CN1796930A - Modeling method of laser auto collimating measurement for angle in 2D - Google Patents

Abstract

The invention belongs to a measuring technique, relating to the improvement of a laser self-aligning measuring method, including the steps of: (1) establishing a reference frame; (2) finding a relationship between the vector coordinates of normal and rotating angle of a plane mirror as rotating the plane mirror at a space angle; (3) finding the coordinate expression of a point F(xIs, yIs, 0) on the surface of an image space xIsOIsyIs; And (4) determining model parameters. The invention is simple in method and convenient to use; and only needs to measure the coordinate values of any one point to be able to calculate its corresponding rotating angle, having good universality.

Description

A kind of modeling method of laser auto collimating measurement for angle in 2 D

Technical field

The invention belongs to measuring technique, relate to improvement the laser auto-collimation measuring method.

Background technology

In many measuring methods, the laser auto-collimation measuring method makes full use of the advantage of laser, has characteristics such as simple in structure, easy to use, obtains application more and more widely in measuring science.The laser auto-collimation measuring method is to utilize the directivity of laser itself, as reference line, adopts CCD, four-quadrant photocell or PSD as photoelectric position detector with laser intensity distribution center, realizes the measurement of angle.Characteristics such as the laser auto-collimation angle-measuring method has noncontact, accuracy height, highly sensitive, and is simple in structure, easy to use.Set up measurement model accurately, the angle that can measure measured object deflection accurately, fast is that the laser auto-collimation measuring method is successfully applied to a gordian technique in the engineering.The method of setting up the laser auto-collimation measurement model at present has:

(1) directly utilizes laser auto-collimation approximate model formula, measure facula position, set up measurement model by different photoelectric receiving devices.Wang Jianlin, Zhu Mingwu, Cui Xiuhua are at article " the two coordinate autocollimators of a kind of single line array CCD of novelty " (Chinese journal of scientific instrument, 2000, Vol.21, No.3:229-232) and Jiang Benhe, Chen Wenyi, Hu Wenfei etc. at article " the small angle measurement system that detects with laser alignment and CCD " (laser and infrared, 1998, Vol.28 has stated this method in No.4:233-235).They adopt CCD to set up the Bidimensional small angle measurement model as photoelectric receiving device.Photoelectric receiving device can also adopt position sensitive detector (PSD).Zhu Xiaoping is in article " PSD autocollimator " (measurement technology, 1999, No.4:8-11) and Guo Xiaosong, Huang Xianxiang, Kong Xiangyu in article " PSD photo electric automatic sighting system " (infrared and laser engineering, 1999, Vol.28 has also described this method in No.1:43-45).

(2) set up measurement model based on polynomial method.Still swan goose, Zhang Guangjun have proposed a kind of modeling method in article " research of the dynamic angle real-time measurement system of Three Degree Of Freedom " (photoelectric project).This method mainly is by testee being installed on accurate three universal stages, and catoptron is sticked on the testee surface.Pitching and following pitch rotation are navigated, gone up to left drift, right avertence that testee is respectively under a certain angle θ, calibrate the horizontal vertical ratio of benchmark zero-bit, PSD of measuring system and the anglec of rotation of PSD coordinate system and pitching/driftage coordinate system, thereby the method that adopts polynomial expression to fit is set up out the mathematical model that laser auto-collimation is measured: θ=Ar ²+ Br+C, wherein A, B, C are the constants that calibrates.

Above-mentioned two kinds of modeling methods only are applicable to the situation that level crossing initial space position is determined, the versatility of model is poor.

Summary of the invention

The objective of the invention is: measure the deficiency that exists in the modeling method at existing laser auto-collimation, propose that a kind of modeling method is simple, usable range wide, use easily laser auto-collimation and measure modeling method, improve the versatility that its engineering is used.

