Double-layer differential grating displacement sensor based on optical lever amplification effect

Abstract

The invention belongs to the technical field of displacement sensing, and particularly relates to a double-layer differential grating displacement sensor based on an optical lever amplification effect, which is characterized in that a laser beam expander is arranged in the light path direction of a laser, an upper grating is arranged in the light path direction of the laser beam expander, and a lower grating is arranged in the light path direction of the upper grating; the objective lens is arranged in the light path direction of the lower grating, and the detector is arranged in the light path direction of the objective lens. Compared with a traditional grating displacement sensor, the grating displacement sensor has the advantages that optical displacement can be amplified spatially, and the amplification factor is gt; 5 times. The high-resolution grating Talbot image type displacement sensor has the advantages that by means of the input displacement amplification effect of the differential structure, high resolution can be achieved under the condition that a large-period grating and a large-pixel-size CCD are used, the problem that a traditional high-resolution grating Talbot image type displacement sensor has high requirements for the grating period and the pixel size of the CCD is solved, and the high-resolution grating Talbot image type displacement sensor has wide application prospects in the fields of mechanical positioning, semiconductor manufacturing and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of displacement sensing, and in particular relates to a double-layer differential grating displacement sensor based on an optical lever amplification effect. Background Art

[0002] As one of the core components of the integrated precision positioning system, the range, resolution, accuracy and other indicators of the optical displacement sensor determine the positioning accuracy of core moving parts such as tool heads / probes in precision processing / detection equipment such as lithography machines / precision machine tools / nano-coordinate measuring machines, which in turn affects core indicators such as processing / detection accuracy and the size of components to be processed / detected.

[0003] At present, a variety of optical displacement sensors have been developed based on different principles such as laser interference, grating interference and Talbot effect. Among them, grating displacement sensors based on micro-nano grating Talbot effect show great application prospects due to their high compactness, high precision and low cost. The resolution of such devices is usually proportional to the grating period. However, since traditional grating Talbot image displacement sensors use the optical Talbot image with the same period as the grating as the detection reference, the grating period and CCD pixel size must be reduced for high-resolution measurement, which puts higher requirements on the grating preparation process and component cost, limiting the actual industrial application of such devices in mechanical processing and other fields. Summary of the invention

[0004] In view of the technical problem that the above-mentioned traditional high-resolution grating Talbot image displacement sensor has high requirements for grating period and CCD pixel size, the present invention provides a double-layer differential grating displacement sensor based on the optical lever amplification effect. The device is based on the principle of double-layer differential grating secondary modulation, adopts a large-period double-layer grating with different periods, and uses the lower grating to perform secondary modulation on the optical Talbot image of the upper grating, and generates a periodic light field distribution with a light field amplification effect based on the optical lever effect. Since the light field distribution undergoes synchronous spatial changes with the upper and lower grating layers, the grating phase displacement detection function can be realized by detecting the change in the intensity of the amplified light field. This method uses the period difference of the double-layer grating to generate a spatial periodic light field, so high-resolution displacement detection can be achieved without a small-period grating, which solves the high requirements of the traditional high-resolution grating Talbot image displacement sensor for the grating period and CCD pixel size.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A double-layer differential grating displacement sensor based on an optical lever amplification effect comprises a laser, a laser beam expander, an upper grating, a lower grating, an objective lens and a detector, wherein the laser beam expander is arranged in the optical path direction of the laser, the upper grating is arranged in the optical path direction of the laser beam expander, the lower grating is arranged in the optical path direction of the upper grating, the objective lens is arranged in the optical path direction of the lower grating, and the detector is arranged in the optical path direction of the objective lens.

[0007] The upper grating is etched on a first light-transmitting substrate, and the lower grating is etched on a second light-transmitting substrate.

[0008] The first light-transmitting substrate and the second light-transmitting substrate are both SiO2 substrates, and the thickness of the first light-transmitting substrate and the second light-transmitting substrate are both 3 μm.

[0009] The input light wavelength of the laser is 635nm, the grating thickness of the upper grating and the lower grating is 150nm, the grating duty ratio of the upper grating and the lower grating is 0.5, the period of the upper grating is 1.5μm, and the period of the lower grating is 1.7μm.

