Device and method for calibrating grating interferometer to measure grating cosine error

Abstract

The present invention relates to the field of displacement measurement technology, and in particular to a device and method for measuring grating cosine error by calibrating a grating interferometer. In the device, there is a cosine error angle between the placement direction of the scale grating and the moving direction of the displacement stage; a spectroscopic system emits two laser beams, the scale grating diffracts one of the laser beams to generate zero-order diffraction light, and the zero-order diffraction light is incident into the spectroscopic system; a reflective component reflects the other laser beam into the spectroscopic system; the spectroscopic system interferes the zero-order diffraction light with the second laser to obtain an interference signal, and a core processing system obtains a cosine error angle according to the interference signal; a measuring method is to solve the phase shift of the scale grating, thereby obtaining the displacement generated by the scale grating interference and the displacement along the direction of the zero-order diffraction light, and with the trigonometric function relationship between the two displacements, the cosine error angle can be calculated and the measurement error introduced thereby can be compensated.

Description

Technical Field

[0001] The invention belongs to the technical field of displacement measurement, and in particular relates to a device and method for calibrating a grating interferometer to measure a grating cosine error. Background Art

[0002] At present, high-precision displacement measurement technologies mainly include laser interferometry and grating interferometry. Among them, the measurement basis of grating interferometry is the grating pitch, and the grating is made of materials with low expansion coefficient, which makes the grating stable and reliable. At the same time, grating interferometry is based on grating Doppler frequency shift. During the measurement process, the optical path from the laser light source to the grating surface is short and does not change with the increase of measured displacement, which makes it more resistant to environmental interference. Therefore, the grating interferometer used to realize grating interferometry has more advantages in terms of system construction cost, volume, and flexibility of use, and is widely used in high-end CNC machine tools, integrated circuit manufacturing equipment, and aerospace fields.

[0003] The error sources that affect the grating interferometric displacement measurement accuracy mainly include: instrument error, installation error and environmental error. The grating pitch error, thermal expansion error and installation cosine error will all introduce linear errors. Multiple errors are coupled together, seriously affecting the grating measurement accuracy. Among them, the cosine error refers to the deviation introduced when the measured displacement is not the actual displacement when the measurement line is not parallel to the displacement line.

[0004] For grating interferometric displacement measurement, since the angle between the measuring light incident on the grating surface and the grating displacement direction is large or even perpendicular, the cosine error causes a significant displacement along the measuring beam direction during the grating displacement process, and the laser interference phase shift introduced by this displacement will overlap with the grating interference Doppler phase shift, which will affect the measurement accuracy of the grating interference displacement. Therefore, how to effectively measure and eliminate the cosine error is crucial to improving the measurement accuracy of grating interferometric linear displacement.

[0005] The Chinese patent publication number is CN102540783A, and the publication date is November 12, 2014. The patent name is "An interferometer Abbe cosine error automatic calibration device and method". By building multiple laser interferometers to simultaneously measure the axial displacement of the system, a mathematical model is established to solve the system displacement to achieve the separation of cosine errors. This type of solution has a complex solution process and a large volume, and is not suitable for miniaturized precision displacement measurement systems.

[0006] The Chinese patent publication number is CN116379972A, the publication date is August 22, 2023, and the patent name is "Method and system for detecting cosine error angle and correcting error and test tooling". The invention patent uses image processing to identify the offset between the measurement spot mass center and the reference spot mass center before and after displacement, and uses this offset to calculate the cosine error angle. The precision and accuracy of this solution completely depends on the back-end image recognition system. If the displacement distance is too small and the moving distance of the spot mass center is less than the image recognition limit, it cannot be effectively used to measure the cosine error, and the measurement sensitivity and accuracy are relatively poor. Summary of the invention

[0007] In view of this, the present invention aims to provide a device and method for calibrating a grating interferometer to measure a grating cosine error, constructing an interference displacement measurement structure with the zero-order diffraction light of the grating, and under the influence of the cosine error angle, by taking advantage of the characteristic that the interference phase of the detection light beam changes in the direction of the zero-order light when the scale grating is translated with the cosine error angle, by measuring the lateral displacement and the displacement change in the direction of the zero-order diffraction light, the cosine error angle is solved based on the inherent trigonometric function relationship between the two, and with the high sensitivity and high precision of laser interferometry itself, high-precision measurement and calibration of the cosine error can be achieved.

