then get the correction value data of the first-order estimate.

The invention provides a method for measuring the dynamic deflection angle of the rotating mirror of the impulse galvanometer by using the above method, which is characterized in that the method comprises the following steps:

1) Use the first convex lens with a focal length of 10mm≤f ₁ ′≤50mm to make the slit illuminated by the light source form a real slit image with reduced equivalent width and convenient width adjustment. After being reflected by the rotating mirror of the meter, it passes through the second convex lens with a focal length of 50mm≤f ₂ ′≤300mm to form a quasi-Gaussian distribution spot on the surface of the CCD detector; fix the impact galvanometer and the components on the same rigid board;

2) Select a linear array CCD detector with a total number of pixels N _p ≥ 7400 and a pixel spacing W = 4.7 μm, the number of signal output bits N = 8, and the error limit of V _Dj uses the formula $\&PlusMinus;u_{V_j}\&ap;\&PlusMinus;(1.5+1.5\%V_{\mathrm{Dj}})$ Indicates that the truncation threshold V _th =6LSBs is selected;

3) Adjust the lateral magnification k and the distance d from the real slit image _Q1 to the point O of the rotating mirror, so that the effective width N _p W of the CCD detector corresponds to the range of the impact charge or current to be measured by the impact galvanometer; at the same time Adjust the distance from the slit to the first lens so that the number of effective pixels within the beam width on the surface of the CCD detector is between 10 and 30;

4) Adjust the brightness of the light source or the circuit gain in the signal acquisition and calculation processing part, so that the maximum value of the digital signal (V _Dj ) _max of the pixel after truncation is ≈200LSB, and the dependent variable y _j = ln in weighted regression after truncation The weight factor of (V _Dj ) is used $w_{{\mathrm{the\; y}}_i}={(V_{\mathrm{Dj}}/u_{V_j})}^2$ Formula to calculate, calculate the estimate of beam center position x _c and then calculate the dynamic deflection angle of the galvanometer rotating mirror.

The present invention also provides a method for measuring displacement or length using the method for measuring beam center position x _c with a linear array CCD, the method comprising the following steps:

1) Using signal acquisition and calculation processing components, CCD detectors and optical components to achieve measurement, the CCD detector adopts a linear array CCD detector with a total number of pixels N _p ≥ 5000 and a pixel interval W ≤ 7 μm; the described The optical component is composed of a semiconductor laser and a lens. The quasi-parallel semiconductor laser beam forms a quasi-Gaussian distribution beam waist on the surface of the CCD detector through the lens; the optical component is composed of a light-emitting diode, a slit or a small hole, and a lens. The lens will transmit The light passing through the slit or small hole converges on the surface of the CCD detector;

随之改变，以直接反映位移或位置改变，实现对位移或长度的测量。2) The number of effective pixels of the light beam emitted by the optical component within the beam width of the CCD detector surface is between 10 and 30, and the CCD detector and the optical component are respectively installed on the stationary part and the movable part that can move linearly Above, the arrangement direction of the CCD detector pixels is parallel to the moving direction of the movable part. When the relative displacement occurs between the beam axis or the center position of the spot and the CCD detector, the value of the weighted regression result

Change accordingly to directly reflect the displacement or position change, and realize the measurement of displacement or length.

The invention provides a method for measuring the center position of the light beam by using the linear array CCD detector to realize the measurement method of 0-360 degree angle, which is characterized in that:

物镜光轴垂直于CCD探测器表面；1) The quasi-parallel semiconductor laser beam with a diameter of not less than 3mm is reflected by any mirror surface of a rotatable metal n-hedron, the serial number of the mirror surface is i, and the reflected beam passes through an objective lens with an effective aperture angle of not less than ±360°/n Converging on the surface of a linear array with a total number of pixels N _p ≥ 5000 and a pixel spacing W ≤ 7 μm, the focal length of the objective lens is

The optical axis of the objective lens is perpendicular to the surface of the CCD detector;

2) Adjust the focus so that the number of effective pixels of the beam within the beam width on the surface of the CCD detector is between 10 and 30, and use truncated processing and weighted regression to obtain the estimate of the beam center coordinate _xc for the digital signal output of the CCD detector ;

3) The azimuth φ of the positive n-hedron is estimated by the mirror serial number i and the beam center coordinate x _c Sure, $\mathrm{\&phi;}=\frac{360}{\mathrm{no}}i+\arctan \left(\frac{{\hat{x}}_c-x_{c0}}{{f_3}^{\&prime;}}\right)+\mathrm{\&epsiv;}({\hat{x}}_c,i)+{\mathrm{\&phi;}}_0,$ In the formula, x _c0 is the coordinate of the optical axis of lens 9 and the surface intersection of CCD detector, and φ ₀ is a constant term, is an angle correction item determined by the degree, and directly outputs or displays the azimuth φ of the n-hedron through the signal acquisition and calculation components.

The present invention provides a method for measuring the wavelength of the linear visible spectrum by using the method of measuring the center position x _c of the light beam with a linear array CCD detector, characterized in that the method includes the following steps:

1) Make the quasi-parallel light beams of different wavelengths with different diffraction angles emitted by the grating dispersion element with no less than 1200 lines per millimeter pass through a lens or concave mirror with a focal length of no less than 150mm, and image it on the surface of the linear array CCD detector. The total number of pixels of the CCD detector N _p ≥ 5000 and the pixel interval W ≤ 7 μm;

2) focusing the lens or the concave reflector so that the number of effective pixels within the beam width on the surface of the CCD detector is between 5 and 15;

再同时或交替测量出波长位于待测谱线附近的He-Ne放电管的若干条已知波长λ_i的参考谱线中心坐标估值

用最小二乘法直线拟合或二次回归求出局域线色散方程 ${\hat{x}}_{\mathrm{ci}}=f\left({\mathrm{\&lambda;}}_i\right),$ 最后将 代入色散方程求出未知谱线波长λ_x来。3) By truncating the digital signal output of the CCD detector pixel and weighted regression, calculate the coordinate estimation of the center of the linear spectral line λ _x to be measured

Then simultaneously or alternately measure the center coordinates of the reference spectral lines of several known wavelengths λ _i of the He-Ne discharge tube whose wavelength is near the spectral line to be measured

Find the local line dispersion equation by linear fitting or quadratic regression ${\hat{x}}_{\mathrm{ci}}=f\left({\mathrm{\&lambda;}}_i\right),$ Finally will Substitute into the dispersion equation to find the wavelength λ _x of the unknown spectral line.

