CN109737893B - Method for increasing measurement range of autocollimator - Google Patents

Method for increasing measurement range of autocollimator Download PDF

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CN109737893B
CN109737893B CN201811269078.8A CN201811269078A CN109737893B CN 109737893 B CN109737893 B CN 109737893B CN 201811269078 A CN201811269078 A CN 201811269078A CN 109737893 B CN109737893 B CN 109737893B
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corner mirror
light
autocollimator
reflected
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CN109737893A (en
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黎人溥
周敏
刘宇
路永乐
文丹丹
郭俊启
邸克
崔巍
夏冰清
杨慧慧
曾理
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Chongqing University of Post and Telecommunications
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Abstract

The invention requests to protect a method for increasing the measurement range of a photoelectric autocollimator, which comprises the following steps: the method includes that a corner mirror with a specific geometrical structure is used as a reflector of the photoelectric autocollimator, and angles of three side surfaces of the corner mirror satisfy the following relation: the angle 1_2 is equal to 90 DEG-12,∠2_3=90°‑23,∠1_3=90°‑13. Analyzing the internal structure of the corner mirror and the reflection of the light, and dividing the light into six beams of light according to different reflection sequences. Researching the relation between the reflection sequence and the measurement parameter to obtain the coordinate matrix M of the corner mirror corresponding to the reflection beamrAngle sensitivity K and reflected light vector B reflected from the corner mirror back to the collimator. Analyzing the imaging condition of the six beams of reflected light on the surface of the photoelectric sensor of the autocollimator to obtain the relation xi between the light spot displacement and the deflection angle of the corner mirrorx≈‑Δ·Θ1·f、ξy≈‑Δ·Θ2F. Controlling the side connecting angle of the corner mirror to give a value to easily increase the measurement range of the photoelectric autocollimator. The invention can be widely applied to the fields of large-scale buildings, warships, wings and the like with large measurement range.

Description

Method for increasing measurement range of autocollimator
Technical Field
The invention belongs to the field of optical measuring instruments, and particularly relates to a method for researching a method for increasing the measuring range of a photoelectric autocollimator by using a specific corner mirror to replace a plane mirror on the basis of the working principle of the two-dimensional photoelectric autocollimator.
Background
The autocollimator is an important measuring instrument for small-angle measurement by using the principle of optical autocollimation. Because of its high accuracy and measurement resolution, it is widely used in precision measurement work, such as: the autocollimator plays an important role in angle measurement, flatness measurement of a flat plate, angle shake measurement of a shaft system, straightness measurement of a guide rail and the like. Autocollimators, due to their high accuracy and measurement resolution, are used in a large number of applications: angle measurement, angle shaking measurement of a shaft system, straightness measurement of a guide rail, angle measurement and the like. In addition to the high requirement for the measurement accuracy of the auto-collimation instrument and the single limitation of the measurement range, the research on the auto-collimation instrument in recent years mainly focuses on the improvement of the accuracy. However, the photoelectric autocollimators sold on the market today are represented by the elcoma hr and elcoma series of MOLLER, germany, and the products thereof have achieved high precision. However, the measurement range of the auto-collimation instrument cannot be effectively improved due to the characteristics of the structure of the auto-collimation instrument, so that the use and development of the auto-collimation instrument in the field of industrial measurement are greatly limited.
The known limiting relation between the working distance and the measuring range of the two-dimensional photoelectric autocollimator and the aperture of the objective lens is as follows:
Figure GDA0001995192290000011
wherein, L represents the working distance of the photoelectric collimator, beta represents the measuring range, and D is the aperture of the objective lens.
According to the formula (15), the existing photoelectric autocollimator will inevitably greatly sacrifice the measurement range when measuring a long-distance measurement target, or increase the measurement range of the autocollimator by increasing the aperture of the objective lens. The former can make the working distance and the measuring range of the autocollimator not be compatible, the latter can increase the cost and the weight of the autocollimator, and the increase of the aperture of the objective lens makes the convergence of some aberrations difficult, so that the design difficulty is increased.