[0010] A measurement method of a double-layer differential grating displacement sensor based on an optical lever amplification effect comprises the following steps:

[0011] S1, the light emitted by the laser is enlarged after passing through the laser beam expander, and then irradiates the upper surface of the upper grating, and then forms a Talbot image light field;

[0012] S2, the lower grating is placed in the Talbot image light field area behind the upper grating and on the optical axis of the incident light, and the objective lens and the detector are placed close to the rear surface of the lower grating;

[0013] S3. The upper grating is relatively displaced relative to the lower grating along the in-plane direction perpendicular to the grating lines. Due to the change in the relative position between the gratings, the light field distribution and the transmitted light intensity behind the lower grating are changed, which causes the light field distribution behind the objective lens to change, resulting in a change in the electrical signal output by the detector. By detecting the electrical change, the relative displacement value of the upper grating is obtained.

[0014] The method for obtaining the relative displacement value of the upper grating by detecting the electrical change in S3 is:

[0015] S3.1, calculate the complex amplitude of the light emitted from the light source plane after reaching the upper grating;

[0016] S3.2, when the light passes through the upper grating and the lower grating, the complex amplitude of the light field on the rear surface of the lower grating is calculated;

[0017] S3.3, calculate the complex amplitude distribution on the detector surface;

[0018] S3.4. Calculate the input displacement using the displacement magnification factor F of the optical lever effect.

[0019] The method for calculating the complex amplitude of the light emitted from the light source plane after reaching the upper grating in S3.1 is:

[0020] U1(x1,x)=exp[iπ(x1―x) 2 / λz0]

[0021] Among them, U1(x1,x) represents the complex amplitude of the light emitted from the light source plane after reaching the upper grating, x0 and x1 represent the coordinate values ​​of the laser plane and the upper grating plane respectively, z0 is the distance from the laser light source to the upper grating, and λ represents the input light wavelength of the laser.

[0022] The method for calculating the complex amplitude of the light field on the rear surface of the lower grating in S3.2 is:

[0023] The amplitude transmittance of the upper and lower gratings is represented by t1(x1) and t2(x2), respectively, which describes the degree of light passing through the grating.

[0024]

[0025] Among them, an and bm are the Fourier coefficients of t1(x1) and t2(x2), and x2 represents the coordinate value of the lower grating plane;

[0026] When light passes through the upper grating and the lower grating, the complex amplitude of the light field on the rear surface of the lower grating is expressed as:

[0027] U2(x2,x)=∫U1(x1,x)t1(x1)exp[iπ(x2―x1) 2 / z1λ]dx1

[0028] Among them, U1(x1,x) represents the complex amplitude of the light emitted from the light source plane after reaching the upper grating, U2(x2,x) represents the complex amplitude of the light field on the back surface of the lower grating, and z1 represents the upper grating to the lower grating.

[0029] The method for calculating the complex amplitude distribution on the detector surface in S3.3 is:

[0030] On the detector surface, the complex amplitude distribution is expressed as:

[0031] U(X,x)=∫U2(x2,x)t2(x2)exp[iπ(X―x2) 2 / z2λ]dx2

[0032] Where X represents the coordinate value of the detector, and z2 represents the distance from the lower grating to the detector.

[0033] The method for calculating the input displacement using the displacement magnification factor F of the optical lever effect in S3.4 is:

[0034] Assuming the intensity distribution of the light source is ω(x), the intensity I(X,x) is expressed as:

[0035] I(X,x)=∫|U(X,x)| 2 ω(x)dx

[0036] Among them, the displacement amplification principle of the system is:

[0037] Substituting the calculated I(X,x) into the expression of intensity I(X,x), we obtain the following expression.

