CN1796928A - Method and devices for measuring dynamic response error of position sensor - Google Patents

Abstract

The invention belongs to the field of measuring technique, relating to a method and device for measuring dynamic response error of a PSD (Position Sensitive Detector). The method includes the steps of: firstly determining a dynamic response model of the PSD under the continuous scanning and irradiation of a light source and then making error measurement. The invention is simple in method, convenient to use, high accuracy and applied to calculating the dynamic response errors of PSD of various electrode structures.

Description

The measuring method and the measurement mechanism of PSD position sensor dynamic response error

Technical field

The invention belongs to field of measuring technique, relate to measuring method and the device of measuring PSD position sensor dynamic response error.

Background technology

(position sensitive detector PSD) is a kind of photoelectric device to the launching spot position sensing to Position-Sensitive Detector, and its principle of work is based on the lateral light electrical effect of large tracts of land PN junction.This photoelectric effect can be described by the Lucovsky equation.When the PSD photosurface is subjected to hot spot part uneven irradiation, on its photosurface, will set up the lateral voltage that be parallel to photosurface relevant with facula position, if hot spot prolonged exposure, and on the electrode of PSD, be connected to external circuit, then form the electric current that flows to the two poles of the earth, the size of bipolar current is relevant with the position of hot spot.Therefore, can calculate the position of hot spot according to the size of electrode current.

In present research, because light source is the focussed laser beam of continous-stable, its irradiation time is far longer than the response time of PSD, so the steady-state response that obtains when utilizing the static light source irradiation of PSD is mostly determined the position of launching spot.The photogenerated current of PSD output is passed through the detecting function that signal circuit is realized the hot spot incoming position, promptly realize electric current-position conversion formula function of PSD.Yet,, will give and measure introducing PSD dynamic response error if still simply adopt this moment electric current-position conversion formula to calculate the incident light spot position when incident light shines the PSD photosurface with certain speed continuous sweep.Therefore just need accurately set up out the dynamic response error model of PSD.

Report is seldom both at home and abroad about the method for building up of the dynamic response error model of PSD under the mobile light source irradiation.That publishes in the document at present has only Michiel de Bakker, Piet W.Verbeek, Gijs K.Steenvoorden etc is at article " The PSD transferfunction " (IEEE Transactions on Electron Devices, 49 (1): 202-206,2002) a kind of modeling method of describing in.

The PSD structural drawing as shown in Figure 1, L is a photosurface length among the figure, j is a photogenerated current, D is the p layer thickness.The resistance of PSD and electric capacity are represented with R, C respectively.Suppose that incident light source is a pulsed light, the position that shines on the PSD photosurface is u _pAt t＞t ₀Constantly, the current pulse signal response expression formula of two ends, PSD left and right sides output:

$\left\{\begin{array}{c}{j}_{\mathrm{left}}^{\mathrm{pulse}}(u_p,t)=-\frac{j_p}{D}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2}{\mathrm{n\π}}{S}_n\left(u_p\right)g_n(t-t_o)\\ j_{\mathrm{right}}^{\mathrm{pulse}}(u_p,t)=+\frac{j_p}{D}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2}{\mathrm{n\π}}{S}_n(-u_p)g_n(t-t_o)\end{array}\right.---\[1\]$

J in the formula _Left ^Pulse, j _Right ^PulseBe respectively the photogenerated current of PSD left and right sides electrode output, j _pBe total photogenerated current intensity that incident light source produces on the PSD photosurface, $S_n\left(u_p\right)=\sin \mathrm{n\&pi;}(\frac{u_p}{L}+\frac{1}{2}),$ $g_n\left(t\right)={\mathrm{\&lambda;}}_n^2{e}^{-{\mathrm{\&lambda;}}_n^{2}t}s\left(t\right),$ ${\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2=\frac{{\left(\mathrm{n\&pi;}\right)}^2}{\mathrm{RC}},$ S (t) is a unit-step function.

When t＞0, light source continuous sweep irradiation PSD photosurface, any one irradiation position u on the track while scan _p(t) expression suppose that incident light source is modulated into sine function, and the amplitude of sine function is very little with respect to photosurface length, and then the light source incoming position can be write as:

u _p(t)＝u _c+Δu?sin(ωt) [2]

U wherein _cBe the amplitude center, Δ u is the amplitude size, and ω is a frequency.

