A precise refractive index measurement method and device based on weak measurement and optical spin hall effect

Abstract

A precision refractive index measurement method and device based on weak measurement and optical spin Hall effect is disclosed, relating to the field of optical precision measurement technology. By introducing weak value amplification technology, the minute physical quantity to be measured is transformed into an easily observable change in the shape of a light spot, and the absolute measurement of light intensity is transformed into the judgment of the relative change of the light spot, thereby overcoming the accuracy bottleneck of traditional methods. At the same time, specific pre-selective and post-selective polarization states are constructed, and the nanometer-level displacement is amplified into a micrometer-level light spot split that can be clearly distinguished by a CCD camera using weak measurement theory. This solves the problem that the traditional geometric optics detection limit cannot identify nanometer-level displacements. On the other hand, by directly using the characteristic incident angle θ measured by a high-precision turntable as a fixed input, the theoretical assumption of constraining it to the theoretical Brewster angle is avoided, thus eliminating the systematic error introduced by the failure to meet theoretical conditions in principle.

Description

Technical Field

[0001] This invention relates to the field of optical precision measurement technology, and more specifically, to a precision refractive index measurement method and apparatus based on weak measurement and the optical spin Hall effect. Background Technology

[0002] In existing technologies, common methods for measuring the refractive index of transparent or translucent materials are mainly based on elliptic polarization or direct calculation by measuring Brewster's angle. The typical optical path structure for such schemes is usually arranged in the following order: laser source → polarizer → sample stage → analyzer → photodetector.

[0003] Its working principle is as follows: The laser beam is converted into linearly polarized light by a polarizer and incident at a certain angle on the surface of the sample placed on the sample stage. The beam is reflected at the air-sample interface, forming reflected light carrying information about the sample's refractive index. This reflected light then passes through an analyzer, and finally, its intensity signal is received by a photodetector. By precisely rotating the sample stage to continuously change the incident angle and monitoring the changes in the reflected light intensity, the incident angle corresponding to the weakest reflected light intensity is the Brewster angle. Finally, based on the Brewster angle... The relationship between n and the sample refractive index n is n=tan( Calculate the refractive index value.

[0004] However, the aforementioned existing technologies have the following objective drawbacks: Limited sensitivity: This method relies on the judgment of the minimum light intensity. When approaching Brewster's angle, the light intensity changes gradually, making it difficult to accurately determine the angle and limiting the accuracy of refractive index measurement.

[0005] Poor anti-interference capability: It relies on absolute light intensity measurement and is easily affected by factors such as laser power fluctuations and environmental stray light.

[0006] Unable to amplify weak signals: Traditional light intensity detection methods cannot detect the nanometer-scale lateral light spot displacement caused by the spin Hall effect of light, and therefore cannot use this physical effect to achieve higher precision measurement.

[0007] A common problem with the aforementioned existing technical solutions is that the optical path structure is too simple, lacking beam expander, collimator, and precision imaging lens groups. The polarizer and analyzer are only separated by a sample stage, making the beam divergence angle and spot size uncontrollable, leading to: 1. The optical path is prone to misalignment; even a slight deviation will cause the light spot to deviate from the center of the detector, resulting in poor system stability. 2. It is impossible to form the specific Gaussian beam pattern (angular spectral broadening and coordinate space transformation) required for weak measurements, making it difficult to effectively extract and amplify nanoscale displacement signals; 3. Photodetectors can only receive total light intensity and cannot distinguish changes in the spatial shape of the light spot, thus missing the possibility of making high-precision judgments using the morphological characteristics of the light spot.

[0008] Based on the above background, the inventors have designed a precision refractive index measurement method and device based on weak measurement and optical spin Hall effect, which solves at least one of the above problems, and thus, this application is filed. Summary of the Invention

[0009] The purpose of this invention is to provide a precise refractive index measurement method and device based on weak measurement and the optical spin Hall effect, aiming to solve the problems of low accuracy and weak anti-interference ability of existing measurement instruments. The core innovation of this solution lies in combining quantum weak measurement technology with the optical spin Hall effect. Through a weak value amplification mechanism, nanoscale physical effects that are difficult to measure directly are amplified into changes in the shape of light spots that can be clearly distinguished by a CCD camera, thereby achieving precise inversion of the refractive index.

[0010] This invention is achieved through the following technical solution: A precise refractive index measurement method based on weak measurement and the optical spin Hall effect includes the following steps: The laser beam emitted from the laser source is passed through a pre-selective polarizer to form incident light, thus constructing a pre-selective state for weak measurement; The incident light is incident on the surface of the sample to be tested and reflected, and the reflected light produces a lateral displacement related to the refractive index of the sample to be tested. The reflected light is passed through a post-selective polarization element, the transmission direction of which is nearly orthogonal to the transmission direction of the pre-selective polarizer, to construct a post-selective state, and the lateral displacement is amplified into observable spot splitting through a weak value amplification mechanism. The incident angle of the incident light relative to the surface of the sample to be tested is changed, the polarization element is rotated and the centroid position of the reflected light spot under different polarization angles is obtained. Based on the change range of the centroid position with the polarization angle and the symmetry about the orthogonal position, the characteristic incident angle is determined. At the characteristic incident angle, the beam is symmetrically deflected and the reflected spot image is acquired with the orthogonal position of the post-selected polarization element as a reference. The magnified beam transverse displacement is obtained through differential operation, and the deviation of the post-selected polarization element relative to the orthogonal position is recorded as the post-selection angle. Substituting the characteristic incident angle, the post-selection angle, and the beam lateral shift into the correlation equation, the refractive index of the sample under test is determined.

[0011] Furthermore, the incident light is configured as linearly polarized light with P-polarization as the main polarization component and a trace S-polarization component; the incident light is focused by a focusing element and then incident on the surface of the sample to be tested; the reflected light is received by a detector after passing through a conversion imaging element; the left-hand circularly polarized component and the right-hand circularly polarized component in the reflected light produce lateral displacements in opposite directions in the direction perpendicular to the incident surface.

