Self-tracing grating interference type in-situ detection method for cosine installation error between workpieces

Abstract

The invention discloses a self-traceability grating interference type inter-workpiece cosine installation error in-situ detection method, and belongs to the technical field of precision measurement, and the method comprises the steps: depositing self-traceability gratings on two to-be-detected workpieces respectively, and measuring grating interference signals at the same time through two self-traceability grating interferometers which move cooperatively; the period direction of a certain self-traceability grating is adjusted to be consistent with the direction of a motion measuring shaft of a high-precision displacement table, and two reading heads of a self-traceability grating interferometer are ideally installed relative to respective gratings by debugging interference optical signals; along with the displacement of the self-traceability gratings, two reading heads of the self-traceability interferometer respectively collect displacement signals of the two self-traceability gratings at the same time; and the cosine installation error between the workpieces is calculated by comparing the ratio of the number of original signal cycles collected by the two reading heads. By adopting the method, the problem of workpiece cosine installation error in-situ detection is solved, and the method has the advantages of magnitude self-calibration, high measurement precision and environmental interference resistance.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and in particular to an in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometric type. Background Technology

[0002] Precision manufacturing and measurement are key technologies supporting the development of strategic and pioneering industries. High-end equipment, as the core support for industrial development, is directly affected by the assembly precision of its components. Taking the dual-stage lithography machine—a core piece of equipment in integrated circuit manufacturing—as an example, the pose accuracy between the two stages and between each stage and the system's main reference is the cornerstone determining the lithography machine's overlay accuracy and yield. The six degrees of freedom errors of the stages during assembly and operation, especially the pitch and roll angle errors in the vertical direction, must be strictly controlled within the microradian range. These angle errors directly introduce Abbe and cosine errors, causing deviations between the actual exposed pattern position and the ideal position. Therefore, high-precision measurement and control of the assembly angle errors between the two stages is crucial for achieving high-end lithography manufacturing. In industrial practice, high-precision measurement of assembly errors is generally achieved using technologies such as laser interferometers and optical microscopy. The principle of laser interferometers for calibrating workpiece installation errors is to use the laser wavelength as a "ruler," calculating displacement or angular deviation by measuring the optical path difference. However, because laser wavelengths are easily affected by environmental disturbances and have poor robustness, they are difficult to adapt to the high-precision measurement requirements of industrial settings. Optical microscopy and imaging techniques capture alignment marks on workpieces using microscopic imaging or diffraction optics, and then calculate the relative position of two workpieces through optical signal processing. However, this method is generally difficult to trace, and its measurement range is limited, failing to meet the needs of large-scale measurements. Therefore, a method for in-situ detection of cosine installation errors between workpieces that is environmentally robust, traceable, and highly accurate is needed. Summary of the Invention

[0003] The purpose of this invention is to provide an in-situ detection method for cosine installation error between workpieces using a self-traceable grating interference type, so as to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides an in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometer, comprising the following steps: S1. Self-traceable gratings are deposited on two workpieces to be tested, and the two workpieces to be tested are coarsely aligned with the two self-traceable gratings parallel to each other along the grating period direction. Then, the grating interference signal is measured simultaneously by two self-traceable grating interferometers that move in coordination. The two workpieces to be tested are the first workpiece and the second workpiece, and the self-traceable grating includes the first grating and the second grating. S2. Align the periodic direction of the first grating with the motion measurement axis direction of the high-precision displacement stage, and adjust the interference light signal to ensure that the two reading heads of the self-traceable grating interferometer are ideally installed relative to their respective gratings; the two reading heads are the first reading head and the second reading head, respectively. S3. As the self-traceable gratings are displaced, the two reading heads of the self-traceable interferometer simultaneously acquire the displacement signals of the two self-traceable gratings. S4. Using the displacement measurement signal of one of the reading heads as a reference, and utilizing the theoretical spacing of the self-traceable grating, the cosine installation error between the workpieces is calculated by comparing the ratio of the number of cycles of the original signals collected by the two reading heads.

