CN110440691B - A Practical Method for Locating the Centroid of Gaussian Spot with High Precision Four-Quadrant Detector - Google Patents

Abstract

The invention is a practical high-precision four-quadrant detector Gaussian spot centroid positioning method, which relates to the field of laser spot positioning. The steps are as follows: step 1, use the four-way output photocurrent of the four-quadrant detector to calculate the solution value of the spot centroid; step 2, take the center of the four-quadrant detector as the coordinate origin, establish a rectangular coordinate system, and use the Gaussian spot energy distribution model , according to the accuracy requirements, construct a look-up table corresponding to the calculated value of the spot centroid and the relative position; step 3, according to the calculated value in step 1, find out the corresponding relative position in the look-up table constructed in step 2; step 4. If the accuracy does not meet the requirements, correct the result searched in step 3, and if the accuracy meets the requirements, proceed to the next step; step 5, calculate the spot centroid according to the spot radius and the relative position in step 4.

Description

A Practical Method for Locating the Centroid of Gaussian Spot with High Precision Four-Quadrant Detector

technical field

The invention relates to the technical field of laser spot positioning, in particular to a practical high-precision four-quadrant detector Gaussian spot centroid positioning method.

Background technique

Quadrant Detector (QD) is a commonly used position detection sensor. It has been widely used due to its simple signal processing circuit, wide wavelength response range, low inherent noise level, high sensitivity and fast response speed. It is used in fields such as laser alignment, laser guidance, laser monitoring, laser tracker and space laser communication that need to provide high-precision micro-displacement or angle measurement.

There are two main factors that affect the detection accuracy of the laser spot position: one is the random error caused by the random fluctuation of the solution value caused by noises such as signal processing circuit, background light and atmospheric turbulence. The other is the inherent error of the system, such as the error of the light spot model, the inconsistency error of the four quadrants, the error of the system optical adjustment and so on. Among the inherent errors, the spot centroid positioning algorithm plays a pivotal role. Due to the nonlinear relationship between the Gaussian spot centroid and the calculated value of the spot centroid, direct calculation is almost impossible, and most related algorithms remain in the theoretical research and numerical simulation stage. , only the approximate algorithm can be applied in real-time applications, but the approximate algorithm only has high accuracy near the center position, and a large error will occur when the spot centroid is far from the detection center. In order to obtain high-precision spot centroid positioning, a feasible way is to use a look-up table. The current look-up table algorithm is to directly use the solution value of the spot centroid or the photocurrent ratio to establish a two-dimensional database, and find and calculate the spot centroid. , the disadvantage of this method is that the database is large, and the search and calculation amount is large, which is not conducive to real-time applications. More importantly, the two-dimensional database is related to the radius. When the radius changes, a two-dimensional database needs to be constructed, which is time-consuming and labor-intensive.

SUMMARY OF THE INVENTION

The technical problem solved by the present invention is to overcome the deficiencies related to the radius of the light spot directly calculated by the existing algorithm, and to provide a practical method for locating the centroid of the Gaussian light spot of a high-precision four-quadrant detector, which greatly improves the positioning accuracy and speeds up the processing. speed and increased ease of use.

In order to solve the above-mentioned technical problems, the technical scheme of the present invention is as follows:

A practical high-precision four-quadrant detector Gaussian spot centroid location method, characterized in that it includes the following steps:

Step 1. Use the four-way output photocurrent of the four-quadrant detector to calculate the solution value of the spot centroid;

Step 2. Taking the center of the four-quadrant detector as the coordinate origin, establish a rectangular coordinate system, and use the Gaussian spot energy distribution model to construct a look-up table corresponding to the calculated value of the spot centroid and the relative position according to the accuracy requirement;

Step 3, find out the corresponding relative position in the lookup table constructed in the step 2 according to the solution value in the step 1;

Step 4. If the accuracy does not meet the requirements, correct the result of the search in step 3, and if the accuracy meets the requirements, proceed to the next step;

Step 5: Calculate the centroid of the light spot according to the radius of the light spot and the relative position in step 4.

