A high-precision displacement measurement system based on metasurface microlens array

Abstract

The present invention provides a high-precision displacement measurement system based on a metasurface microlens array, which belongs to the field of micro-nano optics and high-precision measurement equipment. The system includes two parallel metasurface microlens arrays, a collimated laser light source, a convex lens and an image sensor. The spacing between the two metasurface microlens arrays is the sum of their focal lengths, which is equivalent to a blazed grating whose blaze angle changes with the relative displacement between the two metasurface microlenses; the intensity of adjacent diffraction orders on both sides of the blaze angle of the blazed grating is highly sensitive to relative displacement, and the convex lens projects the far-field diffraction angle spectrum of the outgoing array light beam to the image sensor. The image sensor detects the difference in the intensity of adjacent diffraction orders on both sides of the blaze angle, and the relative displacement between the two metasurface microlens arrays can be obtained. The present invention is a highly sensitive, fast displacement sensing technology that does not require complex post-processing algorithms, and has broad application prospects.

Description

Technical Field

[0001] The present invention belongs to the field of micro-nano optics and high-precision measurement equipment, and in particular relates to a high-precision displacement measurement system based on a super-surface microlens array. Background Art

[0002] High-precision displacement sensing technology plays an important role in many fields in industry and academia, such as semiconductor precision processing, lithography positioning systems, gravitational wave detection devices, and characterization of nanomaterials. Traditional displacement measurement technologies, such as laser interferometers, grating interferometers, and four-quadrant photodetectors, are often limited in detection sensitivity, system complexity, and device portability. With the increasing demand for high-precision positioning and measurement technology in many fields, people are in urgent need of a highly sensitive, fast, and non-complex post-processing algorithm-free displacement sensing technology.

[0003] Metasurfaces provide new design channels for novel optical devices and systems due to their ability to manipulate light fields on a subwavelength scale and their excellent compactness. We can use metasurfaces to design microlens arrays and use them to realize high-precision displacement measurement systems. Summary of the invention

[0004] In view of the problems in the prior art, the present invention provides a high-precision displacement measurement system based on a metasurface microlens array.

[0005] To achieve the above object, the present invention proposes the following technical solutions:

[0006] On the one hand, the present invention provides a high-precision displacement measurement system based on a metasurface microlens array, comprising a first metasurface microlens array and a second metasurface microlens array; the first metasurface microlens array and the second metasurface microlens array are parallel to each other, and the spacing between them is the sum of their focal lengths, forming a blazed grating; the first metasurface microlens array and the second metasurface microlens array are respectively fixed on two objects to be measured, and the relative displacement direction between the two objects to be measured is perpendicular to the optical axis of the metasurface microlens array; the first metasurface microlens array is used to divide the incident light into multiple light beams and focus them separately and then diverge to form an outgoing array light beam, and the second metasurface microlens array is used to collimate the outgoing array light beam of the first metasurface microlens array, and when there is a relative displacement between the two objects to be measured, the outgoing light beam of the second metasurface microlens array forms a certain deflection angle with the optical axis, and the deflection angle is the blazed angle, and the size of the blazed angle varies with the size of the relative displacement.

[0007] As a preferred embodiment of the present invention, the first metasurface microlens array includes a plurality of identical first metasurface microlenses arranged periodically, and the first metasurface microlenses are composed of a first transparent substrate and a plurality of sub-wavelength dielectric columnar structures on the surface of one side of the first transparent substrate; the sub-wavelength dielectric columnar structures of the first metasurface microlens array are all located on its exit surface; the second metasurface microlens array includes a plurality of identical second metasurface microlenses arranged periodically, and the second metasurface microlenses are composed of a second transparent substrate and a plurality of sub-wavelength dielectric columnar structures on the surfaces of both sides of the second transparent substrate; the plurality of sub-wavelength dielectric columnar structures on the first surface of the second transparent substrate are used to collimate the exit array light beam of the first metasurface microlens array, and the plurality of sub-wavelength dielectric columnar structures on the second surface of the second transparent substrate are used to further collimate the array light beam and eliminate stray light; the transparent substrates of all metasurface microlenses in each metasurface microlens array are integrally formed; the number, shape and arrangement of the first metasurface microlenses and the second metasurface microlenses are consistent; the height of each sub-wavelength dielectric columnar structure in each metasurface microlens is the same and the size parameters are different.

