CN115406379A - Wide-range auto-collimation angle measurement method based on light spot deformation - Google Patents
Wide-range auto-collimation angle measurement method based on light spot deformation Download PDFInfo
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Abstract
The invention relates to a wide-range auto-collimation angle measurement method based on light spot deformation, belonging to the field of optical measurement instruments, comprising the following steps: (1) based on an orthogonal structure of a standard conical lens, a space coordinate vector analysis method is applied, an Euler space rotation relation formula is combined, and the reflecting plane of the conical lens is guided to reconstruct the directional structure of the cylindrical surface, so that a hollow cylindrical conical lens with angle sensing on a pitch angle and a yaw angle is designed; (2) constructing an autocollimator measurement system for measuring a pitch angle and a yaw angle by using a hollow cylindrical pyramid as a reflector of the autocollimator measurement system; (3) and establishing a double-coordinate system model between the pyramid mirror and the measuring system, and deducing a mathematical calculation formula of the deformation rule of the reflected imaging light spot and the angle change of the reflector by analyzing the vector information of the reflected light beam. The invention improves the measuring range of the auto-collimation angle measuring method, and simultaneously improves the precision and the dynamic distance measuring performance.
Description
Technical Field
The invention belongs to the field of optical measuring instruments, and particularly provides a method for measuring a pitch angle and a yaw angle of a rotating object by analyzing the reflection condition of light in an autocollimator and analyzing the light, wherein the method is provided with a special-structure conical mirror.
Background
The auto-collimation angle measurement method is used as a representative technology of space traceable optical measurement, has the advantage of a compact system, is widely applied to angle measurement in multiple fields of precision manufacturing, national defense rework and the like, and directly determines the capability and the progress of precision manufacturing and semiconductor technology in the development level. However, the design concept of sharing an optical path by the incident light and the reflected light beams also causes the measurement light to rapidly deviate from the measurement aperture along with the deflection of the reflector, resulting in the performance defect that the measurement range of the autocollimator is usually less than 1 °. Future optical measurement methods are required to have larger measurement range and compact structure, so that the research of the wide-range auto-collimation angle measurement technology becomes a research hotspot in the field of optical measurement.
Y.l. chen (document y.l. chen, y.shimizu, y.kudo, s.ito, and w.gao, mode-locked laser auto collimator with an expanded measurement range [ J ] Optics Express,2016,24 (14): 15554-15569.) uses a diffraction grating as a reflector of an autocollimator, widens a reflected beam diameter by its dispersion effect to obtain an equivalent extension of an objective lens aperture mirror, and thereby a laser Mode-locked autocollimator having a measurement range increased to 11000 arc seconds was developed. However, this improved means of expanding the diameter of the reflected beam results in the measurement beams being separated from each other, and a measurement blind zone is created when the relative distance between the autocollimator and the reflector is dynamically changed. In 2021, we (R.P.Li, Y.ZHen, and K.Di, three-degree-of-free autocollimator with large angle-Measurement range [ J ]. Measuring Science and Technology,2021,32 (11): 115005.) use "space coordinate vector analysis" and "ray tracing theory" to obtain the experimental result of extending the measuring range to 92400 arcsec by designing a nonstandard pyramid with low reflection angle sensitivity, although the scheme does not affect the dynamic measuring distance of the autocollimator, the yaw and pitch angle information has crosstalk with the change of the angle relationship between the reflection surfaces of the pyramid, and the measuring precision can only reach 35 arcsec.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A wide-range auto-collimation angle measurement method based on light spot deformation is provided. The technical scheme of the invention is as follows:
a wide-range auto-collimation angle measurement method based on light spot deformation comprises the following steps:
and 3, establishing a dual-coordinate system model between the hollow cylindrical conical lens and the autocollimator measuring system, analyzing vector information of a reflected light beam to obtain a mathematical calculation formula of a deformation rule of a reflected imaging light spot and the angle change of the reflector, and measuring the width between two vertical axes of the H-shaped light spot and the splitting angle of a vertical axis to respectively obtain the pitching angle information and the yawing angle information of the hollow cylindrical conical lens.