The dynamic response function of PSD can be by t moment light source irradiation u _p(t) the photogenerated current function of PSD output and the convolution of unit-step function are represented during the position.Therefore the photogenerated current dynamic response model of PSD left end electrode output can be written as:

$j_{\mathrm{left}}\left(t\right)=j_{\mathrm{left}}^{\mathrm{pulse}}(u_p\left(t\right),t)*s\left(t\right)$

$=-\frac{j_p}{D}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{2}{\mathrm{n\&pi;}}{\&Integral;}_0^t{S}_n\left(u_p\left(t_o\right)\right)g_n(t-t_o)d{t}_o---\&lsqb;3\&rsqb;$

By approximate, following formula can abbreviation be:

$j_{\mathrm{left}}\left(t\right)=2\frac{j_p}{D}\frac{\mathrm{\&Delta;u}}{L}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{C}_n\left(u_c\right)\&CenterDot;e^{-{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\mathrm{\&epsiv;}}{g}_n\left(t\right)*\sin \mathrm{\&omega;t}---\&lsqb;4\&rsqb;$

In the formula $C_n\left(u_c\right)=\cos \mathrm{n\&pi;}(\frac{u_c}{L}+\frac{1}{2}).$ N, ε are undetermined constants, and be relevant with R, C.

Adopt similar method can obtain the photogenerated current dynamic response model of PSD right-hand member electrode output, no longer provide here.Bring in electric current-position conversion formula, obtain the dynamic response error value that PSD detects, compare with light source actual scanning position then, obtain PSD dynamic response error model.

Adopt said method to build PSD dynamic response error model, have following shortcoming: (1) light source scanning track determines that range of application is limited to very much.Not only need light source to be modulated into sine function, also need the amplitude of sine function very little, this has just limited the usable range of said method.(2) model of Jian Liing only is suitable for one dimension PSD structure.(3) model is very complicated, and two parameter N are wherein arranged, and ε need calculate in addition according to physical parameter R, the C of different structure PSD, uses inconvenient.

Summary of the invention

The objective of the invention is: at the deficiency that exists in the existing PSD dynamic response error modeling method, propose a kind of usable range wide, use PSD dynamic response error modeling method and measurement mechanism easily, further improve the PSD dynamic measurement precision.This measuring method and device can be given in the dynamic response error of optional position on the PSD photosurface to any light source sweep velocity and light source scanning track.

Technical scheme of the present invention is: the measuring method of PSD position sensor dynamic response error is characterized in that the photosurface size of establishing PSD is L ₁* L ₂, R is the electrode resistance of PSD, and C is the Terminal Capacitance of PSD, and φ is the knot electric potential difference, ignores the input impedance and the electrode contact resistance of circuit, and the boundary condition of one dimension PSD and Two-dimensional PSD is:

φ (0, y, t)=φ (L ₁, y, t)=0 and φ (0, y, t)=φ (L ₁, y, t)=φ (x, 0, t)=φ (x, L ₂, t)=0 [5]

A branch of light intensity is constant, and the very little illumination of launching spot is to the PSD photosurface.When light source is done at the uniform velocity rectilinear scanning with speed V, scanning T.T. is t, and true origin is fixed on the left electrodes of PSD, and the X-axis positive dirction is pointed to the right electrodes of PSD, and the step of setting up PSD dynamic response error model is as follows:

(1) determines the light source continuous sweep irradiation dynamic response model of PSD device down, the steps include:

1. whole sweep time of the process of 0～t is divided into the numerous small time interval, get t=τ constantly the d τ of moment analyze; Be located at t=τ moment point light source scanning to P (x ' (τ), y ' (τ)) point, light source is formed on an instantaneous point light source that is positioned at P point place on the PSD photosurface in dr moment, wherein the τ P coordinate of ordering and light source scanning track, light source scanning velocity correlation constantly; In time, the coefficient result of all instantaneous point light sources promptly is that the t photovoltaic electric potential constantly that the transfer point light source causes in PSD distributes at 0～t;

2. based on Ohm law, obtain the light source scanning irradiation photogenerated current of PSD electrode output down, the photogenerated current expression formula that is obtained two electrode outputs about one dimension PSD by Ohm law is expressed as:

$i_1(0,t)=\frac{2a{I}_o}{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}\&CenterDot;{\&Integral;}_0^t\sin \&lsqb;\mathrm{\&lambda;}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\&CenterDot;e^{-{\mathrm{\&lambda;}}^{2}a(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;6a\&rsqb;$