Compared with the prior art, the present invention has the following advantages and outstanding progress:

The present invention improves the detection sensitivity of the central position of the beam by adopting the beam distribution of the quasi-Gaussian distribution; by appropriately increasing the truncation threshold to reduce the influence of interference noise; by appropriately widening the effective width of the beam to make the response characteristics of each pixel uneven, The influence of undetermined system error components such as nonlinearity is "randomized" in the total measurement effective signal, and then the accuracy of beam center position measurement is improved by weighted regression after considering the actual measurement error characteristics of the pixel. The invention can reduce the effective resolution and standard deviation of measuring the central position of the light beam with a linear array CCD detector to less than 0.03W, which is 1-2 orders of magnitude less than the prior art. Therefore, when using the displacement measurement method of the present invention, the standard deviation measured can be less than 0.25 μm, and when N _p ≈7400, the non-linear standard deviation can reach below 1×10 ^-5 of the measurement range; using the method of the present invention The angle measurement method can also effectively improve the measurement precision.

The present invention requires that the light spots form a quasi-Gaussian distribution, which is relatively easy to realize. The invention emphasizes that the weighted regression method with unequal precision of the dependent variable must be adopted to effectively reduce the influence of data errors on the edge of the distribution. Using regression theory, it can be proved that: when the dependent variables of equal weight regression have the same error eigenvalues, the influence of the error of the marginal data with small magnitude on the result -b ₁ /(2b ₂ ) is significantly greater than that of the middle data error; and The weight factor of the dependent variable y _j =lnV _Dj is proportional to the square of the value V _Dj in quasi-Gaussian linear parametric regression, and the error characteristic value of the linear edge dependent variable is large and the weight is small.

Description of drawings

Fig. 1 is a schematic structural diagram of a device for measuring the angle of rotation of a rotating mirror according to the method of the present invention.

Fig. 2 is a schematic diagram of the main structure of the angle measurement method for measuring 0-360 degrees.

Detailed ways

The method for measuring beam center position with linear array CCD described in the present invention and according to this method carry out rotating mirror angle measurement, impact circuit meter rotating mirror dynamic deflection angle measurement, displacement measurement, 0～360 degree angle measurement and linear visible spectrum Specific instructions for wavelength measurement are as follows:

1. The method of measuring the center position of the beam with a linear array CCD

1.1 Beam radiation power density distribution using quasi-Gaussian distribution

The Gaussian distribution is a distribution that is closer to the radiation power density distribution of the common beam cross-section, and it is also a distribution that is easier to approximate. Set the distance between the centers of adjacent pixels of the CCD detector as W (pixel spacing). Let the radiation power line density on the receiving surface be a Gaussian distribution

E _l (x _c , x)＝E _lm exp(-(xx _c ) ² /(2σ ² ))(1)

In the formula, x _c is the coordinates of the center of the beam, and σ is the standard deviation of the distribution. The half-maximum half-width is approximately σ (half-value half-width is equal to 1.177σ), so σ or the relative value σ/W can be used to characterize the receiving surface of the CCD detector Upper Beam Width Characteristic.

For the jth pixel whose central coordinate of the CCD detector is x _j (pixel interval W=x _j -x _j-1 ), the analog signal V _j (x _j , x _c ) transmitted by the pixel is proportional to the pixel The radiation energy on is proportional to the integral of the radiation power line density E _l to the sampling time dt and the position variable x within the effective pixel width in the x direction

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}^{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r\; j</span>}}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dx</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In the formula, x ₁ and x _r are the coordinates of the left and right boundaries of the pixel, and the effective width of the pixel (x _rj -x _1j ) is slightly smaller than W. The coefficient S is the photoelectric conversion factor. The digital signal output V _Dj of the jth pixel is the value corresponding to the binary integer of Nbit. The value corresponding to the last bit "1" of V _Dj is recorded as LSB. Other corresponding quantities also use LSB as the unit.

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; int</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; LSB</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

For a certain beam width parameter σ, only a limited number of neighboring pixels have non-zero outputs. When the beam center x _c changes continuously, the output V _Dj of a limited number of adjacent pixels can only take discrete integer values, and V _Dj is basically proportional to the received radiant energy.

V _Dj -ε _j ＝A _m exp(-(x _j -x _c ) ² /(2σ ² ))(4)

In the above formula, A _m is a proportional constant, ε _j is the error of deviation from the strict Gaussian distribution, and ε _j comprehensively reflects the deviation of the beam distribution from the Gaussian distribution, the non-uniformity and nonlinearity of the CCD detector responsivity, and the conversion of the AD conversion. The influence of errors caused by factors such as integer error and energy integral interval discontinuity. Taking the logarithm on both sides of the above formula can be obtained

$\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Taking the center coordinates x _j and x _j ² of the jth pixel as independent variables and y _j =ln(V _Dj ) as dependent variables, the regression model expressed by the following formula is adopted

y _j =b ₀ +b ₁ x _j +b ₂ x _j ² (6)

In principle, the coefficients b ₀ , b ₁ and b ₂ can be obtained, and then the estimation of the beam center position x _c can be obtained

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="b"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">b</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

1.2 Censored quasi-Gaussian distribution

The pixel digital signal output V _Dj in an interval near x _c presents a quasi-Gaussian distribution. Due to the influence of diffraction effect, background light and interference noise, the output of some pixels outside this interval is also non-zero. Let its maximum value be V _N , and its typical value is 1LSB. In order to reduce the impact of noise and other interference on the regression results, select the truncation threshold V _th slightly larger than V _N or other higher truncation thresholds, and only keep the censored quasi-Gaussian distribution data with V _Dj ≥ _{V th} for regression calculation . After roughly determining the error limit of V _Dj ± U _Vj , select an integer greater than (U _Vj ) _max and less than 2 ^N /20 as the truncation threshold V _th

1.3 Weighted regression to reduce the impact of random error components

When |ε _j |<V _Dj , the left side of (5) can be rewritten as

$\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

It can be seen from the above formula that even if the standard deviation of ε _j is constant and the precision of V _Dj is equal, the approximate error of the dependent variable y _j =ln(V _Dj ) is ε _j /V _Dj , and the precision of y _i is not equal , the precision of y _j is low when V _Dj is small, and the precision of y _j is high when V _Dj is large. Therefore, the following weighted regression method is required:

Assuming that the error limit of V _Dj is ±U _Vj , the relative weight factor of dependent variable y _j =ln(V _Dj ) is $w_{\mathrm{yj}}={\left(u_{\mathrm{yj}}\right)}^{-2}\&ap;{(V_{\mathrm{Dj}}/{u_V}_j)}^2.$ pair equation

The weighted regression of formula (6) can be transformed into the "equal weight" regression problem shown in formula (9) where the constant term is zero

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

The dependent and independent variables in the regression are

$\left\{\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; w</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}}\\ {{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; w</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; Dj</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ;</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; w</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; ;</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; w</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

The estimation of beam center position is still calculated by formula (7), that is ${\hat{x}}_c=-{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">b</figure-callout>}}_1/\left(2b_2\right).$

Estimate the use of V _Dj according to the characteristics of CCD detector and related circuits, output bit number N, noise amplitude, etc. $\&PlusMinus;u_{V_j}=\&PlusMinus;(a+c\%V_{\mathrm{Dj}})$ The error limit expressed in the form, where a is a normal number, c% is a proportional coefficient, and the typical value of U _Vj when the number of bits N=8 is taken as (1.5+1.5% V _Dj ).