[0008] As a preferred embodiment of the present invention, the system also includes a collimated laser light source, a convex lens and an image sensor; the collimated laser light source is used to emit a collimated laser light beam to the incident surface of the first metasurface microlens array; the convex lens is placed in parallel behind the second metasurface microlens array, and is used to project the far-field diffraction angle spectrum of the blazed grating output array light beam to the image sensor; the image sensor is located at the back focal plane of the convex lens, and the image sensor is used to detect the intensity of the far-field diffraction angle spectrum of the output array light beam of the blazed grating.

[0009] On the other hand, the present invention is also based on a high-precision displacement measurement method of the above-mentioned measurement system, the method comprising: respectively installing a first metasurface microlens array and a second metasurface microlens array on two objects to be measured, so that the optical axis of the metasurface microlens array is perpendicular to the relative displacement direction of the object to be measured, and the spacing between the two metasurface microlens arrays is the sum of their focal lengths, forming a blazed grating with an adjustable blaze angle; obtaining the relationship between the relative displacement of the object to be measured and the difference in intensities of adjacent diffraction orders of the blazed grating through calibration; the object to be measured performs a relative displacement, and the far-field diffraction angle spectrum of the output array light beam of the blazed grating is detected by an image sensor, and the difference in diffraction orders and their intensities on both sides of the blaze angle is analyzed based on the far-field diffraction angle spectrum, and the relative displacement between the two objects to be measured is obtained by searching in the calibration results.

[0010] Compared with the prior art, the present invention has the following beneficial effects:

[0011] 1) The present invention provides a high-precision displacement measurement system based on a metasurface microlens array, which can achieve sub-nanometer displacement sensing and improve the measurement sensitivity by increasing the relative aperture of the metasurface microlens array.

[0012] 2) The displacement measurement system of the present invention can measure the absolute position of the current displacement by detecting the intensity of different far-field diffraction orders of the blazed grating.

[0013] 3) The displacement measurement system of the present invention is low in complexity and very simple, and only includes a collimated laser light source, two metasurface microlens arrays, a convex lens and an image sensor.

[0014] 4) The two metasurface microlens arrays of the present invention are highly integrated and light in weight. Due to their lightness, they can be installed on two objects whose relative displacement needs to be measured without affecting the movement of the two objects themselves. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of a high-precision displacement measurement system based on a metasurface microlens array;

[0016] Figure 2 It is a schematic diagram of generating parallel array light beams when two metasurface microlens arrays do not undergo relative displacement;

[0017] Figure 3 The relative displacement between the two metasurface microlens arrays is When Schematic diagram of parallel array beams;

[0018] Figure 4 The transmission amplitude and phase of nano-silicon pillars with different diameters at a wavelength of 1064 nm when the height is 625 nm and the lattice period is 530 nm, calculated using the full-wave simulation software COMSOL;

[0019] Figure 5 A displacement measurement system provided by the present invention is provided for the relative displacement between two metasurface microlens arrays = Far-field diffraction angle spectrum at 412 nm;

[0020] Figure 6 A displacement measurement system provided by the present invention is provided for the relative displacement between two metasurface microlens arrays = Far-field diffraction angle spectrum at 515 nm;

[0021] Figure 7 A displacement measurement system provided by the present invention generates different relative displacements between two metasurface microlens arrays Far-field diffraction angle spectrum at ;

[0022] Figure 8 The intensity difference between the far-field diffraction order 1 and order 0 of a displacement measurement system provided by the present invention and the relative displacement between two metasurface microlens arrays The relationship diagram between

[0023] Fig. 9 The intensity difference between different adjacent diffraction orders in the far field of a displacement measurement system provided by the present invention and the relative displacement between two metasurface microlens arrays The relationship diagram between . DETAILED DESCRIPTION

[0024] The present invention is further described and illustrated below in conjunction with the accompanying drawings and specific embodiments. The embodiments are merely exemplary of the present disclosure and do not define the scope of limitation. The technical features of each embodiment of the present invention may be combined accordingly without conflicting with each other.

[0025] The present invention provides a high-precision displacement measurement system based on a metasurface microlens array. Figure 1 As shown, the high-precision displacement measurement system includes a first metasurface microlens array 1, a second metasurface microlens array 2, a collimated laser light source 3, a convex lens 4 and an image sensor 5.