Preferably, the calculation formula of the solution value of the centroid of the light spot in the step 1 is:

和

分别为x和y方向上的光斑质心解算值。In the formula, I _A , I _B , I _C , and I _D are the photocurrents of the four quadrants, respectively,

and

are the calculated values of the spot centroid in the x and y directions, respectively.

Preferably, the expression of the Gaussian spot energy distribution model in the step 2 is:

In the formula, p ₀ is the light intensity at the center of the spot, (x ₀ , y ₀ ) is the centroid of the spot, and r is the radius of the Gaussian spot.

Preferably, in the step 2, a look-up table is constructed that corresponds to the calculated value of the centroid of the light spot and the relative position, and the relationship between the calculated value of the centroid of the light spot and the relative position is:

In the formula, x _r and y _r are the relative positions of the x and y directions, respectively. The calculation formula of the x direction is x _r = x ₀ /r, which is the ratio of the spot centroid x ₀ to the spot radius r, and the value range is [-1 ,1]; the calculation formula for the y direction is y _r =y ₀ /r, which is the ratio of the spot centroid y ₀ to the spot radius r, and the value range is [-1,1].

Preferably, according to the accuracy requirement in the step 2, the size of the lookup table is set to (2n+1)×1, where 2n+1 is the number of subdivisions for the dynamic range [-r,r] of the four-quadrant detector;

Preferably, according to the symmetry independence of the x and y directions, the method for constructing the lookup table table in the step 2 includes the following:

(1) The x and y directions share a look-up table with the full dynamic range [-r, r], (2n+1) is the number of subdivisions for the dynamic range of the four-quadrant detector, then the size of the table is (2n+1)× 1. The number of tables is 1, and the relative position can be calculated by directly using the solution value to look up the table;

(2) The x and y directions share a look-up table with a positive half dynamic range [0,r], (2n+1) is the number of subdivisions for the dynamic range of the four-quadrant detector, then the size of the table is (n+1)× 1. The number of tables is 1. The calculated value of the positive half dynamic range [0, r] can directly use the calculated value to look up the table to calculate the relative position, while the calculated value of the negative half dynamic range [-r, 0] first takes its absolute value The value look-up table calculates the relative position, and finally takes the negative value of the relative position found;

(3) The x and y directions share a negative half dynamic range [-r, 0] lookup table, (2n+1) is the number of subdivisions for the dynamic range of the four-quadrant detector, then the size of the table is (n+1) ×1, the number of tables is 1, the solution value of the negative half dynamic range [-r, 0] can directly use the solution value to look up the table to calculate the relative position, and the solution value of the positive half dynamic range [0, r] is taken first The negative number look-up table calculates the relative position, and finally takes the negative value of the relative position found;

(4) Considering that there may be differences in the x and y directions of the actual application, x and y construct independent tables respectively. There are also the above three methods, and the number of tables is increased to 2.

Preferably, the sequence in the lookup table constructed in the step 2 may be arranged in ascending order or descending order.

Preferably, the method of searching in the look-up table in the step 3 may be any quick look-up table method suitable for sorting sequences;

Preferably, in the step 4, the relative position of the search is corrected by using a linear interpolation method.

Preferably, the formula for calculating the centroid of the light spot according to the radius of the light spot and the relative position in the step 5 is:

x ₀ =x _r ×r

y ₀ =y _r ×r

The present invention has the following beneficial effects:

Compared with the prior art, a practical high-precision four-quadrant detector Gaussian spot centroid positioning method of the present invention has the following significant advantages:

(1) The present invention can construct look-up tables with different subdivisions according to the requirements of practical applications for accuracy and calculation speed, so as to obtain Gaussian spot centroid positioning algorithms that meet different application requirements.

(2) The algorithm obtained by the present invention can meet various requirements in the actual Gaussian spot centroid location.

(3) The table made by the method of the present invention has nothing to do with the radius of the light spot. When the radius of the light spot changes, there is no need to rebuild the table, so it has the advantages of high positioning accuracy, fast processing speed, strong versatility and easy implementation. When a Gaussian beam is required High-precision positioning occasions (laser communication, laser guidance, laser alignment, etc.), especially in embedded real-time applications that are sensitive to computation, have broad application prospects and practical value.

