Method for simultaneously measuring multi DOF GEs by laser and system therefor

1 . A system for simultaneously measuring multiple DOF GEs by a laser, wherein the system comprises a measuring unit and a target mirror unit; the measuring unit comprising a means for emitting a laser, a polarizing beam splitter, a fixed reflector, a first λ/4 wave plate, a second λ/4 wave plate, a first polarizer, a first photodetector, a means for measuring an interference length, and a means for measuring a two-dimensional angle; the target mirror unit comprises a beam splitter and a reflector;

the means for emitting the laser is used to generate an emitting light L 1 ;

the polarizing beam splitter is used for 1) “beam splitting” which comprises splitting the emitting light L 1 into a measuring light L 11 and a reference light L 12 ; the measuring light L 11 is incident on the target mirror unit, is transmitted by the beam splitter of the target mirror unit, and is reflected back by the reflector as a light L 111 ; the light L 111 carries a 3DOF LGE signal back to the measuring unit as a linear GE measuring light; the reference light L 12 only propagates inside the measurement unit; 2) “beam combining” which comprises transmitting or reflecting the reference light L 12 that passes by the polarizing beam splitter again and the measuring light L 111 that is reflected back 180° toward its original direction by the target mirror unit according to its polarizing status, so that above two beams are superposed in a spatial position, so as to form a combined light L 3 ; and 3) “beam separating” which separates the light L 112 reflected by the beam splitter in the target mirror unit from the measuring light L 11 as a two-dimensional angle measuring light, and the light L 112 is transmitted or reflected by the polarizing beam splitter according to its polarizing state;

the fixed reflector is used for reflecting backward the reference light L 12 propagating only within the measuring unit to return the reference light L 12 to the polarizing beam splitter;

the first λ/4 wave plate is used to change a polarizing direction of the reference light L 12 , so that when the reference light L 12 passes by the polarizing beam splitter again, its transmitting or reflecting status is switched, that is, the reference light L 12 is reflected at the first pass, but is transmitted at the second pass; or is transmitted at the first pass, but is reflected at the second pass; the second λ/4 wave plate is used to change polarizing directions of the LGE measuring light L 111 and a two-dimensional angle measuring light L 112 , so that when the LGE measuring light L 111 and the two-dimensional angle measuring light L 112 pass by the polarizing beam splitter again, their transmitting status or reflecting status is switched;

the first polarizer is arranged between the polarizing beam splitter and the first photodetector; as a light transmitting axial direction of the first polarizer is adjusted, the combined light L 3 interferes after passing through the first polarizer;

the first photodetector is used to receive a superimposed light beam L 3 including the reference light L 12 and the measuring light L 111 , so as to simultaneously measure LGEs along X, Y and Z axes; specifically: 1) according to a spot offset of the LGE measuring light L 111 on the first photodetector, calculating a relative straightness error between the target mirror unit and the measuring unit along Y axis or Z axis; and 2) cooperating with the means for measuring the interference length to measure a relative position error between the target mirror unit and the measuring unit along X-axis;

the means for measuring the two-dimensional angle includes a focusing lens or lens group, and a second photodetector; the focusing lens or lens group is used to focus the two-dimensional angle measuring light L 112 on the second photodetector; and the two-dimensional relative angle error between the target mirror unit and the measuring unit resulted from rotating about Y-axis and Z-axis is calculated according to a spot offset on the second photodetector;

the beam splitter in the target mirror unit is used to split the measuring light L 11 , in which a transmitted light L 111 is reflected back by the reflector in the target mirror unit and returns to the measuring unit with straightness and positioning error information; while a reflected light L 112 carries the two-dimensional angle information back to the measuring unit; and

the reflector in the target mirror unit is used to reflect the measuring light L 111 back 180° toward its original direction and return the measuring light L 111 to the polarizing beam splitter, so as to result in: 1) changing a spatial position of the measuring light L 111 along Y-axis and/or Z-axis, its spatial offset is twice the relative displacement between the reflector in the target mirror unit and the measuring unit along Y axis and/or Z-axis; and 2) changing an optical path and frequency of the measuring light L 111 , and a drift of the optical path and frequency is directly proportional to a relative displacement between the reflector in the target mirror unit and the measuring unit along X-axis.

