A heterodyne six degree of freedom measurement grating interferometer and a six degree of freedom measurement method

Abstract

The application discloses a heterodyne six-degree-of-freedom measurement grating interferometer, a first laser head emits laser with a first frequency, and the laser is vertically incident to a measurement grating after passing through a first polarization beam splitter prism, a first quarter-wave plate and a beam splitter prism, and diffraction is generated; after being reflected by a first right-angle prism group, the diffraction light enters the beam splitter prism; a part of diffraction light components are refracted, enter a four-quadrant photodetector group through a lens to perform angle measurement, another part of diffraction light components are transmitted through the beam splitter prism, enter the first polarization beam splitter prism through the first quarter-wave plate, enter a photodetector group through a second polarization beam splitter prism and a polaroid to perform displacement measurement; a second laser head emits laser with a second frequency, diffraction is generated through a reference grating, the diffraction light is parallel and coincides with the laser with the first frequency to enter the photodetector group together. The application realizes sub-nanometer precision, six-degree-of-freedom measurement, low error level and miniaturization.

Description

Technical Field

[0001] This invention relates to the field of optical precision measurement technology, and in particular to a heterodyne six-degree-of-freedom measurement grating interferometer and a six-degree-of-freedom measurement method. Background Technology

[0002] Multi-degree-of-freedom (DOF) precision measurement is of great significance in fields such as integrated circuits, ultra-precision machine tools, and aerospace manufacturing. In integrated circuit manufacturing, the positioning accuracy of the wafer stage in a lithography machine directly affects the manufacturing precision and yield of chips. Multi-degree-of-freedom precision measurement can ensure high-precision positioning of the wafer stage in multiple dimensions, thereby improving chip production efficiency and yield. In the field of ultra-precision machine tools, tool pose calibration is crucial to ensuring machining accuracy. Through multi-degree-of-freedom precision measurement, the position and angle of the tool during machining can be precisely controlled, ensuring high precision and consistency of the machined parts. In aerospace manufacturing, the installation accuracy of structural components and assemblies is paramount. Multi-degree-of-freedom precision measurement can help achieve high-precision component docking and assembly, improving the performance and safety of aircraft.

[0003] Grating interferometers offer unique advantages in multi-degree-of-freedom precision measurement. First, they possess extremely high resolution, achieving sub-nanometer measurement accuracy, which is crucial for high-precision manufacturing. Second, they can perform multi-dimensional displacement and angle measurements, adapting to complex measurement needs. By combining multiple gratings and readheads, grating interferometers can simultaneously measure displacement and angle across multiple degrees of freedom, providing comprehensive measurement data. Furthermore, they offer high measurement speed and real-time performance, enabling high-precision measurements in dynamic environments, making them suitable for high-speed machining and real-time control applications. Finally, their relatively simple structure facilitates integration and maintenance, and they exhibit high reliability and stability, operating stably in various harsh industrial environments. Therefore, the application of grating interferometers can significantly improve measurement accuracy and production efficiency in fields such as integrated circuits, ultra-precision machine tools, and aerospace manufacturing, driving the development and technological advancement of these high-tech industries. Some representative related technologies are described below.

[0004] In 2011, Lee et al. proposed a system for measuring six-degree-of-freedom motion errors using a single grating. Experimental tests showed an angular resolution of 0.03 arcseconds, Y and Z-axis resolutions of approximately 20 nm, and X-axis resolution of approximately 0.4 nm. Subsequently, in 2012, Lee et al. used the previously proposed grating interferometer to analyze the uncertainty of six-degree-of-freedom motion errors of a linear platform, confirming its application capability in precision positioning scenarios. However, this design suffers from different optical paths for the two measurement targets, leading to different responses to environmental errors, posing challenges in high-precision real-time dynamic measurements.

[0005] In 2013, GaoWei's team proposed a multi-axis surface encoder capable of measuring six-degree-of-freedom (6-DOF) translational and angular motion on a planar motion platform. By using a shared laser light source, a three-axis displacement sensor is combined with a three-axis autocollimator to achieve six-DOF measurement. After design and assembly, the final reading head dimensions are 95mm (X) × 90mm (Y) × 25mm (Z). Experimental testing showed that the surface encoder can distinguish 2nm steps in the XYZ directions, 0.1 arcsecond steps in the XY directions, and 0.3 arcsecond steps in the Z direction. However, the peak error amplitudes in the X, Y, and Z directions are approximately ±6nm, ±7nm, and ±6nm, respectively, which is insufficient to meet current sub-nanometer measurement accuracy requirements.

[0006] In 2013, Hsieh et al. proposed a grating-based interferometer capable of measuring six degrees of freedom of displacement and angle using a heterodyne light source, grating shearing, and Michelson interferometry, with a measurement resolution of approximately 2 nm and 0.05 μrad. However, the system is extremely complex, challenging to install, and its Z-axis and angular range are limited by the lens focal length.

[0007] Subsequently, in 2014, Tohoku University in Japan proposed a three-readhead surface encoder for six-degree-of-freedom measurement. Each readhead can acquire three-degree-of-freedom displacement motion (X, Y, and Z) relative to a grating. By combining and jointly calculating the three readheads, the three-degree-of-freedom angular motion (θ) can also be obtained. X θ Y and θ Z Experimental testing showed that this surface encoder can provide sub-nanometer resolution for XYZ measurements, with interpolation errors below ±4nm, and for θ... X θ Y and θ Z It offers a resolution better than 0.1 arcseconds and a nonlinear error of less than 0.5 arcseconds. However, this technique also faces some challenges. First, it requires high consistency in intensity and polarization among the three measurement points. Furthermore, acquiring small-period, large-area two-dimensional gratings is difficult. Finally, in terms of data readout, issues such as dynamic data switching need to be addressed.