Further, the 1,2 reflecting surfaces of the step 1 hollow cylindrical pyramid mirror are perpendicular to the OX and OY axes respectively, and the unit vectors thereof should satisfy the following relations: n is a radical of hydrogen 1 ＝[1 0 0] T ；N 2 ＝[0 1 0] T ；N 1 、N 2 Respectively, the unit vectors of the 1,2 reflecting surfaces of the hollow cylindrical pyramid mirror. The angle relationship between the cylindrical surface and the other two reflection planes can be expressed as L 2-3 ＝L 1-3 =90 ° - δ, wherein δ is a deviation from 90 °;
normal vector N of the 3 rd cylindrical surface 3 Can be expressed as:
wherein beta is the included angle formed between the unit vector of the 3 rd cylindrical surface and the OZ axis, and the unit vector N of the cylindrical surface 3 Is a set from a point O on the central axis to a horizontal cross-sectional line thereof, wherein the point O is an intersection of the central axis of the cylindrical surface and an extension of the OZ coordinate axis, so that the angle range of beta is from 0 DEG to beta max (ii) a The reflecting matrixes of the three reflecting surfaces can be obtained by combining a unit vector formula of each reflecting surface of the hollow cylindrical pyramid mirror and a relational expression formula of the reflecting matrix:
equation (3) will also be consistent with equation (2) when β = 0.
Further, in the step 2, an autocollimator measurement system for measuring a pitch angle and a yaw angle is constructed by using a hollow cylindrical pyramid as a reflector of the autocollimator measurement system, and specifically includes:
respectively deducing a reflection matrix M of the cylindrical conical mirror according to different reflection sequences of three reflection surfaces in the hollow cylindrical conical mirror 123or321 、M 132or231 、M 213or312 And combining the incident beam vector A to obtain vector expression B of the reflected beam 123or321 、B 213or312 、B 231or132 . Using vector expression B of reflected beam 123or321 、B 213or312 、B 231or132 The initial point and the terminal coordinates of the reflected beam image on the image surface can be respectively calculated, so that the H-shaped integral beam imaging morphology on the system image surface can be deduced.
Further, the step 2 specifically includes the following steps: three pairs of reflected light beam sequences (1-2-3 and 3-2-1, 1-3-2 and 2-3-1, 2-1-3 and 3-1-2), i.e. six different reflection sequences of the reflected light beams, and by exchanging M 1 、M 2 、M 3 The multiplication sequence between the above can be calculated to obtain the reflection matrix of the hollow cylindrical pyramid mirror:
where δ is the effective structural angle, from the unit vector N of the 3 rd cylinder 3 The angle between the three reflecting surfaces caused by the offset beta with the OZ axis is L 1-2 ＝90°，L 2-3 ＝L 1-3 ＝90°-δ；
The beam reflection matrices having the reflection orders 3-2-1,2-3-1 and 3-1-2 have opposite signs to δ of equations (4), (5) and (6), respectively;
since the measurement signal is obtained at the image plane of the autocollimator, the X-ray from the hollow cylindrical pyramid mirror needs to be completed 0 Y 0 Z 0 XYZ reflection matrix conversion from a coordinate system to an autocollimator coordinate system; considering the fact that the angle between the 1 st and 2 nd reflecting surfaces cannot be made absolutely orthogonal in the manufacture of a practical hollow cylindrical pyramid mirror, there is always a constant angular deviation δ _from90 °, and this results in a non-orthogonal deviation angle δ _, between the 3 rd cylindrical surface and the 1 st and 2 nd reflecting surfaces, respectively (βoz)_ And obtaining a reflection matrix of the cylindrical conical mirror in an XYZ coordinate system:
M 213 、M 321 、M 231 respectively, representing a beam reflection matrix with a reflection order of 3-2-1,2-3-1 and 2-3-1. For the reflection matrix with the beam reflection sequence of 3-1-2,1-2-3,1-3-2, the elements on the non-main diagonal are opposite to the elements in the formulas (7), (8) and (9), respectively, and the elements on the main diagonal are consistent.