[0026] The collimated laser light source 3 emits a collimated laser beam, and the first metasurface microlens array 1 focuses the incident beam, and its focus is located on the front focal plane of the second metasurface microlens array 2; when the second metasurface microlens array 2 is displaced perpendicular to the optical axis relative to the first metasurface microlens array 1 , the direction of the outgoing array beam of the second metasurface microlens array 2 will change; the two parallel confocal microlens arrays are equivalent to constructing a blazed grating with adjustable blaze angle, and the angle of the outgoing array beam changed by the relative displacement between the metasurface microlens arrays is the blaze angle of the blazed grating. , according to the geometric relationship of lens imaging, the relative displacement between the two metasurface microlens arrays , Blaze angle of blazed grating , the focal length of the second metasurface microlens array The relationship between The convex lens 4 is placed in parallel behind the second metasurface microlens array 2, and the image sensor 5 is located on the back focal plane of the convex lens 4. The convex lens 4 plays the role of Fourier transform, and projects the far-field diffraction angle spectrum of the outgoing array light beam of the blazed grating onto the image sensor 5 to detect the intensity of different diffraction orders.

[0027] When the relative displacement between the two metasurface microlens arrays changes, the blaze angle of the blazed grating changes, resulting in changes in the intensities of different diffraction orders. The intensities of adjacent diffraction orders on both sides of the blaze angle are highly sensitive to the relative displacement between the two metasurface microlens arrays. The relative displacement between the two metasurface microlens arrays can be obtained by detecting the difference in intensities of adjacent diffraction orders on both sides of the blaze angle through the image sensor 5.

[0028] Two metasurface microlens arrays can be fixedly mounted on two objects whose relative displacement needs to be measured. The optical axis of the metasurface microlens array is perpendicular to the relative displacement direction of the object. The spacing between the two metasurface microlens arrays is adjusted to the sum of the focal lengths of the two metasurface microlens arrays. , forming a blazed grating with adjustable blazed angle; and combining a collimated laser light source 3, a convex lens 4 and an image sensor 5 to form a Figure 1 The high-precision displacement measurement system shown can obtain the relative displacement between two objects by detecting the difference in intensity between adjacent diffraction orders on both sides of the blaze angle of the blazed grating through the image sensor 5.

[0029] The first metasurface microlens array 1 includes a plurality of periodically arranged first metasurface microlenses, which are composed of a first transparent substrate and a plurality of sub-wavelength medium columnar structures on the surface of one side of the first transparent substrate. The sub-wavelength medium columnar structures of the first metasurface microlens array 1 are all located on its exit surface. The second metasurface microlens array 2 includes a plurality of periodically arranged second metasurface microlenses, which are composed of a second transparent substrate and a plurality of sub-wavelength medium columnar structures on the surfaces of both sides of the second transparent substrate. The number, shape and arrangement of the first metasurface microlenses and the second metasurface microlenses are consistent.

[0030] Both the first metasurface microlens and the second metasurface microlens satisfy the following requirements: the transparent substrates of all metasurface microlenses in the metasurface microlens array are integrally formed and are in the shape of a flat plate; the subwavelength medium columnar structures have the same height and different size parameters, so that the microlenses can perform phase modulation on the incident light; the subwavelength medium columnar structures can be in the shape of a cylinder, a square column, etc., and their size parameters refer to the diameter of the cylinder or the side length of the cross section of the square column; the subwavelength medium columnar structures in the metasurface microlenses are arranged in a matrix, and their arrangement period is called the lattice period, the lattice period of all subwavelength medium columnar structures in the first metasurface microlens is equal, and the lattice period of all subwavelength medium columnar structures in the second metasurface microlens is also equal; the ratio of the exit light beam aperture of the second metasurface microlens to the side length of the single-chip metasurface microlens is greater than 0.9, so as to reduce the diffraction side lobes of the exit array light beam when no relative displacement occurs, thereby improving the sensitivity of the high-precision displacement measurement system of the present invention.