[0005] Preferably, the two workpieces to be tested are coarsely aligned with two self-traceable gratings in parallel along the grating period direction, specifically: the first grating period direction is strictly parallel and fixed with the first workpiece reference direction, and the second grating period direction is strictly parallel and fixed with the second workpiece reference direction.

[0006] Preferably, the self-traceable grating is deposited using precision-machined ultra-high perpendicularity orthogonal mirrors and fixtures, ensuring that the deposition direction of the grating lines is strictly parallel to the workpiece reference direction.

[0007] Preferably, the laser wavelength of the light source module of the self-traceable grating interferometer reading head is less than twice the theoretical spacing of the self-traceable grating.

[0008] Preferably, the method for achieving ideal installation of the self-traceable grating and the reading head is to incident a laser at a Litterow angle onto the self-traceable grating and return along the same path, so that the interference signal reaches its maximum.

[0009] Preferably, the read head module of the self-traceable grating interferometer includes at least two read heads; the read head module of the self-traceable grating interferometer adopts any one of the displacement measurement methods of zero-difference interferometry, heterodyne interferometry and self-mixed interferometry.

[0010] Preferably, the read head module of the self-traceable grating interferometer is in the same direction of motion as its corresponding self-traceable grating.

[0011] Preferably, in step S2, the periodic direction of the first grating is aligned with the motion measurement axis direction of the high-precision displacement stage. At this point, no interference signal is generated when a displacement perpendicular to the motion measurement axis is applied, ensuring ideal installation of the first reading head and the first grating. The signal collected by the first reading head at this time is: ; in, This indicates the period of the first grating. This represents the distance the displacement platform has traveled.

[0012] Preferably, step S3 specifically involves: as the first grating and the second grating move simultaneously, the first reading head and the second reading head respectively acquire the original interference signals of the first grating and the second grating. Since the grating period of the second grating and the first grating have installation angle errors, the installation angle errors are respectively rotation angles... Pitch angle and yaw angle Then, the signal collected by the second reading head at this time is: ; in, This indicates the period of the second grating.

[0013] Preferably, step S4 specifically involves: using the displacement measurement signal of the first reading head as a reference, and based on the theoretical spacing of the self-traceable grating... And by comparing the two phase signals and The comparison results of displacement measurement signals from two self-traceable grating interferometers were obtained: ; in, and These represent the displacement measurement results of the second and first reading heads, respectively. The cosine error of the two workpieces was obtained by comparison. as follows: ; Therefore, the present invention employs the above-described in-situ detection method for cosine installation error between workpieces using a self-traceable grating interference type, which has the following beneficial effects: 1. The self-traceable grating is fabricated using atomic lithography, and its periodicity... By directly tracing the transition frequency of chromium atoms, the displacement measurement results are traced back to natural constants based on physical objects. Compared with the traditional method of measuring assembly errors using laser interferometers, this method is more robust and therefore more suitable for field applications. 2. The self-traceable grating has a line density of up to 4700 lines / mm. Combined with the optical subdivision technology of the grating interferometer, it can achieve higher displacement resolution and ensure the accuracy of sinusoidal error measurement. 3. This method is based on the self-calibration mechanism when two self-traceable gratings are arranged in parallel relative to each other. By comparing the phase of the two sets of grating interference displacement signals, the in-situ sinusoidal installation error detection can be easily achieved.