Technical scheme of the present invention is: a kind of modeling method of laser auto collimating measurement for angle in 2 D, it is characterized in that, based on perspective projection transformation, the laser auto-collimation measurement model is regarded as a pin-hole imaging model, mathematical model to set up process as follows:

(1) set up coordinate system,

Set up optical system coordinate system O _Op-x _Opy _Opz _Op, the initial point of optical system coordinate system is positioned on the optical axis, z _OpAxle with optical axis heavy and, direction is identical with the direction of light ray propagation, sets up image space coordinate system (O _Is-x _Isy _Is) and object space coordinate system (O _Ob-x _Oby _Obz _Ob), the initial point of image space coordinate system is positioned on the optical axis, and with the optical system coordinate system at a distance of f, object space coordinate system and O _OpObject distance between the point is L, level crossing minute surface and x _ObO _Oby _ObFace overlaps, and the sensitive area of establishing photoelectric receiving device is x _ImO _Imy _Im, it and x _IsO _Isy _IsFace does not overlap, and the available matrix representation of relation between the two is as follows:

$\left[\begin{array}{c}{x}_{\mathrm{Im}}\\ y_{\mathrm{Im}}\\ z_{\mathrm{Im}}\end{array}\right]=R\left[\begin{array}{c}{x}_{\mathrm{Is}}\\ y_{\mathrm{Is}}\\ z_{\mathrm{Is}}\end{array}\right]+T---\[3\]$

R is the unit orthogonal matrix in the formula, and $R=\left[\begin{array}{ccc}{S}_{11}& S_{12}& S_{13}\\ S_{21}& S_{22}& S_{23}\\ S_{31}& S_{32}& S_{33}\end{array}\right],$ The coordinate of the centre coordinate of photoelectric receiving device sensitive area (0,0) under image space coordinate system is $T=\left[\begin{array}{c}{x}_o\\ y_o\\ z_o\end{array}\right];$

(2) in measuring system, with normal line vector coordinate representation level crossing locus, the unit direction vector of establishing the level crossing normal is $\stackrel{\→}{n_{\mathrm{\π}}}=\{n_x,n_y,n_z\},$ Under the object space coordinate system, when level crossing has rotated a Space Angle, promptly pitch orientation has been rotated the θ angle, and when yaw direction had rotated the angle, the pass between the vectorial coordinate of level crossing normal and the level crossing anglec of rotation was:

And have $n_x^2+n_y^2+n_z^2=1---\[5\]$

(3) from object space O _ObA branch of reflected in parallel light that point sends Through after the refraction of lens, with image space x _IsO _Isy _IsDeliver personally in the F point, reflection ray Moved to the optical system coordinate system

Initial point, i.e. projection centre is established reflection ray and x after the translation _ObO _Oby _ObDeliver personally in the Q point, then Q point, O _OpPoint and F point three point on a straight line based on perspective projection equation and triangle theorem, obtain image space x _IsO _Isy _IsF (x on the face _Is, y _Is, 0) point coordinate be:

$\left[\begin{array}{c}{x}_{\mathrm{Is}}\\ y_{\mathrm{Is}}\end{array}\right]=f\left[\begin{array}{c}\frac{n_x}{\sqrt{n_x^2+n_y^2}}\arccos (2n_z^2-1)\\ \frac{n_y}{\sqrt{n_x^2+n_y^2}}\arccos ({2n}_z^2-1)\end{array}\right]---\[6\]$

(4) simultaneous formula [4] and [6] obtain:

Formula [3] is brought into formula [7], promptly finish the foundation of laser auto collimating measurement for angle in 2 D mathematical model;

(4) determine the parameter of model,

Definite need of laser auto collimating measurement for angle in 2 D mathematical model parameter carry out on the basis of following equipment: a cover need wait to set up the laser auto-collimation measuring system of measurement model, and wherein photoelectric receiving device adopts the PSD photoelectric position sensor; 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; Definite process of model parameter is carried out as follows:

1. open laser instrument, make the outgoing beam of self-collimation measurement system be radiated on the level crossing;

2. rotate the Three Degree Of Freedom universal stage, make 10 known angle (θ of level crossing spatial rotation _i, _i), corresponding 10 the picpointed coordinate value (x that detected by PSD are write down and stored in i=1～10 respectively _i, y _i), i=1～10;

3. 10 point coordinate values that obtain in utilizing 2. and 10 known angles of its correspondence are used the linear solution method, calculate matrix R and T.

