CN101881658B - High-resolution position-sensitive anode detector and anode decoding method thereof - Google Patents

Abstract

The invention relates to a high-resolution position-sensitive anode detector and an anode decoding method thereof, which belong to the technical field of multi-anode detection. The invention provides the electric charge dividing type high-resolution position-sensitive anode detector and the anode decoding method thereof, which have the advantages of extremely high resolution, little image twisting and unlimited anode panel design area. The invention aims at overcoming the defects of complicated read-out circuits and limited anode panel design area of the existing multi-anode detector. The multi-anode detector and the anode decoding method thereof of the invention can realize position measurement and counting imaging of other particles such as photons, electrons and the like, and can be applied to the scientific technical fields such as deep space detection, nuclear radiation and ion detection, biological super faint imaging, quantum communication and the like.

Description

A kind of high-resolution position-sensitive anode detector and anode decoding method thereof

Technical field

The present invention relates to a kind of position-sensitive anode detector and anode decoding method thereof, belong to the multianode technical field of detection.

Background technology

Than coupled mode imageing sensors such as solid state sensors such as CCD, CMOS and CID or ICCD, EBCCD; The multianode detector has the signal to noise ratio (S/N ratio) height; Anti-drift is good; Advantages such as wide dynamic range are therefore to be widely used in survey of deep space, science and technology field such as nuclear radiation and ion detection, biological ultraweak imaging and quantum communications.The quick anode decoding mode of multianode detector step-by-step can be divided into: impedance type and charge division type.Impedance type is to produce different electrode output signals and carry out the incident decoding according to the electrode impedance at diverse location place is different, because the relation of its position decoding and electrode impedance, so the noise of hot charge will limit its spatial resolution.Impedance type position-sensitive anode such as Resistive Anode and Dely-line.Charge division type anode is the quantity of electric charge of receiving according to different electrodes, finds the solution the centroid position of electric charge cloud cluster.The amount of collecting electric charge is proportional with the electrode area that is covered by the electric charge cloud cluster.Charge division type anode such as WSA anode and Cross-Srrip anode.

Much more very the Cross-Srrip anode owing to the output stage that has, so its sensing circuit is very complicated, particularly to large tracts of land, and high-resolution imaging, it is very huge that the electronics of Cross-Srrip anode is read path.

The WSA anode is wedge strip anode again, and its anode plate pattern is by the wedge electrode, strip electrode with the type electrode constitute, separate by insulated wire between electrode.Its basic structure is proposed in nineteen sixty-five by HO.Anger, and in then in the U. S. application patent.Chinese invention patent " folding wedge stripe shape particle two-dimension position-sensitive detector ", application number: 200310121703.1, be a kind of follow-on WSA anode.It is simple that WSA has manufacture craft, the advantage of the corresponding easy design and fabrication of electronics read-out system, but because it only receives the quantity of electric charge of whole electric charge cloud cluster with three electrodes, so its spatial resolution is not high, the distortion of long-term plan picture is big more more for off-center.And because the restriction of dynamic range, the design area of its anode plate is limited, generally within 48 * 48mm.

Summary of the invention

The present invention seeks to solve the very limited shortcoming of area of complicacy, anode plate of existing multianode detector sensing circuit, a kind of have high resolution and less scalloping, anode plate design area unrestricted charge division type high-resolution position-sensitive anode detector and anode decoding method thereof are provided.

Technical solution of the present invention is following:

A kind of high-resolution position-sensitive anode detector; Comprise the input window 1 that has photocathode, microchannel plate 2, germanium inductive layer 3 and the position-sensitive anode 4 of cascade; Described position-sensitive anode 4 comprises dielectric base 5 and is arranged on the conductive layer that is used for the anode surface charge-trapping 6 on the dielectric base 5; Its special character is: said conductive layer 6 comprise a plurality of along the measuring position rectangular electrode unit 7 of Y direction parallel arranged, the length of said rectangular electrode unit is L; Said each rectangular electrode unit 7 comprises three rectangular electrodes of the Y direction parallel arranged along the measuring position, and said three rectangular electrodes are followed successively by A rectangular electrode 81, B rectangular electrode 83 and C rectangular electrode 85; Be provided with straight line insulated trenches 10 between said adjacent in twos rectangular electrode and the adjacent in twos rectangular electrode unit 7;