[0038]

[0039] where A, μ2, ψ2 and ψ1 are constants related to d1, d2, z0, z1 and z2, and the period d0 is defined as the optical magnification period at the detector:

[0040] d0=1 / μ1

[0041] When nn′ = ±1 and mm′ = ±1, the period of the optical transmission field is:

[0042] 1 / d0=|1 / d1―1 / d2|

[0043] Therefore, the displacement magnification factor F using the optical lever effect is:

[0044] F=d0 / d1=d2 / |d1―d2|

[0045] The input displacement calculation formula is:

[0046] d = D' / (L x F)

[0047] Where D' is the displacement value of the magnified light field image, L is the objective lens magnification, and d is the actual displacement value of the upper grating relative to the lower grating.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] Compared with the traditional grating displacement sensor, the present invention can realize the spatial amplification of optical displacement, and the amplification factor is >5 times. Benefiting from the input displacement amplification effect of the differential structure, high resolution (for example, 0.1-1nm level) can be achieved when using large period gratings and large pixel size CCD, which solves the problem of high requirements for grating period and CCD pixel size of traditional high-resolution grating Talbot image displacement sensors, and has broad application prospects in the fields of mechanical positioning and semiconductor manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0051] The structures, proportions, sizes, etc. illustrated in this specification are only used to match the contents disclosed in the specification so as to facilitate understanding and reading by persons familiar with the technology. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantial technical significance. Any structural modification, change in proportion or adjustment of size shall still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0052] Figure 1 It is a structural schematic diagram of the present invention;

[0053] Figure 2 This is the Talbot image of the grating with a single layer period of 1.5 μm according to the present invention;

[0054] Figure 3 This is a schematic diagram of the differential double-layer grating of the present invention;

[0055] Figure 4 This is a schematic diagram of the differential double-layer grating transmission light field of the present invention. The red triangle area in the figure indicates that a large-period light field periodic distribution appears, forming a combined light field;

[0056] Figure 5 This is a schematic diagram of the transmitted light field of the double-layer grating with the same period of the present invention. The uniform red area in the figure indicates that there is no periodic distribution of the large-period light field and no combined light field is formed;

[0057] Figure 6 A diagram showing the relationship between the output displacement and the input displacement of the present invention;

[0058] Figure 7 It is the combined light field image before the upper grating is displaced in the present invention;

[0059] Figure 8 It is the combined light field image after the upper grating is displaced according to the present invention.

[0060] Among them: 1 is a laser, 2 is a laser beam expander, 3 is an upper grating, 4 is a lower grating, 5 is an objective lens, 6 is a detector, 7 is a first light-transmitting substrate, and 8 is a second light-transmitting substrate. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. These descriptions are only to further illustrate the features and advantages of the present invention, rather than to limit the claims of the present invention. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0062] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0063] The terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, unless otherwise specified, "plurality" means two or more.

[0064] In the description of this application, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" 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 this application can be understood according to specific circumstances.

[0065] A double-layer differential grating displacement sensor based on optical lever amplification effect, such as Figure 1 As shown, it includes a laser 1, a laser beam expander 2, an upper grating 3, a lower grating 4, an objective lens 5 and a detector 6. The upper grating 3 is etched on a first light-transmitting substrate 7, and the lower grating 4 is etched on a second light-transmitting substrate 8. The light emitted by the laser 1 is enlarged in diameter after passing through the laser beam expander 2, and then irradiated on the upper surface of the upper grating 3, and then forms a Talbot image light field. The lower grating 4 is placed in the Talbot image light field area behind the upper grating 3 and is on the optical axis of the incident light. The objective lens 5 and the detector 6 are placed close to the rear surface of the lower grating 4.

[0066] During the working process, first, the light emitted from the light source plane with a wavelength of λ reaches the upper grating 3. Using the diffraction effect of the grating, since the sensor is based on the Talbot effect of the grating, the upper grating 3 will form a Talbot image, such as Figure 2As shown, the lower grating 4 should be located in the Talbot region of the upper grating 3. Due to the differential structure, a composite light field with multiple periods is formed behind the lower grating 4. Due to the optical lever effect, the displacement of the composite light field is amplified relative to the actual displacement. The upper grating 3 is perpendicular to the in-plane direction of the grating lines relative to the lower grating 4 ( Figure 1 The relative displacement of the upper grating 3 can be obtained by detecting the electrical change.

[0067] Where x0, x1, x2 and X represent the coordinates of the laser 1 plane, the upper grating 3 plane, the lower grating 4 plane and the detector 6 respectively. z0, z1 and z2 represent the distance from the laser light source to the upper grating 3, from the upper grating 3 to the lower grating 4, and from the lower grating 4 to the detector 6 respectively. Figure 3 As shown, the grating periods of the upper grating 3 and the lower grating 4 are different, forming a differential structure.