[0031] The second metasurface microlens array 2 is composed of a second transparent substrate and a plurality of sub-wavelength dielectric columnar structures on both sides of the second transparent substrate. The function of the plurality of sub-wavelength dielectric columnar structures on the first surface of the second transparent substrate is to collimate the array light beam generated by the first metasurface microlens array 1 after focusing and then diverging. The function of the plurality of sub-wavelength dielectric columnar structures on the second surface of the second transparent substrate is to further collimate and eliminate stray light. The transparent substrate is made of glass, quartz, silicon dioxide and other materials, and the sub-wavelength dielectric columnar structures are made of silicon, silicon nitride, titanium dioxide, gallium nitride and other materials. The specific materials are selected according to the working wavelength. The design method of the metasurface microlens is as follows:

[0032] 1) According to the design index requirements and process limitations of the displacement measurement system, the working wavelength, focal length, aperture and arrangement period of the internal columnar structure of the two metasurface microlenses are determined.

[0033] 2) According to the design parameters determined in step 1, two metasurface microlenses are simulated using binary surfaces in optical simulation software (such as Zemax software), and the phase distribution requirements of the two metasurface microlenses are obtained using damped least squares optimization.

[0034] 3) Use electromagnetic full-wave simulation software to simulate the array formed by the periodic arrangement of the same subwavelength dielectric columnar structure, calculate the transmission amplitude and transmission phase of a single subwavelength dielectric columnar structure in the array under different size parameters at the working wavelength, and select subwavelength dielectric columnar structures with a transmission amplitude greater than 0.9 to construct a unit structure database of the metasurface; during the simulation process, the arrangement period of the subwavelength dielectric columnar structure should be less than the working wavelength, and the transmission phase of the columnar structure under different size parameters should cover 0-2π.

[0035] 4) According to the phase distribution requirements of the metasurface microlens, subwavelength dielectric columnar structures of different sizes are selected from the unit structure database and arranged on a transparent substrate to obtain microlenses that meet the phase distribution requirements, and then the metasurface microlens array is processed.

[0036] Based on the above system, the present invention also provides a high-precision displacement measurement method based on a metasurface microlens array, the method comprising:

[0037] The first metasurface microlens array 1 and the second metasurface microlens array 2 are respectively mounted on two objects to be measured, the optical axis of the metasurface microlens array is adjusted to be perpendicular to the relative displacement direction of the object, and the spacing between the two metasurface microlens arrays is adjusted to be the sum of their focal lengths. , forming a blazed grating with adjustable blaze angle; and Figure 1As shown, a high-precision displacement measurement system is formed by combining a collimated laser light source 3, a convex lens 4 and an image sensor 5; after calibration, the relationship between the relative displacement and the intensity of each diffraction order of the blazed grating is obtained; the object to be measured is relatively displaced, and the far-field diffraction angle spectrum of the outgoing array light beam of the blazed grating is detected by the image sensor 5, and the difference in the diffraction orders and their intensities on both sides of the blazed angle is analyzed based on the far-field diffraction angle spectrum, and the relative displacement between the two objects is obtained by searching in the calibration results.

[0038] In order to more clearly illustrate the displacement measurement system of the present invention, a specific embodiment is described below.

[0039] This embodiment provides a high-precision displacement sensing system based on a metasurface microlens array. The system is composed of Figure 1 As shown, it includes a first metasurface microlens array 1, a second metasurface microlens array 2, a collimated laser light source 3, a convex lens 4 and an image sensor 5. The operating wavelength is 1064 nm, and the array periods of the two metasurface microlens arrays are = 177 nm, and the aperture of the light beam emitted by each microlens in the second metasurface microlens array 2 is = 162 nm, the focal length of the first metasurface microlens array 1 is , the focal length of the second metasurface microlens array 2 is .

[0040] According to the above design parameters, the two metasurface microlens arrays are simulated using binary surfaces in Zemax software, and the phase distribution requirements of the two metasurface microlens arrays are obtained using damped least squares optimization. Figure 4 The transmission amplitude and phase of columnar structures with different diameters at the working wavelength when the columnar structure height is 625 nm and the lattice period is 530 nm are calculated using the full-wave simulation software COMSOL to construct a unit structure database of the metasurface; according to the phase distribution requirements of the two metasurface microlens arrays, columnar structures with different diameters are selected in the unit structure database of the metasurface for arrangement, and the two metasurface microlens arrays are processed according to the arrangement.