Further, the reflected light beam vector B of the autocollimation measurement system in step 3 is determined by the following expression:
B＝M·A (10)
wherein M is a reflector matrix of a cylindrical pyramid mirror in a coordinate system XYZ of the auto-collimation measuring system, and A is a collimated incident beam vector;
since the incident beam is parallel to the optical axis of the auto-collimation measurement system, i.e. the incident beam is parallel to the OZ axis, the vector a of the beam is defined as:
the reflection matrix in the formula (11) is expressed by the expressions (7), (8) and (9), and the reflected light beam vector B can be obtained 213 、B 321 And B 231 ：
B in the formulae (12), (13) and (14) x And B y The elements represent the reflected beam vectors along the OX and OY axes, respectively, where B x And B y Is a function of the effective structural angle delta, since delta is from 0 to delta (βmax) The continuous variable in the range, the light beam images reflected by the hollow cylindrical conical lens are distributed in a continuous line along the OX axis and the OY axis respectively, and the relationship between the coordinate corresponding to each reflection sequence image and the vector of the reflected light beam is as follows:
x＝B x ·f；y＝B y ·f (15)
the equations (12), (13) and (14) are respectively substituted into the equation (15), and assuming that δ =0, the initial point coordinates (X) of the reflected beam image of the reflection sequence 2-1-3,3-2-1,2-3-1 are respectively found s ,Y s) And when δ = δ max The time corresponds to the terminal coordinate (X) of the image e ,Y e ) Thus, the coordinates of the initial points of the three reflected sequential beam images are found to be the same, indicating that the images have a common intersection point C:
in a similar way, the coordinate signs of the boundary points imaged by the reflected light beams of the reflection sequence 3-1-2,1-2-3,1-3-2 are respectively opposite to the signs of 2-1-3,3-2-1,2-3-1, and the common intersection point of the images is D; according to the derivation, the complete H-shaped imaging light spot on the image surface of the autocollimator can be obtained.
Further, said step 4 is that in the actual measurement, the object will probably also follow the OX 0 Shaft rotation pitch angle Θ 1 And OY 0 Axis rotation yaw angle theta 2 The angle, and the free angle change of the object to be measured, relative to the coordinate system of the autocollimation measurement system XYZ, the vector B of the reflected beam is expressed by the following formula:
B'＝R·M·R T ·A (17)
where M is a hollow cylindrical pyramid relative to the coordinate system X 0 Y 0 Z 0 ToA matrix of rays, a being the incident beam vector and R being a rotation matrix around three coordinate axes of the auto-collimation measurement system, wherein the rotation matrix factor θ = Θ 1 ；ψ＝Θ 2 ；
Wherein, theta 1 Denotes pitch angle theta 2 Which is indicative of the angle of yaw,
OZ representing a hollow cylindrical pyramid 0 Axial and auto-collimation measuring system OY 1 The angle between the axes.
According to the formulas (11) and (20), the reflected light beam vector changes caused by the rotation of the pitch angle and the yaw angle of the hollow cylindrical conical lens can be determined by respectively substituting the formulas (7), (8) and (9) into the formula (17); the initial point of the reflected beam image of the reflection sequence 2-1-3,3-2-1,2-3-1, i.e. the coordinate (X) of the common intersection point s_ 、Y s_ ) The rewrite is:
when the hollow cylindrical surface pyramid lens winds the theta 1 And Θ 2 When rotating, the reflected light beam image with the reflection sequence of 2-3-1 will be inclined by the following angle:
ψ＝atan(sinΘ 2 ·tan(γ-Θ 1 ))
where n represents the refractive index of the pyramid mirror.
Similarly, it can be deduced that reflected beam imaging for the reflection sequence 1-3-2 will exhibit a tilt angle change opposite to equation (19); the fracture angle psi between the two reflected beam images is used for realizing the theta of the hollow cylindrical cone lens 2 And (4) measuring.
When wound around theta 1 During rotation, the reflection sequence is 2-1-3,1-3-2 reflected beam imaging will produce a parallel displacement dX along the OX axis of the autocollimator image plane 1 :
dX 1 ＝X s_ -X s (20)
Similarly, it can be deduced that reflected beam images of the reflection sequence 3-1-2,1-3-2 will exhibit a shift change opposite to equation (20); theta of hollow cylindrical pyramid lens is realized by utilizing displacement between longitudinal axes at two ends of reflected light beam imaging 1 And (3) measurement:
wherein f denotes the focal length of the collimator lens, δ max Representing the maximum value of the effective structural angle.