[0068] Wherein, laser 1 is a single-wavelength continuous light laser, and the laser it emits is collimated output;

[0069] The upper grating 3 and the lower grating 4 are both black and white one-dimensional gratings, and the grating lines of the two are in the same direction and are placed in parallel;

[0070] Among them, the complex amplitude of the light emitted from the light source plane after reaching the upper grating 3 is:

[0071] U1(x1,x)=exp[iπ(x1―x) 2 / λz0] (1)

[0072] The amplitude transmittances of the upper grating 3 and the lower grating 4 are represented by t1(x1) and t2(x2) respectively, which describe the extent of light passing through the grating.

[0073]

[0074] Among them, an and bm are the Fourier coefficients of t1(x1) and t2(x2).

[0075] Among them, when the light passes through the upper grating 3 and the lower grating 4, the complex amplitude of the light field on the rear surface of the lower grating 4 can be expressed as:

[0076] U2(x2,x)=∫U1(x1,x)t1(x1)exp[iπ(x2―x1) 2 / z1λ]dx1 (3)

[0077] Among them, on the detector surface, the complex amplitude distribution can be expressed as:

[0078] U(X,x)=∫U2(x2,x)t2(x2)exp[iπ(X―x2) 2 / z2λ]dx2 (4)

[0079] Assuming the intensity distribution of the light source is ω(x), the intensity I(X,x) can be expressed as:

[0080] I(X,x)=∫|U(X,x)| 2 ω(x)dx (5)

[0081] Among them, the displacement amplification principle of the system is as follows:

[0082] Substituting the calculated I(X, x) into equation (5), we can get the following expression.

[0083]

[0084] Where A, μ2, ψ2 and ψ1 are constants related to d1, d2, z0, z1 and z2. The period d0 is defined as the optical amplification period on the detector 6, which can be derived from formula (6).

[0085] d0=1 / μ1 (7)

[0086] When nn′=±1 and mm′=±1, the period of the optical transmission field can be given by the formula.

[0087] 1 / d0=|1 / d1―1 / d2| (8)

[0088] Therefore, the displacement magnification factor F using the optical lever effect can be given by the following formula.

[0089] F=d0 / d1=d2 / |d1―d2| (9)

[0090] Among them, the input displacement calculation formula is:

[0091] d=D′ / (L×F) (10)

[0092] Wherein D' is the displacement value of the magnified light field image, L is the magnification of the objective lens 5, and d is the actual relative displacement value of the upper grating 3.

[0093] From the above, we can know that the double-layer differential grating displacement sensor based on the optical lever amplification effect. Its main structure includes components such as laser, laser beam expander, upper grating, lower grating, objective lens and detector. The upper grating and the lower grating have different periods, forming a double-layer differential structure. When working, the light source is diffracted by the upper grating to form a Talbot image, and the lower grating is placed in the Talbot area of ​​the upper grating, thereby generating a multi-period composite light field, and the amplification of the composite light field displacement relative to the actual displacement is achieved based on the optical lever effect.

[0094] Figure 4 The red triangle area in the figure indicates that a large period light field period distribution has appeared, forming a combined light field, which corresponds to this.

[0095] Figure 5 This is a schematic diagram of the transmitted light field of the double-layer grating with the same period of the present invention. The uniform red area in the figure indicates that there is no periodic distribution of the large-period light field and no combined light field is formed.

[0096] Among them, Figure 6 As shown, the relationship between the output displacement (i.e., the displacement of the amplified light field) and the input displacement is shown. According to formula (9), combined with optical simulation, the amplification factor F in the two cases is 8.5.