Above-mentioned each A rectangular electrode 81 by the sinusoidal insulated trenches 82 of the identical A of two wavelength be divided into three along the measuring position A strip electrodes 811,812,813 of Y direction parallel arranged, and the equiphase point line of the sinusoidal insulated trenches 82 of the same position of all A rectangular electrodes 81 is a straight line;

Above-mentioned each B rectangular electrode 83 by the sinusoidal insulated trenches 84 of the identical B of two wavelength be divided into three along the measuring position B strip electrodes 831,832,833 of Y direction parallel arranged, and the equiphase point line of the sinusoidal insulated trenches 84 of the same position of all B rectangular electrodes 83 is a straight line;

Above-mentioned each C rectangular electrode 85 by the sinusoidal insulated trenches 86 of the identical C of two wavelength be divided into three along the measuring position C strip electrodes 851,852,853 of Y direction parallel arranged, and the equiphase point line of the sinusoidal insulated trenches 85 of the same position of all C rectangular electrodes 85 is a straight line;

The A strip electrodes of the same position of above-mentioned whole A rectangular electrodes is respectively through an A extension line (91,92,93) output; The B strip electrodes of the same position of said whole B rectangular electrodes is respectively through a B extension line (94,95,96) output; The C strip electrodes of the same position of said whole C rectangular electrodes is respectively through a C extension line (97,98,99) output.

Above-mentioned cascade microchannel plate 2 is two microchannel plates of V-shape cascade or three microchannel plates that the Z font is arranged.

Above-mentioned dielectric base 5 is glass, pottery or pcb board material; The width of said straight line insulated trenches 10 is: 10～50 μ m; The width of the sinusoidal wave insulated trenches of said A is: 10～50 μ m; The width of the sinusoidal wave insulated trenches of said B is: 10～50 μ m; The width of the sinusoidal wave insulated trenches of said C is: 10～50 μ m; The thickness of said conductive layer 6 is 1～10 μ m.

A kind of anode decoding method of realizing above-mentioned high-resolution position-sensitive anode detector may further comprise the steps:

1] after position-sensitive anode is directly collected the electric charge cloud cluster or sensed the electric charge cloud cluster through germanium layer, three C strip electrodes of three A strip electrodes of A rectangular electrode, three B strip electrodes of B rectangular electrode, C rectangular electrode are to nine quantity of electric charge signal Q of electronics read-out system output _A1, Q _A2, Q _A3, Q _B1, Q _B2, Q _B3, Q _C1, Q _C2, Q _C3

2] according to nine quantity of electric charge signals according to following formula calculated phase values θ _A, θ _BAnd θ _C:

${\mathrm{\θ}}_A=\arcsin (\frac{{3Q}_{A1}}{Q_{A1}+Q_{A2}+Q_{A3}}-1)$

${\mathrm{\θ}}_B=\arcsin (\frac{{3Q}_{B1}}{Q_{B1}+Q_{B2}+Q_{B3}}-1)$

${\mathrm{\&theta;}}_C=\arcsin (\frac{{3Q}_{C1}}{Q_{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="H2009100224069E00012.png"\; state="\{\{state\}\}">C</figure-callout>}1}+{\mathrm{<figure-callout\; id="2"\; label="Q\; C"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">Q</figure-callout>}}_C+Q_{C3}}-1)$

3] according to the phase value θ that calculates _A, θ _BAnd θ _C, calculate θ according to following formula _XAnd θ _Y:

θ _X＝θ _A+θ _B，

θ _Y＝θ _B+θ _C，

4] calculate electric charge cloud cluster centroid position coordinate (x, y):

$x=\mathrm{\&lambda;}\frac{{\mathrm{\&theta;}}_x}{2\mathrm{\&pi;}}+\mathrm{i\&lambda;}$

$y=\mathrm{\&lambda;}\frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">y</figure-callout>}}}{2\mathrm{\&pi;}}+\mathrm{j\&lambda;}$