[0008] In 2017, Lin Jie et al. from Harbin Institute of Technology proposed a wide-range triaxial grating encoder with nanometer resolution. The ±1st order diffracted beams in the X and Y directions of two planar gratings propagate against their original incident paths, acting as self-collimated diffracted beams. Therefore, the Z-axis measurement range of the proposed system is greatly enhanced. Experimental results show that this grating encoder achieves a Z-axis displacement resolution of 4 nm; however, it fails to achieve six-degree-of-freedom measurement, lacking an angle measurement module.

[0009] In 2022, Li Xinghui's team at Tsinghua University proposed a heterodyne three-degree-of-freedom grating interferometer. This instrument uses a reflective plane grating for the readhead design, ensuring that the main optical path is located on the same side, which helps reduce the impact of Abbe error and environmental interference. Based on a self-made 780nm dual-frequency laser source, experimental tests showed that the three-axis resolution is better than 0.5nm, the short-term repeatability is better than 0.6nm, and the linearity reaches 2*10e. -5 Furthermore, its stability over 300 seconds is better than 5nm. These results fully demonstrate the device's ability to be tested on ultra-precision motion platforms. However, this system lacks an angle measurement module, making it difficult to meet the needs of scenarios requiring simultaneous measurement of position and attitude.

[0010] In summary, six-degree-of-freedom measurement is of great significance in precision engineering and scientific research, especially in fields such as aerospace, manufacturing, and robotics. Among numerous measurement techniques, heterodyne grating interferometry stands out due to its high precision, strong anti-interference capability, and ease of multi-degree-of-freedom extension. However, polarization and frequency aliasing in existing methods can lead to large periodic nonlinear errors, affecting measurement accuracy, and the angle measurement error is also relatively large.

[0011] The above background information is provided only to aid in understanding the concept and technical solution of this invention. It does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above information was disclosed on the filing date of this patent application, the above background information should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0012] To address the aforementioned technical problems, this invention proposes a heterodyne six-degree-of-freedom measurement grating interferometer and a six-degree-of-freedom measurement method, achieving sub-nanometer precision, six-degree-of-freedom measurement, low error level, and miniaturization.

[0013] To achieve the above objectives, the present invention adopts the following technical solution:

[0014] In a first aspect, the present invention discloses a heterodyne six-degree-of-freedom measurement grating interferometer, comprising a first laser head, a second laser head, a first polarizing beam splitter, a second polarizing beam splitter, a first quarter-wave plate, a second quarter-wave plate, a beam splitter, a first right-angle prism group, a second right-angle prism group, a polarizer, a lens, a measurement grating, a reference grating, a photodetector group, and a four-quadrant photodetector group; wherein...

[0015] The first laser head emits a laser of a first frequency, which passes through the first polarizing beam splitter, the first quarter-wave plate, and the beam splitter before being incident perpendicularly onto the measuring grating and diffracting. The diffracted light is reflected by the first right-angle prism group and then enters the beam splitter. A portion of the diffracted light is refracted and incident onto the four-quadrant photodetector group through a lens for angle measurement, while another portion of the diffracted light is transmitted through the beam splitter, then through the first quarter-wave plate, and then incident onto the first polarizing beam splitter. After passing through the second polarizing beam splitter and the polarizer, it is incident onto the photodetector group for displacement measurement.

[0016] The second laser head emits a laser of the second frequency, which passes through the second polarizing beam splitter and the second quarter-wave plate and is then incident perpendicularly onto the reference grating, generating diffraction. The diffracted light is reflected by the second right-angle prism group and then enters the second quarter-wave plate. After being reflected again by the second polarizing beam splitter, it is parallel to and coincides with the laser of the first frequency that has passed through the second polarizing beam splitter. After passing through the polarizer, it is incident onto the photodetector group.

[0017] Preferably, the heterodyne six-degree-of-freedom measurement grating interferometer further includes a half-wave plate.

[0018] The laser emitted by the first laser head is p-polarized light of a first frequency. After passing through the first polarizing beam splitter and the first quarter-wave plate, the p-polarized light is converted into circularly polarized light by the first quarter-wave plate. After passing through the beam splitter, it is incident perpendicularly on the measuring grating and diffracts. The diffraction produces 0th order diffraction light, +1st order diffraction light in the first direction, -1st order diffraction light in the first direction, +1st order diffraction light in the second direction, and -1st order diffraction light in the second direction. The first direction and the second direction are perpendicular to each other.

[0019] The other diffracted light component, transmitted through the beam splitter, passes through the first quarter-wave plate again, and is converted from circularly polarized light to s-polarized light by the first quarter-wave plate before being incident on the first polarizing beam splitter. After being reflected by the first polarizing beam splitter, it passes through the half-wave plate, and is converted from s-polarized light to p-polarized light by the half-wave plate. After being transmitted through the second polarizing beam splitter and the polarizer, it is incident on the photodetector group for displacement measurement.

[0020] Preferably, the laser emitted by the first laser head at a first frequency is s-polarized light. After being reflected by the first polarizing beam splitter, it enters the first quarter-wave plate, where the s-polarized light is converted into circularly polarized light. After passing through the beam splitter, it is perpendicularly incident on the measuring grating and diffracts. The diffraction produces 0th-order diffracted light, +1st-order diffracted light in the first direction, -1st-order diffracted light in the first direction, +1st-order diffracted light in the second direction, and -1st-order diffracted light in the second direction, where the first direction and the second direction are perpendicular to each other.

[0021] The other diffracted light component, transmitted through the beam splitter, passes through the first quarter-wave plate again, and is converted from circularly polarized light to p-polarized light by the first quarter-wave plate before being incident on the first polarizing beam splitter. Then, after passing through the second polarizing beam splitter and the polarizer, it is incident on the photodetector group for displacement measurement.

[0022] Preferably, the laser emitted by the second laser head at the second frequency is p-polarized light. After passing through the second polarizing beam splitter and the second quarter-wave plate, the p-polarized light is converted into circularly polarized light by the second quarter-wave plate and then incident perpendicularly onto the reference grating, generating diffraction. The diffracted light is reflected by the second right-angle prism group and then enters the second quarter-wave plate. The circularly polarized light is converted into s-polarized light by the second quarter-wave plate and then reflected by the second polarizing beam splitter, becoming parallel to and coincident with the emitted laser of the first frequency. The light then enters the photodetector group through a lens.