$i_2({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1,t)=-\frac{2a{I}_o}{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}\&CenterDot;\cos \mathrm{n\&pi;}\&CenterDot;{\&Integral;}_0^t\sin \&lsqb;\mathrm{\&lambda;}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\&CenterDot;e^{-{\mathrm{\&lambda;}}^{2}a(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;6b\&rsqb;$

In the formula $\mathrm{\&lambda;}=\frac{\mathrm{n\&pi;}}{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1},$ $a=\frac{1}{\mathrm{RC}},$ i ₁, i ₂Be the electric current of two electrode outputs about PSD, it is tetragonal establishing the Two-dimensional PSD electrode structure, and the photogenerated current expression formula of four electrode outputs of then two-dimentional quadrilateral PSD is:

${\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">i</figure-callout>}}_1=\frac{4I_o}{\mathrm{RC}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{n}{m}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7a\&rsqb;$

${\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">i</figure-callout>}}_2=-\frac{4I_o}{\mathrm{RC}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{n}{m}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&CenterDot;\cos \mathrm{n\&pi;}\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7b\&rsqb;$

${\mathrm{<figure-callout\; id="3"\; label="i"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">i</figure-callout>}}_3=-\frac{4I_o}{\mathrm{RC}{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{m}{n}\&CenterDot;(1-\cos \mathrm{n\&pi;})\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\&CenterDot;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7c\&rsqb;$

${\mathrm{<figure-callout\; id="4"\; label="i"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">i</figure-callout>}}_4=-\frac{4I_o}{\mathrm{RC}{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{m}{n}\&CenterDot;(1-\cos \mathrm{n\&pi;})\&CenterDot;\cos \mathrm{m\&pi;}\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\&CenterDot;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7d\&rsqb;$

3. the photogenerated current expression formula that provides in 2. is brought in PSD electric current-position conversion formula, obtains the light source continuous sweep irradiation dynamic response model of PSD device down;

(2) dynamic response error of measurement PSD device;

1. use the measurement device of PSD position sensor dynamic response error to go out R, the C of PSD;

2. set the equation of locus and the light source scanning speed of light source scanning;

3. will be 1. and 2. in the parameter value that produces be brought in the PSD dynamic response model of above-mentioned foundation, when obtaining the light source scanning irradiation, the light source incoming position that position, arbitrfary point PSD detects on the light source scanning track;

4. PSD probe source incoming position and the true incoming position of light source that obtains subtracted each other, can obtain the light source continuous sweep irradiation dynamic response error of PSD device down.

A kind of device of measuring PSD position sensor dynamic response error, comprise a power supply 1 and computing machine 2, it is characterized in that, this measurement mechanism is made up of a LRC measuring instrument 3 and a data capture card 4 that has signal output port, the signal output port of LRC measuring instrument 3 is connected with the input end of data collecting card 4, and the output terminal of data collecting card 4 is connected with the data input pin of computing machine 2.

Advantage of the present invention is: PSD dynamic response error measuring method and device have method is simple, easy to use, can access the PSD dynamic response error theoretical solution, precision advantages of higher.Adopt this model and dynamic response error measurement mechanism, can realize the calculating of the dynamic response error that PSD produced when light source was done any track scanning irradiation PSD photosurface with arbitrary speed, applied range is applicable to the PSD dynamic response error that calculates various electrode structures.

Description of drawings

Fig. 1 is the PSD structural representation.

Fig. 2 is the structural representation of measurement mechanism of the present invention.

The S1662 type one dimension PSD dynamic response error curve that Fig. 3 is to use the present invention to measure.

The S1200 type Two-dimensional PSD dynamic response error curve that Fig. 4 is to use the present invention to measure

Embodiment

Below the present invention is described in further details.Measuring method of the present invention is characterized in that, the photosurface size of establishing PSD is L ₁* L ₂, R is the electrode resistance of PSD, and C is the Terminal Capacitance of PSD, and φ is the knot electric potential difference, ignores the input impedance and the electrode contact resistance of circuit, and the boundary condition of one dimension PSD and Two-dimensional PSD is:

φ (0, y, t)=φ (L ₁, y, t)=0 and φ (0, y, t)=φ (L ₁, y, t)=φ (x, 0, t)=φ (x, L ₂, t)=0 [5]