The front koho card fe, the front koho card fe, the front koho card fe, the front koho card fe, the front ge, the front card fe, the front ge, the front card fe Kappa 0/wolf nail tip nail 4 nail tip nail 5 nail tip nail 8 nail tip nail 3 nail tip1Or OY1So that information on the corresponding beam moving on the photo-sensor along the OX or OY axis of the photo-collimator can be obtained.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A method of increasing the measurement range of an autocollimator is proposed. The technical scheme of the invention is as follows:
a method of increasing the measurement range of an autocollimator, comprising the steps of:
1) designing a corner mirror with an improved geometrical structure as a reflector of the photoelectric autocollimator, wherein the improved geometrical structure of the corner mirror mainly consists of angle improvement of three sides, the corner mirror comprises three sides a (1), b (2) and c (3) and a reflector aperture surface (4), and the angles of the three sides of the corner mirror of the improved geometrical structure satisfy the following relation: the angle 1_2 is equal to 90 DEG-12,∠2_3=90°-23,∠1_3=90°-13Wherein122313The effective structural angles between the sides a (1) and b (2), b (2) and c (3), and a (1) and c (3), respectively, are shown. After the autocollimator is maintained to be initialIn the state, the reflector aperture surface (4) of the corner mirror is vertical to the OZ axis of the collimator, and the equivalent aperture (5) of the corner mirror is a hexagram and comprises an entrance pupil (6) and an exit pupil (7);
2) analyzing the internal structure of the corner mirror and the reflection of light, and dividing the reflected light beam into six beams of light according to the different reflection sequence of the collimated light beam along the three sides a (1), b (2) and c (3) of the corner mirror;
3) researching the relation between the reflection sequence and the measurement parameters to obtain the coordinate matrix M of the corner mirror corresponding to the reflection beamrAn angular sensitivity K and a reflected light vector B reflected from the corner mirror back to the collimator;
4) analyzing the imaging condition of the six beams of reflected light on the surface of the photoelectric sensor of the autocollimator to obtain the relation xi between the light spot displacement and the deflection angle of the corner mirrorx≈-△·Θ1·f、ξy≈-△·Θ2F, where Θ1For corner mirrors OX1Angular deflection of the shaft, Θ2As a corner mirror OY1The angular deflection of the axis, f being the focal length of the objective lens of the photoelectric collimator,
Figure GDA0001995192290000033
a slight angle;
5) and the measurement range of the photoelectric autocollimator is increased by the given value through controlling the side connecting angle of the corner mirror.
Furthermore, the equivalent aperture (5) is composed of six parts (8), (9), (10), (11), (12) and (13) which have the same shape and the same area.
Further, six parts of the equivalent aperture receive a part of collimated light beam, and each part of the received collimated light beam is reflected for three times along the surfaces of three side surfaces a (1), b (2) and c (3) of the corner mirror according to a fixed reflection sequence and then reflected back to the photoelectric autocollimator in parallel to the optical axis to form an optical loop;
further, the relationship between the fixed reflection sequence of the light beam along the inside of the corner mirror and the effective fan plane is as follows: a-b-c → 8-11; c-b-a → 11-8; b-a-c → 9-12; c-a-b → 12-9; b-c-a → 10-13; a-c-b → 13-10; the six reflected light sources can be divided into pairs according to the reflection sequence marks of the reflecting surfaces.