[0008] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0009] A device for calibrating a grating interferometer to measure a grating cosine error comprises a spectroscopic system, a reflective component, a core processing system, a displacement stage, and a scale grating placed on the displacement stage, wherein a cosine error angle exists between the placement direction of the scale grating and the movement direction of the displacement stage; the core processing system is connected to the spectroscopic system and the displacement stage at the same time, the core processing system controls the spectroscopic system to complete laser emission and receive signals generated by the spectroscopic system, and at the same time the core processing system controls the displacement stage to drive the scale grating to move; wherein the spectroscopic system comprises a light source, and the light source is connected to the core processing system, the spectroscopic system emits a first laser and a second laser; the first laser is incident on the scale grating; the scale grating diffracts the first laser, and the zero-order diffraction light generated by the diffraction is incident on the spectroscopic system; the second laser is incident on the reflective component; the reflective component reflects the second laser into the spectroscopic system; the spectroscopic system interferes with the zero-order diffraction light and the second laser to obtain an interference signal; the core processing system receives the interference signal, and obtains a cosine error angle according to the interference signal.

[0010] Furthermore, the spectroscopic system also includes a beam splitter and a photodetector; wherein the light source is controlled by the core processing system to emit a laser to the beam splitter, and the beam splitter splits the laser into a first laser and a second laser; the zero-order diffraction light and the second laser are combined in the beam splitter and interfere with each other; the photodetector is connected to the core processing system, and the photodetector detects the interference signal between the zero-order diffraction light and the second laser; the core processing system receives the interference signal and obtains the cosine error angle based on the interference signal.

[0011] Furthermore, the light source is a single-frequency laser.

[0012] A method for calibrating a grating interferometer to measure a grating cosine error is applicable to the device for calibrating a grating interferometer to measure a grating cosine error provided by the present invention, and specifically comprises the following steps:

[0013] S1: Control the translation stage to drive the scale grating to move, so that the position where the first laser is incident on the scale grating changes;

[0014] S2: reading the interference signal in the photodetector to obtain the interference phase of the interference signal;

[0015] S3: continuously monitoring the interference signal to obtain a first phase shift caused by the scale grating moving along the direction of the zero-order diffraction light, and then obtaining a first displacement of the scale grating moving along the direction of the zero-order diffraction light;

[0016] S4: obtaining a second displacement of the scale grating to generate interference according to the interference phase and the first phase shift;

[0017] S5: Obtain a cosine error angle according to the first displacement and the second displacement.

[0018] Furthermore, the first displacement and the second displacement are perpendicular to each other.

[0019] Further, in step S3, the first displacement is obtained by the following formula:

[0020]

[0021] in, represents the first displacement, represents the wavelength of the laser emitted by the light source, n represents the refractive index of air, represents the first phase shift.

[0022] Further, in step S4, the second displacement is obtained by the following formula:

[0023]

[0024] in, represents the second displacement, Indicates the grating pitch of the scale grating, represents the interference phase.

[0025] Further, in step S5, the cosine error angle is obtained by the following formula:

[0026]

[0027] in, Represents the cosine error angle.