The invention has the following advantages and beneficial effects:
the invention provides a hollow cylindrical pyramid mirror, which is designed based on Euler's rotation theorem and through the modulation of included angles between reflecting surfaces of the pyramid mirror, the vector relation of reflecting planes is driven to change. The hollow cylindrical conical lens is used for replacing a plane reflector of a traditional autocollimator, so that an autocollimator with a large measuring range is obtained, an autocollimator measuring system is constructed, and a corresponding algorithm is deduced. And obtaining the relation between the light spot deformation rule and the angle change of the hollow cylindrical pyramid reflector according to the deformation of the reflected imaging light beam on the image surface of the autocollimator, thereby measuring the yaw angle and the pitch angle of the reflector. The invention establishes a measurement formula between the light spot deformation information and the angle of the hollow cylindrical pyramid mirror:
the hollow cylindrical pyramid mirror designed in step 1 according to claim 1, which has the same reflection and incident beam parallel transmission characteristics as the pyramid mirror in the vicinity of the vertex, and can always obtain an imaging spot on the image plane of the autocollimator by using the hollow cylindrical pyramid mirror as the reflector of the autocollimator, and the measurement range of the autocollimator is no longer limited by the aperture of the objective lens because the geometric center of the hollow cylindrical pyramid mirror does not move.
The hollow structure of the hollow cylindrical conical lens effectively avoids the aberration influence caused by glass, is favorable for obtaining high-quality imaging morphology, and is more convenient for an operator to perform sub-pixel-level algorithm processing on an imaging surface. The angle transformation of the reflector is obtained by measuring the displacement and the angle of the imaging light spot, so that the dynamic measurement distance and the measurement precision of the auto-collimation angle measurement are obviously optimized. The angle measuring method of the photoelectric autocollimator based on the hollow cylindrical pyramid lens can be widely applied to the fields of large buildings, warships, wings and the like which require large measuring range and high measuring precision.
Drawings
FIG. 1 is a theoretical block diagram of a preferred embodiment of the present invention providing a hollow cylindrical conical mirror;
FIG. 2 is a dual coordinate system diagram of an auto-collimation measurement system;
FIG. 3 is an image plane spot imaging diagram of an autocollimator;
fig. 4 is an auto-collimation measurement system based on a hollow cylindrical pyramid mirror.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
a wide-range auto-collimation angle measurement method based on spot deformation comprises the following steps:
1) The structure of the cylindrical hollow pyramid mirror reflector structure which has yaw and pitch angle sensing capabilities and simultaneously maintains the local orthogonal relation between the reflecting surfaces is obtained by performing structural reconstruction on one reflecting plane in the standard pyramid mirror reflector to the cylindrical surface. In this process, the angle relationship between the cylindrical surface and the other two reflecting planes can be expressed as L 2-3 ＝L 1-3 (= 90 ° - δ), where δ is a deviation from 90 °, and the deviation is 0 to δ in accordance with the distance between a reflection point on a cylindrical surface and the vertex of an angle cone max Within a range.
2) According to different reflection sequences of three reflecting surfaces in the hollow cylindrical pyramid mirror, respectively deducing a reflecting matrix M of the cylindrical pyramid mirror 123or321 、M 132or231 、M 213or312 And combining the incident beam vector A to obtain vector expression B of the reflected beam 123or321 、B 213or312 、B 231or132 . Using vector expression B of the reflected beam 123or321 、B 213or312 、B 231or132 The initial point and the terminal coordinate of the reflected beam image on the image surface can be respectively calculated, so that the H-shaped integral beam image appearance on the image surface of the system can be deduced.
3) And (3) establishing a measurement formula of the wide-range autocollimator by combining the parameter f of the autocollimator measurement system: x = B x ·f；y＝B y F, where f denotes the focal length of the collimator, B x And B y First and second column vectors in reflected beam vector expression B, respectively. And then thinning and characterizing matrix elements in the reflected light beam vector to obtain deformation information and theta of the imaging light spot 1 Pitch angle and theta 2 Systematic measurement formula between yaw angle changes:
wherein dX 1 Indicating the coordinate change on the OX axis of the reflected beam image of the reflection sequence 2-1-3,3-2-1 and psi indicates the coordinate break angle between the reflected beam images of the reflection sequence 1-3-2 and 2-3-1.