2 . The system according to claim 1 , wherein the means for emitting the laser emits a single frequency laser, and the means for measuring the interference length includes a first non-polarizer beam splitter, a phase retarder, and a third photodetector;

the first non-polarizer beam splitter is arranged between the first polarizer and the first photodetector, and is used to split the interference light, in which one beam is received by the first photodetector, while the other beam is received by the third photodetector; light intensities of interference spots on the first photodetector and the third photodetector are I 1 , I 3 , respectively; and

the phase retarder is arranged in front of the first photodetector or the third photodetector, so as to make a phase difference 90° between the interference spot signals I 1 , I 3 detected by the two photodetectors; a phase difference φ(Δx) between the reference light L 12 and the measuring light L 111 is calculated; and a relative displacement Δx between the target mirror unit and the measuring unit along X-axis is calculated according to the phase difference.

3 . The system according to claim 1 , wherein the means for emitting the laser generates a dual frequency laser; the means for measuring the interference length comprises a third non-polarizing beam splitter, a second polarizer, and a fourth photodetector;

the dual frequency laser is a polarized light with two beams; the two beams are spatially superposed, with a certain frequency difference, and with different polarizing directions;

the third non-polarizing beam splitter is disposed between the means for emitting the laser and the polarizing beam splitter, and the means for emitting the laser emitting light L 1 is split by the third non-polarizing beam splitter, to form another laser beam L 2 ;

the second polarizer is arranged between the third non-polarizer beam splitter and the fourth photodetector; by adjusting a light transmitting axial direction of the second polarizer, the laser light L 2 interferes after passing through the second polarizer; and an interference spot is received by the fourth photodetector as a reference signal/standard signal for heterodyne interference length measurement; and

the combined light L 3 interferes after passing through the first polarizer; and the interference spot is received by the first photodetector as a measuring signal of the heterodyne interference length measurement; according to the reference signal/standard signal and the measuring signal, a relative displacement between the target mirror unit and the measuring unit along X-axis is calculated.

4 . The system according to claim 1 , wherein the means for emitting the laser comprises a multi wavelength laser light source and a means for generating a heterodyne frequency, the means for measuring the interference length comprises a 1st band-pass filter to an Nth band-pass filter and a 1st phase detector to an Nth phase detector, where Nis a natural number greater than or equal to 3; and the polarization beam splitter is replaced with a second non-polarizing beam splitter;

the multi wavelength laser light source emits multi wavelength laser lights λ 1 , λ 2 , λ 3 , . . . , λ N ; their frequencies are v 1 , v 2 , v3, . . . , v N ; after passing through the means for generating the heterodyne frequency, frequencies of the multi wavelength laser become v 1 +f 1 , v 2 +f 2 , v 3 +f 3 , . . . , v N +f N , wherein the multi wavelength laser light is the emitting light L 1 ; the second non-polarizing beam splitter is used for 1) “beam splitting” which comprises splitting the emitting light L 1 into a measuring light L 11 and a reference light L 12 , the measuring light L 11 is incident on the target mirror unit and is reflected back by the target mirror unit as a light L 111 ; the L 111 carries a 3DOF LGE signal to return to the measuring unit as a measuring light, and the reference light L 12 only propagates within the measurement unit; 2) “beam combining” which comprises transmitting or reflecting the reference light L 12 that passes by the non-polarizing beam splitter again and the measuring light L 111 reflected by the target mirror unit, so that above two beams are superposed in a spatial position, so as to form a combined beam L 3 ; and 3 ) “beam separating” which separates a light L 112 reflected by the beam splitter in the target mirror unit from the measuring light L 11 as a two-dimensional angle measuring light;

the combined light L 3 interferes on the first photodetector, and an obtained heterodyne interference signal spectrum only contains components f 1 , f 2 , f 3 , . . . , f N ; and

after the 1st band-pass filter to the Nth bandpass filter separate the components f 1 , f 2 , f 3 , . . . , f N , the 1st phase detector to the Nth phase detector measure ranging phase information φ 1 , φ 2 , φ 3 , . . . , φ N corresponding to each wavelength; taking n pairs of components to form a series of beat signals, in which 2≤n≤N−1, n is a natural number; and a relative displacement Δx between the target mirror unit and the measuring unit along X-axis is calculated according to n pairs of wavelengths and n pairs of phase differences.