[0028] Compared with the prior art, the invention can achieve the following beneficial effects:

[0029] The present invention creates a device and method for measuring grating cosine error by calibrating a grating interferometer. On the basis of retaining the original grating interference displacement measurement optical path structure, the large-angle geometric relationship between the displacement direction of the scale grating and the incident light beam in the grating interference is utilized. Under the influence of the cosine error angle, the scale grating movement will introduce a large displacement in the direction of the grating zero-order diffraction light. With the help of the extremely high detection accuracy and sensitivity of laser interference itself, the displacement change is detected. Combined with simple trigonometric function calculations, the scale grating installation cosine error angle can be efficiently and accurately calculated, and its influence on displacement measurement can be accurately eliminated. The optical path structure involved in the present invention is simple, can be integrated, and is easy to miniaturize, and can be applied to both homodyne grating interference and heterodyne grating interference systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings:

[0031] Figure 1 A schematic diagram of the structure of a device for calibrating a grating interferometer and measuring a grating cosine error according to an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of the optical path structure of the device for calibrating a grating interferometer and measuring a grating cosine error as described in the specific embodiment 1 of the present invention;

[0033] Figure 3 A schematic diagram of the optical path structure of a device for calibrating a grating interferometer and measuring a grating cosine error as described in specific embodiment 2 of the present invention;

[0034] Figure 4 A schematic diagram of the optical path structure of a device for calibrating a grating interferometer and measuring a grating cosine error as described in specific embodiment 3 of the present invention;

[0035] Figure 5 A schematic diagram of the optical path structure of a device for calibrating a grating interferometer and measuring a grating cosine error as described in specific embodiment 4 of the present invention;

[0036] Figure 6 A schematic flow chart of a method for calibrating a grating interferometer to measure a grating cosine error according to an embodiment of the present invention;

[0037] Figure 7 is the motion diagram of the ruler grating;

[0038] Figure 8 This is a schematic diagram of the movement of the ruler grating.

[0039] Description of reference numerals:

[0040] 1. Light source; 2. Beam splitter; 3. Photodetector; 4. Plane reflector; 5. Scale grating; 6. Translation stage; 7. Corner cube prism; 8. Semi-transparent and semi-reflective film; 9. First beam splitter; 10. Second beam splitter; 11. Cosine error angle. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0042] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0043] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0044] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0045] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0046] like Figures 1 to 4 As shown, the device for measuring the grating cosine error of the calibration grating interferometer described in the embodiment of the invention comprises a spectroscopic system, a reflective component, a scale grating 5, a displacement stage 6 and a core processing system. The scale grating 5 is placed on the displacement stage 6, and there is a cosine error angle 11 between the placement direction of the scale grating 5 and the movement direction of the displacement stage 6. The core processing system is connected to the spectroscopic system and the displacement stage 6 at the same time. The core processing system controls the spectroscopic system to complete the laser emission and receive the signal generated by the spectroscopic system, and at the same time, the core processing system controls the displacement stage 6 to drive the scale grating 5 to move.

[0047] The light splitting system includes a light source 1, a beam splitter 2 and a photodetector 3. The light source 1 is connected to the core processing system, so that the core processing system controls the light source 1 to emit laser light to the beam splitter 2, and the beam splitter 2 splits the laser light into a first laser light and a second laser light. The photodetector 3 is connected to the core processing system, so that the core processing system receives the signal emitted by the photodetector 3.

[0048] The first laser is incident on the scale grating 5, which diffracts the first laser and incidents the zero-order diffraction light generated by the diffraction into the beam splitter 2. The second laser is incident on the reflective component, which reflects the second laser into the beam splitter 2. The zero-order diffraction light and the second laser are combined and interfered in the beam splitter 2. The photodetector 3 detects the interference signal between the zero-order diffraction light and the second laser. The core processing system receives the interference signal and obtains the cosine error angle 11 based on the interference signal.