[0097] Among them, Figure 7 The following is a CCD image of the combined light field distribution behind the differential double-layer grating in the experiment. The specific implementation parameters are as follows:

[0098] The input light wavelength is 635nm;

[0099] The thickness of the first light-transmitting substrate 7 is 3 μm;

[0100] The thickness of the second light-transmitting substrate 8 is 3 μm;

[0101] The grating thickness is 150nm;

[0102] The period of the upper grating 3 is 1.5 μm;

[0103] The period of the lower grating 4 is 1.7 μm;

[0104] The grating duty cycle is 0.5;

[0105] Objective lens 5 has a magnification of 40 times;

[0106] The specific analysis is as follows:

[0107] The finite difference time domain (FDTD) method is used to analyze the physical transmission characteristics of the differential double-layer grating and compare it with the simulation results of the double-layer grating with the same period. In the simulation, the wavelength of the plane light source is 635nm, the duty cycle of the grating is 50%, and the grating G2 is located at the Talbot position behind the grating G1 (z1=N·ZT, N=1,2,3…). Figure 4 It can be seen that at this time, a combined light field formed by the superposition of two sine waves with different periods of 1.5μm and 12.75μm appears behind the double-layer grating. The small period in the combined light field is caused by the Talbot effect, which is consistent with the period of grating G1, which is 1.5μm; the large period in the combined light field is formed by differential grating modulation, which is 12.75μm calculated according to formula (7). Figure 5 It can be seen that when the periods of the double-layer gratings are the same, there is only a small-period light field, and no large-period light field appears, so no combined light field appears.

[0108] Depend on Figure 6 It can be seen that in the case of a double-layer grating with the same period, when the grating G1 moves one grating period (such as d1 = 1.5μm), the transmitted field changes with the same period of d1 = 1.5μm. In the case of a differential double-layer grating, the combined light field moves synchronously with the grating. When the grating G1 moves one grating period length (such as d1 = 1.5μm), the amplified light field moves a single period length (d0 ≈ 12.7μm) in the same direction. Therefore, a displacement amplification phenomenon is generated, and the amplification factor is 12.7μm / 1.5μm ≈ 8.5.

[0109] Among them, Figure 7 The figure shows the image of the magnified light field after differential double-layer grating under microscope observation. After experimental testing, it is found that the magnification period of the magnified light field is about 11.6μm.

[0110] like Figure 8 The figure shows the magnified light field image after the upper grating 3 input displacement of 10μm. When the input displacement is 10μm, the magnified light field moves about 77.8μm in the same direction. The results show that the magnification factor F is about 8, which is basically consistent with the theoretical calculation results.

[0111] The linear actuator was used to step 10 nm each time, and the test was repeated 9 times. The output displacement (D') of the CCD imaging system was counted, and the displacement resolution in the experiment was calculated to be about 9.8 nm using formula (10).

[0112] Only the preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention, and various changes should be included in the protection scope of the present invention.

Claims

1. A double-layer differential grating displacement sensor based on optical lever amplification effect, characterized in that: The invention comprises a laser (1), a laser beam expander (2), an upper grating (3), a lower grating (4), an objective lens (5) and a detector (6), wherein the laser beam expander (2) is arranged in the optical path direction of the laser (1), the upper grating (3) is arranged in the optical path direction of the laser beam expander (2), the lower grating (4) is arranged in the optical path direction of the upper grating (3), the objective lens (5) is arranged in the optical path direction of the lower grating (4), and the detector (6) is arranged in the optical path direction of the objective lens (5).

2. The double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 1, characterized in that: The upper grating (3) is etched on a first light-transmitting substrate (7), and the lower grating (4) is etched on a second light-transmitting substrate (8).

3. The double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 2, characterized in that: The first light-transmitting substrate (7) and the second light-transmitting substrate (8) are both SiO2 substrates, and the thickness of the first light-transmitting substrate (7) and the second light-transmitting substrate (8) are both 3 μm.

4. The double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 1, characterized in that: The input light wavelength of the laser (1) is 635 nm, the grating thickness of the upper grating (3) and the lower grating (4) is 150 nm, the grating duty ratio of the upper grating (3) and the lower grating (4) is 0.5, the period of the upper grating (3) is 1.5 μm, and the period of the lower grating (4) is 1.7 μm.