[0023] Preferably, both the first quarter-wave plate and the second quarter-wave plate are placed at a 45° angle.

[0024] Preferably, the photodetector group includes a first photodetector, a second photodetector, a third photodetector, a fourth photodetector, and a fifth photodetector, wherein the first photodetector, the fifth photodetector, and the second photodetector are arranged sequentially along a third direction, and the third photodetector, the fifth photodetector, and the fourth photodetector are arranged sequentially along a fourth direction, wherein the third direction and the fourth direction are perpendicular to each other.

[0025] Preferably, based on the measurement results of the photodetector array, the formula for displacement measurement is obtained as follows:

[0026]

[0027] Where, φ (1) φ (2) φ (3) φ (4) and φ (5)λ represents the phase change on the first photodetector, the second photodetector, the third photodetector, the fourth photodetector, and the fifth photodetector, respectively; g represents the grating period; and λ is the laser wavelength.

[0028] Preferably, the four-quadrant photodetector group includes three four-quadrant photodetectors arranged in a straight line, and the three four-quadrant photodetectors are respectively used to receive +1st order diffraction light, 0th order diffraction light and -1st order diffraction light.

[0029] Preferably, based on the measurement results of the four-quadrant photodetector group, the formula for angle measurement is as follows:

[0030]

[0031] Where, Δv x+1 Δv0 and Δv x-1 Δh0 represents the vertical displacement of the light spot on each of the four quadrant photodetectors receiving +1st order diffraction light, 0th order diffraction light, and -1st order diffraction light, respectively; λ represents the horizontal displacement of the light spot on the four quadrant photodetector receiving 0th order diffraction light; λ is the laser wavelength; and f is the lens focal length.

[0032] Secondly, the present invention discloses a six-degree-of-freedom measurement method, which uses a heterodyne six-degree-of-freedom measurement grating interferometer as described in the first aspect to perform displacement and angle measurements.

[0033] Compared with existing technologies, the beneficial effects of this invention are as follows: The heterodyne six-degree-of-freedom measurement grating interferometer and six-degree-of-freedom measurement method provided by this invention achieve sub-nanometer precision in addressing the measurement accuracy problem. By employing a heterodyne (dual-frequency) grating interferometry method, the accuracy of the measurement system is greatly improved. Regarding the six-degree-of-freedom measurement problem, comprehensive spatial measurement capabilities are achieved. Three-degree-of-freedom displacement measurement is completed by calculating the signal formed by the interference of diffracted light emitted from two two-dimensional gratings, while three-degree-of-freedom angle measurement is completed by calculating the spot displacement on a four-quadrant photodetector. Regarding the error problem, a low error level is achieved. Through a quasi-common optical path design, periodic nonlinear errors caused by polarization / frequency aliasing and optical dead-zone effects are reduced, lowering the measurement error level to the sub-nanometer level. Regarding system miniaturization, an easily achievable miniaturized design is realized. Through careful design of component layout and optical path propagation direction, the size of the engineering prototype can theoretically be less than 10cm*10cm*5cm. These technical effects significantly improve the performance and application range of precision measurement technology, providing strong support for the development of related fields. In summary, the present invention enables a measurement system with sub-nanometer precision, six degrees of freedom, low error level, and miniaturization. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the structure of the heterodyne six-degree-of-freedom measurement grating interferometer of Embodiment 1 of the present invention;

[0035] Figure 2 yes Figure 1 Schematic diagram of the structure of the photodetector array;

[0036] Figure 3 yes Figure 1 A schematic diagram of the detection spot of a photodetector in the middle four quadrants;

[0037] Figure 4 yes Figure 1 A schematic diagram of an angle measurement using a heterodyne six-degree-of-freedom measurement grating interferometer;

[0038] Figure 5 This is a schematic diagram showing the changes in the light spot detected by the four-quadrant photodetector as the light rotates around the XYZ axes.

[0039] Figure 6 This is a schematic diagram of the structure of the heterodyne six-degree-of-freedom measurement grating interferometer of Embodiment 2 of the present invention;

[0040] Figure 7 This is a schematic diagram of the structure of the heterodyne six-degree-of-freedom measurement grating interferometer of Embodiment 3 of the present invention.

[0041] Explanation of icon numbers:

[0042] 11. First laser head; 111. First optical fiber; 12. Second laser head; 121. Second optical fiber;

[0043] 21. First polarizing beam splitter; 22. Second polarizing beam splitter;

[0044] 31. First quarter-wave plate; 32. Second quarter-wave plate; 33. Half-wave plate;

[0045] 40. Beam splitter;

[0046] 51. Measuring grating; 52. Reference grating;

[0047] 61. First right-angle prism group; 62. Second right-angle prism group;

[0048] 70. Four-quadrant photodetector array; QPD x+1 First quadrant photodetector; QPD0; Second quadrant photodetector; QPD x-1 Third and fourth quadrant photodetectors;

[0049] 81. Lens; 82. Polarizing film

[0050] 90. Photodetector group; 91. First photodetector; 92. Second photodetector; 93. Third photodetector; 94. Fourth photodetector; 95. Fifth photodetector. Detailed Implementation

[0051] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and is not intended to limit the scope and application of the present invention.

[0052] It should be noted that when a component is referred to as "fixed to" or "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as "connected to" another component, it can be directly connected to or indirectly connected to that other component. Furthermore, a connection can be used for both fixing and circuit / signal connectivity.

