CN115046475A - High-precision laser spot position detection method based on four-quadrant detector - Google Patents
High-precision laser spot position detection method based on four-quadrant detector Download PDFInfo
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Abstract
The invention provides a high-precision laser spot position detection method based on a four-quadrant detector, which is characterized in that the relation between an actual spot position value and a solution value is obtained according to an infinite integral fitting algorithm; introducing an error compensation factor function, and processing the relation between the actual value and the calculated value of the spot position to obtain a residual error between the estimated value and the actual value of the spot position; obtaining the optimal equivalent spot radius according to the principle of a least square method; introducing parameters for controlling the shape of the waveform based on a Tanh function fitting algorithm to obtain an actual value of the position of the light spot; constructing a mathematical model of the residual error of the light spot position to minimize the sum of squares thereof, so as to obtain the optimal control waveform shape parameter; and obtaining the position of the light spot according to the optimal equivalent radius, the optimal control waveform shape parameter and the establishment of a new mathematical model of the residual error. The invention has the beneficial effects that: the influence of the radius and the dead zone of the detector is fully considered, the requirement of any four-quadrant detector can be met, and the detection precision of the light spot position is improved.
Description
Technical Field
The invention relates to the technical field of laser positioning, in particular to a high-precision laser spot position detection method based on a four-quadrant detector.
Background
The laser spot position detection is an important content in the laser positioning technology, mainly reflects the actual position of a target through the relative position of a laser spot on a detector, obtains the spot position through processing the output signal of the detector, and determines the target position information according to the spot position. According to the difference of the used detector and signal processing method, information such as the energy center position of the light spot, the movement track of the light spot and the like can be obtained, so that the method is widely applied to the fields of basic scientific research, industrial production, laser communication, aerospace military and the like. Therefore, the laser positioning technology represents the development level of the national high-tech laser detection technology to a great extent, and is a hot spot of the modern high-tech technology.
The detection accuracy of the light spot position is not only influenced by the defects of the detector, but also depends on the algorithm of light spot position detection. The essence of the light spot position detection method is that the centroid position of the current light spot is calculated according to four paths of light current signals output by a four-quadrant detector. When the requirement on the detection accuracy of the light spot position is not high, the calculation can be carried out by using a central approximation method, the accuracy of the algorithm is higher in a range with a small light spot center, and when the light spot center moves to the edge of the detector, the calculation deviation value and the actual center of mass are not in a linear relation and show nonlinear change, so that the error is gradually increased. The calculated value of the light spot position can describe the motion trend of the light spot on the photosensitive surface of the detector, but the specific position of the light spot cannot be accurately positioned, so that the key point for solving the problem is to improve the detection precision to the maximum extent according to a corresponding light spot position detection algorithm on the basis of obtaining the calculated value of the light spot position.
In the prior art, the laser spot position detection is researched, the detection precision of the spot position is improved by the provided spot position positioning method, but the research on the self defects of the detector, namely the radius of the detector and a mathematical model of a channel existing during the encapsulation of a photosensitive surface of the detector, is not deep enough, the influence of the self defects of the detector on the detection precision of the spot position of the QD detector cannot be deeply analyzed, and in addition, the research on the spot position detection algorithm does not take the influence of the radius of the detector and the width of a dead zone into consideration, so that the detection precision of the spot position also has a large promotion space to a certain extent.
Aiming at the problems, the invention provides a light spot position detection optimization method based on a four-quadrant detector. In the aspect of the influence factors of the light spot position detection precision, the influence of factors such as the dead zone width and the radius of the detector on the light spot position detection precision is fully considered, and a corresponding error function is established. Meanwhile, in the aspect of a light spot position detection algorithm, an infinite integral algorithm is used for fitting an actual value and a calculation value of a light spot position, an error compensation factor mode is introduced on the basis of the actual value and the calculation value of the light spot position to compensate for the influence of the dead zone width and the radius of a detector on the light spot position detection precision, then a Tanh function is introduced for further improving the light spot position detection precision to fit the relation between the calculation value and the actual value of the light spot, and finally the two algorithms are combined with each other to obtain a new light spot position fitting expression, so that the detection precision of the whole laser light spot position detection system is improved.