1.4 Determine the beam width range by numerically simulating the error distribution with the Monte Carlo method

A). Under the assumption of Gaussian distribution, the integral is calculated for the relative output of each pixel

When the pixel interval W is known, for the center coordinate x _c of the beam, according to the Gaussian distribution formula (1) of the radiation power line density, under a certain value of the standard deviation σ of the distribution, the jth jth with the center coordinate x _j can be calculated by integrating The analog signal V _j of each pixel = V _j (x _j , x _c ) is used as the initial value of the photoelectric measurement signal before analog-to-digital conversion (ADC); V _j is a relative value, and a fixed value is selected when integrating with (2) The proportionality constant makes the peak value of V _j approximately 0.8 × 2 ^N .

B). According to the error limit is $\&PlusMinus;u_{V_j}=\&PlusMinus;(a+c\%V_j)$ Numerical simulation of a set of random error distributions ${\mathrm{\&epsiv;}}_{V_j}=r_{\mathrm{aj}}+r_{\mathrm{cj}}\%V_j,$ Here r _aj and r _cj are uniformly distributed random numbers with error limits of ±a and ±c respectively; take the integer part of (V _j +ε _Vj ) as the digital signal output V _Dj after ADC.

C). A certain integer between (2 ^N ×c%+a) and 2 ^N /20 is used as the truncation threshold V _th to intercept effective digital signals with V _Dj ≥ V _th .

D). pair equation ${\mathrm{the\; y}}_j=\ln \left(V_{\mathrm{Dj}}\right)=b_0+b_1{x}_j+b_2{\mathrm{<figure-callout\; id="2"\; label="x\; j"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">x</figure-callout>}}_j^{}$ Authorization factor is $w_{{\mathrm{the\; y}}_j}={(V_{\mathrm{Dj}}/u_{V_j})}^2$ The weighted regression of ${\hat{x}}_c=-{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">b</figure-callout>}}_1/\left({2b}_2\right),$ and calculate the error ${\mathrm{\&epsiv;}}_{\mathrm{xc}}={\hat{x}}_c-x_c$ Come.

E). Calculate the error ε _xc of each group for multiple groups of simulated error distributions with the same law, and then calculate the standard deviation s _xc of the error, which is the measurement standard deviation of the beam center position x _c corresponding to the beam distribution standard deviation σ .

F). Repeat the steps from A to E above to calculate the corresponding standard deviation s _xc for different σ values, and obtain the relationship curve between s _xc /W and σ/W, and then find out that s _xc /W is not greater than 0.08 The value range of the beam distribution parameter σ/W. A large number of calculations show that the value of x _c has little influence on the relation curve between s _xc /W and σ/W.

The typical results of numerical calculation using the Monte Carlo method are: for an 8-bit linear array CCD detector, even if the measurement error limit is assumed to be zero, only the influence of the random rounding error of the analog-to-digital conversion is considered, and the truncated Gaussian distribution data is calculated. The least square method equal-weight regression, when σ/W=1.8, the error limit caused by the rounding error can be obtained as 0.06W; when σ/W=1.8, the weighting factor w _yj ∝V _Dj ² of the censored Gaussian distribution data Weighted least squares method regression, the error limit caused by the rounding error can be obtained as 0.006W, which is an order of magnitude smaller than the equal weight regression.

Another advantage of the weighted regression is that it is insensitive to the selection of the censored threshold of the continuous V _Dj involved in the regression.

Table 1 CCD pixel serial number and output signal measurement data table

Pixel number j 501 502 503 504 505 506 507 508 509 510 V _D 12 37 87 152 200 193 137 70 27 6

的平均值为505.366。9个结果的标准差仅为0.0035，可见不同的截尾阈值对结果影响甚小。即使自由度仅为3，也影响不大。实际测量中，衍射、散射及其它噪声和误差因素的影响将会使某些本应输出为零的像元输出非零。加权回归对截尾方式不敏感允许提高截尾阈值，为削减噪声影响创造了条件。对8bit输出的线阵CCD探测器，采用 ${\left(V_{D_j}\right)}_{\max }\&ap;200\mathrm{LSBs}$ 及截尾阈值V_th＝4的取值(这里的阈值是计算时取的一个典型数据，取更为保险的阈值V_th＝6也可以算得类似的结果来)，和 $U_{V_{\mathrm{Aj}}}=1.5\mathrm{LSBs}+1.5\%V_{\mathrm{Dj}}$ 的误差分布模型，对辐射功率线密度高斯分布的情形，用蒙特卡罗法计算了s_xc/W和σ/W之间的对应关系.当0.7≤σ/W≤18时0.005＜s_xc/W＜0.045，且s_xc/W和σ/W之间成近似的直线关系。使s_xc/W不大于0.08的光束分布参量σ/W的取值范围约为0.7～25.For example, for the data shown in Table 1, the first row of Table 1 is the pixel number, and the second row is 10 typical measured values V _Dj including errors. If different truncation processes are performed on the distribution data, there are 8 possible truncation methods including the 4 pixels 504-507, and the number of pixels after truncation is not less than 6 (the degrees of freedom are 6-3 respectively). Together with the original array with 7 degrees of freedom, there are 9 kinds in total. Weighted regression is performed on these 9 different data censored results, and it can be obtained

The average value of is 505.366. The standard deviation of the nine results is only 0.0035, which shows that different truncation thresholds have little effect on the results. Even if the degree of freedom is only 3, it has little effect. In the actual measurement, the influence of diffraction, scattering and other noise and error factors will make the output of some pixels that should be zero output non-zero. Weighted regression is not sensitive to the censoring method, allowing the censoring threshold to be increased, creating conditions for reducing the impact of noise. For the linear array CCD detector with 8bit output, use ${\left(V_{{\mathrm{D.}}_j}\right)}_{\max }\&ap;200\mathrm{LSBs}$ And the value of the truncation threshold V _th =4 (the threshold here is a typical data taken during calculation, and a similar result can also be calculated by taking the more secure threshold V _th =6), and $u_{V_{\mathrm{Aj}}}=1.5\mathrm{LSBs}+1.5\%V_{\mathrm{Dj}}$ In the case of the Gaussian distribution of the radiation power line density, the corresponding relationship between s _xc /W and σ/W is calculated by the Monte Carlo method. When 0.7≤σ/W≤18, 0.005＜s _xc / W<0.045, and there is an approximate linear relationship between s _xc /W and σ/W. The value range of the beam distribution parameter σ/W that makes s _xc /W not greater than 0.08 is about 0.7 to 25.