Description of drawings

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

1 is a flow chart of a practical method for locating the Gaussian spot centroid of a high-precision four-quadrant detector according to the present invention;

FIG. 2 is a working schematic diagram of a four-quadrant detector under a Gaussian spot model of a practical high-precision four-quadrant detector Gaussian spot centroid location method of the present invention;

FIG. 3 is an error curve diagram of the spot centroid and the theoretical centroid calculated by the algorithm in a practical high-precision four-quadrant detector Gaussian spot centroid location method of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Please refer to Figure 1-3, a practical high-precision four-quadrant detector Gaussian spot centroid location method, including the following steps:

和

其计算公式为：Step 1. Use the four-way output photocurrent of the four-quadrant detector to calculate the solution value of the spot centroid in the x and y directions

and

Its calculation formula is:

In the formula, I _A , I _B , I _C , and I _D are the photocurrents of the four quadrants, respectively.

Step 2. Using the center of the four-quadrant detector as the coordinate origin, establish a rectangular coordinate system, use the Gaussian spot energy distribution model, and use MATLAB to construct a look-up table corresponding to the solution value of the spot centroid and the relative position according to the accuracy requirements. The expression of the Gaussian spot energy distribution model is:

In the formula, p ₀ is the light intensity at the center of the spot, (x ₀ , y ₀ ) is the centroid of the spot, and r is the radius of the Gaussian beam.

Step 2: Construct a lookup table with one-to-one correspondence between the calculated value of the spot centroid and the relative position. The relationship between the calculated value of the spot centroid and the relative position is:

In the formula, x _r and y _r are the relative positions of the x and y directions, respectively. The calculation formula of the x direction is x _r = x ₀ /r, which is the ratio of the spot centroid x ₀ to the spot radius r, and the value range is [-1 ,1]; the calculation formula for the y direction is y _r =y ₀ /r, which is the ratio of the spot centroid y ₀ to the spot radius r, and the value range is [-1,1].

The lookup table size is set to (2n+1)×1, where 2n+1 is the number of subdivisions for the dynamic range [-r,r] of the four-quadrant detector.

According to the symmetry independence of the x and y directions, the methods for constructing the lookup table table in step 2 include the following:

(1) The x and y directions share a look-up table with the full dynamic range [-r, r], (2n+1) is the number of subdivisions for the dynamic range of the four-quadrant detector, then the size of the table is (2n+1)× 1. The number of tables is 1, and the relative position can be calculated by directly using the solution value to look up the table;

(2) The x and y directions share a look-up table with a positive half dynamic range [0,r], (2n+1) is the number of subdivisions for the dynamic range of the four-quadrant detector, then the size of the table is (n+1)× 1. The number of tables is 1. The calculated value of the positive half dynamic range [0, r] can directly use the calculated value to look up the table to calculate the relative position, while the calculated value of the negative half dynamic range [-r, 0] first takes its absolute value The value look-up table calculates the relative position, and finally takes the negative value of the relative position found;

(3) The x and y directions share a negative half dynamic range [-r, 0] lookup table, (2n+1) is the number of subdivisions for the dynamic range of the four-quadrant detector, then the size of the table is (n+1) ×1, the number of tables is 1, the solution value of the negative half dynamic range [-r, 0] can directly use the solution value to look up the table to calculate the relative position, and the solution value of the positive half dynamic range [0, r] is taken first The negative number look-up table calculates the relative position, and finally takes the negative value of the relative position found;

(4) Considering that there may be differences in the x and y directions of the actual application, x and y construct independent tables respectively. There are also the above three methods, and the number of tables is increased to 2.

In step 2, the sequence in the constructed lookup table can be arranged in ascending order or descending order.

Step 3. Find out the corresponding relative position in the look-up table constructed in step 2 according to the solution value in step 1; the method of looking up in the look-up table can be any quick look-up table method suitable for sorting sequences;

Step 4. According to the accuracy requirements, the relative position of the look-up table in step 3 is corrected by using a linear interpolation method.