[0049] In the device for calibrating a grating interferometer to measure a grating cosine error provided by the present invention, a single-frequency laser is preferably used as the light source 1, and the reflective component can be a plane mirror, a corner cube prism, a semi-transparent and semi-reflective film or other optical elements that play a reflective role, and the number and position of the beam splitters 2 can also be adjusted according to actual needs. In order to clearly demonstrate the device for calibrating a grating interferometer to measure a grating cosine error provided by the present invention, the present invention also provides a specific embodiment of the device for calibrating a grating interferometer to measure a grating cosine error when the reflective components are a plane mirror, a corner cube prism and a semi-transparent and semi-reflective film, and a specific embodiment when the number of beam splitters 2 is 2.

[0050] Specific embodiment 1: When the reflective component is a plane reflector 4, the structure of the device for calibrating a grating interferometer and measuring a grating cosine error provided by the present invention is as follows: Figure 1 As shown, the corresponding optical path structure is as follows Figure 2 shown.

[0051] The laser emitted by the light source 1 first enters the beam splitter 2 to generate the first laser and the second laser. The first laser enters the scale grating 5, which diffracts the first laser. The zero-order diffraction light generated by the diffraction enters the beam splitter 2. The second laser is vertically incident on the surface of the plane reflector 4 and is reflected. The reflected second laser returns along the original path and enters the beam splitter 2 again. The zero-order diffraction light and the second laser are combined in the beam splitter 2 and interfere. The photodetector 3 detects the interference signal between the zero-order diffraction light and the second laser, and transmits the interference signal to the core processing system. The core processing system obtains the cosine error angle 11 based on the interference signal.

[0052] Specific embodiment 2: When the reflective component is a corner cube prism 7, the optical path structure of the device for calibrating a grating interferometer and measuring a grating cosine error provided by the present invention is as follows: Figure 3 shown.

[0053] The laser emitted by the light source 1 first enters the beam splitter 2 to generate the first laser and the second laser. The first laser enters the scale grating 5, which diffracts the first laser. The zero-order diffraction light generated by the diffraction enters the beam splitter 2. The second laser is vertically incident on the corner cube prism 7 and is reflected. The reflected second laser returns along the original path and enters the beam splitter 2 again. The zero-order diffraction light and the second laser are combined in the beam splitter 2 and interfere. The photodetector 3 detects the interference signal between the zero-order diffraction light and the second laser, and transmits the interference signal to the core processing system. The core processing system obtains the cosine error angle 11 based on the interference signal.

[0054] Specific embodiment 3: When the reflective component is a semi-transparent and semi-reflective film 8, the structure of the device for calibrating a grating interferometer and measuring a grating cosine error provided by the present invention is similar to the common optical path structure of a Fizeau interferometer, such as Figure 4As shown, the semi-transparent and semi-reflective film 8 is plated on the side of the beam splitter 2 close to the scale grating 5.

[0055] The laser emitted by the light source 1 is first incident on the beam splitter 2, and then reflected by the beam splitter 2 onto the semi-transparent and semi-reflective film 8. The semi-transparent and semi-reflective film 8 divides the laser into a first laser that can pass through the semi-transparent and semi-reflective film 8, and a second laser reflected by the semi-transparent and semi-reflective film 8. The first laser is incident on the scale grating 5, and the scale grating 5 diffracts the first laser. The zero-order diffraction light generated by the diffraction is input into the beam splitter 2 through the semi-transparent and semi-reflective film 8 in turn. The second laser enters the beam splitter 2. The zero-order diffraction light and the second laser are combined in the beam splitter 2 and interfere. The photodetector 3 detects the interference signal between the zero-order diffraction light and the second laser, and then obtains the cosine error angle 11 based on the interference signal.

[0056] Specific embodiment 4: When the number of beam splitters 2 is 2, the device for measuring the grating cosine error of the calibration grating interferometer provided by the present invention is an oblique incidence structure, which is similar to the Mach-Zehnder interference structure, such as Figure 5 As shown, a plane reflector 4 is selected as the reflective component.