[0012] Furthermore, before constructing the pre-selected state for weak measurement, the process includes moving the detector along the optical axis and acquiring spot images at multiple locations. After extracting the spot radius at each location using a Gaussian model, the beam waist radius is obtained by fitting the Gaussian beam propagation formula.

[0013] Furthermore, the angle between the transmission direction of the subsequent polarizing element and the transmission direction of the preceding polarizing plate is... or ,in .

[0014] Furthermore, changing the incident angle of the incident light relative to the surface of the sample to be tested includes: gradually changing the incident angle in steps over a wide angle range, determining a rough range based on the change of the reflected light spot from a single peak to a concave shape and splitting into two peaks, and gradually changing the incident angle in steps over a second range within the rough range, wherein the first step length is greater than the second step length.

[0015] Furthermore, rotating the selected polarization element and obtaining the centroid position of the reflected light spot includes: at each incident angle, rotating the selected polarization element to change its transmission direction to multiple polarization angles near the orthogonal position, acquiring multiple frames of reflected light spot images at each polarization angle by the detector, calculating the global centroid ordinate of the reflected light spot at each polarization angle, and obtaining the peak-to-peak value of the centroid ordinate as a function of the polarization angle. When the peak-to-peak value exceeds a preset threshold and the centroid ordinate is antisymmetric about the orthogonal position, the corresponding incident angle is determined as a candidate incident angle, and the candidate incident angle with the largest peak-to-peak value is determined as the feature incident angle, wherein the angle corresponding to the orthogonal position is the subsequent selection reference angle.

[0016] Furthermore, at the characteristic incident angle, using the post-selection reference angle as a reference, the post-selection polarization element is rotated to a position deviating from the orthogonal position by a small angle on both sides. The two angular positions, the smaller angle ; Multiple frames of reflected light spot images were continuously acquired at each angular position, and the average centroid coordinates were calculated. The amplified beam lateral displacement is obtained by subtracting the average values ​​of the two centroid coordinates and dividing by 2. Half of the sum of the average values ​​of the two centroid coordinates is taken as the dynamic reference zero point. The beam lateral displacement per pixel is converted into physical length, and the optical path stability is verified based on the drift of the dynamic reference zero.

[0017] Furthermore, a correlation equation is established with the refractive index as the unknown quantity. The theoretical beam lateral displacement is set to be equal to the measured beam lateral displacement. The theoretical beam lateral displacement is related to the characteristic incident angle, the back selection angle, the wavelength of the incident light, the beam waist radius, and the transmission distance. The correlation equation is solved by a numerical iterative algorithm until the absolute error criterion or the relative change criterion is satisfied. The obtained refractive index is then substituted back into the correlation equation for verification. When the difference between the theoretical beam lateral displacement and the measured beam lateral displacement is less than the experimental measurement uncertainty, the measured refractive index value is output.

[0018] A precision refractive index measurement device based on weak measurement and optical spin Hall effect, used to perform the aforementioned precision refractive index measurement method based on weak measurement and optical spin Hall effect, includes: Laser source; A focusing element is disposed on the output light path of the laser source; A pre-selection polarizer is positioned after the focusing element to establish a pre-selection state; A rotary table is used to hold the sample to be tested and to adjust the incident angle. A subsequent polarization element is placed in the reflected light path of the sample under test, and its transmission direction is configured to be approximately orthogonal to the transmission direction of the preceding polarization element. The imaging element is transformed and positioned after the post-selective polarization element; A detector, positioned after the transformation imaging element, is used to receive and observe the shape of the reflected light spot; A displacement stage is used to support the detector and move it precisely along the optical axis.

[0019] Furthermore, the focusing element is a short focal length lens, the transforming imaging element is a long focal length lens, and the short focal length lens and the long focal length lens are configured in a confocal configuration; It also includes a beam splitter and an auxiliary detector. The beam splitter is detachably disposed between the laser source and the focusing element, and the auxiliary detector is disposed on the reflected light path of the beam splitter to calibrate the zero position of the rotating stage.

[0020] Compared with the prior art, the present invention has the following advantages and beneficial effects: 1. The present invention provides a precision refractive index measurement method and device based on weak measurement and optical spin Hall effect. By introducing weak value amplification technology, the minute physical quantity to be measured (the transverse splitting amount of the optical spin Hall effect) is transformed into an easily observable change in the shape of the light spot (such as the rotation and brightness change of the double light spot). The absolute measurement of light intensity is transformed into the judgment of the relative change of the light spot, thereby overcoming the accuracy bottleneck of traditional methods.

[0021] 2. The present invention provides a precision refractive index measurement method and device based on weak measurement and optical spin Hall effect. By constructing specific pre-selective and post-selective polarization states, the weak measurement theory is used to amplify nanoscale displacements into micrometer-level light spot splits that can be clearly distinguished by a CCD camera, thus solving the problem that traditional geometric optics detection limits cannot identify nanoscale displacements.

[0022] 3. The present invention provides a precision refractive index measurement method and apparatus based on weak measurement and optical spin Hall effect, which obtains the characteristic incident angle directly using a high-precision turntable. As a fixed input, rather than assuming it equals the theoretical Brewster angle. This avoids systematic errors caused by actual experimental conditions deviating from the theoretical Brewster conditions, and eliminates systematic errors introduced by the failure to meet theoretical conditions in principle. Attached Figure Description

[0023] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings: Figure 1 This is a logic flowchart of a precision refractive index measurement method based on weak measurement and optical spin Hall effect according to the present invention.

[0024] Figure 2 This is a magnified image of the beam's lateral displacement.

[0025] Figure 3 This is a schematic diagram of the optical spin Hall effect that occurs when light is reflected at an interface.

[0026] Figure 4 This is a schematic diagram of the light spot after the light source and camera are coaxial.

[0027] Figure 5 This is a schematic diagram of the light spot after placing a telephoto lens.

[0028] Figure 6 This is a schematic diagram of the light spot after placing a short focal length lens.