Further, when the reflection sequence of a pair of reflected light beams is b-a-c, c-a-b, the displacement of the two collimated reflected light beams on the photoelectric sensor along the axis OX and OY of the autocollimator is only corresponding to the displacement of the corner mirror along the axis OX1、OY1The rotation quantity of the shaft is correlated to obtain a reflected light vector
Figure GDA0001995192290000031
A collimated incident beam parallel to the corner mirror; the invariant axis U and the corner mirror OX of one of the three pairs of beams1、OY1Perpendicular, i.e. satisfying the following relationship:
Figure GDA0001995192290000032
the following angular relationships are satisfied by the three reflecting surfaces a (1), b (2), c (3) of the corner mirror according to equation (1):
sin(23)·cos(12)·cos(13)+sin(13)=0 (2)
sin(23)·cos(12)·cos(13)-sin(13)+2sin(12)·cos(13)=0 (3)
the action angles among the three reflecting surfaces a (1), b (2) and c (3) of the corner mirror can be obtained by solving the formula122313Comprises the following steps:
13=arctan(sin(12)) (4)
sin(23)=-tan(12) (5)
23=arcsin(-tan(12)) (6)
the invariant axes of the beam pairs a-b-c, c-b-a
Figure GDA0001995192290000041
On the coordinate axis OZ of the corner mirror1The on-axis components are:
Figure GDA0001995192290000042
determining the effective structure angle of the three sides a (1), b (2), c (3) of the corner mirror122313And the constant axis of said light beam a-b-c, c-b-a
Figure GDA0001995192290000043
On the coordinate axis OZ of the corner mirror1Component of the axis:
Figure GDA0001995192290000044
wherein the beam is a small angle and the reflection order is b-a-c
Figure GDA0001995192290000045
Expressed as:
Figure GDA0001995192290000046
beam invariant axis with reflection order b-a-c
Figure GDA0001995192290000047
Is determined by the parameters of three side surfaces a (1), b (2) and c (3) of the corner mirror, and the coordinate matrix of the corner mirror of the light beams b-a-c is as follows according to the sequence of the light beams passing through the reflecting surface:
Figure GDA0001995192290000051
according to the above formula, the light beams reflected in the order of b-a-c are reflected, the coordinate matrix of the corner mirror satisfies the sensing relationship of the euler's rotation equation for the rotation angles of the OX and OY axes, and the angular sensitivity of the corner mirror is obtained as follows:
Figure GDA0001995192290000052
the vector of the reflected light of the light beams b-a-c reflected from the corner mirror to the collimator is as follows:
Figure GDA0001995192290000053
according to the above formula, the displacement information of the reflected light along the OX and OY axes on the two-dimensional surface of the photosensor of the autocollimator corresponds to only the OX corresponding to the corner mirror1、OY1The rotation condition of the shaft is related;
the reflected light vector parameter Delta of the light beams reflected along the b-a-c sequence and the corresponding other light beams reflected along the c-a-b sequence is negative, and the other parameters are the same.
Further, the imaging conditions of the six reflected lights with different reflection sequences on the surface of the photoelectric sensor of the photoelectric collimator are as follows: the light beams with the reflection sequence of b-a-c and c-a-b are imaged on the surface of the photoelectric sensor as light spots (14) and (15), the light spots (16) and (17) are imaged by the light beams with the reflection sequence of a-b-c and c-b-a, the light spots (18) and (19) are imaged by the light beams with the reflection sequence of b-c-a and a-c-b, the light spots (14) and (15), the light spots (16) and (17), and the light spots (18) and (19) are imaging conditions of the light beams when the corner mirror is not deflected, spots (14') and (15'), spots (16') and (17'), spots (18') and (19') representing the imaging of the beam when the corner mirrors are deflected, the displacement of the light spots (14) and (15) and the deflection angle of the corner mirror are in the following relation:
ξx≈-△·Θ1·f (13)
ξy≈-△·Θ2·f (14)
wherein Θ is1For corner mirrors OX1Angular deflection of the shaft, Θ2As a corner mirror OY1The angular deflection of the axis, f, is the focal length of the objective lens of the photoelectric collimator.
Furthermore, the effective structure angle of the three sides a (1), b (2) and c (3) of the corner mirror122313Control according to the angle sensitivity of the corner mirrorDegree of rotation
Figure GDA0001995192290000061
The measurement range of the photoelectric autocollimator can be increased by setting the value as required.
The invention has the following advantages and beneficial effects:
the invention discloses a method for increasing the measuring range of a photoelectric autocollimator, which uses a corner mirror with a specific geometric structure as a reflector of the photoelectric autocollimator to reduce the angular sensitivity of reflected light of a loop, thereby increasing the measuring range of the autocollimator. By controlling the side connecting angle of the corner mirror, the measurement range of the photoelectric autocollimator can be easily increased by giving the value of the inclination angle. The problem that the measuring range of the autocollimator can only be increased by increasing the aperture of the objective lens is solved. The method can effectively and obviously increase the measurement range under the condition of not increasing the caliber of the collimator objective. The novel photoelectric collimator based on the method can be widely applied to the fields of large-scale buildings, warships, wings and the like which require a large measurement range.