Disclosure of Invention
In order to solve the above problems, the present invention provides a high-precision laser spot position detection method based on a four-quadrant detector, which mainly comprises:
s1: obtaining the relation between the actual value and the solution value of the spot position according to an infinite integral fitting algorithm;
s2: introducing an error compensation factor function, and processing the relation between the actual value and the calculated value of the spot position to obtain a residual error between the estimated value and the actual value of the spot position;
s3: obtaining the corresponding optimal equivalent spot radius when the residual error is minimum according to the principle of a least square method;
s4: introducing parameters for controlling the shape of the waveform based on a Tanh function fitting algorithm to obtain an actual value of the position of the light spot;
s5: according to the actual value of the spot position, a mathematical model of the residual error of the spot position is constructed, the sum of squares of the mathematical model is minimized, and the optimal control waveform shape parameter is obtained;
s6: and obtaining the parameters of the new light spot position expression according to the obtained optimal equivalent radius, the optimal control waveform shape parameters, the constructed new light spot position expression and the new mathematical model of the residual error of the light spot position, and then obtaining the light spot position.
Further, in step S1, the relationship between the actual value and the calculated value of the spot position is:
wherein x is the actual value of the spot position, σ x For spot position solution, λ is the beam waist radius of the Gaussian spot, erf -1 (. cndot.) is the inverse of the error function.
Further, in step S2, the residual error between the estimated spot position value and the actual value is:
wherein λ is e N is 1 … N, which is the nth position point of the spot, L n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position of the light spot.
Further, in step S3, the optimal equivalent spot radius is:
wherein the content of the first and second substances,
erf -1 (. cndot.) is the inverse of the error function, N is 1 … N, is the nth location point of the spot, σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position point of the light spot.
Further, in step S4, the actual value of the spot position is:
wherein σ x Alpha is a parameter introduced to control the shape of the waveform, which is a solution of the spot position.
Further, in step S5, a mathematical model of the spot position residual error is constructed as follows:
wherein, J n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n And alpha is an actual value of the nth position point of the light spot, and is a parameter for controlling the shape of the waveform introduced.
Further, in step S5, the optimal control waveform shape parameters are:
wherein epsilon 2 (σ xn )＝ln((1+σ xn )/(1-σ xn ) N is 1 … N, which is the nth position point of the light spot, σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position point of the light spot.
Further, in step S6, a new spot position expression is constructed as follows:
x 0 (σ x )＝β*x 01 (σ x )+(1-β)*x 02 (σ x )
wherein x is 01 (σ x )＝ε 1 (σ x )*λ e ，x 02 (σ x )＝α/2*ε 2 (σ x )，ε 2 (σ xn )＝ln((1+σ xn )/(1-σ xn ))，
ε 2 (σ x )＝ln((1+σ x )/(1-σ x ))，σ x And beta is a parameter to be solved of the light spot position expression.
Further, in step S6, a new spot position residual error mathematical model is constructed as follows:
wherein, K n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position point of the light spot.
Further, in step S6, the parameters of the new spot position expression are:
wherein σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value, x, of the nth position point of the light spot 01 (σ xn )＝ε 1 (σ xn )*λ e ，
Is the nth position point of the light spot, erf -1 (. is an inverse function of the error function, x 02 (σ xn )＝α/2*ε 2 (σ xn )，λ e To the equivalent spot radius, α is the parameter introduced to control the waveform shape.
The technical scheme provided by the invention has the beneficial effects that: the influence of the radius and the dead zone of the detector is fully considered, the requirement of any four-quadrant detector can be met, and the detection precision of the light spot position is improved.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
fig. 1 is a flowchart of a high-precision laser spot position detection method based on a four-quadrant detector in an embodiment of the present invention.
FIG. 2 is a schematic diagram of a four quadrant detector in an embodiment of the present invention.
FIG. 3 is a graph showing a relationship between an actual value and a calculated value of a spot position at different spot radii according to an embodiment of the present invention.
FIG. 4 is a graph of an infinite integration fit error curve for different spot radii in an embodiment of the present invention.
FIG. 5 is an error curve diagram of a Tanh function fitting method under different spot radii in the embodiment of the present invention.
FIG. 6 is a graph of the error curve of the fusion algorithm for different spot radii in the embodiment of the present invention.
Detailed Description
For a more clear understanding of the technical features, objects, and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
The existing common devices for detecting the position of the laser spot comprise three types: (1) the position sensitive detector has the advantages that the photosensitive surface is large, the shape and the energy distribution of light spots hardly influence the detection result of the position of the light spots, but the junction capacitance is large, the position resolution is low and the linearity is poor; (2) the charge coupled device has higher spatial resolution, but has the defects of non-linear response, non-uniform pixel performance and the like; (3) the four-quadrant detector has the advantages of high sensitivity, wide position resolution spectral response range, small size, quick response, wide dynamic range, capability of working under low illumination and the like, and meets the requirement on target positioning.