[0029] Figure 7 This is a diagram of the spin Hall effect light spot splitting observed during Brewster angle determination.

[0030] Figure 8 This is a sequence of light spot morphology changes between the two split light spots after rotation and selection of the polarizer.

[0031] Figure 9 This is a schematic diagram of the structure of a precision refractive index measuring device based on weak measurement and optical spin Hall effect according to the present invention.

[0032] The attached diagram shows the markings and corresponding component names: 1-Laser source; 2-Short focal length lens L1; 3-First polarizer P1; 4-High-precision rotary stage; 5-Sample to be tested; 6-Second polarizer P2; 7-Long focal length lens L2; ​​8-First CCD camera; 9-Front selection optical path; 10-Rear selection optical path; 11-Large circular arc guide rail; 12-Small circular arc guide rail; 13-Front selection optical path guide rail; 14-Rear selection optical path guide rail; 15-Beam splitter prism; 16-Second CCD camera; 17-Transfer stage. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0034] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0035] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0036] The terms “first”, “second”, etc., are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0037] Furthermore, the terms "parallel" and "perpendicular" do not imply that components must be absolutely parallel or perpendicular, but rather that they can be slightly tilted. For example, "parallel" simply means that its direction is more parallel than "perpendicular," not that the structure must be perfectly parallel, but that it can be slightly tilted.

[0038] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0039] When light is reflected at an interface with a sudden change in refractive index (such as an air-sample interface), a spin Hall effect occurs due to spin-orbit coupling. Specifically, the left-handed and right-handed circularly polarized components of the light beam undergo opposite lateral displacements in a direction perpendicular to the incident plane. This displacement is typically on the nanometer scale and is a sensitive function of the sample's refractive index.

[0040] It should be noted that linearly polarized light (such as P-polarized light) can be mathematically decomposed into a superposition of left-handed and right-handed circularly polarized components. During reflection at the air-sample interface, due to spin-orbit interaction, these two circularly polarized components will undergo lateral splitting in opposite directions, resulting in nanoscale displacement. The displacement The refractive index n of the sample and the angle of incidence These parameters exhibit a strict physical correlation. However, the aforementioned nanoscale displacement is far smaller than the resolution limit of conventional detectors and cannot be directly observed. This invention introduces quantum weak measurement theory to amplify this nanoscale displacement. The weak measurement amplification mechanism includes three stages: pre-selection state construction, weak interaction, and post-selection state construction. By constructing specific polarization pre-selection and post-selection states, the nanoscale displacement is amplified into a micrometer-scale light spot split that can be clearly resolved by the detector using weak measurement theory, thereby solving the problem that traditional geometric optics detection limits cannot detect nanoscale displacements.

[0041] like Figures 1 to 9 As shown, this embodiment provides a precise refractive index measurement method based on weak measurement and the optical spin Hall effect, including the following steps: It should be understood that steps S1.1 to S1.8 are the initial system installation, optical path alignment and parameter calibration process, which are only performed after the equipment is first used or after the optical path is overhauled; step S1.9 is the placement and attitude adjustment of the sample to be tested; steps S2 to S6 are the routine measurement process.

[0042] Step S1: Pass the laser beam emitted by the laser source through a pre-selective polarizer to form incident light. The incident light is configured as linearly polarized light with P polarization as the main polarization component and containing a trace S polarization component, so as to construct a pre-selective state for weak measurement.

[0043] Step S1 specifically includes: Step S1.1: Establish the measurement optical path. For example... Figure 9 As shown, a laser source 1, a beam splitter (beam splitter prism 15), a focusing element (short focal length lens L12), a pre-selective polarizer (first polarizer P13), a rotating stage (high-precision rotating stage 4) carrying the sample to be measured, a post-selective polarizer (second polarizer P26), a transformation imaging element (long focal length lens L27), a detector (first CCD camera 8), and a displacement stage 17 for carrying the detector (first CCD camera 8) and moving along the optical axis are arranged sequentially along the optical path to form a complete reflective weak measurement optical path. The focusing element (short focal length lens L12) is used to focus the laser beam and transform it to angular spectral space; the transformation imaging element (long focal length lens L27) is used to transform the beam from angular spectral space back to coordinate space, and works with the focusing element (short focal length lens L12) to achieve beam expansion and collimation; the pre-selective polarizer (first polarizer P13) is used to construct the pre-selective state; the post-selective polarizer (second polarizer P26) is used to construct the post-selective state; and the detector (first CCD camera 8) is used to acquire the reflected light spot image.

[0044] Step S1.2: Coaxial adjustment of the light source and detector (first CCD camera 8). For example... Figure 4 and Figure 9 As shown, to facilitate initial alignment and avoid saturation of the detector (first CCD camera 8) caused by direct laser light, a temporary attenuation filter can be placed in front of the front selection optical path 9. The laser source 1 is turned on, and its height, lateral position, and pitch are adjusted so that the centroid of the light spot remains at the center of the detector's (first CCD camera 8's) field of view when the detector (first CCD camera 8) is moved along the optical axis. At this point, the light source and the detector (first CCD camera 8) are coaxial, establishing the reference optical axis of the entire system.

[0045] Step S1.3: Align the optical axis of the imaging element. For example... Figure 5 and Figure 9 As shown, the transformation imaging element (telephoto lens L27) is placed in the rear selection optical path 10, and its height, lateral position, pitch and yaw are adjusted so that when the detector (first CCD camera 8) is moved along the optical axis, the centroid of the light spot is always approximately located at the center of the field of view of the detector (first CCD camera 8), ensuring that the optical axis of the transformation imaging element (telephoto lens L27) coincides with the reference optical axis.

[0046] Step S1.4: Align the optical axis of the focusing element (short focal length lens L12). For example... Figure 6 and Figure 9As shown, the focusing element (short focal length lens L12) is placed in the front selection optical path 9, and its height, lateral position, pitch and yaw are adjusted. The detector (first CCD camera 8) is moved along the optical axis so that the centroid of the light spot is always approximately located at the center of the field of view of the detector (first CCD camera 8), ensuring that the light beam focused by the focusing element (short focal length lens L12) is coaxial with the reference optical axis.