5 . The system according to claim 1 , wherein the means for emitting the laser emits a single frequency laser, and a second non-polarizing beam splitter is used to replace the polarizing beam splitter, and the means for measuring the interference length includes a first non-polarizing beam splitter, a phase retarder, and a third photodetector;

the second non-polarizing beam splitter is used for 1) “beam splitting” which comprises splitting an emitting light L 1 into a measuring light L 11 and a reference light L 12 , the measuring light L 11 is incident on the target mirror unit and is reflected back by the target mirror unit as a measuring light L 111 which carries a 3DOF LGE signal to return to the measuring unit as a measuring light, and the reference light L 12 only propagates within the measuring unit; 2) “beam combining” which comprises transmitting or reflecting the reference light L 12 that passes by the non-polarizing beam splitter again and the light L 111 reflected by the target mirror unit, so that above two beams are superposed in a spatial position, so as to form a combined light L 3 ; the combined light L 3 is a superimposed beam of the reference light L 12 transmitted by the non-polarizing beam splitter and the measuring light L 111 reflected by the non-polarizing beam splitter, or a superimposed beam of the reference light L 12 reflected by the non-polarizing beam splitter and the measuring light L 111 transmitted by the non-polarizing beam splitter; and 3) “beam separating” which separates a light L 112 reflected by the beam splitter in the target mirror unit from the measuring light L 11 as a two-dimensional angle measuring light;

the first non-polarizer beam splitter is arranged between the first polarizer and the first photodetector, and is used to split the combined beam L 3 that has been interfered, in which one beam L 31 is received by the first photodetector, while the other beam L 32 is received by the third photodetector; light intensities of interference spots on the first photodetector and the third photodetector are I 1 , I 3 , respectively; and

the phase retarder is arranged in front of the first photodetector or the third photodetector, so as to make a phase difference 90° between interference spot signals I 1 , I 3 detected by the two photodetectors; a phase difference q (Δx) between the reference light L 12 and the measuring light L 111 is calculated; and a relative displacement Δx between the target mirror unit and the measuring unit along X-axis is calculated according to the phase difference.

6 . The system according to claim 1 , in which a rolling angle measuring is added so as to simultaneously measure 6DOF GEs, wherein

adding a third λ/4 wave plate at the target mirror unit end, so that the measuring light L 111 passes by the third λ/4 wave plate to return to the measuring unit, passing through the second λ/4 wave plate, and passing by the polarizing beam splitter again, then the measuring light L 111 is divided, in which one beam L 111 ′ is received by the first photodetector, while the other beam L 111 ″ is received by the fifth photodetector; and

when measuring, the third λ/4 wave plate makes a relative angle offset y and a polarizing direction rotated angle γ′ of the measuring light L 111 as the target mirror unit and the measuring unit rotates about X-axis; light intensities received by the first photodetector and the fifth photodetector varies with the angle γ′; according to the measured light intensity changes of the first photodetector and the fifth photodetector, a relationship between the light intensity changes and said angle γ′, and said angle γ′ which is directly proportional to the angle γ, a relative angle change, i.e., a rolling angle γ, between the target mirror unit and the measuring unit about X-axis is obtained.

7 . The system according to claim 1 , wherein the fixed reflector is selected from a group comprising of a corner cube prism, a cat's eye mirror, a corner cube retroreflector composed of three mutually perpendicular reflecting surfaces, a right angle prism, and a retroreflector composed of two plane mirrors; and the target mirror unit reflector is selected from a group comprising of a corner cube prism, a cat's eye mirror, and an angular cube retroreflector composed of three mutually perpendicular reflecting surfaces.

8 . The system according to claim 1 , wherein the first photodetector, the second photodetector, a third photodetector and a fifth photodetector are any one of QD, PSD, CCD and CMOS; and according to a spot offset on any one of the first photodetector, the third photodetector and the fifth photodetector, a relative straightness error between the target mirror unit and the measuring unit along Y-axis or Z-axis is calculated; and a fourth photodetector is any one of QD, PSD, CCD, CMOS and Pin Detector.

9 . A method for simultaneously measuring 5DOF GEs by a laser, wherein the method is applied to the system according to claim 1 , and the method comprises the following steps:

1) measuring a straightness error along Y-axis or Z-axis based on laser collimation principle or called laser autocollimation

1.1) when an emitting light L 1 emitted by a means for emitting a laser passes by a polarizing beam splitter, it is divided into a measuring light L 11 and a reference light or a standard light L 12 ;

1.2) after the measuring light L 11 is emitted from the measuring unit, the measuring light L 11 enters the target mirror unit, and is divided by a beam splitter of the target mirror unit, in which a transmitted light L 111 is reflected back 180° toward its original direction by a reflector of the target mirror unit, a spatial position of the light L 111 is changing being changed with a relative straightness error between the target mirror unit and the measuring unit along Y-axis or Z-axis; the light L 111 carries two-dimensional straightness error information back to the measurement unit; and the light L 111 passes by the polarizing beam splitter again;

