CN100342209C - Calibrating method for laser self-collimation angle measuring system - Google Patents

Abstract

The present invention belongs to measuring technology, which relates to the improvement of a calibration method for a laser auto-collimation angle measuring system based on a laser auto-collimation three-freedom degree angle measuring system. The present invention comprises the steps that a simplified calibration model of a laser auto-collimation angle measuring system is established, calibration data pairs and the parameters of the calibration model are acquired, and a measuring model of the system is obtained. The present invention has the advantages of simple calibration processes, high calibration accuracy, little calibration data amount and short measuring time of the system, and is suitable for on-site calibration.

Description

A kind of scaling method of laser self-collimation angle measuring system

Technical field

The invention belongs to measuring technique, relate to improvement the laser self-collimation angle measuring system scaling method.

Background technology

The laser auto-collimation angle measurement technique is since occurring the sixties, become a low-angle precision measurement technology that becomes more and more important, have unique advantage in realizing low-angle multidimensional, non-cpntact measurement, the angle measuring system of developing based on this technology has characteristics such as highly sensitive, simple in structure, easy to use, as can to realize two dimension angular static state and kinetic measurement.Any one laser self-collimation angle measuring system all needs to determine through a calibration process exact value of unknown parameter in the systematic survey model after structure is finished, its function could correctly be exercised by system then.Effective scaling method of laser self-collimation angle measuring system model parameter is an important research contents always.Mainly contain following method at present:

Polynomial method.

It is right by obtaining a large amount of nominal datas adopting the purpose of polynomial method calibration system, and the method for employing fitting of a polynomial obtains the measurement model of system.Still swan goose, Zhang Guangjun have been described this scaling method in article " research of the dynamic angle real-time measurement system of Three Degree Of Freedom " (photoelectric project is employed).This method mainly is by testee being installed on accurate three universal stages, and catoptron is sticked on the testee surface.The angle of rotating with precise rotating platform is a true value, and it is right to obtain a large amount of nominal datas, and the method that adopts polynomial expression to fit then calibrates the unknown parameter in the laser auto-collimation measurement mathematical model.Adopt polynomial method calibration measurements system, stated accuracy is higher, but the nominal data amount is bigger, and data of calibration point is handled or after match calibrated error compensated, the computation process complexity needing before the match.If the minimizing nominal data then can reduce stated accuracy greatly, be difficult to obtain gratifying result.

Look-up table.

Yang Yongs etc. are in article " a kind of novel small angle measurement systematic research that is used for gyrocompassing " (the accurate manufacturing technology of aviation, 2000,36 (6): described this method 31-34): during system calibrating, the nominal datas that obtain many groups by high-precision surveying instrument are right, the output valve of promptly measured and system.Nominal data to being input in the computing machine, is made form, be stored among the ROM.During actual measurement, obtain measured value thereby table look-up according to the output result of measuring system.The data of calibration point amount that this scaling method needs is very big, and stated accuracy is difficult to guarantee, and it is longer to expend time in the process of tabling look-up, and is not suitable for real-time kinetic measurement.

Summary of the invention

The objective of the invention is: at the deficiency that exists in the existing laser self-collimation angle measuring system scaling method, a kind of precision height is proposed, the simple scaling method of calibration process is the parameter optimization method, further improve the stated accuracy of measuring system and reduce Measuring Time, improve the convenience that its through engineering approaches is used.

Technical scheme of the present invention is: a kind of scaling method of laser self-collimation angle measuring system, based on the dynamic angle measurement system of being made up of following physical equipment of laser auto-collimation Three Degree Of Freedom: precision is at the Three Degree Of Freedom universal stage of rad level, rotation center at universal stage has a plane mirror, the laser angular measurement sensor is the opticator of angle measuring system, photoelectric receiving device, data collecting card and computing machine is characterized in that

1, set up the simplification peg model of laser self-collimation angle measuring system, its step is as follows:

1.1, on Three Degree Of Freedom universal stage and optical system focal plane, set up Three Degree Of Freedom universal stage coordinate system and image coordinate system, be right-handed system;