[0047] Step S1.5: Beam waist radius calibration. Remove the attenuation filter and temporarily move the transformation imaging element (telephoto lens L27). Then, slowly move the detector (first CCD camera 8) back and forth along the optical axis. When the spot size reaches its minimum, this is the coarse positioning of the beam waist. Using this position as the center, control the displacement stage 17 to make equal-interval steps (e.g., 0.1 mm or 0.5 mm per step) along the beam axis. At each step position, acquire and save a clear spot image.

[0048] Extract the light intensity distribution of the cross-section of the light spot at each location and fit it according to the following Gaussian model:

[0049] in Light intensity decays to the center peak value The beam radius at that location Perpendicular to the direction of the incident plane ( In terms of direction, in the horizontal position The light intensity value measured at that location, Let be the peak light intensity on the cross-section of the light spot. The Gaussian beam propagation formula is used on the dataset. Perform fitting:

[0050] in Let z be the radius of the light spot measured at position z. Let the radius of the waist be the unknown. For the precise positioning of the waistband, Rayleigh distance, Where λ is the laser wavelength. This formula is the standard expression for Gaussian beam propagation, and its specific form and fitting method are well known to those skilled in the art. By fitting using the nonlinear least squares method, the accurate beam waist radius can be obtained simultaneously. Waistline position Distance from Rayleigh The minimum value of the fitted curve is... .

[0051] After the measurement is completed, the transformation imaging element (long focal length lens L27) is moved back to its original position, and its position and orientation are adjusted according to the method in step S1.3 to ensure that the optical axis coincides with the reference again.

[0052] Step S1.6: Confocal adjustment of the focusing element (short focal length lens L12) and the transforming imaging element (telephoto lens L27). This is based on the focal lengths of the focusing element (short focal length lens L12) and the transforming imaging element (telephoto lens L27). , Adjust the spacing to approximately The confocal position is determined. The shearing interferometer, used as an auxiliary adjustment tool, is placed between the transformation imaging element (long focal length lens L27) and the detector (first CCD camera 8), at approximately a 45° angle to the optical axis, so that its reflected light is projected onto the observation screen. The pitch and azimuth of the interferometer are adjusted so that the two reflected beams overlap on the screen to create a bright interference area. Slight adjustments are made to the interferometer or the observation screen until clear and appropriately numbered interference fringes appear. Keeping the optical platform stable, the transformation imaging element (long focal length lens L27) is finely adjusted until the fringes are neatly parallel to the reference scribe line and equally spaced. The focusing element (short focal length lens L12) and the transformation imaging element (long focal length lens L27) are precisely in a conjugate position, achieving optimal beam collimation. After adjustment, the shearing interferometer is removed.

[0053] Step S1.7: Zero-point calibration. For example... Figure 9 As shown, the beam splitter (beam splitter prism 15) and auxiliary detector (second CCD camera 16) are placed in the front selection optical path 9. The height, pitch, and yaw of the beam splitter (beam splitter prism 15) are adjusted so that the centroid of the light spot remains at the center of the field of view when the detector (first CCD camera 8) is moved along the optical axis, ensuring that the light source is incident directly on the beam splitter. The position of the auxiliary detector (second CCD camera 16) is adjusted so that the centroid of the light spot reflected by the beam splitter (beam splitter prism 15) is located at the center of the field of view of the auxiliary detector (second CCD camera 16). A standard sample with a known refractive index is placed on the rotary stage (high-precision rotary stage 4). The pitch and yaw of the standard sample are adjusted, and the rotary stage (high-precision rotary stage 4) and the rear selection optical path 10 are rotated in conjunction with this adjustment so that the centroid of the reflected light spot is always approximately located at the center of the field of view when the detector (first CCD camera 8) is moved back and forth. Subsequently, the rotary stage (high-precision rotary stage 4) is rotated until the reflected light energy from the surface of the standard sample returns along its original path and converges at the center of the field of view of the auxiliary detector (second CCD camera 16). This position is the absolute zero position of the rotary stage, corresponding to the state where the beam is incident on the standard sample. The reading of the rotary stage (high-precision rotary stage 4) at this time is recorded as the zero position reference for normal incidence.

[0054] After completing the zero-point calibration, remove the beam-splitting element (beam-splitting prism 15) and the auxiliary detector (second CCD camera 16). During the zero-point calibration process, the light reflected from the surface of the standard sample returns along its original path and converges at the center of the field of view of the auxiliary detector (second CCD camera 16). The optical path state can be referenced... Figure 9 The positional relationship between the central beam splitter 15 and the second CCD camera 16.

[0055] Step S1.8: Pre-selection state reference calibration. For example... Figure 9 As shown, the pre-selection polarizer (first polarizer P13) is moved into the pre-selection optical path 9, keeping the pitch and yaw locks of the standard sample calibrated in step S1.7 unchanged. The rotary stage (high-precision rotary stage 4) is rotated so that the incident angle is close to the theoretical Brewster angle of the standard sample. During this process, the angle of the post-selection optical path 10 is simultaneously adjusted so that the reflected light spot is always kept near the center of the field of view of the detector (first CCD camera 8). The pre-selection polarizer (first polarizer P13) is slowly rotated while monitoring the brightness of the light spot reflected from the surface of the standard sample. When the intensity of the reflected light attenuates to a minimum, the rotation angle of the pre-selection polarizer (first polarizer P13) is locked. At this time, the transmission direction of the pre-selection polarizer (first polarizer P13) is precisely calibrated to the P-polarization direction under the system reference. At the same time, due to the limitation of the extinction ratio of the polarizer, the incident light inevitably contains a trace S-polarization component, constituting a weak measurement pre-selection state. Record the scale of the polarizer rotator at this point for reference during subsequent system reset. After completing the calibration in the forward selection state, remove the standard sample.