λ=L/n wherein, L is the length of anode collecting region, and n is the periodicity of direction of measurement phase change, generally gets n=4, and i and j are the index value of θ Z step;

Wherein ${\mathrm{\&theta;}}_z={\mathrm{\&theta;}}_A+{\mathrm{\&theta;}}_C-{\mathrm{\&theta;}}_X/n^2-{\mathrm{\&theta;}}_Y/n=$

$\left[\begin{array}{cccc}0& \frac{2\mathrm{\&pi;}}{n}& K& \frac{2(n-1)\mathrm{\&pi;}}{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}\\ \frac{2\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}& \frac{2(n+1)\mathrm{\&pi;}}{n^2}& K& \\ & & K& \\ \frac{2(n-1)\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}& \frac{2(2n-1)\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}& & \frac{2(n^2-1)\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}\end{array}\right];$

5] (x y) is the position of incident particle to the centroid position coordinate of electric charge cloud cluster, and the time of electronics read-out system charge pulse output is the time of arrival of incident particle.

Advantage of the present invention is:

1, multianode detector of the present invention and anode decoding method thereof can be realized other particle position measurements such as photon, electronics and be counted as picture, can be applied to science and technology field such as survey of deep space, nuclear radiation and ion detection, biological ultraweak imaging and quantum communications.

2, multianode detector of the present invention and anode decoding method thereof have high resolution and less scalloping.Because position-sensitive anode of the present invention adopts the strip electrodes of nine separations to accept the electric charge cloud cluster, compared with prior art, has higher spatial resolution; Because each strip electrodes is collected the electric charge area along the homogeneity that direction of measurement distributes, and compared with prior art, has less scalloping.

3, multianode detector of the present invention and anode decoding method thereof do not have the restriction of anode plate design area.Because each strip electrodes is collected the homogeneity that the electric charge area distributes along direction of measurement, so there is not the restriction of charge-trapping design area.

Description of drawings

Fig. 1 is a position-sensitive anode detector synoptic diagram of the present invention;

Fig. 2 is the synoptic diagram of an electrode unit of position-sensitive anode pattern of the present invention;

Fig. 3 is the pattern synoptic diagram of position-sensitive anode electric charge collecting region of the present invention;

Fig. 4 is the extension line synoptic diagram of position-sensitive anode electric charge collecting region of the present invention;

Fig. 5 is the equiphase line synoptic diagram of the sinusoidal insulated trenches of position-sensitive anode electric charge collecting region of the present invention;

Fig. 6 is position-sensitive anode decoding process figure of the present invention;

Description of reference numerals: 1-input window, the microchannel plate of 2-cascade, 3-germanium inductive layer, 4-position-sensitive anode; The 5-dielectric base, 6-conductive layer, 7-rectangular electrode unit, 81-A rectangular electrode; 811,812, the 813-A strip electrodes, the sinusoidal wave insulated trenches of 82-A, 83-B rectangular electrode, 831,832, the 833-B strip electrodes; The sinusoidal wave insulated trenches of 84-B, 85-C rectangular electrode, 851,852, the 853-C strip electrodes, the sinusoidal wave insulated trenches of 86-C; 91,92, the 93-A extension line, 94,95, the 96-B extension line, 97,98, the 99-C extension line, 10-straight line insulated trenches.

Embodiment

Fig. 2 is a rectangular electrode synoptic diagram of the rectangular electrode unit of position-sensitive anode of the present invention.Article two, the sinusoidal insulated trenches identical with amplitude is divided into three strip electrodes with rectangular electrode the cycle, the width A1 of these three strip electrodes, proportionate relationship direction X cyclical variation along the measuring position of A2 and A3 (referring to the perpendicular dotted line among Fig. 2).So the bin area Δ S1 of three strip electrodes, Δ S2, the also direction cyclical variation of the proportionate relationship of Δ S3 along the measuring position.Therefore when the electric charge cloud cluster covers these three strip electrodes, can calculate the periodic location of electric charge cloud cluster barycenter according to the proportionate relationship of these three strip electrodes collection electric charges.This is one of basic thought of anode decoding of the present invention.The variation of the width of these three strip electrodes direction along the measuring position can be following with function representation respectively:

N is the width of rectangular electrode.Φ is an initial phase.