[0014] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] Figure 1This is a schematic diagram of the structure of the self-traceable grating according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the self-traceable grating deposition process according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the zero-difference self-traceable grating interferometer according to an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the measurement of installation errors between workpieces according to an embodiment of the present invention; Figure 5 This is an interference signal diagram of an embodiment of the present invention when there is an installation error; Figure 6 This is a flowchart of an in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometer according to an embodiment of the present invention; Figure Labels 1. First grating; 2. Second grating; 3. First reading head; 4. Second reading head; 5. First workpiece; 6. Second workpiece; 201. Cr atomic beam; 202. Converging laser; 203. One-dimensional deposition grating; 301. First reflecting mirror; 302. Polarizing beam splitter prism; 303. First waveplate; 304. Second reflecting mirror; 305. Third reflecting mirror; 306. Second waveplate; 307. First photodetector; 308. First linear polarizer; 309. Second linear polarizer; 310. Second detector; 311. Unpolarizing beam splitter prism; 312. Third waveplate; 313. Fourth waveplate; 314. Fiber collimator. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0017] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0018] Example Reference Figure 6This invention provides an in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometer, comprising the following steps: S1. Deposit self-traceable gratings on two workpieces to be tested respectively, and coarsely align the two workpieces to be tested with the two self-traceable gratings parallel to each other along the grating period direction. Then, measure the grating interference signal simultaneously by two self-traceable grating interferometers that move in coordination. The two workpieces to be tested are workpiece 5 and workpiece 6. The self-traceable grating includes a first grating 1 and a second grating 2. The periodic direction of the first grating 1 is strictly parallel and fixed to the reference direction of the first workpiece 5, and the periodic direction of the second grating 2 is strictly parallel and fixed to the reference direction of the second workpiece 6. Figure 4 .

[0019] The self-traceable grating is made of any one of the following materials: chromium, iron, sodium, aluminum, and ytterbium.

[0020] Employing self-traceable gratings, such as Figure 1 As shown, this embodiment uses chromium as an example, employing a chromium atomic photolithography grating, which is a deposition grating whose grating period is strictly traced back to a natural constant. The chromium atomic photolithography grating is fabricated using atomic photolithography. Due to the inherent characteristics of its fabrication process, its grating period value can be directly traced back to the wavelength corresponding to the atomic transition energy level. Theoretically, its grating period error can be less than 0.001 nm. Furthermore, it can be repeatedly fabricated while maintaining high line density, exhibiting high consistency, high uniformity, and strong resistance to environmental changes.

[0021] The self-traceable grating is fabricated using atomic lithography, specifically including: In a vacuum environment, metal materials are heated and sublimated to form gaseous metal. Metal atomic beams are extracted using a cascading method; Atoms are constrained by a laser standing wave field to deposit a grating periodic structure that is directly traced back to the atomic transition frequency.

[0022] Self-traceable gratings are deposited using precision-machined ultra-high perpendicularity orthogonal mirrors and fixtures, ensuring that the deposition direction of the grating lines is strictly parallel to the workpiece reference direction.

[0023] Chromium atomic lithography is a process that deposits chromium using atomic lithography, the process of which is as follows: Figure 2As shown, generally, a crucible containing chromium powder is heated to between 1550℃ and 1650℃ in a vacuum environment to achieve sublimation, and then drawn out through a 1mm effluent hole to form a metal atom beam. Then, using a theodolite and altimeter, a one-dimensional cooling laser is adjusted to be orthogonal to the beam, and the divergence angle of the metal atom beam is reduced to less than 1mrad based on laser monitoring results. The collimated Cr atom beam 201 is then converged through a standing wave field with the orthogonal laser, and deposited onto a sample under the action of a dipole force to form a one-dimensional deposition grating 203. The wavelength of the converging laser 202 is 425.6nm, corresponding to the resonant transition energy level of the Cr atom, which is the positive detuning (+20MHz) or negative detuning (-250MHz) position of the center frequency corresponding to that resonant energy level when the converging laser frequency is adjusted. Therefore, the period of the formed one-dimensional chromium (Cr) atom photolithography grating structure is half the wavelength of the laser used, which is 212.8nm. Because the one-dimensional chromium atom deposition grating prepared by laser focusing atom deposition technology needs to form a structure, the wavelength of the one-dimensional laser standing wave field must correspond to the wavelength of the atomic transition energy level. Furthermore, the wavelength of the formed one-dimensional chromium atom deposition grating is exactly half the wavelength of the one-dimensional laser standing wave field. Therefore, the one-dimensional chromium atom deposition grating is a self-traceable grating with metrological characteristics, which ensures the uniformity of the quantitative values ​​between different grating periods.