[0056] Step S1.9: Placement and attitude adjustment of the sample under test. The sample under test is mounted on a rotary stage (high-precision rotary stage 4). Only the pitch and yaw of the sample under test are adjusted so that when the detector (first CCD camera 8) is moved back and forth along the optical axis, the centroid of the light spot reflected from the surface of the sample under test is always maintained at the center of the field of view of the detector (first CCD camera 8). Since the reference optical axis of the system has been uniquely determined in steps S1.2 to S1.6, both the standard sample and the sample under test complete the attitude adjustment through the same "spot centering" operation. Provided that the sample mounting surface has sufficient geometrical accuracy, the spatial orientation of the surface normals of both samples is consistent. Therefore, the transmission direction of the pre-selected polarizer calibrated based on the standard sample in step S1.8 remains valid for the sample under test, and the definition of the pre-selected state is maintained after sample replacement.

[0057] Step S2: The incident light is incident on the surface of the sample to be tested and reflected, and the reflected light produces a lateral displacement related to the refractive index of the sample to be tested.

[0058] Step S3: Pass the reflected light through a post-selective polarization element, the transmission direction of which is nearly orthogonal to the transmission direction of the pre-selective polarizer, to construct a post-selective state, and amplify the lateral displacement into observable spot splitting through a weak value amplification mechanism.

[0059] Step S3 specifically includes: Step S3.1: Move the post-selected polarization element into the post-selected optical path and adjust its transmission direction to be nearly orthogonal to the transmission direction of the pre-selected polarization element, thus forming a post-selected state for weak measurement. This near-orthogonal configuration is key to generating a maximum weak amplification.

[0060] It should be noted that when the light beam is reflected at the air-sample interface, photon spin-orbit interaction occurs, producing the optical spin Hall effect. During this process, the photon spin operator... For observable measurements of the system, the transverse splitting δ of the optical spin Hall effect corresponds to the coupling strength between the system and the instrument. The following weak value amplification theoretical framework is based on the Standard Model of quantum weak measurement and the angular spectrum theory of the optical spin Hall effect; the relevant derivations are well-known in the field.

[0061] The theoretical description of the weakness amplification mechanism is as follows: The system's preselection state is The initial state of the instrument | i > represents the spatial pattern of a Gaussian beam, specifically as follows: , The overall initial state consisting of the instruments and the system is: ,in The horizontal polarization basis vector is represented, which in this context corresponds to the pre-selected state |P>, and the V polarization corresponds to the aforementioned S polarization (the electric field vector is perpendicular to the incident plane).

[0062] Spin Operator for Observable Measurement It means (where |+ , |- (Corresponding to the circularly polarized states with positive and negative helicity, respectively), the pointer variable is represented by photon momentum (i.e., wave vector). When the beam is reflected at the interface, spin-orbit interaction occurs, and its wave function evolves as follows: , in = 2π / λ is the wavenumber of the laser in vacuum. These are the transverse components of the reflected light wave vector in the x and y directions, respectively. This represents the change in polarization state of the light beam after reflection (Fresnel reflection coefficient matrix). and , respectively, are the Fresnel reflection coefficients for P-polarization and S-polarization.

[0063] The state of the light beam after passing through the second polarizer P26 is ,in It is called the back selection angle (the angle at which the transmission direction of the back selection polarizer deviates from the orthogonal position).

[0064] The wave function after selection can be expressed as:

[0065] Where z is the transmission distance from the beam waist to the detector surface, and δ is the initial lateral displacement generated by the optical spin Hall effect. For the free evolution of the system, exp(-i 3) is a unitary operator for spin-orbit coupling (representing the weak interaction between photon spin and momentum). For Fresnel reflection coefficient, The state of the system after the light beam is reflected by the air-sample interface.

[0066] After selection, the light field is collimated by the telephoto lens L2 and then enters the first CCD camera 8, recording the overall centroid displacement of the light beam as follows:

[0067] in, This is the transmission amplification factor, which is related to the transmission distance. Rayleigh distance ( , (where z is the waist radius measured in step S1.5), and z is the transmission distance. This is a weak value (the core amplification factor in weak measurements). In the angular spectral representation, the position operator is represented as... .

[0068] In the design of this device, the laser wavelength is 632.8 nm. After being focused by the short focal length lens L12, the beam waist radius w0 = 27 μm; the transmission distance z = 250 mm, and the transmission amplification factor F ≈ 69.

[0069] in addition, ,because = 90° - Therefore, tanβ = Therefore, weak value = Design and debugging standards The weak value magnification factor can be obtained as follows: 286.

[0070] Therefore, through transmission and weak amplification, the initial transverse shift δ of the optical spin Hall effect will be amplified to approximately: , Precise measurements and observations of the optical spin Hall effect have been achieved.

[0071] It should be noted that the theoretical framework of weak measurement, the definition of the weak value, and the relationship between the centroid displacement and the weak value mentioned above are all well-known theories in the field of quantum weak measurement. The contribution of this invention is not to establish a new theory of weak measurement, but to apply this existing theory to the scenario of precise refractive index measurement, and to design the corresponding experimental parameters and optical path system.

[0072] Step S4: Change the incident angle of the incident light relative to the surface of the sample to be tested, rotate the selected polarization element and obtain the centroid position of the reflected light spot under different polarization angles, and determine the characteristic incident angle based on the magnitude of the change of the centroid position with the polarization angle and the symmetry about the orthogonal position.

[0073] Step S4 specifically includes: Step S4.1: Coarse Scan to Locate the Approximate Brewster Angle Range. Control the rotary stage to gradually increase the laser beam incident angle from a preset starting angle in large increments (e.g., 2° to 3°), traversing a wide angle range (e.g., 40° to 80°) to cover the expected range where the Brewster angle is located. While rotating the rotary stage to change the incident angle, simultaneously drive the subsequent selection optical path to rotate around the center of the sample surface, ensuring that the angle of the subsequent selection optical path always changes synchronously with the incident angle. This guarantees that the reflected beam always propagates along the principal optical axis, and the centroid of the reflected spot always remains near the center of the detector's field of view. At each incident angle, observe the morphological changes of the reflected spot through the detector. When the incident angle is far from the Brewster angle, the spot is a single peak; as the incident angle gradually approaches the Brewster angle, a depression appears at the center of the spot, eventually splitting into approximately symmetrical double peaks. Record the range of incident angles where the spot first shows obvious splitting as the approximate range where the Brewster angle is located.