Use a CCD detector with a total number of pixels N _p ≈ 7400 and a pixel interval W = 4.7 μm, so that when the beam width parameter σ/W ≈ 2.5 to 5 on the surface of the CCD detector (corresponding to a truncation threshold of 4 and a peak value of 200 The censored full width is about 14W to 28W), a large number of measured data show that: the standard deviation of repeated measurements of the same beam center position is not greater than 0.04W; for repeated measurements in groups, the time interval between adjacent measurements in each group 0.5ms～100ms, the standard deviation of each group’s average value is not more than 0.02W, and the maximum deviation between each group’s average value is not more than 0.02W, thus proving that the effective resolution of the present invention can reach 0.02W, that is, like 1/50 of the meta interval

The value range of the beam distribution reference /W that makes s _xc /W not greater than 0.08 is relatively large, and the error in actual measurement is often smaller than the estimated error limit. When σ/W is large, the central part of the quasi-Gaussian distribution basically presents a flat-top type with little change. The number of effective digital output signals V _Dj of pixels that are not less than the threshold V _th after truncation is actually selected, that is, the number of effective pixels within the beam width is between 5 and 50.

Second, the method of measuring the angle of the rotating mirror

Fig. 1 is a schematic structural diagram of a device for measuring the angle of rotation of a rotating mirror according to the method of the present invention. The device comprises a light source 3, a slit 4, a first convex lens 1, a rotating mirror 5, a second convex lens 2 and a CCD detector 6; the first convex lens 1 with a focal length of 10mm≤f ₁ '≤50mm makes it illuminated by the light source 3 The slit 4 forms a slit real image whose equivalent width is reduced and the width adjustment is convenient at point Q ₁ below the rotating mirror 5 to be measured in the figure. The second convex lens 2 with 50mm≤f ₂ '≤300mm forms a quasi-Gaussian distribution spot with an effective pixel number between 5 and 50 in the beam width at point Q ₂ on the surface of the CCD detector 6;

Use the CCD detector 6 and the signal acquisition and calculation processing part 7 to realize truncated processing and weighted regression, and give an estimate of the beam center position x _c in real time; use the deflection angle α of the rotating mirror 5 and the beam center position x on the surface of the CCD detector The first-order approximate relationship between the offset of _c (x _c -x _c0 ) is (x _c -x _c0 )=(k ₂ d)sin(2α), and the first-order of the rotation angle α of the rotating mirror can be obtained Estimation, where k ₂ is the lateral magnification of lens 2, d is the distance from the slit real image Q ₁ to the rotation axis O of the rotating mirror, and x _c0 is the center of the light beam at the surface of the CCD detector and the lens 2 when the rotation angle of the rotating mirror α=0 Beam center coordinates at intersection point Q ₂₀ of optical axes P ₂₀ Q ₂₀ . After the installation and adjustment of the measuring device, the actual measurement data of the relationship between the deflection angle α and the beam center position _xc on the surface of the CCD detector is obtained through calibration, and then the correction value data of the first-order estimation is obtained.

Calculation and Supplementary Explanation of Optical Path

Suppose the distance from the precision slit 4 with width w ₀ to the principal point of the object space of lens 1 with focal length f ₁ ′ is l _{1 and} the equivalent light source slit width at Q ₁ with the center of the real image is w ₁ , from Q ₁ to lens 1 The distance of the principal point of the image square is l ₁ ′, we can get

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="w"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">w</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\frac{{{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="l"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">l</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="l"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">l</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Assuming that the optical axis of lens 1 passes through point O of the rotation axis of plane rotating mirror 5, the optical axis of lens 2 also passes through point O. At the initial position of the rotating mirror, the optical axes of the lenses 1 and 2 are symmetrical with respect to the normal of the plane rotating mirror 5 . The symmetry plane of Q ₁ and its virtual image P ₂₀ in the plane mirror is a mirror surface. Assume that the lengths of the line segments OQ ₁ and OP ₂₀ are both d. When the mirror rotates through a small angle α, the midpoint of the new virtual image is at P ₂ , and the angle between the line OP ₂ and OP ₂₀ is 2α. The vertical distance of P ₂ to the optical axis is dsin(2α). The midpoint P ₂ of the virtual image is imaged on the surface of the CCD detector Q 2 through the lens ₂ , and the distance from Q ₂ to the optical axis (x _c -x _c0 ) is

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="x\; Q"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">x</figure-callout></span><figure-callout\; id="2"\; label="x\; Q"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}_{}{\mathrm{<span\; class="notranslate">Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

where _k2 is the lateral magnification of lens 2. When only the standard deviation s _xc of the CCD detector’s detection of the center of the truncated Gaussian distribution beam is considered, the standard deviation s _α of the system’s measurement of the rotation angle α is approximately proportional to s _xc and inversely proportional to d and k ₂ , s _α ≈s _xc /( 2dk ₂ ).

3. Realized linear array CCD photoelectric measurement method for the dynamic deflection angle of the rotating mirror of the impulse galvanometer

Adopt the device as described in Figure 1, the shock galvanometer host and the device are installed on the same rigid plate with shockproof measures, the rotating mirror 5 in Figure 1 is exactly the rotating mirror of the shock galvanometer, and the CCD detector 6 The surface spot is quasi-Gaussian distribution; 1) Use the first convex lens (1) with a focal length of 10mm≤f ₁ '≤50mm to make the slit (4) illuminated by the light source (3) form an equivalent width that is reduced and adjusted Convenient slit real image, the light emitted by the slit real image is reflected by the shock galvanometer rotating mirror (5), and then passes through the second convex lens (2) with a focal length of 50mm≤f ₂ ′≤300mm, and then passes through the CCD detector (6 ) surface to form a quasi-Gaussian distribution spot; the shock galvanometer and the components are fixed on the same rigid plate with anti-vibration measures;

2) Select a linear array CCD detector with a total number of pixels N _p ≥ 7400 and a pixel spacing W = 4.7 μm, the number of signal output bits N = 8, and the error limit of V _Dj uses the formula $\&PlusMinus;u_{V_j}\&ap;\&PlusMinus;(1.5+1.5\%V_{\mathrm{Dj}})$ Indicates that the truncation threshold V _th =6LSBs is selected;

3) Adjust the lateral magnification k and the distance d from the real slit image _Q1 to the point O of the rotating mirror, so that the effective width N _p W of the CCD detector corresponds to the range of the impact charge or current to be measured by the impact galvanometer; at the same time Adjust the distance from the slit (4) to the first lens (1), so that the number of effective pixels within the beam width on the surface of the CCD detector is between 10 and 30;

4) Adjust the brightness of the light source (3) or the circuit gain in the signal acquisition and calculation processing part (7), so that the maximum value of the digital signal (V _Dj ) _max of the pixel after truncation is ≈200LSB, and the value during weighted regression after truncation The weight factor of dependent variable y _j =ln(V _Dj ) is used $w_{{\mathrm{the\; y}}_j}={(V_{\mathrm{Dj}}/u_{V_j})}^2$ Formula to calculate, calculate the estimate of beam center position x _c and then calculate the dynamic deflection angle of the galvanometer rotating mirror.