So the width A1 of these three strip electrodes, the proportionate relationship of A2 and A3 can be used a phase theta _Aθ in one-period is described _AIn [0,2 Л], change.Therefore the variation of the proportionate relationship of the collection electric charge of three strip electrodes can be summed up as phase value, has greatly simplified decoding.This also is one of basic thought of anode decoding of the present invention.Position-sensitive anode of the present invention is exactly to be made up of some sinusoidal insulated trenches wavelength rectangular electrode unit different with initial phase.

Fig. 3 is the synoptic diagram of position-sensitive anode electric charge collecting region of the present invention, and electric charge collecting region is a rectangular area, and the rectangular area is long to be L, and wide is W.Anode is made up of the different above-mentioned rectangular electrode of some insulated trenches wavelength, presses the difference of wavelength, can be divided into three kinds of different electrode type, i.e. A rectangular electrode, B rectangular electrode and C rectangular electrode.

The wavelength of the sinusoidal insulated trenches of a plurality of electrodes of the same type equates but initial phase does not wait, as being called the equiphase line to the line of the equiphase point of the sinusoidal insulated trenches of electrode of the same type.Because initial phase do not wait, the equiphase line is not orthogonal to the length direction of rectangular area, is straight line like the equiphase line of all the A rectangular electrodes among Fig. 5.

To sum up; The synoptic diagram of position-sensitive anode pattern of the present invention such as Fig. 3; Electric charge collecting region is the rectangular area that the rectangular electrode unit cell arrangement of three kinds of sinusoidal insulated trenches wavelength of difference forms; Put in order like Fig. 3, A rectangular electrode, B rectangular electrode and C rectangular electrode are a rectangular electrode unit, and the electric charge collecting region pattern is made up of a plurality of rectangular electrode unit combination.The combination of only having drawn 3 rectangular electrode unit among Fig. 3.The wavelength of the sinusoidal insulated trenches of each electrode unit and prima facies place value have above-mentioned definite value relation.Position-sensitive anode pattern of the present invention has nine electrode outputs, and the connected relation of each strip electrodes is as shown in Figure 4, and the place, point of crossing is not communicated with.Position-sensitive anode is exactly on dielectric base, to make electric conductivity favorable conductive layer, and processes above-mentioned electrode pattern through the method for microelectronic technique or laser ablation.

Tell about the decoding principle and the flow process of position-sensitive anode of the present invention below in conjunction with Fig. 6: when the quantity of A rectangular electrode is many, when electrode width N was very little, (x was y) corresponding to a phase theta in two dimensional surface any point _A, in like manner can draw two dimensional surface any point (x, y) all corresponding three phase theta _A, θ _BAnd θ _CSo, can calculate two-dimensional coordinate with these three phase places.The quick positive design of patterns in position according to the present invention, the phase place of X coordinate axis and Y coordinate axis can be by θ _A, θ _BAnd θ _CCalculate, expression formula is following:

θ _A+θ _B＝θ _X，

θ _B+θ _C＝θ _Y，

θ _z＝θ _A+θ _C-θ _X/n ²-θ _Y/n

Because θ _A, θ _BAnd θ _CCyclical variation, θ _XAnd θ _YBe cyclical variation along X axle and Y direction.Variation range is [0,2 Л], and length of periodicity is: λ=L/n, (λ=L/n wherein, L is the length of anode collecting region, the periodicity of n direction of measurement phase change is generally got n=4).According to the expression formula of θ Z, θ Z is some discrete values in the distribution value of two dimension, and each discrete value is represented a step.θ Z discrete value can be following with matrix representation:

$\left[\begin{array}{cccc}0& \frac{2\mathrm{\&pi;}}{n}& K& \frac{2(n-1)\mathrm{\&pi;}}{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}\\ \frac{2\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}& \frac{2(n+1)\mathrm{\&pi;}}{n^2}& K& \\ & & K& \\ \frac{2(n-1)\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}& \frac{2(2n-1)\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}& & \frac{2(n^2-1)\mathrm{\&pi;}}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}\end{array}\right]$