[0053] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0054] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0055] Six-degree-of-freedom (6DOF) measurement is of great significance in precision engineering and scientific research, especially in aerospace, manufacturing, and robotics. Among numerous measurement techniques, heterodyne grating interferometry stands out for its high accuracy, strong anti-interference capability, and ease of multi-DOF extension. However, existing methods have some problems: first, polarization and frequency aliasing can lead to large periodic nonlinear errors, affecting measurement accuracy; second, the angle measurement model based on spot displacement is not perfect, resulting in large angle measurement errors; and finally, current 6DOF sub-nanometer resolution measurement techniques are still lacking. To address these issues, a quasi-common-path heterodyne interferometer system was designed and constructed to reduce periodic nonlinear errors. Furthermore, this invention employs a quadrant photodetector (QPD) to measure the angle of the spot position, improving the angle measurement model and thus reducing modeling errors. Ultimately, this system can achieve sub-nanometer resolution measurements both in-plane and out-of-plane. Therefore, this invention designs a 6DOF heterodyne grating interferometer, providing a new solution for complex multi-DOF measurements with sub-nanometer precision.

[0056] The heterodyne six-degree-of-freedom measurement grating interferometer disclosed in Embodiment 1 of this invention employs a dual-frequency light source, two two-dimensional reflective diffraction gratings, detectors, optical fibers, and optical component assemblies to achieve six-degree-of-freedom measurement. The dual-frequency light source needs to have two separable laser heads capable of outputting lasers with a certain frequency difference. The detector includes five photodetectors and three four-quadrant photodetectors. Its structure is as follows... Figure 1 As shown. The coordinate system is set as follows. Figure 1 As shown, the direction perpendicular to the surface of the measuring grating 51 is the Z-axis. The X and Y directions within the surface of the measuring grating 51 are orthogonal, with the X-axis being horizontal and the Y-axis vertical. The rotation angle R around the X, Y, and Z axes is... x R y R z Defined by the right-hand screw rule.

[0057] The laser propagation path is as follows: The dual-frequency laser generates two laser beams with frequencies f1 and f2, which are emitted from the first laser head 11 and the second laser head 12, respectively. These are described below:

[0058] First, let's introduce the measurement light. The first laser head 11 emits a laser with an RF rate of f1 as the measurement light.

[0059] After being collimated by the fiber collimator in the first laser head 11, the laser light is emitted in the negative Z-axis direction and is p-polarized. After passing through the first fiber 111, the laser light passes through the first polarizing beam splitter (PBS) 21, the first quarter-wave plate (QWP) 31 placed at a 45° angle, and the beam splitter (BS) 40 and is incident perpendicularly on the measuring grating 51. The function of the first quarter-wave plate 31 is to convert the laser light from p-polarized light to circularly polarized light.

[0060] After the laser is incident on the measurement grating 51, due to the grating pitch being less than 10 micrometers, the laser produces a diffraction phenomenon and forms 5 beams of light. These 5 beams of light are composed of: 0th order diffraction light, X-direction positive first order diffraction light, X-direction negative first order diffraction light, Y-direction positive first order diffraction light, and Y-direction negative first order diffraction light.

[0061] After the four first-order diffracted beams propagate a short distance in space, they are reflected by the first right-angle prism group 61, which consists of four symmetrically arranged right-angle prisms, and become parallel beams propagating along the positive Z-axis. The reflecting surface of each right-angle prism in the first right-angle prism group 61 is the surface containing the hypotenuse, which is total internal reflection.

[0062] After the propagation direction is adjusted by the first right-angle prism group 61, the five diffracted beams enter the beam splitter 40. According to the beam splitter 40's beam splitting efficiency, they are divided into two components: one component of the diffracted beam is refracted at the cemented surface of the beam splitter 40 and propagates in the negative X-axis direction. Among them, the 0th order diffracted beam, the positive first order diffracted beam in the X-axis direction, and the negative first order diffracted beam in the X-axis direction are collimated by the lens and incident on the center of the three four-quadrant photodetectors in the four-quadrant photodetector group 70 for angle measurement; the other component is transmitted through the beam splitter 40 and continues to propagate in the positive Z-axis direction for displacement measurement.

[0063] The latter beam, after passing through the first quarter-wave plate 31 placed at a 45° angle, is converted from circularly polarized light to s-polarized light and then incident on the first polarizing beam splitter 21. It is reflected on the cemented surface of the first polarizing beam splitter 21 and propagates parallel to the negative X-axis. Subsequently, passing through the half-wave plate (HWP) 33 placed at a 45° angle, the five parallel beams achieve the conversion from s-polarized light to p-polarized light, and then pass through the second polarizing beam splitter 22. After passing through the polarizer (P) 82 placed at a 45° angle, they are incident on the photosensitive elements of the five photodetectors (PDs) in the photodetector group 90. It should be noted that, due to... Figure 1 The diagram shown is an XZ plan view, therefore only 3 photodetectors are displayed. There are actually 5 photodetectors; the detailed structure is as follows... Figure 2 As shown, the photodetector group 90 includes a first photodetector 91, a second photodetector 92, a third photodetector 93, a fourth photodetector 94, and a fifth photodetector 95. The first photodetector 91 receives the positive first-order interference signal in the X direction, the second photodetector 92 receives the negative first-order interference signal in the X direction, the third photodetector 93 receives the positive first-order interference signal in the Y direction, the fourth photodetector 94 receives the negative first-order interference signal in the Y direction, and the fifth photodetector 95 receives the zero-order interference signal.

[0064] Next, the reference light is introduced. The second laser head 12 emits a laser with an RF rate of f2 as the reference light.

[0065] The laser beam is collimated by the fiber collimator in the second laser head 12 and emitted as p-polarized light. The laser beam passes through the second fiber 121, the second polarizing beam splitter 22, and the second quarter-wave plate 32 placed at a 45° angle, and is incident perpendicularly on the reference grating 52. The second quarter-wave plate 32 converts the p-polarized light into circularly polarized light. Similarly, five diffracted beams are formed, and four of the first-order diffracted beams are reflected by the reflecting surfaces of the right-angle prisms in the second right-angle prism group 62, becoming parallel light propagating along the Z-axis. These beams then pass again through the second quarter-wave plate 32 placed at a 45° angle, converting from circularly polarized light to s-polarized light before entering the second polarizing beam splitter 22 and being reflected by the cemented surface of the second polarizing beam splitter 22. At this point, the five beams propagate along the X-axis, parallel to and coinciding with the laser beam of frequency f1 emitted from the first laser head 11, and together they enter the photosensitive elements of the five photodetectors in the photodetector group 90.