1.3) after the reference light L 12 is reflected back 180° toward its original direction by the fixed reflector, it passes by the polarizing beam splitter again, and is combined with the light L 111 passing by the polarizing beam splitter again in Step 1.2), so as to form a combined light L 3 which is received by the first photodetector;

1.4) recording an initial position of a spot of the combined light measured by the first photodetector; and

1.5) according to a real-time position of the spot of the combined light on the first photodetector, comparing the real-time position with the initial position of the spot of the combined light, to obtain an offset of the spot of the combined light; since the offset of the spot of the combined light is only resulted from a position drift of the measuring light L 111 , a relative straightness error between the target mirror unit and the measuring unit along Y-axis or Z-axis is calculated according to the position offset of the spot of the combined light;

2) measuring a position error along X-axis based on laser interference

2.1) after the reference light L 12 in Step 1.1) is reflected back 180° toward its original direction by the fixed reflector of the measuring unit, its polarizing state, frequency and phase are kept as what they are, so the light L 12 is used as a reference light of the interference length measuring signal;

2.2) frequency and phase of the light L 111 in Step 1.2) keep changing with a relative displacement between the target mirror unit and the measuring unit along X-axis, so the light L 111 carries straightness error information along X-axis to return to the measuring unit as a measuring light of a heterodyne interference length measuring signal; and

2.3) after the reference light L 12 in Step 2.1) and the measuring light L 111 in Step 2.2) pass through the polarizing beam splitter, above two beams are superposed in a space; after passing through the means for measuring the interference length, a relative displacement between the target mirror unit and the measuring unit along X-axis is calculated by referring to a signal measured on the first photodetector; and

3) measuring an angle error resulted from rotating around Y-axis or Z-axis based on laser collimation

3.1) the reflected light of the beam splitter of the target mirror unit in Step 1.2) is as a two-dimensional angle measuring light L 112 ;

3.2) the light L 112 carries the two-dimensional angle error information back to the measuring unit, and passes by the second λ/4 wave plate and the polarizing beam splitter, and focuses on a second photodetector by a focusing lens or lens group;

3.3) recording an initial position of a light spot measured by the second photodetector; and

3.4) according to a real-time position of the light spot on the second photodetector, comparing the same with its initial position of the light spot, so as to obtain a spot offset, and a two-dimensional relative angle error between the target mirror unit and the measuring unit resulted from rotating around Y-axis or Z-axis is calculated according to the spot offset.

10 . The method according to claim 9 , wherein calculating a straightness error along Y-axis or Z-axis according to a position offset of a spot of a combined light is as follows:

the initial position and the real-time position of the spot on the first photodetector are (y1 0 , z1 0 ), (y1 t , z1 t ), respectively, then relative straightness errors between the target mirror unit and the measuring unit along Y-axis and Z-axis are Δy=2(y1 t −y1 0 ), Δz=2(z1 t −z1 0 ), respectively.

11 . The method according to claim 9 , wherein when a single frequency length measurement is applied, the position error along X-axis based on laser interferometry comprises the following steps:

1) the reference light L 12 and the measuring light L 111 are superposed in a spatial position after passing by the polarizing beam splitter or a second non-polarizing beam splitter, and are denoted as a combined light L 3 ; as a light transmitting axial direction of a first polarizer is adjusted, the combined light L 3 interferes after passing through the first polarizer;

2) the interference light L 3 is divided into a light L 31 and a light L 32 after passing by a first non-polarizing beam splitter;

3) one of the light L 31 and the light L 32 is delayed 90° by a phase retarder, then they are received by the first photodetector and a third photodetector, respectively, light intensities of interference spots thereon are I 1 , I 3 , respectively; and

4) processing the I 1 , I 3 , so as to obtain a phase difference φ(Δx) between the reference light L 12 and the measuring light L 111 , and a number N(Δx) of light and dark changes of interference fringes caused by φ(Δx); a laser emitting laser wavelength is λ, so a relative displacement between the target mirror unit and the measuring unit along X-axis is Δx=N(Δx)·λ/2.