Preferably, the 1,2 reflecting surfaces of the hollow cylindrical pyramid mirror in the step 1) are perpendicular to the OX and OY axes respectively, and unit vectors thereof should satisfy the following relations: n is a radical of 1 ＝[1 0 0] T ；N 2 ＝[0 1 0] T 。
Normal vector N of the 3 rd cylinder 3 Can be expressed as:
wherein β is formed between the unit vector of the 3 rd cylindrical surface and the OZ axisAngle of cylinder, unit vector N of cylinder 3 Is a set from a point O on the central axis to a horizontal cross-sectional line thereof, wherein the point O is an intersection of the central axis of the cylindrical surface and an extension of the OZ coordinate axis, so that the angle range of beta is from 0 DEG to beta max . The structure of the hollow cylindrical pyramid mirror is shown in the attached figure 1. The reflecting matrixes of the three reflecting surfaces can be obtained by combining a unit vector formula of each reflecting surface of the hollow cylindrical pyramid mirror and a relational expression formula of the reflecting matrix:
equation (3) will also be consistent with equation (2) when β = 0. Thus, it can be concluded that: the area near the vertex of the hollow cylindrical conical lens has the same reflection and incident light beam parallel transmission characteristics as the conical lens, so when the hollow cylindrical conical lens is used as a reflector of the autocollimator, partial reflected light beams are not limited by the aperture size of the collimator lens, and an image can be formed on the image surface of the autocollimator in a large angle change range of the reflector.
3. Preferably, the step 2) specifically comprises: according to different arrangement sequences of three reflectors in the hollow cylindrical pyramid, there are three pairs of reflected light beam sequences (1-2-3 and 3-2-1, 1-3-2 and 2-3-1, 2-1-3 and 3-1-2), namely six reflected light beams with different reflection sequences, and the reflected light beams are obtained by exchanging M 1 、M 2 、M 3 The multiplication sequence between the above can be calculated to obtain the reflection matrix of the hollow cylindrical pyramid mirror:
where δ is the effective structural angle, from the unit vector N of the 3 rd cylinder 3 The angle between the three reflecting surfaces caused by the offset beta with the OZ axis is L 1-2 ＝90°，L 2-3 ＝L 1-3 ＝90°-δ。
The light beam reflection matrices having the reflection orders of 3-2-1,2-3-1 and 3-1-2 have the opposite signs of δ of equations (4), (5) and (6), respectively.
Since the measurement signal is finally obtained at the image plane of the autocollimator, the X from the hollow cylindrical pyramid needs to be completed 0 Y 0 Z 0 XYZ reflection matrix transformation of the coordinate system to the autocollimator coordinate system as shown in figure 2. Considering that the angle between the 1 st and 2 nd reflecting surfaces cannot be made absolutely orthogonal in the manufacture of a practical hollow cylindrical pyramid mirror, there is always a constant angular deviation δ _from90 °, and this results in a non-orthogonal deviation angle δ between the 3 rd cylindrical surface and the 1 st and 2 nd reflecting surfaces, respectively (βoz)_ . Obtaining a reflection matrix of the cylindrical conical mirror in an XYZ coordinate system:
for the reflection matrix with the beam reflection sequence of 3-1-2,1-2-3,1-3-2, the elements on the non-main diagonal are opposite to those in the formulas (7), (8) and (9), respectively, and the elements on the main diagonal are consistent.
4. The reflected beam vector B at the autocollimation measurement system is determined by the following expression:
B＝M·A (31)
wherein M is a reflector matrix of the cylindrical pyramid mirror in a coordinate system XYZ of the auto-collimation measuring system, and A is a collimated incident beam vector.
Since the incident beam is parallel to the optical axis of the auto-collimation measurement system, i.e. the incident beam is parallel to the OZ axis, the vector a of the beam is defined as:
the reflection matrix in the formula (11) is expressed by the expressions (7), (8) and (9), and the reflected light beam vector B can be obtained 213 、B 321 And B 231 ：
B in the formulae (12), (13) and (14) x And B y The elements represent the reflected beam vectors along the OX and OY axes, respectively, where B x And B y Is a function of the effective structural angle delta, again because delta is 0-delta (βmax) And continuously changing the range, and respectively arranging the light beam images reflected by the hollow cylindrical conical mirror in a continuous linear distribution along the OX axis and the OY axis, wherein the relation between the coordinate corresponding to each reflection sequence image and the vector of the reflected light beam is as follows:
x＝B x ·f；y＝B y ·f (36)
the equations (12), (13) and (14) are respectively substituted into the equation (15), and if δ =0, the reflection order can be respectively obtainedInitial point coordinate (X) of reflected beam image of 2-1-3,3-2-1,2-3-1 s ,Y s) And when δ = δ max The time corresponds to the terminal coordinate (X) of the image e ,Y e ) Thus, the coordinates of the initial points of the three reflected sequential beam images are found to be the same, indicating that the images have a common intersection point C:
similarly, the coordinate signs of the boundary points imaged by the reflected light beams of the reflection sequence 3-1-2,1-2-3,1-3-2 are respectively opposite to the signs of 2-1-3,3-2-1,2-3-1, and the common intersection point of the images is D. According to the derivation, the complete imaging light spot on the image surface of the autocollimator can be obtained.