An effective light spot position detection algorithm is the key for improving the light spot positioning accuracy of a four-quadrant detector, the existing light spot position detection algorithm has a central approximation method, a micro-motion positioning method and the like, most of the methods use uniform light spots as research objects, and the problem that the actual laser light spots are Gaussian light spots is ignored; the research aiming at the Gaussian spot model comprises a geometric approximation method, a database query method and the like, but the influence of the radius of the detector and the dead zone of the detector on the detection precision of the position of the Gaussian spot is ignored. Therefore, how to compensate for the influence of the factors and further improve the detection accuracy of the position of the light spot is a challenging task.
The invention mainly solves the problem that the radius and dead zone of a four-quadrant detector influence the detection precision of a light spot position, and provides a method based on infinite integral fitting and hyperbolic tangent functionAnd (4) a number-fitting fused light spot position detection algorithm. Because the actual value and the calculated value of the light spot position are in an S-shaped curve relation, the invention uses an infinite integration algorithm to fit the relation between the actual value and the calculated value, and considers the influence of the radius and the dead zone of the detector on the light spot detection on the basis of the relation, thereby introducing an error compensation factor to improve the detection precision of the light spot position. In addition, in order to further represent the relationship between the actual value and the calculated value of the four-quadrant detector, the hyperbolic tangent function (Tanh) model is deeply linked with the curve relationship between the calculated value and the actual value of the light spot, and new physical meanings are given to parameters in the Tanh function model. Finally, a new spot position fitting expression is obtained, and the position detection precision of the laser spot is improved. However, the two algorithms are not simply combined with each other, and firstly, the two algorithms can represent the S-shaped curve relation between the spot position solution value and the actual value; secondly, the equivalent spot radius λ needs to be found from a suitable mathematical model e And a waveform control parameter alpha (which is one of the improvement points of the application), so that the light spot position error curve of the infinite integration algorithm and the Tanh function fitting algorithm can simultaneously achieve the effect of higher light spot position detection precision on the basis of presenting opposite change trends.
Referring to fig. 1, fig. 1 is a flowchart of a high-precision laser spot position detection method based on a four-quadrant detector in an embodiment of the present invention, and a spot position detection algorithm studied by the present invention is a fusion algorithm based on a combination of an infinite integration method and a Tanh function fitting method, and specifically includes:
(1) infinite integral fitting algorithm
When the detector receives illumination, a photocurrent proportional to the light intensity is generated, and the position of the light spot can be calculated according to the four photocurrents. As shown in fig. 2, due to the manufacturing process, there is a channel d between the four photodiodes, which is not sensitive to light, and the size of the channel d affects the detection accuracy of the four-quadrant detector. Firstly, laser is emitted by a laser, and is focused on a four-quadrant detector to form light spots after being converted by an optical system, and the light energy received by the four quadrants is assumed to be E respectively A 、E B 、E C 、E D Meridian/channelThe output currents after photoelectric conversion are respectively I A 、I B 、I C 、I D The different positions of the spots on the detector directly results in different currents being output by the quadrants. Therefore, the approximate position of the light spot can be calculated by different output currents, and the expression is as follows:
wherein σ x ，σ y Respectively represents the offset of the centroid of the light spot in the x-axis direction and the y-axis direction of the photosensitive surface, and k is a proportionality coefficient. Because the four-quadrant detector is in a highly symmetrical structure, the method only carries out research on the direction of the x axis of the detector, and the y axis has the same property and research result in the same way.