[0074] Step S4.2: Quantitatively determine the high-sensitivity measurement range. Within the coarse range, adjust the incident angle with a fine step size (e.g., 0.2° to 0.5°). At each candidate incident angle, rotate the selected polarization element and scan through multiple polarization angles (e.g., within a neighborhood where its transmission direction is approximately orthogonal to the transmission direction of the previously selected polarizer, from 88° to 92°, rotating and scanning at least 5 angular positions with a fixed step size, such as 0.2° to 0.5°), simultaneously acquiring spot images at each angle. Rotate the selected polarization element to different angles, and record the i-th scanning angle as... The corresponding centroid ordinate is

[0075] At each angular position, the detector acquires no fewer than 5 frames of spot images, and the global centroid ordinate of the spot at each angle is calculated using the intensity-weighted centroid method. .

[0076] For each preprocessed frame of the light spot image, the intensity-weighted centroid method is used to calculate the following formula in the direction perpendicular to the incident plane:

[0077] in, For the first The ordinate of a pixel. This is the grayscale value of the pixel after subtracting the dark background. Image preprocessing uniformly includes dark background subtraction and Gaussian smoothing filtering (standard deviation). The process involves pixel extraction, region of interest (ROI) extraction (selecting a rectangular area containing all the energy of the light spot, or automatically determining it through thresholding), and intensity threshold setting (taking 10% of the peak intensity within the ROI as the threshold, retaining only pixels above the threshold to eliminate edge noise). The average value of multiple frames is taken as the representative centroid value for that angle.

[0078] Calculate the centroid ordinate at this incident angle. Peak value as a function of the scanning angle of the second polarizer P26 .

[0079] Set the judgment threshold Threshold The selection method is as follows: at a distance far from Brewster's angle (e.g., a deviation of more than 5°), the light spot is always a single peak. At this time, the change in centroid shift caused by the scanning of the second polarizer P26 is minimal, and this background change is recorded. ,Pick (That is, the threshold is set to 3 to 5 times the amount of background fluctuation), or it is set to an absolute threshold (such as 3 to 5 pixels) according to the pixel resolution of the first CCD camera 8.

[0080] The current incident angle is considered to have entered the high-sensitivity measurement range, deviating from the Brewster angle by 0.5° to 2°, when the following two conditions are met: Condition 1 (Sensitivity Condition): The peak value of the centroid shift exceeds the threshold, i.e. This condition ensures that the light spot exhibits a significant asymmetric change when the second polarizer P26 rotates, indicating that the linear term has become dominant and the system is in a high-sensitivity state.

[0081] Condition 2 (Symmetry Condition): Within the scan range, find the maximum value of the global centroid's ordinate. and minimum value Calculate the arithmetic mean of the two. .

[0082] In a weak measurement system, when the light spot splits into two peaks due to the spin Hall effect and the second polarizer P26 is nearly orthogonal, the global centroid ordinate of the light spot is... The deviation from the post-selection angle is linearly related and antisymmetric about the orthogonal position. That is, when the second polarizer P26 deviates from the orthogonal position by equal amounts in the positive and negative directions, the centroid offset is equal in magnitude and opposite in direction. Let the centroid ordinate in the precisely orthogonal state be... Then we have:

[0083] Therefore, the arithmetic mean of the maximum and minimum values ​​within the scanning range is exactly equal to the centroid ordinate when orthogonal:

[0084] In the data sequence, following the increasing order of the second polarizer P26 angle, find the global centroid ordinate spanning... The interval of adjacent data points satisfies:

[0085] If multiple sign change intervals are detected, select one of them. The largest interval corresponds to the linear segment with the steepest centroid change near the orthogonal position, and this interval corresponds to the region with the best linearity and highest signal-to-noise ratio. Because the scan step size is sufficiently small, within the local interval... The ordinate of the incenter of mass changes approximately linearly with the angle; therefore, within the selected interval... Perform linear interpolation within the range and solve for... The corresponding angle :

[0086] like If the deviation from the center angle of the scanning range does not exceed twice the scanning step length, the symmetry condition is satisfied. This condition ensures that the light spot restores symmetry at orthogonal positions (the linear term coefficient is zero), eliminating false signals caused by optical path deviation or other factors.

[0087] at the same time, This is the post-selection reference angle, which is the scale value of the rotary table corresponding to the strict orthogonality between the transmission direction of the second polarizer P26 and the transmission direction of the first polarizer P13. All post-selection angles in subsequent steps will use this as the absolute zero point. For ease of operation, this orthogonal reference position is calibrated as the zero point (denoted as ). ( ), serving as the absolute reference for all subsequent angle selections.

[0088] Step S4.3: Determine the characteristic incident angle. Record the incident angles that simultaneously satisfy both of the above conditions, and select the centroid offset peak value among them. The largest candidate incident angle is used as the measured characteristic incident angle. (i.e., the high-sensitivity measurement interval angle near Brewster's angle).

[0089] The physical mechanism for adopting the above selection criteria is that when the incident angle approaches the theoretical Brewster angle, i.e., the deviation angle Δθ → 0, the P-polarization reflection coefficient... Approaching zero. As can be seen from the aforementioned expression for light intensity distribution, the linear term carrying displacement information is proportional to... Therefore, this term also approaches zero. In this case, although the weak-value amplification factor theoretically approaches its maximum value, the absolute value of the amplified signal is extremely weak and easily drowned out by system noise in actual measurements, leading to a centroid shift in peak-to-peak value. Instead, it remains at a lower level. And when the angle of incidence deviates appropriately from the theoretical Brewster angle, As the value of increases, the absolute value of the linear term signal is significantly enhanced. At this point, although the theoretical amplification factor decreases compared to the extreme point, the amplified effective centroid shift signal is significantly enhanced, and the measured peak-to-peak value of the centroid shift... The maximum value can be obtained. Therefore, we know that... It is a measured index that comprehensively reflects signal strength and amplification factor. Its maximum value corresponds to the optimal signal-to-noise ratio and the highest response sensitivity of the measurement system.