4. matrix R that calculates and T are brought in the formula [10], thereby obtain the mathematical model of laser auto collimating measurement for angle in 2 D.

Advantage of the present invention is: the modeling method that the present invention is based on the laser auto collimating measurement for angle in 2 D of perspective projection transformation principle is avoided the concrete structure of optical system own, employing is more than or equal to 3 groups of picpointed coordinates and corresponding level crossing rotational angle value, just can set up out the mathematical model of laser auto collimating measurement for angle in 2 D, simplified the process of modelling and demarcation, characteristics such as it is simple to have method, easy to use.Based on this laser auto collimating measurement for angle in 2 D model, only need measure the coordinate figure of arbitrary picture point, just can calculate the rotational angle corresponding with it, versatility is good.

Description of drawings

Fig. 1 is the perspective projection geometric representation.

Fig. 2 is the perspective projection transformation synoptic diagram that laser auto-collimation is measured.

Embodiment

Below the present invention is described in further details.

Perspective projection transformation.

The characteristics of perspective projection imaging model are all from the light of scene all by a projection centre, and it is corresponding to the center of lens.Be called axis of projection or optical axis through projection centre and perpendicular to the straight line of imaging plane, as shown in Figure 1.Wherein xyz is the rectangular coordinate system that is fixed on the lens, follows right-hand rule, and its initial point is positioned at projection centre, z axle and axis of projection heavy and and point to scene, coordinate system x ' the axle on x axle, y axle and picture plane is parallel with y ' axle, and the distance of xy plane and imaging plane is f, is called the focal length of lens.

((z) vertical line segment and the z axle to the z axle formed a triangle to point for x, y for sight line z), point for x, y.Become the sight line, point (x ', y ') of point on the image plane (x ', y ') to form another triangle to vertical line segment of z axle and z axle.These two triangles are similar triangles, obtain the perspective projection equation thus:

$\frac{x^{\′}}{x}=\frac{y^{\′}}{y}=\frac{f}{z}---\[1\]$

Point (z) position in becoming image plane is provided by following formula for x, y:

$x^{\′}=\frac{f}{z}x,$ $y^{\′}=\frac{f}{z}y---\[2\]$

The foundation of laser auto collimating measurement for angle in 2 D mathematical model.

Fig. 2 is the projection Perspective transformation model synoptic diagram that laser auto-collimation is measured.Black dotted line is the approach that actual reflection ray is propagated among the figure.Based on perspective projection transformation, the laser auto-collimation measurement model is regarded as a pin-hole imaging model.It is as follows that mathematical model is set up process:

(1) sets up coordinate system.

Set up optical system coordinate system O _Op-x _Opy _Opz _Op, the initial point of optical system coordinate system is positioned on the optical axis, z _OpAxle with optical axis heavy and, direction is identical with the direction of light ray propagation, as shown in Figure 2.Set up image space coordinate system (O _Is-x _Isy _Is) and object space coordinate system (O _Ob-x _Oby _Obz _Ob).The initial point of image space coordinate system is positioned on the optical axis, and with the optical system coordinate system at a distance of f.Object space coordinate system and O _OpObject distance between the point is L.Level crossing minute surface and x _ObO _Oby _ObFace overlaps.

The sensitive area of photoelectric receiving device (is made as x _ImO _Imy _Im) and x _IsO _Isy _IsFace does not overlap, and the available matrix representation of relation between the two is as follows:

$\left[\begin{array}{c}{x}_{\mathrm{Im}}\\ y_{\mathrm{Im}}\\ z_{\mathrm{Im}}\end{array}\right]=R\left[\begin{array}{c}{x}_{\mathrm{Is}}\\ y_{\mathrm{Is}}\\ z_{\mathrm{Is}}\end{array}\right]+T---\[3\]$

R is the unit orthogonal matrix in the formula, and $R=\left[\begin{array}{ccc}{S}_{11}& S_{21}& S_{13}\\ S_{21}& S_{22}& S_{23}\\ S_{31}& S_{32}& S_{33}\end{array}\right];$ The coordinate of the centre coordinate of photoelectric receiving device sensitive area (0,0) under image space coordinate system is $T=\left[\begin{array}{c}{x}_o\\ y_o\\ z_o\end{array}\right].$

(2) in measuring system, with normal line vector coordinate representation level crossing locus.