[0041] The spacing between the first metasurface microlens array 1 and the second metasurface microlens array 2 is controlled to be the sum of their focal lengths. , forming a blazed grating with adjustable blaze angle; and Figure 1 As shown, a collimated laser light source 3, a convex lens 4 and an image sensor 5 are combined to form a high-precision displacement measurement system; after calibration, the relationship between the relative displacement and the intensity of each diffraction order of the blazed grating is obtained; by detecting the difference in the intensity of adjacent diffraction orders on both sides of the blazed angle of the blazed grating by the image sensor 5, the relative displacement between the two objects can be obtained.

[0042] Figure 5 Shown is the relative displacement between two metasurface microlens arrays. = Far-field diffraction angle spectrum at 412 nm; Figure 6 Shown is the relative displacement between two metasurface microlens arrays. = Far-field diffraction angle spectrum at 515 nm. The far-field diffraction angle spectrum is equal to the product of the interference term and the diffraction term, where the angle at which the diffraction term intensity peaks is the current blaze angle ( Figure 5 and Figure 6 Angles marked by dotted lines ), the angles of the two highest angular spectrum peaks on both sides of the blaze angle are the diffraction orders on both sides of the blaze angle. Figure 5 and Figure 6 In the case shown, the diffraction orders are both diffraction 1st and 0th order. =412 nm, the intensities of the 1st and 0th diffraction orders are equal; when = 515 nm, the intensity of the 1st diffraction order is greater than that of the 0th order. Figure 7 Different relative displacements are shown The far-field diffraction angle spectrum at the time of the diffraction, the intensity of the 1st and 0th order diffraction increases with the relative displacement The changes in this situation lead to increases in some areas while decreases in others. Figure 8 Shown is the difference in intensity and relative displacement between the 1st and 0th diffraction orders Therefore, the relative displacement can be obtained from the difference in the intensity of the 1st and 0th diffraction orders. .

[0043] As the relative displacement increases, the blaze angle increases, and the diffraction order used to detect the relative displacement will change. Usually, the intensity difference between the mth and m-1th orders is used for sensing (the blaze angle is between the angles corresponding to the mth and m-1th orders or on the mth order). Fig. 9 Shown is the intensity difference (I m -I m-1 , where I m and I m-1 represents the intensity of the mth and m-1th diffraction orders, where m is an integer) and the relative displacement between the two metasurface microlens arrays The relationship diagram between . Fig. 9 In = 824 nm, which is the relative displacement required for the blaze angle to shift from the m-1 order to the corresponding angle of the m order.

[0044] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is not intended to limit the scope of the present invention. For those skilled in the art, several modifications and improvements may be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention.

Claims

1. A high-precision displacement measurement system based on a metasurface microlens array, characterized in that: including a first metasurface microlens array and a second metasurface microlens array; The first metasurface microlens array and the second metasurface microlens array are parallel to each other, and the spacing between them is the sum of their focal lengths, forming a blazed grating; the first metasurface microlens array and the second metasurface microlens array are respectively fixed on two objects to be measured, and the relative displacement direction between the two objects to be measured is perpendicular to the optical axis of the metasurface microlens array; The first metasurface microlens array is used to divide the incident light into multiple light beams and respectively focus and then diverge to form an outgoing array light beam. The second metasurface microlens array is used to collimate the outgoing array light beam of the first metasurface microlens array. When there is a relative displacement between the two objects to be measured, the outgoing light beam of the second metasurface microlens array is deflected at a certain angle with the optical axis. The deflection angle is the blaze angle, and the size of the blaze angle varies with the size of the relative displacement. The first metasurface microlens array comprises a plurality of identical first metasurface microlenses arranged periodically, and the first metasurface microlenses are composed of a first transparent substrate and a plurality of sub-wavelength dielectric columnar structures on a surface of one side of the first transparent substrate; the sub-wavelength dielectric columnar structures of the first metasurface microlens array are all located on its exit surface; The second metasurface microlens array includes a plurality of identical second metasurface microlenses arranged periodically, and the second metasurface microlenses are composed of a second transparent substrate and a plurality of subwavelength dielectric columnar structures on the surfaces of both sides of the second transparent substrate; the plurality of subwavelength dielectric columnar structures on the first surface of the second transparent substrate are used to collimate the outgoing array light beams of the first metasurface microlens array, and the plurality of subwavelength dielectric columnar structures on the second surface of the second transparent substrate are used to further collimate the array light beams and eliminate stray light; The transparent substrates of all the supersurface microlenses in each supersurface microlens array are integrally formed; the number, shape and arrangement of the first supersurface microlenses and the second supersurface microlenses are consistent; the height of each subwavelength medium columnar structure in each supersurface microlens is the same, and the size parameters are different.