1.2, to establish measuring distance be L, the focal length of optical system is f, the normal line vector coordinate of plane mirror is { n _x, n _y, n _z, plane mirror initial space position is ( _o, θ _o), the installation site between optical system and the Three Degree Of Freedom universal stage is: pitch orientation is inclined to one side θ _vThe angle, yaw direction is inclined to one side  _vThe angle, the coordinate of optical system center in Three Degree Of Freedom universal stage coordinate system is (Δ H _x, Δ H _y, L).The installation site of photoelectric receiving device is: the pitch orientation u angle that tilted, the yaw direction v angle that tilted, the coordinate of photosurface central point in image coordinate system is (x _Uo, y _Uo, z _Uo);

1.3, obtain the peg model of laser self-collimation angle measuring system, with plane mirror space rotation , behind the θ, measure the method for mathematical model according to set up laser auto-collimation based on perspective projection transformation, obtain the peg model of laser self-collimation angle measuring system;

1.4, simplify peg model,

1. suppose Δ H in the peg model _x=Δ H _y=0,

2. the position rotation relationship of photoelectric receiving device is approximated to an anglec of rotation β, i.e. the angle that rotates on optical axis as the plane,

3. set the horizontal vertical ratio that unknown parameter J demarcates picpointed coordinate,

Based on the simplification of above-mentioned model parameter, the simplification peg model that obtains laser self-collimation angle measuring system is:

$\left\{\begin{array}{c}{x}_{\mathrm{Im}}=(x_{\mathrm{Is}}-x_{\mathrm{uo}})\cos \mathrm{\β}+(y_{\mathrm{Is}}-y_{\mathrm{uo}})\sin \mathrm{\β}\\ y_{\mathrm{Im}}=\frac{-(x_{\mathrm{Is}}-x_{\mathrm{uo}})\sin \mathrm{\β}+(y_{\mathrm{Is}}-y_{\mathrm{uo}})\cos \mathrm{\β}}{J}\end{array}\right.---\left(1\right)$

Wherein:

$\left\{\begin{array}{c}{x}_{\mathrm{Is}}=(f-z_{\mathrm{uo}})\frac{n_x}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="C20051006943100111.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}}}\arccos (2n_z^2-1)\\ y_{\mathrm{Is}}=(f-z_{\mathrm{uo}})\frac{n_y}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="C20051006943100111.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}}}\arccos (2n_z^2-1)\end{array}\right.,$

r ₁～r ₉The expression formula of nine coefficients is

2, it is right to obtain nominal data, and testee is installed on the Three Degree Of Freedom universal stage, and plane mirror is sticked on the testee surface, testee is done driftage/pitch rotation respectively, angular turn scope≤1.0000 °, with t be measurement point at interval, 0＜t＜0.1000 °, obtain P angle, P＞10 under each angle, are carried out left drift, right avertence boat respectively, are gone up pitching and following pitch rotation, read two output voltage values of photoelectric receiving device, it is right to obtain 4 * P data altogether;

3, the parameter of peg model,

Right according to the nominal data that obtains, adopt the Levenberg-Marquardt optimized Algorithm 9 unknown parameter (θ in the above-mentioned simplification peg model _o,  _o, θ _v,  _v, β, x _Uo, y _Uo, z _Uo, J) demarcate;

4, the measurement model of system is as follows: when photoelectric receiving device detects a picpointed coordinate (x _Im, y _Im) time, according to systematic survey model given below, just can calculate the plane mirror spatial rotation angle (, θ):

In the formula $\left\{\begin{array}{c}{n}_z=\sqrt{\frac{1}{2}(1+\cos \frac{\sqrt{x_{\mathrm{Is}}^2+y_{\mathrm{Is}}^2}}{f-z_{\mathrm{uo}}})}\\ n_y=\frac{y_{\mathrm{Is}}}{\sqrt{x_{\mathrm{Is}}^2+y_{\mathrm{Is}}^2}}\sqrt{1-n_z^2}\\ n_x=\frac{x_{\mathrm{Is}}}{y_{\mathrm{Is}}}{n}_y\end{array}\right.,$ $\left\{\begin{array}{c}{x}_{\mathrm{Is}}=x_{\mathrm{Im}}\cos \mathrm{\&beta;}-y_{\mathrm{Is}}\sin \mathrm{\&beta;}\&CenterDot;J+x_{\mathrm{uo}}\\ y_{\mathrm{Is}}=x_{\mathrm{Im}}\sin \mathrm{\&beta;}+y_{\mathrm{Is}}\cos \mathrm{\&beta;}\&CenterDot;J+y_{\mathrm{uo}}\end{array}\right..$