[0024] S2. Align the periodic direction of the first grating 1 with the motion measurement axis direction of the high-precision displacement stage, and adjust the interference light signal to ensure that the two reading heads of the self-traceable grating interferometer are ideally installed relative to their respective gratings. The two reading heads are the first reading head 3 and the second reading head 4.

[0025] The laser wavelength of the readhead light source module of the self-traceable grating interferometer is less than twice the theoretical spacing of the self-traceable grating.

[0026] The ideal method for installing the self-traceable grating and the readhead is to incident a laser at a Litterow angle onto the self-traceable grating and return along the same path, so that the interference signal reaches its maximum.

[0027] The read head module (i.e., the reading head) of the self-traceable grating interferometer can adopt any of the displacement measurement methods among zero-difference interferometry, heterodyne interferometry, and self-mixed interferometry.

[0028] The read head module of a self-traceable grating interferometer includes at least two read heads.

[0029] The read head module of the self-traceable grating interferometer and its corresponding self-traceable grating move in the same direction.

[0030] The first reading head 3 and the second reading head 4 use the same optical path. Taking zero-difference interference as an example, the internal optical paths of the first reading head 3 and the second reading head 4 are as follows: Figure 3As shown, the system mainly includes a diffraction light generating unit and a signal receiving unit. The diffraction light generating unit includes a fourth waveplate 313, a polarizing beam splitter 302, a first waveplate 303, a second waveplate 306, a first reflecting mirror 301, a second reflecting mirror 305, and a third reflecting mirror 304. The signal receiving unit includes a third waveplate 312, a non-polarizing beam splitter 311, a first polarizer 308, a second polarizer 309, a first detector 307, and a second detector 310. The fourth waveplate 313 is a half-waveplate, and the first waveplate 303, second waveplate 306, and third waveplate 312 are quarter-waveplates. The fast axes of the first waveplate 303, second waveplate 306, and third waveplate 312 are all at 45° to the light incident plane. The polarization direction of the first linear polarizer 308 is at 45° to the light incident plane, and the polarization direction of the second linear polarizer 309 is at 22.5° to the light incident plane.

[0031] The process of acquiring the interference signal using a reading head in this embodiment is as follows: A 405nm laser beam enters from the fiber collimator 314, passes through the first reflecting mirror 301, and enters the diffraction light generating unit. The rotatable fourth waveplate 313 is adjusted so that the polarization direction of the incident laser beam forms a 45° angle with the incident plane. The laser beam is decomposed into two components, vertical polarization and horizontal polarization, by the polarizing beam splitter 302. The vertically polarized light is transmitted and then passes through the second waveplate 306, becoming right-hand circularly polarized light. The right-hand circularly polarized light passes through the third reflecting mirror 305 and enters the first grating 1 at a Littrow angle. The incident light diffracts at the grating, and the -1st order diffracted light returns along the same path, passes through the second waveplate 306 again, and becomes horizontally polarized light. The horizontally polarized light is reflected after passing through the polarizing beam splitter 302 and enters the signal receiving unit. The other reflected horizontally polarized light becomes left-hand circularly polarized light after passing through the first waveplate 303. Left-handed circularly polarized light is incident on the first grating 1 at a Littrow angle through the second reflecting mirror 304. The incident light is diffracted on the grating, and the -1st order diffracted light returns along the original path. It passes through the first waveplate 303 again and becomes vertically polarized light. The vertically polarized light is transmitted through the polarizing beam splitter 302 and merges with the previous diffracted light, and together they enter the receiving unit.

[0032] Two perpendicularly polarized diffracted beams are converted into circularly polarized light by a third waveplate. They are then proportionally split into two paths by an unpolarized beam splitter prism 311. One path passes through a first linear polarizer 308 and enters a first photodetector 307, while the other path passes through a second linear polarizer 309 and enters a second photodetector 310. The two orthogonal interference signals collected by the photodetectors are fed into a signal processing module. By calculating the arctangent and unwrapping the phase of the interference signals, the motion distance and direction of motion of the first grating 1 can be obtained. The light intensity of each interference signal exhibits the following relationship: ; In the formula, The period of a chromium atom photolithography grating. This represents the distance the displacement platform has traveled.