[0066] The following uses the grating sensor from an embodiment of the present invention to perform six-degree-of-freedom measurements.

[0067] The principle for calculating the XYZ linear displacement in a six-degree-of-freedom measurement is as follows:

[0068] (1) Principle of linear displacement measurement in the X direction.

[0069] In the actual measurement process, the laser emitted by the first laser head 11 at a frequency of f1 is the measurement light, and the incident grating is called the measurement grating. The laser emitted by the second laser head 12 at a frequency of f2 is the reference light, and the incident grating is called the reference grating 52. The reference grating 52 is fixed. The laser emitted by the second laser head 12 has a stable initial spatial phase on the photodetector after passing through the optical path. The measurement grating 51 is fixed to the object under test. When the object under test is stationary, the laser emitted by the first laser head 11 has a stable initial phase on each photodetector. When the object under test is displaced, the measurement grating 51 moves together with the object. Due to the Doppler effect and the grating diffraction effect, the five laser beams generated by the first laser head 11 and the incident measurement grating 51 each carry different phase information caused by the displacement.

[0070] When the grating undergoes an X-axis displacement *x*, since the grating displacement is perpendicular to the Z-axis and the reflected light propagates along the Z-axis, the X-axis displacement has no effect on the phase of the 0th order diffracted light. According to the Doppler frequency shift and the grating equation, the effect of the X-axis displacement of the grating on the phase change of the positive and negative first-order diffracted light in the X-axis is as follows:

[0071]

[0072] Where φ x(1) φ represents the phase change on the first photodetector 91 caused by the movement of the grating in the X direction. x(2)denoted by , g represents the phase change on the second photodetector 92 caused by the X-direction motion of the grating; g represents the grating period. Therefore, the expression for the X-direction displacement Δx can be derived as follows:

[0073]

[0074] (2) Principle of linear displacement measurement in the Y direction.

[0075] Based on the properties of two-dimensional gratings, the X-axis grating lines are orthogonal to the Y-axis grating lines, and the X and Y directions share the same measurement principle. Therefore, for Y-axis displacement measurement, when the measuring grating 51 generates a Y-axis displacement y, since the grating displacement is perpendicular to the Z-axis and the reflected light propagates along the Z-axis, the Y-axis displacement has no effect on the phase of the 0th order diffracted light. According to the Doppler frequency shift and the grating equation, the effect of the grating's Y-axis displacement on the phase change of the positive and negative first-order diffracted light in the Y-axis is as follows:

[0076]

[0077] Where φ y(3) φ represents the phase change on the third photodetector 93 caused by the movement of the grating in the Y direction. y(4) denoted by , g represents the phase change on the fourth photodetector 94 caused by the Y-axis motion of the grating; g represents the grating period. Therefore, the expression for the Y-axis displacement Δy can be derived as follows:

[0078]

[0079] (3) The principle of linear displacement measurement in the Z direction.

[0080] When a Z-axis displacement z occurs, the phase change of the 0th order diffracted light is:

[0081]

[0082] Where φ z(5) The phase change on the fifth photodetector 95 due to the Z-direction motion of the grating is represented by n, where n is the air refractive index, λ is the laser wavelength, and z is the displacement in the Z-direction. The phase change on the first photodetector 91 and the second photodetector 92 caused by the Z-direction displacement of the grating is as follows:

[0083]

[0084] Similarly, the phase change on the third photodetector 93 and the fourth photodetector 94 caused by the Z-axis displacement of the grating is:

[0085]

[0086] According to formulas (5), (6), and (7), the formula for calculating the Z-direction displacement Δz is as follows:

[0087]

[0088] Where, φ z(1) φ z(2) φ z(3) φ z(4) and φ z(5) θ represents the phase change on the first photodetector 91, the second photodetector 92, the third photodetector 93, the fourth photodetector 94, and the fifth photodetector 95 caused by the Z-direction displacement of the grating, respectively; z is the displacement in the Z direction; θ is the angle between the positive and negative first-order diffracted light and the normal.

[0089] In summary, the X-axis displacement, Y-axis displacement, and Z-axis displacement can be obtained by solving the phase changes of the signals on the five photodetectors in the photodetector group 90.

[0090] The following introduces R in six-degree-of-freedom measurement. X R Y R Z Angle calculation principle. Grating rotation angle measurement is achieved by calculating the positional changes of the diffracted light spot on each of the four-quadrant photodetectors in the four-quadrant photodetector group 70. The working principle of the four-quadrant photodetector is as follows: Figure 3 As shown.

[0091] In a four-quadrant photodetector, the same photosensitive element exists in each of the four quadrants. When a laser beam illuminates the four-quadrant photodetector, the relative position of the light spot can be determined by the light intensity values ​​in the four quadrants. When the light intensities received by the photosensitive elements in the four quadrants of the four-quadrant photodetector are I1, I2, I3, and I4, respectively, the relative horizontal offset Δh of the light spot center relative to the origin of the four-quadrant photodetector is:

[0092]

[0093] The relative vertical offset Δv of the light spot center relative to the origin of the four-quadrant photodetector is:

[0094]

[0095] Figure 4This is an optical path structure containing only the angle measurement module; the optical path structures related to displacement measurement have been ignored. All lenses have the same focal length, f. The effective detection plane of the four-quadrant photodetector coincides with the focal plane of the lens. If the measurement grating is in an ideal orientation, the laser emitted from the first laser head 11 will be incident directly onto the measurement grating 51. Three diffracted beams (positive first-order diffraction in the X-axis, 0th-order diffraction, and negative first-order diffraction in the X-axis) propagate along the ideal optical axis and are ultimately projected onto the first four-quadrant photodetector QPD in the four-quadrant photodetector group 70. x+1 Second quadrant photodetector QPD0, third quadrant photodetector QPD x-1 Above, the center of the diffracted light spot coincides with the center of each of the four quadrant photodetectors.