Drawings
FIG. 1 is a block diagram of a corner mirror of an optoelectronic autocollimator according to the preferred embodiment of the invention.
Fig. 2 shows the equivalent aperture of the corner mirror of the present invention.
Fig. 3 shows the imaging of the light beam on the photoelectric sensor after the corner mirror of the present invention replaces the plane 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 method of increasing the measurement range of an autocollimator, comprising the steps of:
firstly, a corner mirror with an improved geometric structure is used as a reflector of the photoelectric autocollimator. As shown in FIG. 1, the corner mirror includes three sides a 1, b 2, c 3, and oneMirror aperture plane 4. The angles of the three sides a 1, b 2, c 3 of the corner mirror satisfy the following relationship: the angle 1_2 is equal to 90 DEG-12,∠2_3=90°-23,∠1_3=90°-13Wherein122313The effective structural angles between the sides a (1) and b (2), b (2) and c (3), and a (1) and c (3) are respectively shown; the mirror aperture plane 4 of the corner mirror is perpendicular to the OZ axis of the collimator when the autocollimator is in the initial state. As shown in fig. 2, the equivalent aperture 5 of the corner mirror is a hexagonal star, and includes an entrance pupil 6 and an exit pupil 7. The equivalent caliber 5 consists of six parts 8, 9, 10, 11, 12 and 13 which have the same shape and the same area;
analyzing the internal structure of the corner mirror and the reflection of light, and dividing the reflected light beam into six beams of light according to the different reflection sequences of the collimated light beam along the three side surfaces a (1), b (2) and c (3) of the corner mirror;
step three, researching the relation between the reflection sequence and the measurement parameter to obtain the coordinate matrix M of the corner mirror corresponding to the reflection beamrAn angular sensitivity K and a reflected light vector B reflected from the corner mirror back to the collimator;
analyzing the imaging condition of the six beams of reflected light on the surface of the photoelectric sensor of the autocollimator to obtain the relation xi between the light spot displacement and the deflection angle of the corner mirrorx≈-△·Θ1·f、ξy≈-△·Θ2F, where Θ1For corner mirrors OX1Angular deflection of the shaft, Θ2As a corner mirror OY1The angular deflection of the axis, f being the focal length of the objective lens of the photoelectric collimator,
Figure GDA0001995192290000071
a slight angle;
fifthly, the measurement range of the photoelectric autocollimator can be easily increased by controlling the side connecting angle of the corner mirror according to the given value.
Six parts of the equivalent aperture receive a part of collimated light beam, and each part of the received collimated light beam is reflected three times along three sides a 1, b 2 and c 3 of the corner mirror according to a fixed reflection sequence and then reflected back to the photoelectric autocollimator in parallel with the optical axis to form an optical loop. The relationship between the fixed reflection sequence of the light beam along the inside of the corner mirror and the effective sector is as follows: a-b-c → 8-11; c-b-a → 11-8; b-a-c → 9-12; c-a-b → 12-9; b-c-a → 10-13; a-c-b → 13-10. The six reflected light sources can be divided into pairs according to the reflection sequence marks of the reflecting surfaces, for example, the six reflected light sources can be divided into a pair of light beams with opposite reflection sequences according to the reflection sequence of a-b-c and c-b-a.