12 . The method according to claim 9 , wherein when a double frequency length measurement is performed, determining a position error along X-axis measured by laser interferometry comprises:

1) the emitting light L 1 emitted from the means for emitting the laser contains two polarized lights with a certain frequency difference, the two polarized lights have frequencies f 1 , f 2 , respectively; when the emitting light L 1 is split by the polarization beam splitter, a frequency of the measuring light L 11 is f 1 , while a frequency of the reference light L 12 is f 2 ;

2) a relative displacement Δx of the measuring light L 111 along X-axis between the target mirror unit and the measuring unit is measured; a frequency variation due to Doppler effect is f(Δx); and a frequency of the measuring light L 111 is f 1 +f(Δx);

3) setting a first polarizer in front of the first photodetector; by adjusting a light transmitting axial direction of the first polarizer, the linearly polarized light L 12 and the light L 111 interfere after passing by the first polarizer; an interference spot is received by the first photodetector as a measuring signal of a heterodyne interference length measurement, and a frequency of a measured beat signal is f m =f 1 +f(Δx)−f 2 ;

4) when the emitting light L 1 passes by a third non-polarizing beam splitter, it is split by the third non-polarizing beam splitter to form another laser beam L 2 ; as a light transmitting axial direction of a second polarizer is adjusted, the light L 2 interferes after passing through the second polarizer; an interference spot is received by the fourth photodetector as a standard signal for the heterodyne interference length measurement, and a frequency of the standard signal is f s =f 1 −f 2 ; and

5) the frequency of the measured beat signal obtained in Step 3), f m =f 1 +f(Δx)−f 2 , subtracts the standard beat signal frequency obtained in Step 4), f s =f 1 −f 2 , so as to obtain f(Δx)=f m −f s ; a number of light and dark changes of interference fringes caused by f(Δx) is N(Δx), and a laser emitting laser wavelength is λ, so that a relative displacement between the target mirror unit and the measuring unit along X-axis is Δx=N (Δx)·λ/2.

13 . The method according to claim 9 , wherein when measuring a length of multiple wavelengths, determining a position error along X-axis based on laser interferometry comprises the following steps:

1) the multi wavelength laser light source emits multi wavelength laser lights λ 1 , λ 2 , λ 3 , . . . , λ N ; their frequencies are v 1 , v 2 , v 3 , . . . , v N ; after passing through the means for measuring the heterodyne frequency, the frequencies of the multi wavelength laser become v 1 +f 1 , v 2 +f 2 , v 3 +f 3 , . . . , v N +f N , the multi wavelength laser light is the emitting light L 1 ;

2) the emitting light L 1 is split into a measuring light L 11 and a reference light L 12 by a second non-polarizing beam splitter, and the measuring light L 11 and the reference light L 12 both contain multi wavelength laser light v 1 +f 1 , v 2 +f 2 , v 3 +f 3 , . . . , v N +f N ;

3) the measuring light L 11 is emitted from the measuring unit and enters the target mirror unit, and is reflected back 180° toward its original direction by the reflector of the target mirror unit; a retroreflected light is a light L 111 which carries straightness error information along X-axis and returns to the measuring unit as a measuring light of the heterodyne interference length measuring signal;

4) after the reference light L 12 is reflected back 180° toward its original direction by the fixed reflector of the measuring unit, it passes by the non-polarizing beam splitter, and then combines with the light L 111 ; by adjusting a light transmitting axial direction of a first polarizer, the reference light L 12 and the measuring light L 111 interfere with each other on the first photodetector; and

5) the first photodetector detects components, such as f 1 , f 2 , f 3 , . . . , f N , of the heterodyne interference signal spectrum; the 1st band-pass filter to the Nth band-pass filter separate the components such as f 1 , f 2 , f 3 , . . . , f N ; the 1st phase detector to the Nth phase detector measure ranging phase information φ 1 , φ 2 , φ 3 , . . . , φ N corresponding to each wavelength; taking n pairs thereof to form a series of beat signals, a relative displacement Δx between the target mirror unit and the measuring unit along X-axis is calculated according to n pairs of combined wavelengths and of n pairs phase differences.

14 . The method according to claim 9 , wherein calculating a two-dimensional angle error resulted from rotating about Y-axis or Z-axis according to a spot offset is as follows:

an initial position and a real-time position of the light L 112 's spot on the second photodetector are (γ 0 , z 0 ), (y t , z t ), respectively, relative angle errors between the target mirror unit and the measuring unit resulted from rotating around Y-axis and Z-axis are Δα=(y t −y 0 )/2f, Δβ=(z t −z 0 )/2f, respectively, where f is a focal length of a focusing lens or lens group.