[0096] If the measurement grating deflects, the diffracted light deviates from the ideal optical axis, and the center of the diffracted light spot shifts relative to the centers of the photodetectors in each of the four quadrants. For example... Figure 4 As shown, the grating has a rotation angle R of α angle (α angle is small enough) around the Y-axis. y For example, the incident light vector and the normal vector of the measuring grating 51 have an angle α. According to the grating diffraction equation, the diffracted light vectors are all rotated by an angle 2α around the Y-axis relative to the ideal diffracted light vector. After being reflected by the cemented surface of the first right-angle prism 31 and the beam splitter prism 40, the diffracted light is incident on the front surface of the lens 81. According to geometric relationships, the incident light has an angle of 2α with the ideal optical axis and a horizontal offset. The light is refracted in the lens 81, and the outgoing light deviates from the ideal optical axis and illuminates the photodetectors in each of the four quadrants, forming light spots.

[0097] Based on the paraxial relationship of the lenses, the horizontal offset Δh of the light spot (including the first four-quadrant photodetector QPD) x+1 The horizontal displacement Δh of the upper light spot x+1 The horizontal displacement Δh0 of the light spot on the second quadrant photodetector QPD0, and the third quadrant photodetector QPD0. x-1 The horizontal displacement Δh of the upper light spot x-1 The incident light deflection angle 2α satisfies:

[0098] Δh0=f·tan2α (11)

[0099] Δh x±1 = -f·tan2α (12)

[0100] Therefore, the turning angle R y The approximate solution formula is as follows:

[0101] R y =Δh0 / 2f=-Δh x±1 / 2f (13)

[0102] Δh can be obtained from the relationship between the light intensity signals detected by each of the four quadrant photodetectors.

[0103] Similarly, the rotation angle R of the grating around the X-axis x The approximate solution formula is as follows:

[0104] R x =Δv0 / 2f=Δv x+1 / 2f=Δv x-1 / 2f (14)

[0105] In the formula, Δv x+1 Δv0 and Δv x-1 These represent the first and fourth quadrant photodetectors (QPDs). x+1 The second and fourth quadrant photodetectors QPD0 and the third and fourth quadrant photodetectors QPD x-1 The amount of displacement of the upper light spot in the vertical direction.

[0106] When the measured grating attitude has a rotation angle R around the Z-axis... z At that time, the diffracted light vector will rotate around the Z-axis by the same angle as the grating line.

[0107] In this case, the propagation direction of the 0th order diffracted light remains unchanged, and its spot remains at the center of QPD0, with Δh0 = Δv0 = 0. The equivalent optical paths of the positive and negative first-order diffracted light in the X direction rotate around the grating normal, and the spots on each of the four quadrant photodetectors will simultaneously shift in both the horizontal and vertical directions, resulting in a curved trajectory.

[0108] When R z When the light spot is sufficiently small, its horizontal offset is negligible, and its vertical offset can be expressed as:

[0109] Δv x±1 =±L·tanR z (15)

[0110] Where L is the equivalent rotation radius of the light spot, satisfying

[0111] L=f·tanφ (16)

[0112] Where φ is the positive and negative first-order diffraction angle of the grating, which can be obtained from the grating equation gsinφ=λ.

[0113] Combining the above equations, the rotation angle R of the grating around the Z-axis z The approximate solution formula is as follows:

[0114]

[0115] like Figure 5 As shown, when the grating rotation angle R x R y Rz Simultaneously, the first four-quadrant photodetector QPD also exists. x+1 Second quadrant photodetector QPD0, third quadrant photodetector QPD x-1 The position of the upper light spot is as follows Figure 5 As shown. The relative positions of the light spots satisfy:

[0116]

[0117] To achieve grating rotation angle R x R y R z Simultaneous measurement, the rotation formula is determined as follows:

[0118]

[0119] This completes the derivation of the displacement measurement module and the angle measurement module.

[0120] The formulas for the results of the above six-degree-of-freedom measurements are summarized as follows:

[0121]

[0122] Where, φ (1) φ (2) φ (3) φ (4) and φ (5) These represent the phase changes on the first photodetector 91, the second photodetector 92, the third photodetector 93, the fourth photodetector 94, and the fifth photodetector 95, respectively; Δv x+1 Δv0 and Δv x-1 These represent the first and fourth quadrant photodetectors (QPDs). x+1 The second and fourth quadrant photodetectors QPD0 and the third and fourth quadrant photodetectors QPD x-1 The vertical displacement of the upper light spot, Δh0, represents the horizontal displacement of the light spot on the second four-quadrant photodetector QPD0. Therefore, six degrees of freedom measurement can be achieved by varying the signals from the five photodetectors and the three four-quadrant photodetectors.

[0123] The design advantages of the grating interferometer proposed in this embodiment are analyzed below: For displacement measurement in the X direction, after the laser source with frequency f1 is incident, the optical path reaching the first photodetector 91 and the second photodetector 92 is consistent after passing through a series of optical elements. This avoids the influence of environmental and frequency fluctuations (dead zone effect) due to unequal optical path lengths, thereby improving measurement accuracy. The same applies to Y-direction measurement. Moreover, the optical dead zone effect in the Z direction is also minimized. In summary, the structural design of the grating interferometer proposed in this embodiment can eliminate the optical dead zone through a quasi-common optical path, while also avoiding the frequency / polarization confusion effect caused by single-beam dual-frequency light incident beam splitting, thereby improving measurement accuracy.

[0124] like Figure 6 As shown, this is a heterodyne six-degree-of-freedom measurement grating interferometer disclosed in Embodiment 2 of the present invention. It is a variant structure with symmetrical incident structure of the grating interferometer in Embodiment 1. The derivation of the principle is similar to that in Embodiment 1, and will not be repeated here.

[0125] like Figure 7 The image shows a heterodyne six-degree-of-freedom measurement grating interferometer disclosed in Embodiment 3 of the present invention. It is a variant structure arranged vertically with respect to the grating interferometer in Embodiment 1. The optical propagation direction of the grating interferometer is briefly described below.