In the embodiment, the impulse galvanometer adopts the AC43 type, selects a linear array CCD detector with a total number of pixels N _p ≈ 7400, and a pixel spacing W = 4.7 μm, and the number of signal output bits N = 8, and the error limit of V _Dj uses the formula $u_{V_j}\&ap;1.5+1.5\%V_{\mathrm{Dj}}$ Indicates that the selected truncation threshold V _th =6LSBs. Adjust the lateral magnification k ₂ and the distance d between the real slit image Q ₁ and the point O of the rotation axis of the rotating mirror, so that the effective width N _p W of the CCD detector roughly corresponds to the range of the impact charge (or current) to be measured by the impact galvanometer; At the same time, adjust the distance from the slit 4 to the lens 1, so that the number of effective pixels in the beam width on the surface of the CCD detector is between 8 and 18; adjust the brightness of the light source using light-emitting diodes or the circuit gain in the signal acquisition and calculation processing components Make the maximum value of the digital signal (V _Dj ) _max ≈200LSB of the censored pixel, and the weight factor of the dependent variable y _j = ln(V _Dj ) is $w_{{\mathrm{the\; y}}_j}={(V_{\mathrm{Dj}}/u_{V_j})}^2$ Formula to calculate, calculate the estimate of beam center position x _c and then calculate the dynamic deflection of the galvanometer rotating mirror.

The parameters used in the design of the optical path are: the distance between the rotation axis O of the rotating mirror and the surface of the CCD detector L=560mm, the focal length f ₂ ′=150mm of the second convex lens 2, the distance d=110mm from the slit real image _Q1 to the rotation axis O of the rotating mirror, The focal length f ₁ ′ of a convex lens 1 is 35mm. The lateral magnification of the second convex lens 2 is calculated as k ₂ =1.96, x _α ≈216tan(2α) at a small angle, and the unit is mm. The corner corresponding to the pixel pitch IW=4.7 μm is 0.01 mrad. The minimum value of the theoretical resolution is not pursued in parameter selection. The main consideration is to make the influence of undetermined system error components such as uneven response characteristics and nonlinearity of each pixel fully "randomized" in the total effective signal of measurement, and also to The device is compact, the adjustment is convenient, and the measurement range is taken into account. The effective resolution of the deflection angle of the traditional impulse galvanometer rotating mirror is $\frac{0.2\mathrm{<figure-callout\; id="2"\; label="mm"\; filenames="C20051001206600181.png"\; state="\{\{state\}\}">mm</figure-callout>}}{2\&times;1000\mathrm{mm}}\&ap;1\&times;{10}^{-4}\mathrm{rad}=0.1\mathrm{mrad}.$

With the device of the present invention, when s _x ≈0.1W～0.47μm, the effective resolution of the corner can reach about 0.001mrad. The current division value of the original AC4/3 type impulse galvanometer is 8× when the scale distance of the light source is 1.3m. ^10-10 A/mm. The current "division value" corresponding to a single pixel of the new measurement system using a linear array CCD detector has reached 24pA, and the standard deviation of the measured microcurrent has reached s _I ≈ 4pA. For the measured microcurrent between 200 and 60000pA, some measurement data are shown in Table 2. The beam center deflection reading x _α on the CCD detector has a good proportional relationship with the current I, ${\hat{I}}_i=b_1{x}_{\mathrm{\&alpha;\; i}},$ The current residual v _Ii obtained by straight line fitting = the absolute value of I _i -b ₁ x _αi |v _Ii |≤3.6pA+0.25%I _i . The effective resolution of a conventional impulse galvanometer is only about 0.1% of the range, and the resolution of the rotation angle is about 0.1mrad. In this embodiment, the standard deviation of the rotation angle corresponding to 3.6pA can be reduced to below 0.002mrad. Compared with the scale reading device of the original AC4/3 type shock galvanometer, the precision and rotation angle resolution of the current measurement of the embodiment are both improved by two orders of magnitude.

Table 2 The measurement data of measuring the deflection angle of the impulse galvanometer with linear array CCD

Current I/pA 232.4 473.2 940.8 1877.9 3766.9 7515.3 14914.3 60561.2 Deflection x _α /W 9.64 19.66 39.45 78.26 157.41 314.55 623.48 2541.62 residual(x _α -41.86081)/W -0.09 -0.15 0.07 -0.35 -0.28 -0.04 -0.85 6.48

Fourth, the method of realizing displacement or length measurement

1) Using signal acquisition and calculation processing components, CCD detectors and optical components to achieve measurement, the CCD detector adopts a linear array CCD detector with a total number of pixels N _p ≥ 5000 and a pixel interval W ≤ 7 μm; the described The optical component is composed of a semiconductor laser and a lens. The quasi-parallel semiconductor laser beam forms a quasi-Gaussian distribution beam waist on the surface of the CCD detector through the lens; the optical component is composed of a light-emitting diode, a slit or a small hole, and a lens. The lens will transmit The light passing through the slit or small hole converges on the surface of the CCD detector;

随之改变，以直接反映位移或位置改变，实现对位移或长度的测量。2) The number of effective pixels of the light beam emitted by the optical component within the beam width of the CCD detector surface is between 10 and 30, and the CCD detector and the optical component are respectively installed on the stationary part and the movable part that can move linearly Above, the arrangement direction of the CCD detector pixels is parallel to the moving direction of the movable part. When the relative displacement occurs between the beam axis or the center position of the spot and the CCD detector, the value of the weighted regression result

Change accordingly to directly reflect the displacement or position change, and realize the measurement of displacement or length.

In the embodiment, a linear array CCD detector with a total number of pixels N _p ≈ 7400 and a pixel spacing W = 4.7 μm is used; the light-emitting diode light source is used, and the main beam diffracted by a slit is focused on the CCD detector by a lens superficial approach.

A displacement measurement device experiment was carried out, the optical components were fixed, and the CCD detector was installed on the translation platform of the Abbe ratio instrument. When the CCD detector is shifted, the reading value of the Abbe ratio meter, the regression value of the center position of the beam with the pixel interval W as the unit, and the residual value of the measurement point deviating from the regression line are listed in Table 3, respectively. The residual standard deviation of the data of 19 consecutive measurement positions is 0.67 μm. The uncertainty of the Abbe ratio meter is 1.5 μm. The measured values of each group of CCD detectors in Table 3 are the average values of 20 scans of the CCD detectors at the same position, and the standard deviation of each group of average values is not greater than 0.02W.