5. In actual measurement, it is likely that the object will also be along OX 0 Shaft rotation pitch angle Θ 1 And OY 0 Axis rotation yaw angle theta 2 And (4) an angle. The free angle change of the object to be measured is expressed by the following formula relative to the coordinate system of the autocollimation measurement system XYZ:
B'＝R·M·R T ·A (38)
where M is a hollow cylindrical pyramid relative to the coordinate system X 0 Y 0 Z 0 A is the incident beam vector and R is the rotation matrix around the three coordinate axes of the auto-collimation measurement system, wherein the rotation matrix factor θ = Θ 1 ；ψ＝Θ 2 ；
According to the formulas (11) and (20), the reflected light beam vector changes caused by the rotation of the pitch angle and the yaw angle of the hollow cylindrical conical mirror can be determined by respectively substituting the formulas (7), (8) and (9) into the formula (17). The initial point of the reflected beam image of the reflection sequence 2-1-3,3-2-1,2-3-1, i.e. the coordinate (X) of the common intersection point s_ 、Y s_ ) The rewrite is:
when the hollow cylindrical surface pyramid lens winds the theta 1 And Θ 2 When rotating, the reflected beam image with the reflection sequence of 2-3-1 will be inclined, as shown in fig. 4, by the angle:
similarly, it can be deduced that reflected beam imaging for the reflection sequence 1-3-2 will exhibit a tilt angle change opposite to equation (19). The angle phi of fracture between the two reflected light beam images is used to realize the theta of the hollow cylindrical cone lens 2 And (6) measuring.
When wound around theta 1 When rotated, the reflected beam images of the reflection sequence 2-1-3,1-3-2 will produce a parallel displacement dX along the OX axis at the image plane of the autocollimator 1 :
dX 1 ＝X s_ -X s (41)
Similarly, it can be deduced that reflected beam images of the reflection sequence 3-1-2,1-3-2 will exhibit a shift change opposite to equation (20). Theta of hollow cylindrical pyramid lens is realized by utilizing displacement between longitudinal axes at two ends of reflected light beam imaging 1 And (3) measurement:
finally, according to the invention, by designing the hollow cylindrical surface conical mirror structure with the cylindrical surface partially orthogonal to the two reflecting planes, the corresponding relation of the spot deformation, the yaw and the pitch deduced by the experimental device is constructed, and the wide-range angle measurement of the autocollimator is realized. Based on the method, the measuring range performance is increased from +/-30' to +/-30 degrees, and the dynamic measuring distance can reach 0.2-5 m. In addition, the hollow cylindrical pyramid mirror is provided with two groups of extreme crosstalk states: theta 1 =30 ° and Θ 2 =30 °, measurement accuracy for pitch and yaw verified to be better than 66 "and 51", no significant yaw and pitch phaseThe phenomenon of cross talk.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising one of 8230; \8230;" 8230; "does not exclude the presence of additional like elements in a process, method, article, or apparatus that comprises that element.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure in any way whatsoever. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (6)
1. A wide-range auto-collimation angle measurement method based on spot deformation is characterized by comprising the following steps:
step 1, based on an orthogonal structure of a standard conical mirror, applying a space coordinate vector analysis method and combining an Euler space rotation relation formula to complete reconstruction of a directional structure of a reflecting plane of the conical mirror to a cylindrical surface, thereby designing a hollow cylindrical conical mirror with angle sensing for a pitch angle and a yaw angle;
step 2, constructing an autocollimator measurement system for measuring a pitch angle and a yaw angle by using a hollow cylindrical pyramid as a reflector of the autocollimator measurement system;
and 3, establishing a dual-coordinate system model between the hollow cylindrical conical lens and the autocollimator measurement system, analyzing vector information of a reflected light beam to obtain a mathematical calculation formula of a deformation rule of a reflected imaging light spot and the angle change of the reflector, and measuring the width between two vertical axes of the H-shaped light spot and the splitting angle of a longitudinal axis to respectively obtain the pitching and yawing angle information of the hollow cylindrical conical lens.