Advantage of the present invention is: compare with the scaling method of existing laser self-collimation angle measuring system, the calibration process of this method is simple, and stated accuracy height, nominal data amount are less, and the Measuring Time of system is shorter.This method is fit to on-site proving, and the measurement model that obtains by this method is fit to the real-time measurement of system dynamics angle.

Description of drawings

Fig. 1 is the dynamic angle measurement system synoptic diagram of laser auto-collimation Three Degree Of Freedom of the present invention.1 testee among the figure; 2 plane mirrors; 3 collimation eyepieces; 4 laser instruments; 5 photoelectric receiving devices; 6 semi-transparent semi-reflecting lens; 7 three-axle tables; 8 supports; 9 data acquisitions and display part.

Embodiment

Below the present invention is described in further details.Referring to Fig. 1, the simplification peg model of laser self-collimation angle measuring system of the present invention to set up process as follows:

On Three Degree Of Freedom universal stage and optical system focal plane, set up turntable coordinate system and image coordinate system, be right-handed system.

If measuring distance is L, the focal length of optical system is f, and the normal line vector coordinate of level crossing is { n _x, n _y, n _z, level crossing initial space position is ( _o, θ _o), the installation site between optical system and the turntable is: pitch orientation is inclined to one side θ _vThe angle, yaw direction is inclined to one side  _vThe angle, the coordinate of optical system center in the turntable coordinate system is (Δ H _x, Δ H _y, L).The installation site of photoelectric receiving device is: the pitch orientation u angle that tilted, the yaw direction v angle that tilted, the coordinate of photosurface central point in image coordinate system is (x _Uo, y _Uo, z _Uo).

As level crossing space rotation , behind the θ, (application number: that describes 200410102586.9) sets up the method that laser auto-collimation is measured mathematical model based on perspective projection transformation, obtains the peg model of laser self-collimation angle measuring system according to patent " a kind of modeling method of laser auto collimating measurement for angle in 2 D ".

Directly adopt the peg model of above-mentioned foundation to carry out system calibrating, have two problems: 1. right by many group nominal datas, can't directly find the solution the value that obtains unknown parameter in the peg model.If adopt the nonlinear optimization method to find the solution the value that obtains calibrating parameters, through inverse, the stated accuracy that obtains is poor especially.2. can't from peg model, derive the explicit expression of systematic survey model.

The present invention reaches the purpose that obtains the systematic survey model by the abbreviation peg model.

The abbreviation of peg model.

1. suppose Δ H in the peg model _x=Δ H _y=0.

2. the position of rotation of photoelectric receiving device relation is approximated to an anglec of rotation β, the i.e. angle that rotates on optical axis as the plane.

3. set the horizontal vertical ratio that unknown parameter J demarcates picpointed coordinate.

Based on the simplification of above-mentioned model parameter, the simplification peg model that obtains laser self-collimation angle measuring system is:

$\left\{\begin{array}{c}{x}_{\mathrm{Im}}=(x_{\mathrm{Is}}-x_{\mathrm{uo}})\cos \mathrm{\&beta;}+(y_{\mathrm{Is}}-y_{\mathrm{uo}})\sin \mathrm{\&beta;}\\ y_{\mathrm{Im}}=\frac{-(x_{\mathrm{Is}}-x_{\mathrm{uo}})\sin \mathrm{\&beta;}+(y_{\mathrm{Is}}-y_{\mathrm{uo}})\cos \mathrm{\&beta;}}{J}\end{array}\right.----\left(1\right)$