Table 3 The data of measuring the table displacement of the Abbe ratio meter with linear array CCD

Reading value of ratio meter/mm 3.0000 4.0000 5.0000 6.0000 8.0000 10.0000 12.0000 14.0000 16.0000 18.0000 CCD measured value/W 714.95 927.45 1139.83 1352.09 1776.69 2201.52 2626.01 3050.46 3475.02 3899.90 Residual deviation from straight line/mm 0.0010 0.0001 -0.0003 -0.0001 -0.0001 -0.0011 -0.0006 0.0002 0.0004 -0.0009 Reading value of ratio meter/mm 20.0000 22.0000 24.0000 26.0000 28.0000 30.0000 31.0000 32.0000 33.0000 CCD measured value/W 4324.35 4748.81 5173.30 5598.01 6022.55 6447.33 6659.72 6872.16 7084.44 Residual deviation from straight line/mm -0.0001 0.0005 0.0011 0.0007 0.0010 0.0001 -0.0003 -0.0009 -0.0008

According to data analysis, the standard deviation of the reading indication error of Abbe's ratio meter itself is about 0.6 μm, and it is integrated with the error of the device of the present invention, and the standard deviation is no more than 0.7 μm, which shows that the method of the present invention can be used in Within the measurement range of 30mm, the relative standard deviation of non-linearity is not greater than $\frac{0.67\&times;0.001}{30}\&ap;2.3\&times;{10}^{-5}.$

The second kind of displacement measurement device experiment was realized. The CCD detector box was fixed on the micro-actuation table manufactured according to the principle of elastic deformation, and 22 sets of micro-actuation table drum readings z and CCD detector beam center position x _c were measured continuously. worthy Listed in Table 4. The fitted line is ${\hat{x}}_c=b_0+b_{1}z,$ Standard deviation of strain ${\mathrm{the\; s}}_{x_c}\&ap;0.039W~0.18\mathrm{\&mu;m},$ The maximum nonlinear residual is 0.45μm. The standard deviation and residual here also include the influence of the nonlinear error between the displacement of the micro-actuator itself and the reading of the drum (the impact of this error has not been verified and referenced. expression). The data in Table 4 shows that: for the measured displacement of the quasi-continuous change not smaller than the pixel interval, the non-linear standard deviation is not greater than 0.20 μm.

Table 4 The data of measuring the displacement of the micro-actuated table with linear array CCD

The measurement serial number 1 2 3 4 5 6 7 8 9 10 11   Micro-actuation table reading z/division 2 4 6 8 10.2 12 14 16 19.2 twenty two 24.2 Beam center position x _c /W 7.095 7.179 7.191 7.203 7.226 7.308 7.307 7.357 7.514 7.504 7.645

Beam center position x _c /μm 33.35 33.74 33.80 33.85 33.96 34.35 34.34 34.58 35.32 35.27 35.93   Residual error/μm 0.12 0.30 0.13 -0.04 -0.17 0.01 -0.22 -0.20 0.18 -0.18 0.24 The measurement serial number 12 13 14 15 16 17 18 19 20 twenty one twenty two   Micro-actuation table reading z/division 26 28.2 30.2 32.2 34 36 38 40 42 44 46 Beam center position x _c /W 7.619 7.675 7.64 7.803 7.802 7.887 7.918 7.968 8.045 8.103 8.124 Beam center position x _c /μm 35.81 36.07 35.91 36.67 36.67 37.07 37.21 37.45 37.81 38.08 38.18   Residual error/μm -0.08 -0.06 -0.45 0.09 -0.11 0.06 -0.01 0.00 0.14 0.19 0.07

5. Realize the measurement method of 0-360 degree angle

使物镜光轴垂直于CCD探测器表面；调焦使CCD探测器表面汇聚的准高斯分布光束宽度内的有效像元数在8～18之间，对CCD探测器像元的数字信号输出采用截尾处理和加权回归求出光束中心坐标xc的估值。正24面体8的方位角φ由反射镜面序号i和光束中心坐标x_c的估值

确定， $\mathrm{\&phi;}=15i+\arctan$ $\left(\frac{{\hat{x}}_c-x_{c0}}{{f_3}^{\&prime;}}\right)$ $+\mathrm{\&epsiv;}$ $({\hat{x}}_c,i)+{\mathrm{\&phi;}}_0,$ 式中x_c0是透镜9的光轴与CCD探测器表面交点的坐标，φ₀是常量项， 是可以通过定度来确定的角度修正项，φ₀及ε(x_c，i)固定在计算程序之中。信号采集和计算处理部件直接输出或显示正24面体8的方位角φ。Fig. 2 is a schematic diagram of the main structure of the angle measurement method for measuring 0-360 degrees. The quasi-parallel semiconductor laser beam with a diameter not less than 3mm is reflected by any mirror surface of the rotatable metal n-hedron 8, where n=24, when one face of the regular 24-hedron rotates ±180°/n=±7.5°, the reflected beam turns over ±15°. The reflected light beam is converged on the surface of the linear array CCD detector 6 with the total number of pixels N _p ≈ 7400 and the pixel spacing W = 4.7 μm through the lens 9 whose effective aperture angle is not less than ±15°. The focal length of the lens 9 is

Make the optical axis of the objective lens perpendicular to the surface of the CCD detector; adjust the focus so that the number of effective pixels within the width of the quasi-Gaussian distribution beam converged on the surface of the CCD detector is between 8 and 18, and the digital signal output of the CCD detector pixel is cut. Tail processing and weighted regression find an estimate of the beam center coordinate xc. The azimuth angle φ of the regular 24-hedron 8 is estimated by the serial number i of the mirror surface and the coordinate x _c of the beam center

Sure, $\mathrm{\&phi;}=15i+\arctan$ $\left(\frac{{\hat{x}}_c-x_{c0}}{{f_3}^{\&prime;}}\right)$ $+\mathrm{\&epsiv;}$ $({\hat{x}}_c,i)+{\mathrm{\&phi;}}_0,$ In the formula, x _c0 is the coordinate of the optical axis of lens 9 and the surface intersection of CCD detector, and φ ₀ is a constant term, It is an angle correction item that can be determined by a fixed degree, and φ ₀ and ε(x _c , i) are fixed in the calculation program. The signal acquisition and calculation processing unit directly outputs or displays the azimuth φ of the regular 24-hedron 8 .

The metal-distance 24-hedron adopts a shaped product with a nominal diameter of 120mm and an error level of 2". The actually selected lens 9 is a photographic objective lens with a relative aperture f ₃ ′/D=1.4 and a focal length f ₃ ′=50mm.

6. The realized method of measuring the wavelength of the linear visible spectrum

1) Make the quasi-parallel light beams of different wavelengths with different diffraction angles emitted by the grating dispersion element with no less than 1200 lines per millimeter pass through a lens or concave mirror with a focal length of no less than 150mm, and image it on the surface of the linear array CCD detector. The total number of pixels of the CCD detector N _p ≥ 5000 and the pixel interval W ≤ 7 μm;

2) focusing the lens or the concave reflector so that the number of effective pixels within the beam width on the surface of the CCD detector is between 5 and 15;

3) By truncating the digital signal output of the CCD detector pixel and weighted regression, calculate the coordinate estimation of the center of the linear spectral line λ _x to be measured Then simultaneously or alternately measure the center coordinates of the reference spectral lines of several known wavelengths λ _i of the He-Ne discharge tube whose wavelength is near the spectral line to be measured Find the local line dispersion equation by linear fitting or quadratic regression ${\hat{x}}_{\mathrm{ci}}=f\left({\mathrm{\&lambda;}}_i\right),$ Finally will Substitute into the dispersion equation to find the wavelength λ _x of the unknown spectral line.