2. The high-precision displacement measurement system based on the metasurface microlens array according to claim 1, characterized in that: The arrangement period of all sub-wavelength dielectric columnar structures on the surface of the first metasurface microlens is the same, and the arrangement period of all sub-wavelength dielectric columnar structures on the surface of the second metasurface microlens is also the same.

3. The high-precision displacement measurement system based on the metasurface microlens array according to claim 1, characterized in that: The ratio of the exit light beam aperture of the second metasurface microlens to the side length of the single-chip metasurface microlens is greater than 0.

9.

4. The high-precision displacement measurement system based on the metasurface microlens array according to claim 1, characterized in that: The material of the transparent substrate is glass, quartz or silicon dioxide, and the material of the sub-wavelength medium columnar structure is silicon, silicon nitride, titanium dioxide or gallium nitride.

5. The high-precision displacement measurement system based on the metasurface microlens array according to claim 1, characterized in that: The relationship between the relative displacement Δx between the first metasurface microlens array and the second metasurface microlens array, the blaze angle Δθ of the blazed grating, and the focal length f2 of the second metasurface microlens array satisfies Δx=f2×tan(Δθ).

6. The high-precision displacement measurement system based on the metasurface microlens array according to claim 1, characterized in that: The system also includes a collimated laser light source, a convex lens and an image sensor; the collimated laser light source is used to emit a collimated laser light beam to the incident surface of the first metasurface microlens array; the convex lens is placed in parallel behind the second metasurface microlens array, and is used to project the far-field diffraction angle spectrum of the blazed grating output array light beam to the image sensor; the image sensor is located at the back focal plane of the convex lens, and is used to detect the intensity of the far-field diffraction angle spectrum of the output array light beam of the blazed grating.

7. The high-precision displacement measurement system based on the metasurface microlens array according to claim 1, characterized in that: The design method of the first metasurface microlens and the second metasurface microlens is as follows: 1) respectively determining the operating wavelength, focal length, aperture and side length of the first metasurface microlens and the second metasurface microlens; 2) According to the design parameters determined in step 1, two metasurface microlenses are simulated using a binary surface in an optical simulation software, and the damped least squares method is used for optimization to obtain the phase distribution requirements of the first metasurface microlens and the second metasurface microlens; 3) By performing full-wave simulation on an array formed by periodic arrangement of the same subwavelength dielectric columnar structure, the transmission amplitude and transmission phase of a single subwavelength dielectric columnar structure in the array under different size parameters are calculated, and subwavelength dielectric columnar structures with a transmission amplitude greater than 0.9 are selected to construct a unit structure database; during the simulation process, subwavelength dielectric columnar structures with a transmission phase covering 0-2π should be traversed, and the arrangement period of the columnar structure should be less than the working wavelength; 4) According to the phase distribution requirements of the first metasurface microlens and the second metasurface microlens, subwavelength dielectric columnar structures of different sizes are selected from the unit structure database and arranged on the transparent substrate to form the first metasurface microlens and the second metasurface microlens, so that the first metasurface microlens and the second metasurface microlens meet the phase distribution requirements.

8. A high-precision displacement measurement method according to the measurement system of claim 6, characterized in that: The method comprises: The first metasurface microlens array and the second metasurface microlens array are respectively mounted on two objects to be measured, so that the optical axis of the metasurface microlens array is perpendicular to the relative displacement direction of the objects to be measured, and the spacing between the two metasurface microlens arrays is the sum of their focal lengths, forming a blazed grating with an adjustable blazed angle; The relationship between the relative displacement of the object to be measured and the difference in intensity of each adjacent diffraction order of the blazed grating is obtained through calibration; The object to be measured is subjected to relative displacement, and the far-field diffraction angle spectrum of the outgoing array light beam of the blazed grating is detected by an image sensor. The difference in diffraction orders and their intensities on both sides of the blazed angle are analyzed based on the far-field diffraction angle spectrum, and the relative displacement between the two objects to be measured is obtained by searching in the calibration results.

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