Step 5. Calculate the centroid of the light spot according to the radius of the light spot and the relative position in step 4. The calculation formula is:

x ₀ =x _r ×r

y ₀ =y _r ×r.

The specific implementation of the present invention is described in detail below in conjunction with specific embodiments:

With reference to FIG. 1 , a practical method for locating the centroid of a Gaussian spot with a high-precision four-quadrant detector of the present invention includes the following steps:

和

其计算公式为：Step 1. Combined with Figure 2, use the four-way output photocurrent of the four-quadrant detector to calculate the solution value of the centroid of the light spot in the x and y directions

and

Its calculation formula is:

In the formula, I _A , I _B , I _C , and I _D are the photocurrents of the four quadrants, respectively.

Step 2. Combined with Fig. 2, with the center of the four-quadrant detector as the coordinate origin, establish a rectangular coordinate system, use the Gaussian spot energy distribution model, and use MATLAB to construct a one-to-one correspondence between the solution value of the spot centroid and the relative position according to the accuracy requirements. surface. The expression of the Gaussian spot energy distribution model is:

In the formula, p ₀ is the light intensity at the center of the spot, which is taken as 1, (x ₀ , y ₀ ) at the centroid of the spot, and r is the radius of the Gaussian spot, which is taken as 0.75mm.

Step 2: Construct a lookup table with one-to-one correspondence between the calculated value of the spot centroid and the relative position. The relationship between the calculated value of the spot centroid and the relative position is:

In the formula, x _r and y _r are the relative positions of the x and y directions, respectively. The calculation formula of the x direction is x _r = x ₀ /r, which is the ratio of the spot centroid x ₀ to the spot radius r, and the value range is [-1 ,1]; the calculation formula for the y direction is y _r =y ₀ /r, which is the ratio of the spot centroid y ₀ to the spot radius r, and the value range is [-1,1].

In this embodiment, the full dynamic range subdivision number (2n+1) of the four-quadrant detector is set to 151, that is, the resolution of the lookup table is 10 μm, and x and y share an ascending order table. The location lookup table is shown in Table 1.

Table 1 Part of the spot centroid solution value and relative position lookup table calculation results

serial number Spot centroid (mm) Spot centroid solution value Relative position of spot centroid 1 -0.7500 -0.9545 -1.0000 2 -0.7400 -0.9515 -0.9867 3 -0.7300 -0.9484 -0.9733 4 -0.7200 -0.9451 -0.9600 5 -0.7100 -0.9417 -0.9467 6 -0.7000 -0.9381 -0.9333 7 -0.6900 -0.9342 -0.9200 8 -0.6800 -0.9302 -0.9067 9 -0.6700 -0.9260 -0.8933 10 -0.6600 -0.9216 -0.8800 … … … … 151 0.7500 0.9545 1.0000

Step 3. Use the quick look-up table dichotomy method to find the relative position corresponding to the calculated value in the look-up table of step 2.

Step 4. Use linear interpolation to correct the relative position.

Step 5. Calculate the centroid of the light spot by using the formula x ₀ =x _r ×r. Figure 3 shows the calculated error curve of the spot centroid and the spot centroid. It can be seen that the maximum error is 66.21nm, which can meet the needs of most applications. If higher precision is required, it is sufficient to increase the full dynamic range subdivision of the four-quadrant detector.

Obviously, the above-mentioned embodiments are only examples for clear description, and are not intended to limit the implementation manner. For those of ordinary skill in the art, changes or modifications in other different forms can also be made on the basis of the above description. There is no need and cannot be exhaustive of all implementations here. And the obvious changes or changes derived from this are still within the protection scope of the present invention.