Wherein: $\left\{\begin{array}{c}{x}_{\mathrm{Is}}=(f-z_{\mathrm{uo}})\frac{n_x}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="C20051006943100111.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}}}\arccos (2n_z^2-1)\\ y_{\mathrm{Is}}=(f-z_{\mathrm{uo}})\frac{n_y}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="C20051006943100111.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}}}\arccos (2n_z^2-1)\end{array}\right.,$

r ₁～r ₉The expression formula of nine coefficients is

It is right to obtain nominal data, and testee is installed on accurate three universal stages, and catoptron is sticked on the testee surface, testee is done driftage/pitch rotation respectively, angular turn scope≤1.0000 °, with t be measurement point at interval, 0＜t＜0.1000 ° obtains P angle, P＞10.Under each angle, carry out left drift, right avertence boat respectively, go up pitching and following pitch rotation, read two output voltage values of PSD, it is right to obtain 4 * P data altogether.

The demarcation of model parameter.

Nominal data by acquisition is right, adopts the Levenberg-Marquardt optimized Algorithm 9 unknown parameter (θ in the above-mentioned simplification peg model _o,  _o, θ _v,  _v, β, x _Uo, y _Uo, z _Uo, J) demarcate.(Chen Baolin, Optimum Theory and algorithm, publishing house of Tsing-Hua University, 1989)

The measurement model of system.

When photoelectric receiving device detects a picpointed coordinate (x _Im, y _Im) time, according to systematic survey model given below, just can calculate the level crossing spatial rotation angle (, θ):

In the formula $\left\{\begin{array}{c}{n}_z=\sqrt{\frac{1}{2}(1+\cos \frac{\sqrt{x_{\mathrm{Is}}^2+y_{\mathrm{Is}}^2}}{f-z_{\mathrm{uo}}})}\\ n_y=\frac{y_{\mathrm{Is}}}{\sqrt{x_{\mathrm{Is}}^2+y_{\mathrm{Is}}^2}}\sqrt{1-n_z^2}\\ n_x=\frac{x_{\mathrm{Is}}}{y_{\mathrm{Is}}}{n}_y\end{array}\right.,$ $\left\{\begin{array}{c}{x}_{\mathrm{Is}}=x_{\mathrm{Im}}\cos \mathrm{\&beta;}-y_{\mathrm{Is}}\sin \mathrm{\&beta;}\&CenterDot;J+x_{\mathrm{uo}}\\ y_{\mathrm{Is}}=x_{\mathrm{Im}}\sin \mathrm{\&beta;}+y_{\mathrm{Is}}\cos \mathrm{\&beta;}\&CenterDot;J+y_{\mathrm{uo}}\end{array}\right..$

Embodiment

The dynamic angle measurement system of laser auto-collimation Three Degree Of Freedom among Fig. 1 mainly is made up of following physical equipment: 1. precision is at the Three Degree Of Freedom universal stage of rad level, and places a plane mirror at the rotation center of universal stage.2. laser angular measurement transducing part, i.e. the opticator of angle measuring system, measurement range ± 1 °, focal distance f=168.44mm.Optical system is L=1.2m to the distance of testee.3. photoelectric receiving device is the two dimension pillow type Position-Sensitive Detector PSD that the loose company in Japanese shore produces, and model is S1880.4. data acquisition and display part: mainly form by data collecting card, computing machine etc.

What nominal data was right obtains.

Testee is installed on accurate three universal stages, and catoptron is sticked on the testee surface.Testee is done driftage/pitch rotation respectively, angular turn scope≤0.8500 °.Beginning with 0.1500 ° of measurement point, and carry out left drift, right avertence boat respectively, go up pitching and following pitching with 0.0500 ° at measurement point interval, read two output voltage values of PSD simultaneously, is 0.8500 ° up to rotational angle.Obtain 15 angles altogether, 60 data are right, as shown in table 1.