[0033] The periodic direction of the first grating 1 is aligned with the motion measurement axis direction of the high-precision displacement stage. At this point, no interference signal is generated when a displacement perpendicular to the motion measurement axis is applied, ensuring ideal installation of the first reading head 3 and the first grating 1. The signal collected by the first reading head 3 at this time is: ; in, This indicates the period of the first grating.

[0034] S3. As the self-traceable gratings shift, the two reading heads of the self-traceable interferometer simultaneously acquire the displacement signals of the two self-traceable gratings. With the first grating 1 and the second grating 2 moving simultaneously, the first reading head 3 and the second reading head 4 respectively acquire the original interference signals of the first grating 1 and the second grating 2. Due to the installation angle error between the grating period of the second grating 2 and the first grating 1, the installation angle errors are respectively the rotation angles... Pitch angle and yaw angle Then, at this time, the signal collected by the second reading head 4 is: ; in, This indicates the period of the second grating.

[0035] S4. Using the displacement measurement signal of one of the reading heads as a reference, and effectively utilizing the theoretical spacing of the self-traceable grating, the cosine installation error between the workpieces is calculated by comparing the ratio of the number of cycles of the original signals acquired by the two reading heads, thus achieving in-situ detection. Specifically, this is based on the theoretical spacing of the self-traceable grating. The cosine error is calculated by comparing the ratio of the periods of the original signals acquired by the two reading heads, and the installation error of the second grating 2 is calculated to facilitate correction.

[0036] By comparing the two phase signals and The comparison results of displacement measurement signals from two self-traceable grating interferometers were obtained: ; in, and These represent the displacement measurement results of the second and first reading heads, respectively.

[0037] The cosine error of the two workpieces was obtained by comparison. as follows: ; Reference Figure 5 As the first reading head 3 and the second reading head 4, serving as the reference, move at a constant speed simultaneously, they simultaneously acquire the interference signals of the two self-traceable gratings, with each reading head taking one signal. The signal period of the reference grating is... The grating period time to be adjusted is Due to the existence of cosine error, At this point, the measured cosine error is: ; Correction is achieved by adjusting the installation pitch and yaw parameters. A value of 0 allows for in-situ correction of the cosine error during installation.

[0038] The self-traceable grating is fabricated using atomic lithography, and its theoretical periodicity is directly traced back to the transition frequency of Cr atoms, corresponding to the chromium atom transition spectral lines. 7 S3→ 7 P4 0 The theoretical period value is 212.7787±0.0049nm (k=2), which is the materialization of a natural constant. In this invention, the period value of the self-traceable grating was determined by German PTB to be 212.781±0.008nm (k=2), with an accuracy reaching the picometer level. The accuracy and consistency of the period have been verified, and it has significant advantages such as fine scribing density, high accuracy, and strong robustness.

[0039] Grating interferometers, using grating spacing as the measurement reference, possess significant advantages such as short traceability chains, high precision, and strong environmental robustness. Embedding a self-traceable grating into a grating interferometer can construct a self-traceable grating interferometer with direct traceability of measurement values. Compared to laser interferometers, which use physical gratings as the reference, this offers stronger environmental robustness and is more suitable as an on-site angle measurement tool. This invention proposes to achieve in-situ detection of the installation cosine error of two workpieces by comparing the difference in interference signals between two self-traceable grating interferometers, combined with the consistency of the standard period value of the self-traceable gratings. Furthermore, it can quantify the installation error and provide correction guidance. The self-traceable grating, with its high precision and direct traceability, ensures the accuracy and traceability of the detection results, demonstrating significant application advantages.