15 . The method according to claim 9 , wherein for measuring a rolling angle with a single frequency length measurement, a third λ/4 wave plate is added in the target mirror unit to measure an angular error resulted from rotating around X-axis, i.e., to measure 6DOF GEs, said method comprises the following steps:

1) adding a third λ/4 wave plate in the target mirror unit, the measuring light L 111 passes by the third λ/4 wave plate to return to the measuring unit, then passing through the second λ/4 wave plate, the measuring light L 111 is split again when passing through the polarizing beam splitter, in which one beam L 111 ′ is received by the first photodetector and a third photodetector, while the other beam L 111 ″ is received by the fifth photodetector;

2) blocking the measuring light L 111 , so that only the reference light L 12 is received on the first photodetector and the third photodetector, and recording light intensities I 10 , I 30 of the first photodetector and the third photodetector, respectively;

3) recovering the measuring light L 111 ; with the third λ/4 wave plate, making a variation γ of a relative angle between the target mirror unit and the measuring unit around X-axis; when the measuring light passes by the polarizing beam splitter again, its polarizing direction increases γ′ with respect to its original polarizing direction, γ′ is in a direct proportion to γ; γ′=k 1 γ; when the measuring light passes by the second λ/4 wave plate in the target mirror unit for the first time, k 1 =1; when the measuring light passes by the second λ/4 wave plate in the target mirror unit for the second time, k 1 =2;

4) the measuring light L 111 passes by the polarizing beam splitter and is split by the polarizing beam splitter, in which one beam is received by the first photodetector and the third photodetector, light intensities thereon are I 1 (γ), I 3 (γ), while the other beam is received by the fifth photodetector with a light intensity thereon I 5 (γ), there is formed a function f(γ)=[I 1 (γ)−I 10 +I 3 (γ)−I 30 −I 5 (γ)]/[I 1 (γ)−I 10 +I 3 (γ)−I 30 +I 5 (γ)];

5) turning the target mirror unit around X-axis by several specific angles γ 1 , γ 2 , . . . , measuring the corresponding f(γ 1 ), f(γ 2 ), . . . , and calibrating a function curve of f(γ) v·γ; and

6) measuring light intensities I 1 (γ), I 3 (γ), I 5 (γ) in real time, calculating f(γ) according to Step 4); calculating a relative rotation angle γ between the target mirror unit and the measuring unit about X-axis according to a calibrated function f(γ)v·γ in Step 5).

16 . The method according to claim 9 , wherein for measuring a rolling angle with a dual frequency length measurement, a third λ/4 wave plate is added in the target mirror unit to measure an angular error resulted from rotating around X-axis, the method comprises the following steps:

1) adding a third λ/4 wave plate in the target mirror unit, the measuring light L 111 passes by the third λ/4 wave plate to return to the measuring unit; after passing by the second λ/4 wave plate, the measuring light L 111 is split again when passing by the polarizing beam splitter, in which one beam L 111 ′ is received by the first photodetector, while the other beam L 111 ″ is received by the fifth photodetector;

2) blocking the measuring light L 111 , so that only the reference light L 12 is received on the first photodetector, and recording a light intensity I 10 of the first photodetector;

3) recovering the measuring light L 111 ; with the third λ/4 wave plate, a relative angle variation γ is made between the target mirror unit and the measuring unit around X-axis; when the measuring light passes by the polarizing beam splitter again, its polarizing direction increases by γ′ with respect to its original polarizing direction, γ′ is in a direct proportion to γ; γ′=k 1 γ; when the measuring light passes by the second λ/4 wave plate in the target mirror unit for the first time, k 1 =1; when the measuring light passes by the second λ/4 wave plate in the target mirror unit for the second time, k 1 =2;

4) the measuring light L 111 passes by the polarizing beam splitter and is split by the polarizing beam splitter, in which one beam is received by the first photodetector and its light intensity is I 1 (γ), while the other beam is received by the fifth photodetector, and its light intensity is I 5 (γ), f(γ)=[I 1 (γ)−I 10 −I 5 (γ)]/[I 1 (γ)−I 10 +I 5 (γ)];

5) turning the target mirror unit around X-axis by several specific angles γ 1 , γ 2 , . . . , measuring the corresponding f(γ 1 ), f(γ 2 ), . . . , and calibrating a functional curve of f(γ)v·γ; and

6) measuring light intensities I 1 (γ), I 5 (γ) in real time; calculating f(γ) according to Step 4); and calculating a rotation angle γ of the target mirror unit about X-axis according to the functional curve of f(γ)v·γ calibrated in Step 5).