2. The method for wide-range auto-collimation angle measurement based on spot deformation as claimed in claim 1, wherein the 1,2 reflecting surfaces of the hollow cylindrical pyramid of step 1 are perpendicular to the OX and OY axes respectively, and the unit vectors thereof should satisfy the following relations: n is a radical of 1 ＝[1 0 0] T ；N 2 ＝[0 1 0] T ；N 1 、N 2 Respectively representing the unit vectors of 1,2 reflecting surfaces of the hollow cylindrical pyramid mirror, and the included angle relationship between the cylindrical surface and the other two reflecting surfaces can be represented as L 2-3 ＝L 1-3 =90 ° - δ, where δ is the deviation from 90 °;
normal vector N of the 3 rd cylindrical surface 3 Can be expressed as:
wherein beta is the included angle formed between the unit vector of the 3 rd cylindrical surface and the OZ axis, and the unit vector N of the cylindrical surface 3 Is a set from a point O on the central axis to a horizontal cross-sectional line thereof, wherein the point O is an intersection of the central axis of the cylindrical surface and an extension of the OZ coordinate axis, so that the angle range of beta is from 0 DEG to beta max (ii) a The reflecting matrixes of the three reflecting surfaces can be obtained by combining a unit vector formula of each reflecting surface of the hollow cylindrical conical mirror and a relational expression formula of the reflecting matrix:
equation (3) will also be consistent with equation (2) when β = 0.
3. The wide-range auto-collimation angle measurement method based on the light spot deformation according to claim 1, wherein in the step 2, a hollow cylindrical cone mirror is used as a reflector of an auto-collimation measurement system to construct an auto-collimation measurement system for measuring a pitch angle and a yaw angle, and specifically comprises:
according to different reflection sequences of three reflecting surfaces in the hollow cylindrical pyramid mirror, respectively deducing a reflecting matrix M of the cylindrical pyramid mirror 123or321 、M 132or231 、M 213or312 And combining the incident beam vector A to obtain vector expression B of the reflected beam 123or321 、B 213or312 、B 231or132 . Using vector expression B of reflected beam 123or321 、B 213or312 、B 231or132 The initial point and the terminal coordinate of the reflected beam image on the image surface can be respectively calculated, so that the H-shaped integral beam image appearance on the image surface of the system can be deduced.
4. The method according to claim 3, wherein the step 2 specifically comprises the following steps: according to different arrangement sequences of three reflectors in the hollow cylindrical pyramid, there are three pairs of reflected light beam sequences (1-2-3 and 3-2-1, 1-3-2 and 2-3-1, 2-1-3 and 3-1-2), namely reflected light beams of six different reflection sequences, and the reflected light beams are obtained by exchanging M 1 、M 2 、M 3 The multiplication sequence between them can be calculated as the reflection matrix of the open cylinder pyramid:
where δ is the effective structural angle, from the unit vector N of the 3 rd cylinder 3 With the OZ axisThe angle between the three reflecting surfaces caused by the offset beta is L 1-2 ＝90°，L 2-3 ＝L 1-3 ＝90°-δ；
The beam reflection matrices having the reflection orders 3-2-1,2-3-1 and 3-1-2 have opposite signs to δ of equations (4), (5) and (6), respectively;
since the measurement signal is finally obtained at the image plane of the autocollimator, the X from the hollow cylindrical pyramid needs to be completed 0 Y 0 Z 0 XYZ reflection matrix conversion from a coordinate system to an autocollimator coordinate system; considering the fact that the angle between the 1 st and 2 nd reflecting surfaces cannot be made absolutely orthogonal in the manufacture of a practical hollow cylindrical pyramid mirror, there is always a constant angular deviation δ _from90 °, and this results in a non-orthogonal deviation angle δ _, between the 3 rd cylindrical surface and the 1 st and 2 nd reflecting surfaces, respectively (βoz)_ And obtaining a reflection matrix of the cylindrical conical mirror in an XYZ coordinate system:
M 213 、M 321 、M 231 the light beam reflection matrixes with the reflection sequence of 2-1-3,3-2-1 and 2-3-1 are respectively shown, and for the reflection matrixes with the light beam reflection sequence of 3-1-2,1-2-3,1-3-2, the elements on the non-main diagonal lines are opposite numbers to the elements in the formulas (7), (8) and (9), and the elements on the main diagonal lines are kept consistent.