If the unit direction vector of level crossing normal is $\stackrel{\→}{n_{\mathrm{\π}}}=\{n_x,n_y,n_z\}\·$ Under the object space coordinate system, when level crossing had rotated a Space Angle (be that pitch orientation has been rotated the θ angle, yaw direction has rotated the angle), the pass between the vectorial coordinate of level crossing normal and the level crossing anglec of rotation was:

And have

$n_x^2+n_y^2+n_z^2=1---\[5\]$

(3) among Fig. 2, from object space O _ObA branch of reflected in parallel light that point sends

Through after the refraction of lens, with image space x _IsO _Isy _IsDeliver personally in the F point.Reflection ray Moved to the initial point of optical system coordinate system, i.e. projection centre.If reflection ray after the translation and x _ObO _Oby _ObDeliver personally in the Q point, then Q point, O _OpPoint and F point three point on a straight line.

Based on perspective projection equation and triangle theorem, obtain image space x _IsO _Isy _IsF (x on the face _Is, y _Is, 0) point coordinate be:

$\left[\begin{array}{c}{x}_{\mathrm{Is}}\\ y_{\mathrm{Is}}\end{array}\right]=f\left[\begin{array}{c}\frac{n_x}{\sqrt{n_x^2+n_y^2}}\arccos (2n_z^2-1)\\ \frac{n_y}{\sqrt{n_x^2+n_y^2}}\arccos (2n_z^2-1)\end{array}\right]---\[6\]$

(4) simultaneous formula [4] and [6] obtain:

Formula [3] is brought into following formula, can set up out the mathematical model of laser auto collimating measurement for angle in 2 D.

Determining of model parameter.

The following physical equipment of definite need of laser auto collimating measurement for angle in 2 D mathematical model parameter is finished: a cover need wait to set up the laser auto-collimation measuring system of measurement model, and wherein photoelectric receiving device adopts the PSD photoelectric position sensor; 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.Definite process of model parameter is carried out as follows:

1. open laser instrument, make the outgoing beam of self-collimation measurement system be radiated on the level crossing.

2. rotate the Three Degree Of Freedom universal stage, make 10 known angle (θ of level crossing spatial rotation _i, _i), corresponding 10 the picpointed coordinate value (x that detected by PSD are write down and stored in i=1～10 respectively _i, y _i), i=1～10.

3. 10 point coordinate values that obtain in utilizing 2. and 10 known angles of its correspondence are used the linear solution method, calculate matrix R and T.

4. matrix R that calculates and T are brought in the formula [17], thereby obtain the mathematical model of laser auto collimating measurement for angle in 2 D.

Embodiment

Make up parameter and determine required physical equipment, the photoelectric receiving device PSD that wherein need wait to set up the laser auto-collimation measuring system of measurement model is that Japanese shore pine company produces, and model is S1880.According to the above-mentioned process of setting up according to the laser auto collimating measurement for angle in 2 D mathematical model, obtain 10 groups of picpointed coordinates and corresponding level crossing rotational angle value, calculate matrix R and T and be:

$R=\left[\begin{array}{ccc}1.0000& 0.0000& -0.0016\\ 0.0000& 1.0000& 0.0041\\ 0.0024& 0.0041& 1.0000\end{array}\right],$ $T=\left[\begin{array}{c}0.331\\ 0.140\\ 1.272\end{array}\right]$

Thereby the mathematical model of the laser auto collimating measurement for angle in 2 D of setting up is:

Adopt the measurement mechanism of the inventive method modeling to carry out the laser auto-collimation measurement of angle, measurement range ± 2 °, static measurement precision 0.25 '.