In the embodiment, the grating has 1200 lines per millimeter, and the quasi-parallel beam passes through an objective lens with a focal length of _150mm to be imaged on the surface of the linear array CCD detector. Adjust the focus of the objective lens so that the surface of the CCD detector forms a quasi-Gaussian spectral line with an effective pixel number between 5 and 10 within the beam width; use this method to measure the distance between the two blue light 483nm in the H and D spectra is about 0.13 The wavelength difference of the spectral line in nm makes the effective number of pixels within the beam width of the surface of the CCD detector between 5 and 10. The diffraction order of the existing spectrometer with CCD is fixed at 1, and the position resolution corresponding to the effective resolution is Generally, it is 1W. In the measurement example, the diffraction order of blue light is selected to be 3, and the incident angle is greater than 75 degrees. On the focal plane of the objective lens with a focal length of 150mm, the distance between the centers of the blue spectral lines of H and D is about 0.100mm when observed with a micrometer eyepiece. About 20W. Since the effective resolution of the linear array CCD of the present invention can reach below 0.03W, the effective resolution of wavelength difference measurement can be improved by about two orders of magnitude. The relative standard deviation of the wavelength difference measurement of the blue spectral line of H and D is not greater than 0.3% by adopting censoring treatment and weighted regression.

When measuring the wavelength λ _x of the spectral line to be measured, there are nearly 60 spectral lines with accurately known wavelengths in the side spectrum of the glow discharge He-Ne discharge tube. Select 5-7 spectral lines with known wavelength λ _i near the spectral line to be measured for measurement. Whether to use straight line fitting or quadratic regression to find the local line dispersion equation is mainly based on the standard deviation of the dependent variables of different models after fitting (regression). Generally, the model with a significantly smaller standard deviation is selected; if the standard deviation of the two models is the same If it is large, the linear model should be used. Generally, grating spectrometers rely on the repeatability of the mechanical system to achieve wavelength measurement accuracy of about 0.2nm. Since the wavelength uncertainty of the reference spectral line in this embodiment is generally less than 0.005 nm, this method is essentially a comparative measurement method, so it can achieve a higher measurement accuracy of the wavelength of the line spectrum.

Claims (7)

1. A method for measuring beam center position with a linear array CCD, characterized in that: 1) Make the radiation power line density of the light spot on the surface of the CCD detector along the line array direction be Gaussian distribution or quasi-Gaussian distribution; 2) Find the truncation threshold: suppose the digital signal output of the pixel whose center coordinates of the jth CCD detector is x _j is V _Dj , and the V _Dj is an integer multiple of LSB; according to the characteristics of the CCD detector and related circuits, Output bit number N and noise amplitude, use the formula $\&PlusMinus;u_{V_j}=\&PlusMinus;(a+c\%V_j)$ Indicates the error limit of V _Dj , where a is a normal number, and c% is the lower proportional coefficient; an integer between (a+c%×2 ^N ) and 2 ^N /20 is used as the truncation threshold V _th , Make the effective digital output signal V _Dj of the pixel not less than the threshold V _th after the truncation be a truncated quasi-Gaussian distribution; 3) For the effective digital signal output V _Dj of the truncated quasi-Gaussian distribution of the pixel whose center coordinate is _xj , the regression equation model is adopted ${\mathrm{the\; y}}_j=b_0+b_1{x}_j+b_2{x}_j^2$ , taking x _j and x _j ² as independent variables and y _j =ln(V _Dj ) as dependent variables respectively, the weighting factor is $w_{\mathrm{yj}}={(V_{\mathrm{Dj}}/u_{v_j})}^2$ Calculate the weighted regression of b ₁ and b ₂ , and then calculate the estimated position of the center of the beam ${\hat{x}}_c=-b_1/\left({2b}_2\right)$ ; 4) Determine the beam width range by numerically simulating the error distribution with the Monte Carlo method, and the specific steps are: A). When the pixel spacing W is known, for the beam center position x _c , according to the Gaussian distribution of the radiation power line density E _l (x _c , x)=E _lm exp(-(xx _c ) ² /(2σ ² )), under the value of a certain distribution standard deviation σ, integrate the fixed sampling time interval and the position variable x in the pixel to calculate the analog signal V _j = V _j of the jth pixel whose center coordinate is x _j (x _j , x _c ), as the initial value of the photoelectric measurement signal before analog-to-digital conversion; V _j is a relative value, and a proportional constant is selected during integration so that the peak value of V _j is 0.8×2 ^N ; B). According to the error limit is $\&PlusMinus;u_{V_j}\&PlusMinus;(a+c\%V_j)$ Numerical simulation of a set of random error distributions ${\mathrm{\&epsiv;}}_{V_j}=r_{\mathrm{aj}}+r_{\mathrm{cj}}\%V_j$ , where r _aj and r _cj are uniformly distributed random numbers with error limits of ±a and ±c respectively; take the integer part of (V _j +ε _Vj ) as the digital signal output V _Dj after analog-to-digital conversion; C). Intercept the effective digital signal of V _Dj ≥ V _th ; D). pair equation ${\mathrm{the\; y}}_j=1\mathrm{no}\left(V_{\mathrm{Dj}}\right)=b_0+b_1{x}_j+b_2{x}_j^2$ Authorization factor is $w_{\mathrm{yj}}={(V_{\mathrm{Dj}}/u_{v_j})}^2$ The weighted regression of ${\hat{x}}_c=-b_1/\left(2b_2\right),$ and calculate the error ${\mathrm{\&epsiv;}}_{\mathrm{xc}}={\hat{x}}_c-x_c$ Come; E). Calculate the error ε _xc of each group for multiple groups of simulation error distributions with the same law, and then calculate the standard deviation s _xc of the error, which is the measurement standard deviation of the beam center position x _c corresponding to the beam distribution standard deviation σ ; F). Repeat the steps from A to E above to calculate the corresponding standard deviation s _xc for different σ values, and obtain the relationship curve between s _xc /W and σ/W, and then find out that s _xc /W is not greater than 0.08 The value range of the beam distribution parameter σ/W. 2. according to the described method of claim 1, it is characterized in that: the number of effective digital output signal V _Dj of the picture element that is not less than threshold value V _th after truncation, promptly the number of effective picture elements in the beam width is 5～50 between. 3. A method of using the method claimed in claim 1 to measure the angle of rotation of the mirror, characterized in that the method may further comprise the steps: 1) Use the first convex lens (1) with a focal length of _{10mm≤f1'≤50mm} to make the slit (4) illuminated by the light source (3) form a real slit image with reduced equivalent width and convenient width adjustment. The light emitted by the slit real image is reflected by the rotating mirror (5), and then passes through the second convex lens (2) with a focal length of 50mm≤f ₂ ′≤300mm to form an effective pixel within the beam width on the surface of the CCD detector (6) The number of spots between 5 and 50; 2) Utilize the CCD detector (6), signal acquisition and calculation processing part (7), according to the method of step 2) and 3) in claim 1, to the truncated quasi-Gaussian distribution output signal V _Dj weighted regression, give in real time Estimation of beam center position _xc ; 3) Utilize the first-order approximate relationship between the deflection angle α of the rotating mirror (5) and the offset (x _c -x _c0 ) of the beam center position x _c on the surface of the CCD detector: (x _c -x _c0 )= (κ ₂ d)sin(2α), the first-order estimate of the rotation angle α of the rotating mirror can be obtained, where κ ₂ is the lateral magnification of the second convex lens, and d is the distance from the slit real image Q ₁ to the rotation axis O of the rotating mirror Distance, x _c0 is the coordinate of the beam center at the intersection of the CCD detector surface and the second convex lens optical axis when the rotation angle of the rotating mirror α=0; the deflection angle α and the beam center of the CCD detector surface are obtained by calibration after the installation and adjustment of the measuring device Quantitative measured data of the relationship between position x _c , and then obtain the revised value data of the first-order estimate. 4. A method of utilizing claim 1 or 3 described method to measure the dynamic deflection angle of the rotating mirror of impulse galvanometer, it is characterized in that the method comprises the steps: 1) Use the first convex lens (1) with a focal length of _{10mm≤f1'≤50mm} to make the slit (4) illuminated by the light source (3) form a real slit image with reduced equivalent width and convenient width adjustment. The light emitted by the slit real image is reflected by the rotating mirror (5) of the shock galvanometer, and then passes through the second convex lens (2) with a focal length of 50mm≤f ₂ ′≤300mm, forming a quasi-Gaussian distribution on the surface of the CCD detector (6) Light spot: fix the shock galvanometer, the first convex lens, the light source, the slit, the second convex lens and the CCD detector on the same rigid plate with anti-vibration measures; 2) Select a linear array CCD detector device with a total number of pixels N _p ≥ 7400 and a pixel spacing W = 4.7 μm, the number of signal output bits N = 8, and the error limit of V _Dj uses the formula $\&PlusMinus;u_{V_j}\&ap;\&PlusMinus;(1.5+1.5\%V_{\mathrm{Dj}})$ Indicates that the truncation threshold V _th =6LSBs is selected; 3) Adjust the lateral magnification κ and the distance d between the real slit image _Q1 and the point O of the rotating mirror, so that the effective width N _p W of the CCD detector corresponds to the range of the impact charge or current to be measured by the impact galvanometer; at the same time Adjust the distance from the slit (4) to the first convex lens (1), so that the number of effective pixels within the beam width on the surface of the CCD detector is between 10 and 30; 4) Adjust the brightness of the light source (3) or the circuit gain in the signal acquisition and calculation processing part (7), so that the maximum value of the digital signal (V _Dj ) _max of the pixel after truncation is ≈200LSB, and the value during weighted regression after truncation The weight factor of dependent variable y _j =ln(V _Dj ) is used $w_{{\mathrm{the\; y}}_j}={(V_{\mathrm{Dj}}/u_{V_j})}^2$ Formula to calculate, calculate the estimate of beam center position x _c and then calculate the dynamic deflection angle of the galvanometer rotating mirror. 5. A method for measuring displacement or length using the method of claim 1, the method may further comprise the steps: 1) Using signal acquisition and calculation processing components, CCD detectors and optical components to achieve measurement, the CCD detector adopts a linear array CCD detector with a total number of pixels N _p ≥ 5000 and a pixel interval W ≤ 7 μm; the described The optical component is composed of a semiconductor laser and a lens. The quasi-parallel semiconductor laser beam forms a quasi-Gaussian distribution beam waist on the surface of the CCD detector through the lens; the optical component is composed of a light-emitting diode, a slit or a small hole, and a lens. The lens will transmit The light passing through the slit or small hole converges on the surface of the CCD detector; 2) The number of effective pixels of the light beam emitted by the optical component within the beam width of the CCD detector surface is between 10 and 30, and the CCD detector and the optical component are respectively installed on the stationary part and the movable part that can move linearly Above, the arrangement direction of the CCD detector pixels is parallel to the moving direction of the movable part. When the relative displacement occurs between the beam axis or the center position of the spot and the CCD detector, the value of the weighted regression result