[0126] First, the measurement light is emitted. The laser beam from the first laser head 11, with a radio frequency of f1, is collimated by an optical fiber collimator and emitted in the negative Z-axis direction. At this point, the beam is s-polarized. After passing through the first optical fiber 111, it enters the first polarizing beam splitter 21, is reflected upwards, and becomes circularly polarized after passing through the first quarter-wave plate 31. It then enters the beam splitter 40, where one beam is reflected to the right (discarded), and another continues upwards into the measurement grating 51, emitting five diffracted beams. After passing through the first right-angle prism group 61, it becomes five parallel beams. Three beams aligned in the z-direction are split by the beam splitter 40 and enter the four-quadrant photodetector group 70 for angle measurement. These three angle measurement beams are recorded. The remaining beams propagate downwards, becoming p-polarized after passing through the first quarter-wave plate 31, and then are transmitted through the first polarizing beam splitter 21 into the beam-splitting surface of the second polarizing beam splitter 22. These are recorded as the five measurement diffracted beams.

[0127] Next comes the reference light. The laser emitted from the second laser head 12, with a radio frequency of f2, is collimated by the fiber collimator and emitted in the negative Z-axis direction as p-polarized light. After passing through the second quarter-wave plate 32, it becomes circularly polarized light and enters the reference grating 52, emitting five diffracted beams. After being collimated by the second right-angle prism group 62, it becomes five parallel beams. It then re-enters the second quarter-wave plate 32 and becomes s-polarized light, reaching the beam-splitting surface of the second polarizing beam splitter 22. The five reference diffracted beams are recorded.

[0128] Finally, let's discuss the beam combining. The five measurement diffracted beams formed in the two sections above, along with the five reference diffracted beams, combine on the beam-splitting plane of the second polarizing beam splitter 22, forming an interference signal. This signal is then sent to the five photodetectors in the photodetector group 90 for three-degree-of-freedom displacement measurement. The three angle measurement beams mentioned above enter the three four-quadrant photodetectors in the four-quadrant photodetector group 70, achieving three-degree-of-freedom angle measurement. Thus, the six-degree-of-freedom measurement is completed. The specific calculation principle and accuracy are the same as in Example 1, and will not be repeated here.

[0129] Correspondingly, the embodiments of the present invention also disclose methods for displacement measurement and angle measurement using a heterodyne six-degree-of-freedom measurement grating interferometer as described in Embodiment 1, Embodiment 2, or Embodiment 3.

[0130] The heterodyne six-degree-of-freedom measurement grating interferometer and corresponding six-degree-of-freedom measurement method proposed in the above embodiments of the present invention can achieve the following four technical effects:

[0131] (1) To address the measurement accuracy issue, sub-nanometer precision was achieved by employing a heterodyne (dual-frequency) grating interferometry method, which greatly improved the accuracy of the measurement system.

[0132] (2) For the six-degree-of-freedom measurement problem, a comprehensive spatial measurement capability has been realized. The three-degree-of-freedom displacement measurement is completed by solving the five signals formed by the mutual interference of the five diffraction beams emitted by two two-dimensional gratings. The three-degree-of-freedom angle measurement is completed by solving the light spot displacement on three four-quadrant photodetectors (QPDs).

[0133] (3) To address the error problem, a low error level was achieved. Through quasi-common optical path design, the periodic nonlinear error caused by polarization / frequency aliasing and the optical path dead zone effect were reduced, and the measurement error level was reduced to the sub-nanometer level.

[0134] (4) To address the issue of system miniaturization, an easily achievable miniaturized design was implemented. Through careful design of component layout and optical path propagation direction, the size of the engineering prototype can theoretically be less than 10cm*10cm*5cm. The realization of these technical effects significantly improves the performance and application range of precision measurement technology, providing strong support for the development of related fields.

[0135] Compared to existing six-degree-of-freedom measurement schemes, laser interferometers are relatively large due to their inherent limitations, while ordinary six-degree-of-freedom grating interferometers, although miniaturized, only achieve sub-micron precision. The heterodyne six-degree-of-freedom measurement grating interferometer proposed in this invention simultaneously achieves "six degrees of freedom + sub-nanometer precision + miniaturization" by eliminating "optical dead zone + frequency / polarization aliasing" through a quasi-common optical path scheme and by using QPD for angle measurement with maximum efficiency, thereby simultaneously meeting the above requirements.

[0136] In summary, the present invention enables a measurement system with sub-nanometer precision, six degrees of freedom, low error level, and miniaturization. Furthermore, this measurement system can be applied to fields such as lithography wafer stage positioning, ultra-precision machine tool processing, atomic force microscopes, and atomic-level manufacturing probes.

[0137] The background section of this invention may include background information about the problems or circumstances surrounding the invention, rather than a description of prior art by others. Therefore, the content included in the background section is not an admission of prior art by the applicant.

[0138] The above description provides a further detailed explanation of the present invention in conjunction with specific / preferred embodiments, and it should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various substitutions or modifications can be made to these described embodiments without departing from the concept of the present invention, and all such substitutions or modifications should be considered within the scope of protection of the present invention. In the description of this specification, the reference to terms such as "an embodiment," "some embodiments," "preferred embodiment," "example," "specific example," or "some examples," etc., indicates that the specific features, structures, materials, or characteristics described in connection with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate different embodiments or examples and features of different embodiments or examples described in this specification without contradiction. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions, and modifications can be made herein without departing from the scope defined by the appended claims.