[0090] When none of the candidate incident angles meet condition one (i.e., the peak value of the centroid offset is always less than the threshold), it indicates that the current angle deviates too far from the Brewster angle, and the scanning range needs to be expanded or the sample placement posture needs to be checked.

[0091] Compared with the traditional minimum light intensity criterion, this morphological criterion has the advantages of being visually intuitive, having high judgment accuracy, and being unaffected by fluctuations in light source power. It directly solves the fundamental problems of difficulty in judging the minimum light intensity and low accuracy in traditional methods.

[0092] Step S5: At the characteristic incident angle, the beam is symmetrically deflected and the reflected light spot image is acquired with the orthogonal position of the post-selected polarization element as the reference. The magnified beam transverse displacement is obtained through differential operation, and the deviation of the post-selected polarization element relative to the orthogonal position is recorded as the post-selection angle.

[0093] Step S5 specifically includes: Step S5.1: Select a small deviation angle .

[0094] Choose a small angle based on the required amplification factor and signal strength. ,generally . The smaller the value, the greater the amplification factor of the weak signal, but the weaker the signal light intensity. It is necessary to make a trade-off between the sensitivity and signal-to-noise ratio of the first CCD camera 8.

[0095] Step S5.2: Set the symmetry selection angle and acquire the image. Use the orthogonal reference angle determined in step S4. Using this as a reference, the second polarizer P26 is rotated sequentially to the following two angular positions: Status A:

[0096] State B:

[0097] In state A, after the light spot stabilizes, the first CCD camera 8 continuously acquires data. Frame spot image ( (), stored as sequence A. In state B, the same data is collected. The frame of the light spot image is stored as sequence B.

[0098] Step S5.3: Determine the post-selection angle used for refractive index inversion. The angle corresponding to state A. The small angle deviating from the orthogonal direction is denoted as the subsequent selection angle Δ, and the accuracy of the angle reading should be better than [previous value]. This post-selection angle will be used as a reference in the refractive index-beam lateral displacement correlation model in step S6. value.

[0099] Step S5.4: Calculate the average centroid values ​​for states A and B. For each frame in sequence A, after image preprocessing, calculate the global centroid ordinate of the light spot using the intensity-weighted centroid method. ,Pick The arithmetic mean of the frames, denoted as The same calculation applies to sequence B, denoted as... .

[0100] Step S5.5: Calculate the beam lateral displacement and reference zero point. Using the average centroid values ​​from states A and B, calculate using the following formula: Magnified beam lateral shift (in pixels): Dynamic reference zero point (pixel coordinates):

[0101] This reference zero point corresponds to the splitting point without the spin Hall effect (i.e., the initial transverse shift). (Ideal case) The absolute position of the spot centroid on the first CCD camera 8. Differential operation eliminates systematic errors such as beam common-mode drift, mechanical vibration, and bias of the first CCD camera 8, and doubles the effective signal.

[0102] Step S5.6: Pixel Size Calibration. Convert the beam lateral displacement per pixel unit to the actual physical length. Utilize a pre-calibrated pixel size conversion factor. (μm / pixel), or via imaging system parameters (L2 focal length of the telephoto lens). First CCD camera pixel size ) Calculated by combining the beam transmission matrix The final physical beam lateral displacement is obtained as follows: this This is the "beam shift" used in the refractive index inversion model in step S6.

[0103] Step S5.7: Zero-point calibration. If zero-point calibration is found at multiple measurement points or during the scanning process... Significant drift indicates instability in the optical path, requiring system recalibration or drift subtraction before further calculations. This can be addressed through real-time monitoring. This can effectively ensure the reliability of measurement data.

[0104] Step S6: Substitute the characteristic incident angle, the back selection angle, and the beam lateral shift into the correlation equation to determine the refractive index of the sample to be tested.

[0105] Step S6 specifically includes: Step S6.1: Establish the nonlinear equation. The characteristic incident angle measured in step S4.3... The post-selection angle determined in step S5.3 The beam transverse shift measured in step S5.6 Including the already calibrated waist radius Laser wavelength Transmission distance Substitute the system parameters into the refractive index-beam transverse displacement correlation model established based on the optical spin Hall effect. .in This represents the theoretical beam lateral displacement.

[0106] The refractive index-beam lateral displacement correlation model is based on the angular spectrum theory of quantum weak measurement and the optical spin Hall effect. The following is a brief explanation of its derivation to clearly demonstrate the physical origin of the final inversion equation.

[0107] In the weak measurement framework, the system state is described by the polarization state of the photon. Taking the pre-selected state as... That is, the P-polarization direction; then, the transmission direction of the selected polarizer is approximately orthogonal to the P-direction, and the subsequent selected state can be written as: in The post-selection angle (i.e., the angle between the transmission direction of the post-selection polarizer and the orthogonal direction).

[0108] The spatial pattern of the laser beam, known as the pointer state, is used to indicate and record minute changes caused by system interactions. In this device, the focusing element (short focal length lens L12) focuses the laser beam to form a Gaussian beam, and the angular spectrum of this Gaussian beam constitutes the pointer state. (The text then abruptly shifts to a seemingly unrelated topic about beam waist radius.) and wave number ( (Description of the transverse wave vector, where the wavelength is the laser wavelength) The initial distribution is: .