60 data of table 1 are right

Sequence number	The object corner	Left drift (V)	Right avertence boat (V)	Last pitching (V)	Following pitching (V)
						1	0.1500	-0.9570， -0.1758	0.7129， 0.1611	0.0488， -0.8447	-0.2881， 0.8252
2	0.2000	-1.2305， -0.2393	0.9814， 0.2246	0.0977， -1.1133	-0.3418， 1.1035
						3	0.2500	-1.5039， -0.2930	1.2598， 0.2832	0.1514， -1.3965	-3.3955， 1.3818
4	0.3000	-1.7773， -0.3613	1.5381， 0.3320	0.2100， -1.6797	-0.4443， 1.6357
						5	0.3500	-2.0605， -0.4053	1.8115， 0.3906	0.2637， -1.9434	-0.4883， 1.8848

6	0.4000	-2.3291， -0.4736	2.0850， 0.4395	0.3223， -2.2266	-0.5420， 2.1338
						7	0.4500	-2.6074， -0.5420	2.3682， 0.4932	0.3809， -2.4951	-0.5908， 2.3828
8	0.5000	-2.8809， -0.5957	2.6416， 0.5469	0.4443， -2.7637	-0.6348， 2.6416
						9	0.5500	-3.1396， -0.6641	2.9150， 0.6055	0.4932， -3.0420	-0.6934， 2.9053
10	0.6000	-3.4131， -0.7178	3.1885， 0.6543	0.5518， -3.3057	-0.7373， 3.1494
						11	0.6500	-3.6865， -0.7666	3.4570， 0.7129	0.6006， -3.5596	-0.7910， 3.4229
12	0.7000	-3.9502， -0.8350	3.7256， 0.7666	0.6592， -3.8184	-0.8398， 3.6816
						13	0.7500	-4.2090， -0.8789	3.9795， 0.8154	0.7129， -4.0674	-0.9033， 3.9795
14	0.8000	-4.4580， -0.9424	4.2383， 0.8691	0.7568， -4.3213	-0.9616， 4.2676
						15	0.8500	-4.7266， -0.9912	4.5020， 0.9326	0.8203， -4.5703	-1.0205， 4.5654

Calibration result.

Based on the peg model of simplifying is formula 1, and the result who adopts the Levenberg-Marquardt optimized Algorithm to optimize is as follows:

 _o＝0.1036°，θ _o＝0.0648°， _v＝0.0994°，θ _v＝0.1831°，x _uo＝0.188mm，y _uo＝0.660mm，z _uo＝4.465mm，β＝-11.9523°，J＝1.0164。

The measurement model that the value of the calibrating parameters of above-mentioned acquisition is brought into system is in the formula 2, nominal data centering picpointed coordinate (x _Im, y _Im) as the input value of measurement model, the output valve of computation model.Utilize following formula:

$\mathrm{RMS}=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\mathrm{\&Delta;}\right)}^2}{n}}---\left(3\right)$

Calculating the angle of pitch of level crossing rotation and the RMS error of crab angle is: the RMS of the angle of pitch equals 0.23, and the RMS of crab angle equals 0.45, the about 3 μ s of Measuring Time.

Claims (1)

1, a kind of scaling method of laser self-collimation angle measuring system, based on the dynamic angle measurement system of being made up of following physical equipment of laser auto-collimation Three Degree Of Freedom: precision is at the Three Degree Of Freedom universal stage of rad level, rotation center at universal stage has a plane mirror, the laser angular measurement sensor is the opticator of angle measuring system, photoelectric receiving device, data collecting card and computing machine is characterized in that

1.1, set up the simplification peg model of laser self-collimation angle measuring system, its step is as follows:

1.1.1, on Three Degree Of Freedom universal stage and optical system focal plane, set up Three Degree Of Freedom universal stage coordinate system and image coordinate system, be right-handed system;

1.1.2, to establish measuring distance be L, the focal length of optical system is f, the normal line vector coordinate of plane mirror is { n _x, n _y, n _z, plane mirror initial space position is ( _o, θ _o), the installation site between optical system and the Three Degree Of Freedom universal stage is: pitch orientation is inclined to one side θ _vThe angle, yaw direction is inclined to one side  _vThe angle, the coordinate of optical system center in Three Degree Of Freedom universal stage coordinate system is (Δ H _x, Δ H _y, L).The installation site of photoelectric receiving device is: the pitch orientation u angle that tilted, the yaw direction v angle that tilted, the coordinate of photosurface central point in image coordinate system is (x _Uo, y _Uo, z _Uo);