5. A measurement method for a double-layer differential grating displacement sensor based on an optical lever amplification effect according to any one of claims 1 to 4, characterized in that: The following steps are involved: S1, the light emitted by the laser (1) passes through the laser beam expander (2), the beam diameter is enlarged, and then irradiates the upper surface of the upper grating (3), and then forms a Talbot image light field; S2, the lower grating (4) is placed in the Talbot image light field area behind the upper grating (3) and on the optical axis of the incident light, and the objective lens (5) and the detector (6) are placed close to the rear surface of the lower grating (4); S3, the upper grating (3) is relatively displaced relative to the lower grating (4) along the in-plane direction perpendicular to the grating lines. Due to the change in the relative position between the gratings, the light field distribution and the transmitted light intensity behind the lower grating (4) are changed, so that the light field distribution behind the objective lens (5) is changed, resulting in a change in the electrical signal output by the detector (6). By detecting the electrical change, the relative displacement value of the upper grating (3) is obtained.

6. The measurement method of a double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 5, characterized in that: The method for obtaining the relative displacement value of the upper grating (3) by detecting the electrical change in S3 is: S3.1, calculate the complex amplitude of the light emitted from the light source plane after reaching the upper grating (3); S3.2, when the light passes through the upper grating (3) and the lower grating (4), the complex amplitude of the light field on the rear surface of the lower grating (4) is calculated; S3.3, calculating the complex amplitude distribution on the surface of the detector (6); S3.

4. Calculate the input displacement using the displacement magnification factor F of the optical lever effect.

7. The measurement method of a double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 5, characterized in that: The method for calculating the complex amplitude of the light emitted from the light source plane after reaching the upper grating (3) in S3.1 is: U1(x1,x)=exp[iπ(x1―x) 2 / λz0] Wherein, Y1(x1,x) represents the complex amplitude of the light emitted from the light source plane after reaching the upper grating (3), x0 and x1 represent the coordinate values ​​of the laser (1) plane and the upper grating (3) plane respectively, z0 represents the distance from the laser (1) light source to the upper grating (3), and λ represents the input light wavelength of the laser (1).

8. The measurement method of a double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 5, characterized in that: The method for calculating the complex amplitude of the light field on the rear surface of the lower grating (4) in S3.2 is: The amplitude transmittance of the upper grating (3) and the lower grating (4) are represented by t1(x1) and t2(x2) respectively, which describe the degree of light passing through the grating. Where an and bm are the Fourier coefficients of t1(x1) and t2(x2), and x2 represents the coordinate value of the plane of the lower grating (4); When light passes through the upper grating (3) and the lower grating (4), the complex amplitude of the light field on the rear surface of the lower grating (4) is expressed as: U2(x2,x)=∫U1(x1,x)t1(x1)exp[iπ(x2―x1) 2 / z1λ]dx1 Among them, U1(x1,x) represents the complex amplitude of the light emitted from the light source plane after reaching the upper grating (3), U2(x2,x) represents the complex amplitude of the light field on the back surface of the lower grating (4), and z1 represents the distance from the upper grating (3) to the lower grating (4).

9. The measurement method of a double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 5, characterized in that: The method for calculating the complex amplitude distribution on the surface of the detector (6) in S3.3 is: On the detector surface, the complex amplitude distribution is expressed as: U(X,x)=∫U2(x2,x)t2(x2)exp[iπ(X―x2) 2 / z2λ]dx2 Wherein, X represents the coordinate value of the detector (6), and z2 represents the distance from the lower grating (4) to the detector (6).

10. The measurement method of a double-layer differential grating displacement sensor based on optical lever amplification effect according to claim 5, characterized in that: The method for calculating the input displacement using the displacement magnification factor F of the optical lever effect in S3.4 is: Assuming the intensity distribution of the light source is ω(x), the intensity I(X,x) is expressed as: I(X,x)=∫|U(X,x)| 2 ω(x)dx Among them, the displacement amplification principle of the system is: Substituting the calculated I(X,x) into the intensity I(X,x) expression, we get the following expression: where A, μ2, ψ2 and ψ1 are constants related to d1, d2, z0, z1 and z2, and the period d0 is defined as the optical amplification period at the detector (6): d0=1 / μ1 When nn′ = ±1 and mm′ = ±1, the period of the optical transmission field is: 1 / d0=|1 / d1―1 / d2| Therefore, the displacement magnification factor F using the optical lever effect is: F=d0 / d1=d2 / |d1―d2| The input displacement calculation formula is: d = D' / (L x F) Wherein D' is the displacement value of the magnified light field image, L is the magnification of the objective lens (5), and d is the actual displacement value of the upper grating (3) relative to the lower grating (4).

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