Therefore the decoding of position-sensitive anode of the present invention can be represented with following two formulas:

$x=\mathrm{\&lambda;}\frac{{\mathrm{\&theta;}}_x}{2\mathrm{\&pi;}}+\mathrm{i\&lambda;}$

$y=\mathrm{\&lambda;}\frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="H2009100224069E00011.png,H2009100224069E00012.png"\; state="\{\{state\}\}">y</figure-callout>}}}{2\mathrm{\&pi;}}+\mathrm{j\&lambda;}$

Wherein λ is the length in each cycle, (λ=L/n wherein, L is the length of anode collecting region, the periodicity of n direction of measurement phase change is generally got n=4), i and j are the index value of θ Z step.

To sum up, position-sensitive anode detector of the present invention is as shown in Figure 1, and the course of work is following: particles (if photon, the energy situation of looking photon adds photocathode) such as the photon of entering input window 1 or electronics through the microchannel plate 2 back multiplications of cascade, form the electric charge cloud cluster.The microchannel plate 2 of cascade can be two microchannel plates of V-shape cascade or three microchannel plates that the Z font is arranged.The electric charge cloud cluster quickens through electric field, beats at germanium layer and perhaps directly beats on position-sensitive anode.Position-sensitive anode is after directly collecting the electric charge cloud cluster or sensing the electric charge cloud cluster through germanium inductive layer 3, and nine strip electrodes calculate phase value θ to nine quantity of electric charge signals of electronics read-out system output according to these nine quantities of electric charge _A, θ _BAnd θ _C, calculate θ then _XAnd θ _Y, at last according to above-mentioned two formulas can calculate electric charge cloud cluster centroid position coordinate (x, y).The centroid position of electric charge cloud cluster has just been represented the position of incident particle.Through the time of recorded electronic read-out system charge pulse output, survey the time of arrival of incident particle.Therefore utilize position-sensitive anode detector of the present invention can survey the position and the time of arrival of incident particle.Therefore can be widely used in survey of deep space, science and technology field such as nuclear radiation and ion detection, biological ultraweak imaging and quantum communications.

Claims (4)

1. high-resolution position-sensitive anode detector; Comprise the input window (1) that has photocathode, microchannel plate (2), germanium inductive layer (3) and the position-sensitive anode (4) of cascade; Described position-sensitive anode (4) comprises dielectric base (5) and is arranged on the conductive layer that is used for the anode surface charge-trapping (6) on the dielectric base (5); It is characterized in that: said conductive layer (6) comprise a plurality of along the measuring position rectangular electrode unit (7) of Y direction parallel arranged, the length of said rectangular electrode unit is L; Said each rectangular electrode unit (7) comprises three rectangular electrodes of the Y direction parallel arranged along the measuring position, and said three rectangular electrodes are followed successively by A rectangular electrode (81), B rectangular electrode (83) and C rectangular electrode (85); Be provided with straight line insulated trenches (10) between said adjacent in twos rectangular electrode and the adjacent in twos rectangular electrode unit (7);

Said each A rectangular electrode (81) by the identical sinusoidal insulated trenches of A (82) of two wavelength be divided into three along the measuring position A strip electrodes (811,812,813) of Y direction parallel arranged, and the equiphase point line of the sinusoidal insulated trenches (82) of the same position of all A rectangular electrodes (81) is a straight line;

Said each B rectangular electrode (83) by the identical sinusoidal insulated trenches of B (84) of two wavelength be divided into three along the measuring position B strip electrodes (831,832,833) of Y direction parallel arranged, and the equiphase point line of the sinusoidal insulated trenches (84) of the same position of all B rectangular electrodes (83) is a straight line;

Said each C rectangular electrode (85) by the identical sinusoidal insulated trenches of C (86) of two wavelength be divided into three along the measuring position C strip electrodes (851,852,853) of Y direction parallel arranged, and the equiphase point line of the sinusoidal insulated trenches (85) of the same position of all C rectangular electrodes (85) is a straight line;

The A strip electrodes of the same position of said whole A rectangular electrodes is respectively through an A extension line (91,92,93) output; The B strip electrodes of the same position of said whole B rectangular electrodes is respectively through a B extension line (94,95,96) output; The C strip electrodes of the same position of said whole C rectangular electrodes is respectively through a C extension line (97,98,99) output.