When the reflection sequence of a pair of reflected light beams is b-a-c, c-a-b, the displacement of the two collimated reflected light beams on the photoelectric sensor along the axis OX of the autocollimator and the axis OY is only equal to that of the corner mirror along the axis OX1、OY1The rotation quantity of the shaft is correlated to obtain a reflected light vector
Figure GDA0001995192290000081
A collimated incident beam parallel to the corner mirror; the invariant axis U and the corner mirror OX of one of the three pairs of beams1、OY1Perpendicular, i.e. satisfying the following relationship:
Figure GDA0001995192290000082
the following angular relationships are satisfied by the three reflecting surfaces a (1), b (2), c (3) of the corner mirror according to equation (1):
sin(23)·cos(12)·cos(13)+sin(13)=0 (2)
sin(23)·cos(12)·cos(13)-sin(13)+2sin(12)·cos(13)=0(3)
the action angles among the three reflecting surfaces a (1), b (2) and c (3) of the corner mirror can be obtained by solving the formula122313Comprises the following steps:
13=arctan(sin(12)) (4)
sin(23)=-tan(12) (5)
23=arcsin(-tan(12)) (6)
the invariant axis U of the beam pair a-b-c, c-b-a is on the coordinate axis OZ of the corner mirror1The on-axis components are:
Figure GDA0001995192290000083
determining the effective structure angle of the three sides a (1), b (2), c (3) of the corner mirror122313And the constant axis of said light beam a-b-c, c-b-a
Figure GDA0001995192290000084
On the coordinate axis OZ of the corner mirror1Component of the axis:
Figure GDA0001995192290000091
wherein the beam is a small angle and the reflection order is b-a-c
Figure GDA0001995192290000092
Expressed as:
Figure GDA0001995192290000093
when the error is less than or equal to 5 degrees, the error of the operation is less than 0.5 percent.
Beam invariant axis with reflection order b-a-c
Figure GDA0001995192290000094
Is determined by the parameters of three side surfaces a (1), b (2) and c (3) of the corner mirror, and the coordinate matrix of the corner mirror of the light beams b-a-c is as follows according to the sequence of the light beams passing through the reflecting surface:
Figure GDA0001995192290000095
according to the above formula, the light beams reflected in the order of b-a-c are reflected, the coordinate matrix of the corner mirror satisfies the sensing relationship of the euler's rotation equation for the rotation angles of the OX and OY axes, and the angular sensitivity of the corner mirror is obtained as follows:
Figure GDA0001995192290000096
the vector of the reflected light of the light beams b-a-c reflected from the corner mirror to the collimator is as follows:
Figure GDA0001995192290000097
according to the above formula, the displacement information of the reflected light along the OX and OY axes on the two-dimensional surface of the photosensor of the autocollimator corresponds to only the OX corresponding to the corner mirror1、OY1The rotation of the shaft is relevant.
The reflected light vector parameter Delta of the light beams reflected along the b-a-c sequence and the corresponding other light beams reflected along the c-a-b sequence is negative, and the other parameters are the same.
The imaging condition of the six beams of reflected light with different reflection sequences on the surface of the photoelectric sensor of the photoelectric collimator is as follows: the light beams with the reflection sequence of b-a-c and c-a-b are imaged on the surface of the photoelectric sensor as light spots (14) and (15), the light spots (16) and (17) are imaged by the light beams with the reflection sequence of a-b-c and c-b-a, the light spots (18) and (19) are imaged by the light beams with the reflection sequence of b-c-a and a-c-b, the light spots (14) and (15), the light spots (16) and (17), and the light spots (18) and (19) are imaging conditions of the light beams when the corner mirror is not deflected, spots (14') and (15'), spots (16') and (17'), spots (18') and (19') representing the imaging of the beam when the corner mirrors are deflected, the displacement of the light spots (14) and (15) and the deflection angle of the corner mirror are in the following relation:
ξx≈-△·Θ1·f (13)
ξy≈-△·Θ2·f (14)
wherein Θ is1For corner mirrors OX1Angular deflection of the shaft, Θ2As a corner mirror OY1Of shaftsThe angular deflection, f, is the focal length of the objective lens of the photoelectric collimator.
For the current general two-dimensional photoelectric autocollimator, the angular sensitivity is 2, the whole precision is less than or equal to 0.3 ", the measuring range is about 700", the resolution is 0.01 ", the focal length is 860mm, the aperture of the objective lens is 60mm, the photoelectric sensor adopts a high-resolution area array CCD and an electronic eyepiece, the measurement control is triggered by notebook software, a corner mirror is fixed with a measuring object, the diameter of the corner mirror is 62mm, and the measuring object is formed by glass K8(n-1.5163).
In this example, the angle sensitivity of the angle mirror can be determined by adjusting the effective structural angles of the three side surfaces a 1, b 2, c 3 of the angle mirror according to the invention to 91 ° 39' ═ 1_2 and 89 ° 20'46 ', respectively, to 1 ° 39 ″
Figure GDA0001995192290000101
Angular sensitivity K compared to current two-dimensional photoelectric collimator0The reduction of 2 is 20 times, i.e. the measurement range of the photoelectric collimator is also increased by at least 20 times.