Since the energy of the beam actually output by the laser is closer to the gaussian distribution, the energy distribution on the four-quadrant detector can be approximately regarded as a spot model of the gaussian distribution, and the formula is shown in formula (3), that is:
wherein E is 0 Is the total energy of the spot, λ is the beam waist radius of the Gaussian spot, (x) 0 ,y 0 ) Is the coordinate position of the spot centroid. The photocurrent is proportional to the incident light energy reaching the detector, written as an integral, in the form:
where η is the conversion factor, n1 is the quadrant representing the detector, and S is the area occupied by the spot in each quadrant of the detector. Substituting equation (4) into equation (1) may result in a spot position solution expression as follows:
ignoring the presence of the detector channel d, equation (5) is simplified to equation (6):
since the above expression cannot be directly solved, the integration limit in equation (6) is changed to infinity in consideration of neglecting the influence of the radius R of the detector, and an error function is used
And (3) simplifying the expression (6) to obtain the relation between the actual value and the solution value of the spot position, wherein the expression is as follows:
in order to obtain higher accuracy, and considering the influence of the radius of the detector on the calculation model, an error compensation factor function ρ (λ, R) is introduced, the error compensation factor considers the influence of neglecting R because the integral limit becomes infinite, and then the position of the centroid of the light spot is estimated as follows:
in this case, λ × ρ (λ, R) in the above formula is newly defined as λ e It represents the degree of contribution of λ and R to the influence of the spot position. Lambda [ alpha ] e Referred to as the equivalent spot radius, the spot position estimate at this time is as follows:
is provided with
Then x ═ epsilon 1 (σ x )*λ e . Parameter lambda e The value of (c) can be solved using calibrated data according to a strategy that minimizes empirical risk. The actual value x of the light spot can be obtained through experiments n And the calculated value σ xn Thereby obtaining epsilon of each point 1 (σ x ) Values, then substituting each set of values into the above equation, solving for λ based on known parameters e The value of (c) is critical to solving the problem. Let the actual values of the spot positions be x respectively 1 ，x 2 ，…，x n The spot position estimates are each x (λ) e ,σ x1 )，x(λ e ,σ x2 )，…，x(λ e ,σ xn ) The residual errors are respectively expressed as L 1 ，L 2 ，…，L n Therefore, the residual error between the estimated spot position and the actual value has the following relationship:
the essence of improving the spot position detection accuracy is to minimize the difference between the spot position estimate and the actual value. Therefore, according to the principle of least squares, the estimated spot position value closest to the actual value should minimize the sum of the squares of the residual error (L) min ) If so, the following expression should be satisfied:
to facilitate the calculation, the coefficients of the equation are
The residual error expression is constructed as follows:
wherein λ is e N is 1 … N, which is the nth position point of the spot, L n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position of the spot.
The minimum value L of the sum of the squares of the residual errors is calculated min Thus for the parameter λ of the above formula e By taking the first derivative and making it zero, the optimum lambda can be found e The values, namely:
(2) tanh function fitting algorithm
When laser is incident on a photosensitive surface of the four-quadrant detector, a relation curve between a resolving value of the four-quadrant detector and an actual position value of a spot centroid presents an S shape. In order to enable the change between the light spot position calculation value and the actual value to conform to a certain mathematical function relation, the method deeply links the hyperbolic tangent function model with the curve relation between the calculation value of the detector and the light spot centroid actual position value. Therefore, the method provides a light spot position detection algorithm based on the hyperbolic tangent function, which is called Tanh fitting algorithm for short. The hyperbolic tangent function is:
in order to describe the variation relationship between the calculated value and the actual value of the light spot position more closely, a parameter alpha for controlling the waveform shape is introduced, and the improved relationship is shown as the formula (15):
and (3) obtaining an expression of the actual value of the spot position by taking an inverse function of the formula (15):
wherein σ x Alpha is a parameter introduced to control the shape of the waveform, which is a solution of the spot position.
Let ε 2 (σ x )＝ln((1+σ x )/(1-σ x ) X ═ α/2 ∈ ═ then 2 (σ x ) The value of the parameter α can be solved using calibrated data according to an empirical risk minimization strategy. Similar to the infinite integration algorithm, let the actual value of the spot position be x respectively 1 ，x 2 ，…，x n The estimated values of the positions of the light spots are x (alpha, sigma) respectively x1 )，x(α,σ x2 )，…，x(α,σ xn ) The residual errors are respectively represented as J 1 ，J 2 ，…，J n Therefore, the residual error between the estimated spot position and the actual value has the following relationship:
to minimize the sum of squared residual errors, a mathematical model of the positional residual error is constructed as follows:
wherein, J n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n And alpha is the introduced parameter for controlling the waveform shape, and is the actual value of the nth position point of the light spot.
By taking the partial derivative of α in the above equation and making it zero, the optimal α value can be found, i.e.:
wherein epsilon 2 (σ xn )＝ln((1+σ xn )/(1-σ xn ) N is 1 … N, which is the nth position point of the light spot, σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position point of the light spot.
(3) Fusion algorithm
The light spot position detection precision can be improved by carrying out infinite integral algorithm fitting on the light spot position solution value and the actual value and introducing an error compensation factor for analysis; and secondly, through analysis of the influence of the hyperbolic tangent function fitting compensation detector channel on the detection precision, the detection errors of the light spot positions of the hyperbolic tangent function fitting compensation detector channel and the hyperbolic tangent function fitting compensation detector channel are opposite in trend in the same detection range and can be mutually offset in a certain range. Therefore, the method comprehensively considers that the two algorithms are fused and then adopts a weighting mode to reduce the position detection error.