[0057] The laser emitted by the light source 1 is first incident on the first beam splitter 9 to generate the first laser and the second laser. The first laser is incident on the scale grating 5, and the scale grating 5 diffracts the first laser, and the zero-order diffraction light generated by the diffraction enters the second beam splitter 10. The second laser is incident on the surface of the plane reflector 4 and is reflected, and the reflected second laser is incident on the second beam splitter 10. The zero-order diffraction light and the second laser are combined and interfered in the second beam splitter 10. The photodetector 3 detects the interference signal of the zero-order diffraction light and the second laser, and then obtains the cosine error angle 11 according to the interference signal.

[0058] Based on the proposed device for calibrating a grating interferometer to measure a grating cosine error, the present invention also provides a method for calibrating a grating interferometer to measure a grating cosine error. Figure 1 to Figure 6 , specifically including the following steps:

[0059] S1: Control the translation stage 6 to drive the scale grating 5 to move, so that the position where the first laser generated by the spectroscopic system is incident on the scale grating 5 changes.

[0060] like Figure 7 and Figure 8 As shown, when the displacement stage 6 drives the scale grating 5 to move the actual displacement L, the position where the first laser is incident on the scale grating 5 changes from point P1 to point P2. At this time, the displacement caused by the interference of the scale grating 5 is the second displacement L. d , corresponding to the second phase The initial phase of the interference of scale grating 5 is 0, so the second phase The corresponding second phase shift is equal to the second phase .

[0061] Since there is a cosine error angle between the placement direction of the scale grating 5 and the moving direction of the translation stage 6 , so the second displacement L d It is not equal to the actual displacement L of the scale grating 5, but produces a first displacement L along the direction of the zero-order diffraction light. i , corresponding to the first phase The initial phase of the scale grating 5 along the zero-order diffraction light direction is 0, so the first phase The corresponding first phase shift is equal to the first phase .

[0062] S2: Read the interference signal between the zero-order diffraction light and the second laser from the photodetector 3 to obtain the interference phase of the interference signal.

[0063] Taking the +1-order diffracted light as an example, the interference signal detected by the photodetector 3 can be expressed as:

[0064]

[0065] in, represents the interference signal of +1-order diffracted light, represents the DC component of the interference signal, which can be directly read on the photodetector 3. It represents the interference phase actually detected by the photodetector 3 and can be read using a phase meter.

[0066] There is a cosine error angle between the placement direction of the scale grating 5 and the moving direction of the translation stage 6. , so that the first phase shift The corresponding phase is coupled into the interference of the scale grating 5, resulting in the interference phase The first phase shift With the second phase shift The sum is:

[0067]

[0068] At this time, the interference signal of the +1-order diffracted light detected by the photodetector 3 can be expressed as:

[0069]

[0070] Due to the introduction of cosine error, there is an additional first phase shift in the +1st order diffraction light. , so it is necessary to use zero-order light for calculation, which can shift the first phase Extracted separately.

[0071] S3: Continuously monitor the interference signal to obtain a first phase shift caused by the scale grating 5 moving along the direction of the zero-order diffraction light, and then obtain a first displacement of the scale grating 5 moving along the direction of the zero-order diffraction light.

[0072] In step S3, for the zero-order diffraction light interference, the interference signal received by the photodetector 3 is continuously monitored, and the first phase shift is obtained by arc cosine calculation or the like. The first phase shift With the first displacement L i The relationship is:

[0073]

[0074] in, represents the wavelength of the laser light emitted by the light source 1, and n represents the refractive index of air.

[0075] Therefore, the first displacement L is obtained by the following formula i :

[0076]

[0077] S4: According to the interference phase and the first phase shift, a second displacement of the scale grating 5 perpendicular to the first displacement is obtained.

[0078] In step S4, the second displacement L is obtained by the following formula: d :

[0079]

[0080] in, Indicates the grating pitch of the scale grating 5.

[0081] S5: Obtain a cosine error angle according to the first displacement and the second displacement.