Claims (7)

1. A practical high-precision four-quadrant detector Gaussian spot mass center positioning method is characterized by comprising the following steps:

step 1, calculating a resolving value of a light spot centroid by four paths of output photoelectric currents of a four-quadrant detector;

step 2, establishing a rectangular coordinate system by taking the center of the four-quadrant detector as the origin of coordinates, and constructing a lookup table in which spot centroid solution values and relative positions correspond to one another according to precision requirements by using a Gaussian spot energy distribution model;

step 3, finding out the corresponding relative position in the lookup table constructed in the step 2 according to the resolving value in the step 1;

step 4, if the precision does not meet the requirement, correcting the result searched in the step 3, and if the precision meets the requirement, performing the next step;

step 5, calculating the centroid of the light spot according to the radius of the light spot and the relative position in the step 4;

and (3) constructing a lookup table in which the light spot centroid solution value and the relative position correspond to each other one by one in the step (2), wherein the relationship between the light spot centroid solution value and the relative position is as follows:

in the formula, x_rAnd y_rRelative positions in x and y directions, respectively, and the calculation formula in the x direction is x_r＝x₀/r is the spot centroid x₀The ratio of the radius of the light spot to the radius r of the light spot is in the range of [ -1,1 [)](ii) a The calculation formula of the y direction is y_r＝y₀R is the spot centroid y₀The ratio of the radius of the light spot to the radius r of the light spot is in the range of [ -1,1 [)]；

In the step 2, according to the precision requirement, the size of the lookup table is set to be (2n +1) × 1, wherein 2n +1 is a subdivision number of the dynamic range [ -r, r ] of the four-quadrant detector;

according to the symmetric independence of the x and y directions, the method for constructing the lookup table in the step 2 comprises the following steps:

(1) the x and y directions share a lookup table of a full dynamic range [ -r, r ], (2n +1) is a subdivision number of the dynamic range of the four-quadrant detector, the size of the table is (2n +1) × 1, the number of the tables is 1, and the relative position can be calculated by directly using a solution value lookup table;

(2) the x and y directions share a lookup table of positive semi-dynamic range [0, r ], (2n +1) is the subdivision number of the dynamic range of the four-quadrant detector, the size of the table is (n +1) x 1, the number of the tables is 1, the solution value of the positive semi-dynamic range [0, r ] can directly use the solution value to lookup the table to calculate the relative position, and the negative semi-dynamic range

The resolving value of [ -r,0] firstly takes the absolute value thereof to look up a table to calculate the relative position, and finally takes the negative value of the relative position;

(3) the x and y directions share a lookup table of a negative semi-dynamic range [ -r,0], (2n +1) is a subdivision number of the dynamic range of the four-quadrant detector, the size of the table is (n +1) × 1, the number of the tables is 1, the solution value of the negative semi-dynamic range [ -r,0] can directly use the solution value lookup table to calculate the relative position, the solution value of the positive semi-dynamic range [0, r ] firstly uses the negative number lookup table to calculate the relative position, and finally uses the negative value of the relative position;

(4) considering that the x and y directions may have differences in practical application, x and y construct independent tables respectively, and there are the above three methods, and the number of tables increases to 2.

2. The practical high-precision four-quadrant detector Gaussian spot mass center positioning method according to claim 1, characterized in that the calculation formula of the calculated value of the spot mass center in step 1 is as follows:

in the formula I_A、I_B、I_C、I_DThe photocurrent of the four quadrants respectively,

and

the values are calculated for the spot centroid in the x and y directions, respectively.

3. The practical high-precision four-quadrant detector Gaussian spot mass center positioning method according to claim 1, wherein the expression of the Gaussian spot energy distribution model in the step 2 is as follows:

in the formula, p₀Is the light intensity of the center of the light spot (x)₀,y₀) Is the spot centroid and r is the gaussian spot radius.

4. The practical high-precision four-quadrant detector Gaussian spot centroid positioning method according to claim 1, wherein the number sequence in the lookup table constructed in the step 2 is arranged in an ascending order or a descending order.

5. The practical high-precision four-quadrant detector Gaussian spot centroid positioning method according to claim 1, wherein the method for searching in the lookup table in step 3 is any fast lookup table suitable for sorting sequences.

6. The practical high-precision four-quadrant detector Gaussian spot centroid positioning method according to claim 1, wherein the relative position searched in the step 4 is corrected by adopting a linear interpolation method.

7. The practical high-precision four-quadrant detector Gaussian spot centroid positioning method according to claim 1, wherein the formula for calculating the spot centroid according to the spot radius and the relative position in the step 5 is as follows:

x₀＝x_r×r

y₀＝y_r×r。

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