Assuming that the spot position can be expressed as:
x 0 (σ x )＝β*x 01 (σ x )+(1-β)*x 02 (σ x ) (20)
wherein: x is the number of 01 (σ x )＝ε 1 (σ x )*λ e ，x 02 (σ x )＝α/2*ε 2 (σ x )，ε 2 (σ xn )＝ln((1+σ xn )/(1-σ xn ))，
ε 2 (σ x )＝ln((1+σ x )/(1-σ x ) λ) can be introduced according to the steps of sections (1) and (2) above e And alpha value, beta is a parameter to be solved of the light spot position expression, and then a mathematical model of the residual error is established:
wherein, K n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n The actual values of the n-th position points of the light spot are x 1 ，x 2 ，…，x n The estimated values of the positions of the light spots are x respectively 0 (β,σ x1 )，x 0 (β,σ x2 )，…，x 0 (β,σ xn ) The partial derivative of β in the above equation is found and made zero, and the optimal β value can be found, that is:
wherein σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value, x, of the nth position point of the light spot 01 (σ xn )＝ε 1 (σ xn )*λ e ，
Is the nth position point of the light spot, erf -1 (. is an inverse function of the error function, x 02 (σ xn )＝α/2*ε 2 (σ xn )，λ e To the equivalent spot radius, α is the parameter introduced to control the waveform shape.
By the algorithm derivation, the parameter lambda is obtained e The values of alpha and beta are the key points for obtaining a new spot position fitting expression. To further analyze the proposed algorithmic model, numerical analysis was performed by MATLAB simulation software. Assuming that the radius R of the four-quadrant detector is 1.5mm, the width d of the detector channel is 0.045mm, and the total energy E of the light spot 0 The incident spot radius λ is 0.65mm, 0.75mm, 0.85mm, 0.95mm, respectively. Drawing an actual value x and a calculated value sigma of the spot position by using a formula (5) x The curves are shown in fig. 3. Then, simulation is carried out by respectively utilizing an infinite integral fitting method, a hyperbolic tangent function fitting method and a fusion algorithm to obtain a light spot position detection error sigma x The comparison curves are shown in fig. 4, 5 and 6, respectively.
According to the simulation result, the variation trends of the error curves of the infinite integral fitting algorithm and the hyperbolic tangent function fitting algorithm are oppositeThe trend, and therefore the error curve of the composite algorithm, is obtained by combining the two. Aiming at incident light spots with different radiuses, the maximum error and the root mean square error of the composite algorithm in the whole detection range are far lower than those of an infinite integral fitting algorithm and a Tanh function fitting algorithm, and the maximum error of the composite algorithm can reach 10 -4 Of the order of mm. Therefore, the fusion algorithm for detecting the light spot position, which is provided by the patent, considers the influence of the radius of the detector and the dead zone on the detection precision of the light spot position on the basis of a geometric approximation method, improves the detection precision of the light spot position, and finally verifies the effectiveness and the rationality of the algorithm through simulation.
The light spot position detection optimization algorithm provided by the invention can be used for light spot position detection systems of all four-quadrant detectors, and can obtain the optimal light spot radius aiming at detectors with different radii, so that the high-precision positioning of the light spot position is realized in the maximum effective detection range.
Parameter lambda of the algorithm in the invention e The solving methods of alpha and beta and the Tanh function fitting algorithm can be replaced, and in the light spot position detection algorithm implementation flow chart provided by the invention, the specific algorithm replacement still belongs to the innovation point of the invention.
The key points and points to be protected of the invention are as follows:
1. aiming at the influence of the radius and the channel of the detector in the light spot position detection process, an error model of the radius and the dead zone width of the detector is determined according to an error theory, the system is suitable for light spot position detection systems of four-quadrant detectors with different radius sizes and dead zone widths, and has better universality;
2. aiming at the infinite integral algorithm part, simplifying a light spot position calculation value expression by using an error compensation function, then introducing an error compensation factor, compensating the influence of the radius and the dead zone of a detector on the light spot position detection precision, and providing a specific processing method of the algorithm;
3. aiming at infinite integral fitting method, Tanh function fitting method and fusion algorithm of light spot position detection, solving key parameter lambda corresponding to each algorithm by using residual error mathematical model e Alpha and beta, and then giving a spot position fitting expression corresponding to each algorithm.