Claims (1)

1, a kind of modeling method of laser auto collimating measurement for angle in 2 D is characterized in that, based on perspective projection transformation, the laser auto-collimation measurement model is regarded as a pin-hole imaging model, mathematical model to set up process as follows:

(1) set up coordinate system,

Set up optical system coordinate system O _Op-x _Opy _Opz _Op, the initial point of optical system coordinate system is positioned on the optical axis, z _OpAxle with optical axis heavy and, direction is identical with the direction of light ray propagation, sets up image space coordinate system (O _Is-x _Isy _Is) and object space coordinate system (O _Ob-x _Oby _Obz _Ob), the initial point of image space coordinate system is positioned on the optical axis, and with the optical system coordinate system at a distance of f, object space coordinate system and O _OpObject distance between the point is L, level crossing minute surface and x _ObO _Oby _ObFace overlaps, and the sensitive area of establishing photoelectric receiving device is x _ImO _Imy _Im, it and x _IsO _Isy _IsFace does not overlap, and the available matrix representation of relation between the two is as follows:

$\left[\begin{array}{c}{x}_{\mathrm{Im}}\\ y_{\mathrm{Im}}\\ z_{\mathrm{Im}}\end{array}\right]=R\left[\begin{array}{c}{x}_{\mathrm{Is}}\\ y_{\mathrm{Is}}\\ z_{\mathrm{Is}}\end{array}\right]+T----\left[3\right]$

R is the unit orthogonal matrix in the formula, and $R=\left[\begin{array}{ccc}{S}_{11}& S_{12}& S_{13}\\ S_{21}& S_{22}& S_{23}\\ S_{31}& S_{32}& S_{33}\end{array}\right],$ The coordinate of the centre coordinate of photoelectric receiving device sensitive area (0,0) under image space coordinate system is $T=\left[\begin{array}{c}{x}_o\\ y_o\\ z_o\end{array}\right];$

(2) in measuring system, with normal line vector coordinate representation level crossing locus, the unit direction vector of establishing the level crossing normal is $\stackrel{\→}{n_{\mathrm{\π}}}=\{n_x,n_y,n_z\},$ Under the object space coordinate system, when level crossing has rotated a Space Angle, promptly pitch orientation has been rotated the θ angle, and when yaw direction had rotated the angle, the pass between the vectorial coordinate of level crossing normal and the level crossing anglec of rotation was:

And have $n_x^2+n_y+n_z^2=1----\left[5\right]$

(3) from object space O _ObA branch of reflected in parallel light that point sends

Through after the refraction of lens, with image space x _IsO _Isy _IsDeliver personally in the F point, reflection ray

Moved to the initial point of optical system coordinate system, i.e. projection centre is established reflection ray and x after the translation _ObO _Oby _ObDeliver personally in the Q point, then Q point, O _OpPoint and F point three point on a straight line based on perspective projection equation and triangle theorem, obtain image space x _IsO _Isy _IsF (x on the face _Is, y _Is, 0) point coordinate be:

$\left[\begin{array}{c}{x}_{\mathrm{Is}}\\ y_{\mathrm{Is}}\end{array}\right]=f\left[\begin{array}{c}\frac{n_x}{\sqrt{n_x^2+n_y^2}}\arccos ({2n}_z^2-1)\\ \frac{n_y}{\sqrt{n_x^2+n_y^2}}\arccos (2n_z^2-1)\end{array}\right]----\left[6\right]$

(4) simultaneous formula [4] and [6] obtain:

Formula [3] is brought into formula [7], promptly finish the foundation of laser auto collimating measurement for angle in 2 D mathematical model;

(4) determine the parameter of model,

Definite need of laser auto collimating measurement for angle in 2 D mathematical model parameter carry out on the basis of following equipment: a cover need wait to set up the laser auto-collimation measuring system of measurement model, and wherein photoelectric receiving device adopts the PSD photoelectric position sensor; 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; Definite process of model parameter is carried out as follows:

1. open laser instrument, make the outgoing beam of self-collimation measurement system be radiated on the level crossing;

2. rotate the Three Degree Of Freedom universal stage, make 10 known angle (θ of level crossing spatial rotation _i, _i), corresponding 10 the picpointed coordinate value (x that detected by PSD are write down and stored in i=1～10 respectively _i, y _i), i=1～10;

3. 10 point coordinate values that obtain in utilizing 2. and 10 known angles of its correspondence are used the linear solution method, calculate matrix R and T.

4. matrix R that calculates and T are brought in the formula [5], thereby obtain the mathematical model of laser auto collimating measurement for angle in 2 D.

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