Finally, the method for increasing the measurement range of the autocollimator can effectively increase the measurement range by 20 times while ensuring the working distance.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. 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 (7)

1. A method of increasing the measurement range of an autocollimator, comprising the steps of:
1) designing a corner mirror with an improved geometrical structure as a reflector of the photoelectric autocollimator, wherein the improved geometrical structure of the corner mirror is characterized by angle improvement of three sides of the corner mirror, the corner mirror comprises three sides a (1), b (2) and c (3) and a reflector aperture surface (4), and the angles of the three sides of the corner mirror of the improved geometrical structure satisfy the following relation: angle 1_2 is 90°-12,∠2_3=90°-23,∠1_3=90°-13Wherein122313Respectively representing effective structural angles between side surfaces a (1) and b (2), b (2) and c (3), and a (1) and c (3), wherein when the autocollimator is kept in an initial state, a reflector aperture surface (4) of the corner mirror is perpendicular to an OZ axis of the autocollimator, and an equivalent aperture (5) of the corner mirror is a hexagram and comprises an entrance pupil (6) and an exit pupil (7);
2) analyzing the internal structure of the corner mirror and the reflection of light, and dividing the reflected light beam into six beams of light according to the different reflection sequence of the collimated light beam along the three sides a (1), b (2) and c (3) of the corner mirror;
3) researching the relation between the reflection sequence and the measurement parameters to obtain the coordinate matrix M of the corner mirror corresponding to the reflection beamrAn angular sensitivity K and a reflected light vector B reflected from the corner mirror back to the collimator;
4) analyzing the imaging condition of the six beams of reflected light on the surface of the photoelectric sensor of the autocollimator to obtain the relation xi between the light spot displacement and the deflection angle of the corner mirrorx≈-△·Θ1·f、ξy≈-△·Θ2F, where Θ1For corner mirrors OX1Angular deflection of the shaft, Θ2As a corner mirror OY1The angular deflection of the axis, f being the focal length of the objective lens of the photoelectric collimator,
Figure FDA0002691929320000011
a slight angle;
5) and the measurement range of the photoelectric autocollimator is increased by the given value through controlling the side connecting angle of the corner mirror.
2. A method for increasing the measurement range of an autocollimator according to claim 1, characterized in that the equivalent aperture (5) consists of six sectors of the same shape and equal area, a first sector (8), a second sector (9), a third sector (10), a fourth sector (11), a fifth sector (12) and a sixth sector (13).
3. A method for increasing the measurement range of an autocollimator according to claim 2, wherein six parts of the equivalent aperture will receive a portion of the collimated light beam, and each portion of the collimated light beam will be reflected three times along the three surfaces a (1), b (2) and c (3) of the corner mirror in a fixed reflection sequence, and then reflected back to the photoelectric autocollimator parallel to the optical axis and forming an optical circuit.
4. A method of increasing the measurement range of an autocollimator according to claim 3, wherein the fixed reflection sequence of the beam along the inside of the corner mirror is related to the effective fan by: a-b-c → the first sector (8) -the fourth sector (11); c-b-a → fourth sector (11) -the first sector (8); b-a-c → the second sector (9) -the fifth sector (12); c-a-b → the fifth sector (12) -the second sector (9); b-c-a → the third sector (10) -the sixth sector (13); a-c-b → the sixth sector (13) -the third sector (10); the six reflected light sources can be divided into pairs according to the reflection sequence marks of the reflecting surfaces.