The beneficial effects of the invention are: the invention mainly solves the problem of low light spot position detection precision caused by neglecting the influence of the radius and the dead zone of the detector in the light spot position detection of a four-quadrant detector, and provides a fused light spot position detection algorithm combining an infinite integration method and a Tanh function fitting method. In the actual laser spot position detection, the four-quadrant detector has a dead zone which cannot sense light, so that the spot energy of the laser is lost; in addition, simulation research shows that for a determined four-quadrant detector, the corresponding light spot detection error and the effective detection range are different when the sizes of the light spot radiuses are different, so that a proper light spot radius is selected, the effective detection range is as large as possible, and better light spot position detection accuracy can be obtained. The invention fully considers the influence of the radius and the dead zone of the detector, the proposed fusion algorithm can meet the requirements of any four-quadrant detector, and the detection precision of the light spot position is effectively improved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (10)
1. A high-precision laser spot position detection method based on a four-quadrant detector is characterized by comprising the following steps: the method comprises the following steps:
s1: obtaining the relation between the actual value and the solution value of the spot position according to an infinite integral fitting algorithm;
s2: introducing an error compensation factor function, and processing the relation between the actual value and the calculated value of the spot position to obtain a residual error between the estimated value and the actual value of the spot position;
s3: obtaining the corresponding optimal equivalent spot radius when the residual error is minimum according to the principle of a least square method;
s4: introducing parameters for controlling the shape of the waveform based on a Tanh function fitting algorithm to obtain an actual value of the position of the light spot;
s5: according to the actual value of the spot position, a mathematical model of the residual error of the spot position is constructed, the sum of squares of the mathematical model is minimized, and the optimal control waveform shape parameter is obtained;
s6: and obtaining the parameters of the new light spot position expression according to the obtained optimal equivalent radius, the optimal control waveform shape parameter, the constructed new light spot position expression and the new mathematical model of the residual error of the light spot position, and further obtaining the light spot position.
2. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S1, the relationship between the actual value of the spot position and the calculated value is:
wherein x is the actual value of the spot position, σ x For spot position solution, λ is the beam waist radius of the Gaussian spot, erf -1 (. cndot.) is the inverse of the error function.
3. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S2, the residual error between the estimated spot position value and the actual spot position value is:
wherein λ is e N is 1 … N as the equivalent spot radius, the nth position point of the spot, L n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position of the spot.
4. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S3, the optimal equivalent spot radius is:
wherein the content of the first and second substances,
erf -1 (. h) is the inverse of the error function, N is 1 … N, and is the nth position point of the spot, σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position point of the light spot.
5. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S4, the actual value of the spot position is:
wherein σ x Alpha is a parameter introduced to control the shape of the waveform, which is a solution of the spot position.
6. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S5, a mathematical model of the spot position residual error is constructed as follows:
wherein, J n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n And alpha is the introduced parameter for controlling the waveform shape, and is the actual value of the nth position point of the light spot.
7. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S5, the optimal control waveform shape parameters are:
wherein epsilon 2 (σ xn )＝ln((1+σ xn )/(1-σ xn ) N is 1 … N, which is the nth position point of the light spot, σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position point of the light spot.
8. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S6, a new spot position expression is constructed as follows:
x 0 (σ x )＝β*x 01 (σ x )+(1-β)*x 02 (σ x )
wherein x is 01 (σ x )＝ε 1 (σ x )*λ e ，x 02 (σ x )＝α/2*ε 2 (σ x )，ε 2 (σ xn )＝ln((1+σ xn )/(1-σ xn ))，
ε 2 (σ x )＝ln((1+σ x )/(1-σ x ))，σ x And beta is a parameter to be solved of the light spot position expression.
9. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S6, the new spot position residual error mathematical model is constructed as follows:
wherein, K n Residual error of the nth position point of the light spot, sigma xn Calculated value, x, for the nth position point of the light spot n Is the actual value of the nth position point of the light spot.
10. The high-precision laser spot position detection method based on the four-quadrant detector as claimed in claim 1, wherein: in step S6, the parameters of the new spot position expression are:
wherein σ xn Calculated value, x, for the nth position point of the light spot n Is the actual value, x, of the nth position point of the light spot 01 (σ xn )＝ε 1 (σ xn )*λ e ，
Is the nth position point of the light spot, erf -1 (. is an inverse function of the error function, x 02 (σ xn )＝α/2*ε 2 (σ xn )，λ e To the equivalent spot radius, α is the parameter introduced to control the waveform shape.
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