A branch of light intensity is constant, and the very little illumination of launching spot is to the PSD photosurface.When light source is done at the uniform velocity rectilinear scanning with speed V, scanning T.T. is t, and true origin is fixed on the left electrodes of PSD, and the X-axis positive dirction is pointed to the right electrodes of PSD, and the step of setting up PSD dynamic response error model is as follows:

1. whole sweep time of the process of 0～t is divided into the numerous small time interval, get t=τ constantly the d τ of moment analyze; Be located at t=τ moment point light source scanning to P (x ' (τ), y ' (τ)) point, light source is formed on an instantaneous point light source that is positioned at P point place on the PSD photosurface in dr moment, wherein the τ P coordinate of ordering and light source scanning track, light source scanning velocity correlation constantly; In time, the coefficient result of all instantaneous point light sources promptly is that the t photovoltaic electric potential constantly that the transfer point light source causes in PSD distributes at 0～t.

2. based on Ohm law, obtain the light source scanning irradiation photogenerated current of PSD electrode output down, the photogenerated current expression formula that is obtained two electrode outputs about one dimension PSD by Ohm law is expressed as:

$i_1(0,t)=\frac{2a{\mathrm{<figure-callout\; id="1"\; label="I\; o\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">I</figure-callout>}}_o}{L_{}}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}\&CenterDot;{\&Integral;}_0^t\sin \&lsqb;\mathrm{\&lambda;}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\&CenterDot;e^{-{\mathrm{\&lambda;}}^{2}a(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;6a\&rsqb;$

$i_2({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1,t)=-\frac{2a{\mathrm{<figure-callout\; id="1"\; label="I\; o\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">I</figure-callout>}}_o}{L_{}}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}\&CenterDot;\cos \mathrm{n\&pi;}\&CenterDot;{\&Integral;}_0^t\sin \&lsqb;\mathrm{\&lambda;}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\&CenterDot;e^{-{\mathrm{\&lambda;}}^{2}a(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;6b\&rsqb;$

In the formula $\mathrm{\&lambda;}=\frac{\mathrm{n\&pi;}}{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1},$ $a=\frac{1}{\mathrm{RC}},$ i ₁, i ₂Be the electric current of two electrode outputs about PSD, it is tetragonal establishing the Two-dimensional PSD electrode structure, and the photogenerated current expression formula of four electrode outputs of then two-dimentional quadrilateral PSD is:

$i_1=-\frac{4I_{\mathrm{<figure-callout\; id="1"\; label="o\; RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">o</figure-callout>}}}{\mathrm{RC}{L}_{}^{}}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{n}{m}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{<figure-callout\; id="1"\; label="RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">RC</figure-callout>}{L}_{}^{}{}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7a\&rsqb;$

$i_2=-\frac{4I_{\mathrm{<figure-callout\; id="1"\; label="o\; RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">o</figure-callout>}}}{\mathrm{RC}{L}_{}^{}}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{n}{m}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&CenterDot;\cos \mathrm{n\&pi;}\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{<figure-callout\; id="1"\; label="RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">RC</figure-callout>}{L}_{}^{}{}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7b\&rsqb;$

$i_3=\frac{4I_{\mathrm{<figure-callout\; id="2"\; label="o\; RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">o</figure-callout>}}}{\mathrm{RC}{L}_{}^{}}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{m}{n}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{<figure-callout\; id="1"\; label="RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">RC</figure-callout>}{L}_{}^{}{}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7c\&rsqb;$

$i_4=-\frac{4I_{\mathrm{<figure-callout\; id="2"\; label="o\; RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">o</figure-callout>}}}{\mathrm{RC}{L}_{}^{}}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{m}{n}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&CenterDot;\cos \mathrm{m\&pi;}\&times;{\&Integral;}_0^t\sin \&lsqb;\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;\sin \&lsqb;\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\&rsqb;e^{-\frac{({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{<figure-callout\; id="1"\; label="RC\; L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">RC</figure-callout>}{L}_{}^{}{}_1^2{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20041010258400112.png"\; state="\{\{state\}\}">L</figure-callout>}}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}---\&lsqb;7d\&rsqb;$

3. the photogenerated current expression formula that provides in 2. is brought in PSD electric current-position conversion formula, obtains the light source continuous sweep irradiation dynamic response model of PSD device down.

4. use the measurement device of PSD position sensor dynamic response error to go out R, the C of PSD.Set the equation of locus and the light source scanning speed of light source scanning.