5. The method of claim 4, wherein when the reflected light beams of a pair are reflected in the order b-a-c, c-a-b, the displacement of the two collimated reflected light beams on the photosensor along the axis OX and OY of the autocollimator is only combined with the displacement of the corner mirror along the axis OX1、OY1The rotation quantity of the shaft is correlated to obtain a reflected light vector
Figure FDA0002691929320000021
A collimated incident beam parallel to the corner mirror; the invariant axis U and the corner mirror OX of one of the three pairs of beams1、OY1The axes are vertical, that is, the following relationship is satisfied:
Figure FDA0002691929320000022
the following angular relationships are satisfied by the three reflecting surfaces a (1), b (2), c (3) of the corner mirror according to equation (1):
sin(23)·cos(12)·cos(13)+sin(13)=0 (2)
sin(23)·cos(12)·cos(13)-sin(13)+2sin(12)·cos(13)=0 (3)
the effective structure angle between the three reflecting surfaces a (1), b (2) and c (3) of the corner mirror can be obtained by solving the above formula122313Comprises the following steps:
13=arctan(sin(12)) (4)
sin(23)=-tan(12) (5)
23=arcsin(-tan(12)) (6)
invariant axes of the beam pairs a-b-c, c-b-a
Figure FDA0002691929320000023
On the coordinate axis OZ of the corner mirror1The on-axis components are:
Figure FDA0002691929320000031
determining the effective structure angle of the three sides a (1), b (2), c (3) of the corner mirror122313And the constant axis of said light beam a-b-c, c-b-a
Figure FDA0002691929320000032
On the coordinate axis OZ of the corner mirror1Component of the axis:
Figure FDA0002691929320000033
wherein the beam is a small angle and the reflection order is b-a-c
Figure FDA0002691929320000034
Expressed as:
Figure FDA0002691929320000035
beam invariant axis with reflection order b-a-c
Figure FDA0002691929320000036
Is determined by the parameters of three side surfaces a (1), b (2) and c (3) of the corner mirror, and the coordinate matrix of the corner mirror of the light beams b-a-c is as follows according to the sequence of the light beams passing through the reflecting surface:
Figure FDA0002691929320000037
according to the above formula, the light beams reflected in the order of b-a-c are reflected, the coordinate matrix of the corner mirror satisfies the sensing relationship of the euler's rotation equation for the rotation angles of the OX and OY axes, and the angular sensitivity of the corner mirror is obtained as follows:
Figure FDA0002691929320000038
the vector of the reflected light of the light beams b-a-c reflected from the corner mirror to the collimator is as follows:
Figure FDA0002691929320000041
according to the above formula, the displacement information of the reflected light along the OX and OY axes on the two-dimensional surface of the photosensor of the autocollimator corresponds to only the OX corresponding to the corner mirror1、OY1The rotation condition of the shaft is related;
the reflected light vector parameter Delta of the light beams reflected along the b-a-c sequence and the corresponding other light beams reflected along the c-a-b sequence is negative, and the other parameters are the same.
6. The method for increasing the measurement range of the autocollimator according to claim 5, wherein the six reflected lights with different reflection sequences are imaged on the surface of the photoelectric sensor of the autocollimator as follows: the light beams with the reflection sequence of b-a-c and c-a-b are imaged on the surface of the photoelectric sensor as a first light spot (14) and a second light spot (15), a third light spot (16) and a fourth light spot (17) are imaged by the light beams with the reflection sequence of a-b-c and c-b-a, a fifth light spot (18) and a sixth light spot (19) are imaged by the light beams with the reflection sequence of b-c-a and a-c-b, the first light spot (14) and the second light spot (15), the third light spot (16) and the fourth light spot (17), the fifth light spot (18) and the sixth light spot (19) are imaged by the light beams when the corner mirror is not deflected, the seventh light spot (14') and the eighth light spot (15'), the ninth light spot (16') and the tenth light spot (17'), and the eleventh light spot (18') and the twelfth light spot (19') represent imaged by the light beams when the corner mirror is deflected The relationship between the displacement amount of the first light spot (14) and the second light spot (15) and the deflection angle of the corner mirror is as follows:
ξx≈-△·Θ1·f (13)
ξy≈-△·Θ2·f (14)
wherein Θ is1For corner mirrors OX1Angular deflection of the shaft, Θ2As a corner mirror OY1The angular deflection of the axis, f, is the focal length of the objective lens of the photoelectric collimator.
7. A method of increasing the measuring range of an autocollimator according to claim 6, characterized by the effective constructional angle of the three sides a (1), b (2), c (3) of the corner mirror122313Control is made according to the angular sensitivity of the corner mirror
Figure FDA0002691929320000042
The measurement range of the photoelectric autocollimator can be increased by setting the value as required.
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