Change accordingly to directly reflect the displacement or position change, and realize the measurement of displacement or length. 6. A method for measuring angles of 0 to 360 degrees using the method of claim 1, characterized in that: 1) The quasi-parallel semiconductor laser beam with a diameter of not less than 3 mm is reflected by any mirror surface of the rotatable metal n-hedron (8), the serial number of the mirror surface is set to i, and the reflected beam has an effective aperture angle of not less than ±360°/ The objective lens (9) of n converges on the surface of the linear array CCD detector (6) with the total number of pixels N _p ≥ 5000 and the pixel spacing W ≤ 7 μm, and the focal length of the objective lens is The optical axis of the objective lens is perpendicular to the surface of the CCD detector; 2) Adjust the focus so that the number of effective pixels of the beam within the beam width on the surface of the CCD detector is between 10 and 30, and use truncated processing and weighted regression to obtain the beam center coordinate _xc for the digital signal output of the CCD detector pixel the valuation of 3) The azimuth φ of the n-hedron (8) is evaluated by the mirror surface serial number i and the beam center coordinate x _c

Sure, $\mathrm{\&phi;}=\frac{260}{\mathrm{no}}i+\arctan \left(\frac{{\hat{x}}_c-x_{c0}}{f_3^{\&prime;}}\right)\mathrm{\&epsiv;}({\hat{x}}_c,i)+{\mathrm{\&phi;}}_0,$ In the formula, x _c0 is the coordinate of the optical axis of lens 9 and the surface intersection of CCD detector, and φ ₀ is a constant term,

It is an angle correction item determined by the degree, and directly outputs or displays the azimuth φ of the n-hedron (8) through the signal acquisition and calculation components. 7. A method for measuring the linear visible spectrum wavelength using the method claimed in claim 1 is characterized in that the method comprises the steps: 1) Make the quasi-parallel light beams of different wavelengths with different diffraction angles emitted by the grating dispersion element with no less than 1200 lines per millimeter pass through a lens or concave mirror with a focal length of no less than 150mm, and image it on the surface of the linear array CCD detector. The total number of pixels of the CCD detector N _p ≥ 5000 and the pixel interval W ≤ 7 μm; 2) focusing the lens or the concave reflector so that the number of effective pixels within the beam width on the surface of the CCD detector is between 5 and 15; 3) By truncating the digital signal output of the CCD detector pixel and weighted regression, calculate the coordinate estimation of the center of the linear spectral line to be measured with a wavelength of λ _x Then simultaneously or alternately measure the center coordinates of the reference spectral lines of several known wavelengths λ _i of the He-Ne discharge tube whose wavelength is near the spectral line to be measured Find the local line dispersion equation by linear fitting or quadratic regression ${\hat{x}}_{\mathrm{ci}}=f\left({\mathrm{\&lambda;}}_i\right),$ Finally will

Substitute into the dispersion equation to find the wavelength λ _x of the unknown spectral line.

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