1.1.3, obtain the peg model of laser self-collimation angle measuring system, with plane mirror space rotation , behind the θ, measure the method for mathematical model according to set up laser auto-collimation based on perspective projection transformation, obtain the peg model of laser self-collimation angle measuring system;

1.1.4, simplify peg model,

1. suppose Δ H in the peg model _x=Δ H _y=0,

2. the position rotation relationship of photoelectric receiving device is approximated to an anglec of rotation β, i.e. the angle that rotates on optical axis as the plane,

3. set the horizontal vertical ratio that unknown parameter J demarcates picpointed coordinate,

Based on the simplification of above-mentioned model parameter, the simplification peg model that obtains laser self-collimation angle measuring system is:

$\left\{\begin{array}{c}{x}_{\mathrm{Im}}=(x_{\mathrm{Is}}-x_{\mathrm{uo}})\cos \mathrm{\&beta;}+(y_{\mathrm{Is}}-y_{\mathrm{uo}})\sin \mathrm{\&beta;}\\ y_{\mathrm{Im}}=\frac{-(x_{\mathrm{Is}}-x_{\mathrm{uo}})\sin \mathrm{\&beta;}+(y_{\mathrm{Is}}-y_{\mathrm{uo}})\cos \mathrm{\&beta;}}{J}\end{array}\right....\left(1\right)$

Wherein: $\left\{\begin{array}{c}{x}_{\mathrm{Is}}=(f-z_{\mathrm{uo}})\frac{n_x}{\sqrt{n_x^2+n_y^2}}\arccos (2n_z^2-1)\\ y_{\mathrm{Is}}=(f-z_{\mathrm{uo}})\frac{n_y}{\sqrt{n_x^2+n_y^2}}\arccos (2n_z^2-1)\end{array}\right.,$

r ₁～r ₉The expression formula of nine coefficients is

1.2, to obtain nominal data right, and testee is installed on the Three Degree Of Freedom universal stage, plane mirror is sticked on the testee surface, testee is done driftage/pitch rotation respectively, angular turn scope≤1.0000 °, with t be measurement point at interval, 0＜t＜0.1000 °, obtain P angle, P＞10 under each angle, are carried out left drift, right avertence boat respectively, are gone up pitching and following pitch rotation, read two output voltage values of photoelectric receiving device, it is right to obtain 4 * P data altogether;

1.3, the parameter of peg model,

Right according to the nominal data that obtains, adopt the Levenberg-Marquardt optimized Algorithm 9 unknown parameter (θ in the above-mentioned simplification peg model _o,  _o, θ _v,  _v, β, x _Uo, y _Uo, z _Uo, J) demarcate;

1.4, the measurement model of system is as follows: when photoelectric receiving device detects a picpointed coordinate (x _Im, y _Im) time, according to systematic survey model given below, just can calculate the plane mirror spatial rotation angle (, θ):

In the formula $\left\{\begin{array}{c}{n}_z=\sqrt{\frac{1}{2}(1+\cos \frac{\sqrt{x_{\mathrm{Is}}^2+y_{\mathrm{Is}}^2}}{f-z_{\mathrm{uo}}})}\\ n_y=\frac{y_{\mathrm{Is}}}{\sqrt{x_{\mathrm{Is}}^2+y_{\mathrm{Is}}^2}}\sqrt{1-n_z^2}\\ n_x=\frac{x_{\mathrm{Is}}}{y_{\mathrm{Is}}}{n}_y\end{array}\right.,$ $\left\{\begin{array}{c}{x}_{\mathrm{Is}}=x_{\mathrm{Im}}\cos \mathrm{\&beta;}-y_{\mathrm{Is}}\sin \mathrm{\&beta;}\&CenterDot;J+x_{\mathrm{uo}}\\ y_{\mathrm{Is}}=x_{\mathrm{Im}}\sin \mathrm{\&beta;}+y_{\mathrm{Is}}\cos \mathrm{\&beta;}\&CenterDot;J+y_{\mathrm{uo}}\end{array}\right..$

Images