5. the 4. middle parameter value that produces is brought in the PSD dynamic response model of above-mentioned foundation, when obtaining the light source scanning irradiation, the light source incoming position that position, arbitrfary point PSD detects on the light source scanning track.The PSD probe source incoming position and the true incoming position of light source that obtain are subtracted each other, can obtain the light source continuous sweep irradiation dynamic response error of PSD device down.

Dynamic response error measurement mechanism of the present invention is made up of R and C measuring system, data collecting card and the computing machine of PSD.The photosurface size of dynamic response error model, light source scanning track, light source scanning speed and PSD device is stored in the computing machine.A kind of embodiment of measurement mechanism is shown in 2 figure, it comprises a power supply 1 and computing machine 2, it is characterized in that, this measurement mechanism is made up of a LRC measuring instrument 3 and a data capture card 4 that has signal output port, the signal output port of LRC measuring instrument 3 is connected with the input end of data collecting card 4, and the output terminal of data collecting card 4 is connected with the data input pin of computing machine 2.The R of PSD and C adopt the LRC measuring instrument to measure.The LRC measuring instrument is the automatic LRC measuring instrument that has adopted radio six factories in Tianjin to produce, and model is YY2811, has increased the signal output port of measured value on the basis of this instrument.

During measurement mechanism work, two comparative electrodes of PSD device are connected on two terminals of measuring instrument, select different function button on the measuring instrument, parameter value R and C that acquisition will be measured are by being stored in the computing machine after the data collecting card collection.Equation of locus and light source scanning speed to computing machine input light source scanning according to above-mentioned PSD device dynamic response error measuring process, can obtain the dynamic response error of PSD device.

Embodiment

Measure one dimension PSD dynamic response error.

The one dimension PSD (model S1662) and the above-mentioned measurement mechanism that adopt the loose Optronics APS in Japanese shore to produce.When at the uniform velocity rectilinear scanning of light source, track while scan is PSD photosurface center line (y=L ₂/ 2mm, x=L ₁* 0.05～L ₁* 0.95mm) time,, obtain under the Different Light scan velocity V (m/s) curve map that the dynamic response error that S1662 type PSD device produces changes with scanning position according to above-mentioned PSD dynamic response error model.

Measure two-dimentional quadrilateral PSD dynamic response error.

The Two-dimensional PSD (model S1200) and the above-mentioned measurement mechanism that adopt the loose Optronics APS in Japanese shore to produce, when at the uniform velocity rectilinear scanning of light source, track while scan is PSD photosurface center line (y=L ₂/ 2mm, x=L ₁* 0.10～L ₁* 0.90mm) time,, obtain under the Different Light scan velocity V (m/s) curve map that the dynamic response error that S1200 type PSD device produces changes with scanning position according to above-mentioned PSD dynamic response error model.

Claims (2)

1, the measuring method of PSD position sensor dynamic response error is characterized in that, the photosurface size of establishing PSD is L ₁* L ₂, R is the electrode resistance of PSD, and C is the Terminal Capacitance of PSD, and φ is the knot electric potential difference, ignores the input impedance and the electrode contact resistance of circuit, and the boundary condition of one dimension PSD and Two-dimensional PSD is:

φ (0, y, t)=φ (L ₁, y, t)=0 and φ (0, y, t)=φ (L ₁, y, t)=φ (x, 0, t)=φ (x, L ₂, t)=0 [5]

A branch of light intensity is constant, and the very little illumination of launching spot is to the PSD photosurface.When light source is done at the uniform velocity rectilinear scanning with speed V, scanning T.T. is t, and true origin is fixed on the left electrodes of PSD, and the X-axis positive dirction is pointed to the right electrodes of PSD, and the step of setting up PSD dynamic response error model is as follows:

(1) determines the light source continuous sweep irradiation dynamic response model of PSD device down, the steps include:

1. whole sweep time of the process of 0～t is divided into the numerous small time interval, get t=τ constantly the d τ of moment analyze; Be located at t=τ moment point light source scanning to P (x ' (τ), y ' (τ)) point, light source is formed on an instantaneous point light source that is positioned at P point place on the PSD photosurface in d τ moment, wherein the τ P coordinate of ordering and light source scanning track, light source scanning velocity correlation constantly; In time, the coefficient result of all instantaneous point light sources promptly is that the t photovoltaic electric potential constantly that the transfer point light source causes in PSD distributes at 0～t;