2. high-resolution position-sensitive anode detector according to claim 1 is characterized in that: said cascade microchannel plate (2) is two microchannel plates of V-shape cascade or three microchannel plates that the Z font is arranged.

3. high-resolution position-sensitive anode detector according to claim 1 and 2 is characterized in that: said dielectric base (5) is glass, pottery or pcb board material; The width of said straight line insulated trenches (10) is: 10～50 μ m; The width of the sinusoidal insulated trenches of said A is: 10～50 μ m; The width of the sinusoidal insulated trenches of said B is: 10～50 μ m; The width of the sinusoidal insulated trenches of said C is: 10～50 μ m; The thickness of said conductive layer (6) is 1～10 μ m.

4. anode decoding method according to the said high-resolution position-sensitive anode detector of claim 1 is characterized in that: may further comprise the steps:

1] after position-sensitive anode is directly collected the electric charge cloud cluster or sensed the electric charge cloud cluster through germanium layer, three C strip electrodes of three A strip electrodes of A rectangular electrode, three B strip electrodes of B rectangular electrode, C rectangular electrode are to nine quantity of electric charge signal Q of electronics read-out system output _A1, Q _A2, Q _A3, Q _B1, Q _B2, Q _B3, Q _C1, Q _C2, Q _C3

2] according to nine quantity of electric charge signals according to following formula calculated phase values θ _A, θ _BAnd θ _C:

${\mathrm{\&theta;}}_A=\arcsin (\frac{{3Q}_{A1}}{Q_{A1}+Q_{A2}+Q_{A3}}-1)$

${\mathrm{\&theta;}}_B=\arcsin (\frac{{3Q}_{B1}}{Q_{B1}+Q_{B2}+Q_{B3}}-1)$

${\mathrm{\&theta;}}_C=\arcsin (\frac{{3Q}_{C1}}{Q_{C1}+Q_{C2}+Q_{C3}}-1)$

3] according to the phase value θ that calculates _A, θ _BAnd θ _C, calculate θ according to following formula _XAnd θ _Y:

θ _X＝θ _A+θ _B，

θ _Y＝θ _B+θ _C，

4] calculate electric charge cloud cluster centroid position coordinate (x, y):

$x=\mathrm{\&lambda;}\frac{{\mathrm{\&theta;}}_x}{2\mathrm{\&pi;}}+\mathrm{i\&lambda;}$

$y=\mathrm{\&lambda;}\frac{{\mathrm{\&theta;}}_y}{2\mathrm{\&pi;}}+\mathrm{j\&lambda;}$

λ=L/n wherein, L is the length of anode collecting region, and n is the periodicity of direction of measurement phase change, gets n=4, and i and j are θ _ZThe index value of step;

θ wherein _z=θ _A+ θ _C-θ _X/ n ²-θ _Y/ n=

$\left[\begin{array}{cccc}0& \frac{2\mathrm{\&pi;}}{n}& \&CenterDot;\&CenterDot;\&CenterDot;& \frac{2(n-1)\mathrm{\&pi;}}{n}\\ \frac{2\mathrm{\&pi;}}{n^2}& \frac{2(n+1)\mathrm{\&pi;}}{n^2}& \&CenterDot;\&CenterDot;\&CenterDot;& \\ & & \&CenterDot;\&CenterDot;\&CenterDot;& \\ \frac{2(n-1)\mathrm{\&pi;}}{n^2}& \frac{2(2n-1)\mathrm{\&pi;}}{n^2}& \&CenterDot;\&CenterDot;\&CenterDot;& \frac{2(n^2-1)\mathrm{\&pi;}}{n^2}\end{array}\right];$

5] (x y) is the position of incident particle to the centroid position coordinate of electric charge cloud cluster, and the time of electronics read-out system charge pulse output is the time of arrival of incident particle.

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