5. The method for wide-range auto-collimation angle measurement based on spot deformation of claim 3, wherein the reflected beam vector B of the step 3 in the auto-collimation measurement system is determined by the following expression:
B＝M·A (10)
wherein M is a reflector matrix of the cylindrical conical mirror in a coordinate system XYZ of the auto-collimation measuring system, and A is a collimation incident beam vector;
since the incident beam is parallel to the optical axis of the auto-collimation measurement system, i.e. the incident beam is parallel to the OZ axis, the vector a of the beam is defined as:
the reflection matrix in the formula (11) is expressed by the expressions (7), (8) and (9), and the reflected light beam vector B can be obtained 213 、B 321 And B 231 ：
B in the formulas (12), (13) and (14) x And B y The elements represent the reflected beam vectors along the OX and OY axes, respectively, where B x And B y Is a function of the effective structural angle delta, since delta is from 0 to delta (βmax) The continuous variable in the range, the light beam images reflected by the hollow cylindrical conical lens are distributed in a continuous line along the OX axis and the OY axis respectively, and the relationship between the coordinate corresponding to each reflection sequence image and the vector of the reflected light beam is as follows:
x＝B x ·f；y＝B y ·f (15)
substituting the equations (12), (13) and (14) into the equation (15), respectively, andassuming that δ =0, the coordinates (X) of the initial point of the reflected beam image of the reflection sequence 2-1-3,3-2-1,2-3-1 can be found separately s ,Y s) And when δ = δ max The time corresponds to the terminal coordinate (X) of the image e ,Y e ) Thus, the coordinates of the initial points of the three reflected sequential beam images are found to be the same, indicating that the images have a common intersection point C:
in a similar way, the coordinate signs of the boundary points imaged by the reflected light beams of the reflection sequence 3-1-2,1-2-3,1-3-2 are respectively opposite to the signs of 2-1-3,3-2-1,2-3-1, and the common intersection point of the images is D; according to the derivation, the complete H-shaped imaging light spot on the image surface of the autocollimator can be obtained.
6. A wide-range auto-collimation angle measurement method based on spot deformation as claimed in claim 5, wherein in step 4, in actual measurement, the object is likely to follow OX 0 Shaft rotation pitch angle Θ 1 And OY 0 Axis rotation yaw angle Θ 2 The angle, and the free angle change of the object to be measured, relative to the coordinate system of the autocollimation measurement system XYZ, the vector B of the reflected beam is expressed by the following formula:
B'＝R·M·R T ·A (17)
where M is a hollow cylindrical pyramid relative to the coordinate system X 0 Y 0 Z 0 A is the incident beam vector and R is the rotation matrix around the three coordinate axes of the auto-collimation measurement system, wherein the rotation matrix factor θ = Θ 1 ；ψ＝Θ 2 ；
Wherein Θ is 1 Denotes pitch angle theta 2 The angle of yaw is represented as the angle of yaw,
OZ representing a hollow cylindrical pyramid 0 Axial and auto-collimation measuring system OY 1 The included angle between the axes;
according to the formulas (11) and (20), the reflected beam vector changes caused by the rotation of the pitch angle and the yaw angle of the hollow cylindrical conical mirror can be determined by respectively substituting the formulas (7), (8) and (9) into the formula (17); the initial point of the reflected beam image of the reflection sequence 2-1-3,3-2-1,2-3-1, i.e. the coordinate (X) of the common intersection point s_ 、Y s_ ) The rewrite is:
when the hollow cylindrical surface pyramid lens winds the theta 1 And Θ 2 When rotating, the reflected light beam image with the reflection sequence of 2-3-1 will be inclined by the following angle:
wherein n represents the refractive index of the pyramid mirror;
similarly, it can be deduced that reflected beam imaging for the reflection sequence 1-3-2 will exhibit a tilt angle change opposite to equation (19); the fracture angle psi between the two reflected beam images is used for realizing the theta of the hollow cylindrical cone lens 2 And (6) measuring.
When winding theta 1 When rotated, the reflected beam images of the reflection sequence 2-1-3,1-3-2 will produce a parallel displacement dX along the OX axis at the image plane of the autocollimator 1 :
dX 1 ＝X s_ -X s (20)
Similarly, it can be deduced that reflected beam images of the reflection sequence 3-1-2,1-3-2 will exhibit a shift change opposite to equation (20); method for realizing theta of hollow cylindrical pyramid lens by utilizing longitudinal axis displacement of two ends of reflected light beam imaging 1 Measurement:
wherein f represents the focal length of the collimator lens, δ max Representing the maximum value of the effective structural angle.
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