2. based on Ohm law, obtain the light source scanning irradiation photogenerated current of PSD electrode output down, the photogenerated current expression formula that is obtained two electrode outputs about one dimension PSD by Ohm law is expressed as:

$i_1(0,t)=\frac{2a{I}_o}{L_1}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}\&CenterDot;{\&Integral;}_0^t\sin \left[\mathrm{\&lambda;}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;e^{-{\mathrm{\&lambda;}}^{2}a(t-\mathrm{\&tau;})}\mathrm{d\&tau;}----\left[6a\right]$

$i_2(L_1,t)=-\frac{2a{I}_o}{L_1}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{\&lambda;}\&CenterDot;\cos \mathrm{n\&pi;}\&CenterDot;{\&Integral;}_0^t\sin \left[\mathrm{\&lambda;}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;e^{-{\mathrm{\&lambda;}}^{2}a(t-\mathrm{\&tau;})}\mathrm{d\&tau;}----\left[6b\right]$

In the formula $\mathrm{\&lambda;}=\frac{\mathrm{n\&pi;}}{L_1},$ $a=\frac{1}{\mathrm{RC}},$ i ₁, i ₂Be the electric current of two electrode outputs about PSD, it is tetragonal establishing the Two-dimensional PSD electrode structure, and the photogenerated current expression formula of four electrode outputs of then two-dimentional quadrilateral PSD is:

$i_1=\frac{4I_o}{\mathrm{RC}{L}_1^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{n}{m}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&times;{\&Integral;}_0^t\sin \left[\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\sin \left[\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]e^{-\frac{(L_2^2{n}^2+L_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{L}_1^2{L}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}----\left[7a\right]$

$i_2=\frac{4I_o}{\mathrm{RC}{L}_1^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{n}{m}\&CenterDot;(1-\cos \mathrm{m\&pi;})\&times;\cos \mathrm{n\&pi;}\&times;{\&Integral;}_0^t\sin \left[\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\sin \left[\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]e^{-\frac{(L_2^2{n}^2+L_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{L}_1^2{L}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}----\left[7b\right]$

$i_3=\frac{4I_o}{\mathrm{RC}{L}_2^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{m}{n}\&CenterDot;(1-\cos \mathrm{n\&pi;})\&times;{\&Integral;}_0^t\sin \left[\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\&CenterDot;\sin \left[\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]e^{-\frac{(L_2^2{n}^2+L_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{L}_1^2{L}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}----\left[7c\right]$

$i_4=-\frac{4I_o}{\mathrm{RC}{L}_2^2}\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{m}{n}\&CenterDot;(1-\cos \mathrm{n\&pi;})\&CenterDot;\cos \mathrm{m\&pi;}\&times;{\&Integral;}_0^t\sin \left[\frac{\mathrm{n\&pi;}}{L_1}{x}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]\sin \left[\frac{\mathrm{m\&pi;}}{L_2}{y}^{\&prime;}\left(\mathrm{\&tau;}\right)\right]e^{-\frac{(L_2^2{n}^2+L_1^2{m}^2){\mathrm{\&pi;}}^2}{\mathrm{RC}{L}_1^2{L}_2^2}(t-\mathrm{\&tau;})}\mathrm{d\&tau;}----\left[7d\right]$

3. the photogenerated current expression formula that provides in 2. is brought in PSD electric current-position conversion formula, obtains the light source continuous sweep irradiation dynamic response model of PSD device down;

(2) dynamic response error of measurement PSD device.

1. use the measurement device of PSD position sensor dynamic response error to go out R, the C of PSD;

2. set the equation of locus and the light source scanning speed of light source scanning;

3. will be 1. and 2. in the parameter value that produces be brought in the PSD dynamic response model of above-mentioned foundation, when obtaining the light source scanning irradiation, the light source incoming position that the PSD of place, arbitrfary point detects on the light source scanning track;

4. PSD probe source incoming position and the true incoming position of light source that obtains subtracted each other, can obtain the light source continuous sweep irradiation dynamic response error of PSD device down.

2, a kind of device of measuring PSD position sensor dynamic response error, comprise a power supply [1] and computing machine [2], it is characterized in that, this measurement mechanism is made up of a LRC measuring instrument [3] and a data capture card [4] that has signal output port, the signal output port of LRC measuring instrument [3] is connected with the input end of data collecting card [4], and the output terminal of data collecting card [4] is connected with the data input pin of computing machine [2].

Images