[0040] Therefore, the present invention employs the above-mentioned in-situ detection method for cosine installation error between workpieces using a self-traceable grating interference type, providing an efficient and reliable solution for the perfect installation of two workpieces, which has significant research significance and application value.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for in-situ detection of cosine installation error between workpieces using a self-traceable grating interferometric type, characterized in that, Includes the following steps: S1. Self-traceable gratings are deposited on two workpieces to be tested, and the two workpieces to be tested are coarsely aligned with the two self-traceable gratings parallel to each other along the grating period direction. Then, the grating interference signal is measured simultaneously by two self-traceable grating interferometers that move in coordination. The two workpieces to be tested are the first workpiece and the second workpiece, and the self-traceable grating includes the first grating and the second grating. S2. Align the periodic direction of the first grating with the motion measurement axis direction of the high-precision displacement stage, and adjust the interference light signal to ensure that the two reading heads of the self-traceable grating interferometer are ideally installed relative to their respective gratings; the two reading heads are the first reading head and the second reading head, respectively. S3. As the self-traceable gratings are displaced, the two reading heads of the self-traceable interferometer simultaneously acquire the displacement signals of the two self-traceable gratings. S4. Using the displacement measurement signal of one of the reading heads as a reference, and utilizing the theoretical spacing of the self-traceable grating, the cosine installation error between the workpieces is calculated by comparing the ratio of the number of cycles of the original signals collected by the two reading heads.

2. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometric type as described in claim 1, characterized in that, The two workpieces to be tested are coarsely aligned with two self-traceable gratings in parallel along the grating period direction. Specifically, the period direction of the first grating is strictly parallel and fixed with the reference direction of the first workpiece, and the period direction of the second grating is strictly parallel and fixed with the reference direction of the second workpiece.

3. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometric type as described in claim 1, characterized in that, Self-traceable gratings are deposited using precision-machined ultra-high perpendicularity orthogonal mirrors and fixtures, ensuring that the deposition direction of the grating lines is strictly parallel to the workpiece reference direction.

4. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometry method according to claim 1, characterized in that, The laser wavelength of the readhead light source module of the self-traceable grating interferometer is less than twice the theoretical spacing of the self-traceable grating.

5. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometric type as described in claim 1, characterized in that, The ideal method for installing the self-traceable grating and the readhead is to incident a laser at a Litterow angle onto the self-traceable grating and return along the same path, so that the interference signal reaches its maximum.

6. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometric type as described in claim 1, characterized in that, The read head module of the self-traceable grating interferometer includes at least two read heads; the read head module of the self-traceable grating interferometer adopts any one of the displacement measurement methods of zero-difference interferometry, heterodyne interferometry and self-mixed interferometry.

7. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometric type as described in claim 1, characterized in that, The read head module of the self-traceable grating interferometer moves in the same direction as its corresponding self-traceable grating.

8. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometry method according to claim 1, characterized in that, In step S2, the periodic direction of the first grating is aligned with the motion measurement axis direction of the high-precision displacement stage. At this point, no interference signal is generated when a displacement perpendicular to the motion measurement axis is applied, ensuring ideal installation of the first reading head and the first grating. The signal collected by the first reading head at this time is: ； in, This indicates the period of the first grating. This represents the distance the displacement platform has traveled.

9. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometry method according to claim 8, characterized in that, Step S3 specifically involves: As the first and second gratings move simultaneously, the first and second reading heads respectively acquire the original interference signals of the first and second gratings. Due to the installation angle error between the grating period of the second grating and the first grating, the installation angle errors are respectively the rotation angle... Pitch angle and yaw angle Then, the signal collected by the second reading head at this time is: ； in, This indicates the period of the second grating.

10. The in-situ detection method for cosine installation error between workpieces using a self-traceable grating interferometry method according to claim 9, characterized in that, Step S4 specifically involves: using the displacement measurement signal of the first reading head as a reference, and based on the theoretical spacing of the self-traceable grating... And by comparing the two phase signals and The comparison results of displacement measurement signals from two self-traceable grating interferometers were obtained: ； in, and These represent the displacement measurement results of the second and first reading heads, respectively. The cosine error of the two workpieces was obtained by comparison. as follows: 。

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