[0082] In step S5, the cosine error angle It is obtained by the following formula:

[0083]

[0084] After completing the above steps and obtaining the cosine error angle between the placement direction of the scale grating 5 and the moving direction of the translation stage 6 Then, based on the second displacement L generated by the interference of the scale grating 5 obtained in step S4, d The actual displacement L of the scale grating 5 driven by the displacement stage 6 is obtained by the following formula:

[0085]

[0086] After the actual displacement L is obtained, the displacement of the scale grating 5 driven by the translation stage 6 can be corrected according to the actual displacement L, so as to compensate for the cosine error angle in subsequent measurements and calculations. The measurement error caused.

[0087] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0088] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calibrating a grating interferometer to measure a grating cosine error, characterized in that: The device for measuring the cosine error of a grating comprises a spectroscopic system, a reflective component, a core processing system, a displacement stage, and a scale grating placed on the displacement stage, wherein a cosine error angle exists between the placement direction of the scale grating and the moving direction of the displacement stage; the core processing system is connected to the spectroscopic system and the displacement stage at the same time, the core processing system controls the spectroscopic system to complete laser emission and receive the signal generated by the spectroscopic system, and at the same time, the core processing system controls the displacement stage to drive the scale grating to move; wherein the spectroscopic system comprises a light source, and the light source is connected to the core processing system, the spectroscopic system emits a first laser and a second laser; the first laser is incident on the scale grating; the scale grating diffracts the first laser, and the zero-order diffraction light generated by the diffraction is incident on the spectroscopic system; the second laser is incident on the reflective component; the reflective component reflects the second laser into the spectroscopic system; the spectroscopic system interferes with the zero-order diffraction light and the second laser to obtain an interference signal; the core processing system receives the interference signal, and obtains the cosine error angle according to the interference signal; Methods for measuring grating cosine error include: S1: controlling the translation stage to drive the scale grating to move, so that the position where the first laser is incident on the scale grating changes; S2: reading the interference signal in a photodetector to obtain an interference phase of the interference signal; S3: continuously monitoring the interference signal to obtain a first phase shift caused by the scale grating moving along the direction of the zero-order diffraction light, and further obtaining a first displacement of the scale grating moving along the direction of the zero-order diffraction light; S4: obtaining a second displacement of the scale grating to generate interference according to the interference phase and the first phase shift; S5: Obtain the cosine error angle according to the first displacement and the second displacement.

2. The method for measuring grating cosine error by calibrating a grating interferometer according to claim 1, characterized in that: The spectroscopic system also includes a beam splitter and a photodetector; wherein the light source is controlled by the core processing system to emit laser light to the beam splitter, and the beam splitter splits the laser light into the first laser light and the second laser light; the zero-order diffraction light and the second laser light are combined and interfere with each other in the beam splitter; the photodetector is connected to the core processing system, and the photodetector detects an interference signal between the zero-order diffraction light and the second laser light; the core processing system receives the interference signal and obtains the cosine error angle according to the interference signal.

3. The method for measuring grating cosine error by calibrating a grating interferometer according to claim 2, characterized in that: The light source is a single-frequency laser.

4. The method for measuring grating cosine error by calibrating a grating interferometer according to claim 1, characterized in that: The first displacement and the second displacement are perpendicular to each other.

5. The method for measuring grating cosine error by calibrating a grating interferometer according to claim 1, characterized in that: In the step S3, the first displacement is obtained by the following formula: in, represents the first displacement, represents the wavelength of the laser emitted by the light source, n represents the refractive index of air, represents the first phase shift.

6. The method for measuring grating cosine error by calibrating a grating interferometer according to claim 5, characterized in that: In the step S4, the second displacement is obtained by the following formula: in, represents the second displacement, represents the grating pitch of the scale grating, represents the interference phase.

7. The method for measuring grating cosine error by calibrating a grating interferometer according to claim 6, characterized in that: In step S5, the cosine error angle is obtained by the following formula: in, represents the cosine error angle.

Images