Claims

1. A heterodyne six-degree-of-freedom measurement grating interferometer, characterized in that, It includes a first laser head, a second laser head, a first polarizing beam splitter, a second polarizing beam splitter, a first quarter-wave plate, a second quarter-wave plate, a beam splitter, a first right-angle prism group, a second right-angle prism group, a polarizer, a lens, a measuring grating, a reference grating, a photodetector group, and a four-quadrant photodetector group; among which, The first laser head emits a laser of a first frequency, which, after passing through the first polarizing beam splitter, the first quarter-wave plate, and the beam splitter, is perpendicularly incident on the measurement grating and diffracts. The diffracted light is reflected by the first right-angle prism group and then enters the beam splitter. A portion of the diffracted light component is refracted and incident on the four-quadrant photodetector group through a lens for three-degree-of-freedom angle measurement. Another portion of the diffracted light component is transmitted through the beam splitter and then through the first quarter-wave plate to the first polarizing beam splitter. After passing through the second polarizing beam splitter and the polarizer, it is incident on the photodetector group for three-degree-of-freedom displacement measurement. The beam splitter is positioned in the optical path between the first right-angle prism group and the first quarter-wave plate. It is used to split the diffracted light into a refracted beam and a transmitted beam after the diffracted light is reflected by the first right-angle prism group and before it returns to the first quarter-wave plate. The refracted beam is used for three-degree-of-freedom angle measurement, and the transmitted beam is used for three-degree-of-freedom displacement measurement, thus maintaining a quasi-common path design for the displacement measurement optical path. The second laser head emits a laser of the second frequency, which passes through the second polarizing beam splitter and the second quarter-wave plate and is then perpendicularly incident on the reference grating, generating diffraction. The diffracted light is reflected by the second right-angle prism group and then enters the second quarter-wave plate. After being reflected by the second polarizing beam splitter, it is parallel to and coincides with the laser of the first frequency that has passed through the second polarizing beam splitter. After passing through the polarizer, it is incident on the photodetector group. The three-degree-of-freedom displacement measurement is calculated by using the signal formed by the interference of the diffracted light emitted from the measuring grating and the reference grating, while the three-degree-of-freedom angle measurement is calculated by the spot displacement on the four-quadrant photodetector group.

2. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 1, characterized in that, It also includes half-wave plates, The laser emitted by the first laser head is p-polarized light of a first frequency. After passing through the first polarizing beam splitter and the first quarter-wave plate, the p-polarized light is converted into circularly polarized light by the first quarter-wave plate. After passing through the beam splitter, it is incident perpendicularly on the measuring grating and diffracts. The diffraction produces 0th order diffraction light, +1st order diffraction light in the first direction, -1st order diffraction light in the first direction, +1st order diffraction light in the second direction, and -1st order diffraction light in the second direction. The first direction and the second direction are perpendicular to each other. The other diffracted light component, transmitted through the beam splitter, passes through the first quarter-wave plate again, and is converted from circularly polarized light to s-polarized light by the first quarter-wave plate before being incident on the first polarizing beam splitter. After being reflected by the first polarizing beam splitter, it passes through the half-wave plate, and is converted from s-polarized light to p-polarized light by the half-wave plate. After being transmitted through the second polarizing beam splitter and the polarizer, it is incident on the photodetector group for displacement measurement.

3. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 1, characterized in that, The laser emitted by the first laser head is s-polarized light of the first frequency. After being reflected by the first polarizing beam splitter, it enters the first quarter-wave plate. The first quarter-wave plate converts the s-polarized light into circularly polarized light. After passing through the beam splitter, it is incident perpendicularly on the measuring grating and diffracts. The diffraction produces 0th order diffracted light, +1st order diffracted light in the first direction, -1st order diffracted light in the first direction, +1st order diffracted light in the second direction, and -1st order diffracted light in the second direction. The first direction and the second direction are perpendicular to each other. The other diffracted light component, transmitted through the beam splitter, passes through the first quarter-wave plate again, and is converted from circularly polarized light to p-polarized light by the first quarter-wave plate before being incident on the first polarizing beam splitter. Then, after passing through the second polarizing beam splitter and the polarizer, it is incident on the photodetector group for displacement measurement.

4. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 2 or 3, characterized in that, The second laser head emits p-polarized light at a second frequency. This light passes through the second polarizing beam splitter and the second quarter-wave plate. The second quarter-wave plate converts the p-polarized light into circularly polarized light, which is then incident perpendicularly onto the reference grating and diffracts. The diffracted light is reflected by the second right-angle prism group and then enters the second quarter-wave plate. The second quarter-wave plate converts the circularly polarized light into s-polarized light, which is then reflected by the second polarizing beam splitter and becomes parallel to and coincides with the emitted laser at the first frequency. The light then passes through a lens and enters the photodetector group.

5. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 1, characterized in that, Both the first quarter-wave plate and the second quarter-wave plate are placed at a 45° angle.

6. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 1, characterized in that, The photodetector group includes a first photodetector, a second photodetector, a third photodetector, a fourth photodetector, and a fifth photodetector, wherein the first photodetector, the fifth photodetector, and the second photodetector are arranged sequentially along a third direction, and the third photodetector, the fifth photodetector, and the fourth photodetector are arranged sequentially along a fourth direction, wherein the third direction and the fourth direction are perpendicular to each other.

7. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 6, characterized in that, Based on the measurement results of the photodetector array, the formula for displacement measurement is as follows: in, , , , and These represent the phase changes on the first photodetector, the second photodetector, the third photodetector, the fourth photodetector, and the fifth photodetector, respectively. Represents the size of the grating period. is the laser wavelength.

8. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 1, characterized in that, The four-quadrant photodetector group includes three four-quadrant photodetectors arranged in a straight line. The three four-quadrant photodetectors are used to receive +1st order diffraction light, 0th order diffraction light and -1st order diffraction light, respectively.

9. The heterodyne six-degree-of-freedom measurement grating interferometer according to claim 8, characterized in that, Based on the measurement results of the four-quadrant photodetector group, the formula for angle measurement is as follows: in, and These represent the displacements in the vertical direction of the photodetector spots in each of the four quadrants that receive +1st-order, 0th-order, and -1st-order diffracted light, respectively. This represents the horizontal displacement of the light spot on a four-quadrant photodetector that receives 0th-order diffracted light. The wavelength of the laser. This is the focal length of the lens.

10. A six-degree-of-freedom measurement method, characterized in that, Displacement and angle measurements were performed using a heterodyne six-degree-of-freedom measurement grating interferometer as described in any one of claims 1 to 9.

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