[0109] When light is reflected at the air-sample interface, spin-orbit coupling occurs, corresponding to the optical spin Hall effect. Let the Fresnel reflection coefficients for P-polarization and S-polarization be respectively... and And let Angle of incidence Place The first-order partial derivative. Retained to... The first-order reflected light angular spectrum is in The following can be written as (this expansion is based on the well-known quantum weak measurement angular spectrum theory):

[0110] After the reflected beam passes through the selective polarizer, the effective angular spectrum of the output light is:

[0111] in, ,

[0112] In this device, the detector is placed on the rear focal plane of the telephoto lens, and the light field on this plane is related to... They are mutually Fourier transforms. The centroid of the light spot shifts laterally. The expected value of the transverse momentum of the output angular spectrum satisfy

[0113] The transmission distance from the beam waist to the detector surface is equal to the focal length of the telephoto lens in a confocal configuration. The expected value of the momentum is calculated using Gaussian integration, yielding:

[0114] Will Substitute the expression and use Rayleigh distance After simplification, the analytical expression for the theoretical beam displacement is finally obtained as follows:

[0115] This expression fully reflects the transmission amplification (including the factor). ), weak value amplification (including) ) and Fresnel coefficient partial derivatives (including The combined effect on the centroid displacement of the light spot. The two terms in the denominator are respectively proportional to... and This describes the intensity changes and nonlinear saturation behavior caused by post-selection. Specifically, near Brewster's angle, although... ,but Keeping finite, in the numerator and denominator The terms guarantee good behavior of the formula and the absence of singularities, thus making the model suitable as an accurate basis for numerical inversion of the refractive index.

[0116] The specific definitions of each parameter in the above formula are as follows: , The wavelength of the laser; , The beam waist radius after focusing by the focusing element (short focal length lens L12); , , are the Fresnel reflection coefficients for P-polarization and S-polarization, respectively, both being the refractive index of the medium. and angle of incidence The function; ; The measured characteristic angle of incidence; The post-selection angle (i.e., the angle between the measured transmission direction of the post-selection polarizer and the orthogonal direction, which is a small angle deviating from orthogonality). The transmission distance is equal to the focal length of the telephoto lens; This is the beam lateral displacement calculated theoretically.

[0117] The Fresnel coefficients mentioned above and its partial derivatives By explicitly substituting the basic parameters into the analytical expression, one can obtain the result completely using the basic parameters. The expansion of the expression:

[0118] Where, λ, , z, , All of these are known constants (obtained through measurement or calibration). Therefore, the problem of solving for the refractive index n is transformed into solving for the roots of the following equation:

[0119] Step S6.2: Numerical Iterative Solution. The above equations are solved using Newton's iterative method. In each iteration, the current estimated refractive index is calculated. Corresponding objective function value and its derivative value Derivative The refractive index can be obtained through automatic differentiation, sign differentiation, or manual derivation of the analytical expression followed by programming calculation. The estimated value of the refractive index is updated based on Newton's iterative formula.

[0120] in, The refractive index to be measured is... For the first The refractive index estimate of the next iteration. For the first The estimated value after the next iteration update objective function For the objective function in The first derivative at that point.

[0121] Set a sufficiently small convergence threshold. (For example When the iteration satisfies the absolute error criterion. or relative change criteria When the computation is considered to have converged, then take... This is the final solution. If the number of iterations exceeds the preset maximum limit (e.g., 100 times) and convergence is still not achieved, the algorithm will terminate with an error, and the input parameters need to be checked or the initial values ​​adjusted.

[0122] Step S6.3: Reverse verification. Substitute the obtained refractive index back into the theoretical model to calculate the theoretical beam shift. ,Compare Compared with measured values Its absolute difference The uncertainty should be less than the range of the experimental measurement. Once verification is successful, the precise refractive index measurement of the sample under the experimental configuration will be output.

[0123] It should be noted that the numerical iterative method described above for solving nonlinear equations is a well-known algorithm in mathematical computation in this field. The contribution of this invention lies not in inventing this algorithm, but in combining this well-known algorithm with the physical model of the optical spin Hall effect, forming a complete measurement technical route of fixed polarization state—measured angle—direct numerical inversion. This bypasses the technical solutions of polarization scanning and database fitting, and eliminates systematic errors caused by theoretical assumptions.

[0124] Through the above embodiments, this invention achieves approximately 20,000-fold amplification of the initial nanometer-scale displacement of the optical spin Hall effect, enabling the detector to directly resolve light spot splitting. Compared to the minimum light intensity determination scheme relied upon by the traditional Brewster angle method, this invention transforms the determination criterion into an intuitive light spot shape criterion, significantly improving the determination accuracy and repeatability. Simultaneously, by directly using the measured incident angle for numerical inversion, systematic errors introduced by the theoretical Brewster angle assumption are avoided, ensuring the accuracy and reliability of the final refractive index output.

[0125] Example 2

[0126] This embodiment provides a precision refractive index measurement device based on weak measurement and the optical spin Hall effect, used to perform the method described in Embodiment 1. Figure 9 As shown, the device includes: Laser source 1 is used to provide a stable coherent beam. In this embodiment, a helium-neon laser with a wavelength of 632.8 nm is used; The beam splitter 15 is detachably disposed in the front optical path between the laser source 1 and the short focal length lens L12; A short-focal-length lens L12 is disposed in the output optical path of the laser source 1 to converge the incident collimated beam to its focal point. In this embodiment, the focal length of the short-focal-length lens L12 is 50 mm. The first polarizer P13 is disposed after the short focal length lens L12 to construct a pre-selection state, configuring the incident light as linearly polarized light containing a main polarization component and a small amount of orthogonal polarization components. A high-precision rotary stage 4 is used to hold the sample 5 to be tested and to precisely adjust the incident angle. In this embodiment, the angular resolution can reach the arcsecond level. The sample to be tested, 5, is placed on the high-precision rotating stage 4, and its surface to be tested is a light-reflecting interface. The second polarizer P26 is disposed on the reflected light path of the sample 5 to be tested. Its transmission direction is configured to be nearly orthogonal to the transmission direction of the first polarizer P13, in order to construct the post-selected state and amplify the lateral displacement generated by the optical spin Hall effect. A telephoto lens L27, positioned after the second polarizer P26, has its focal point coinciding with that of the short-focal-length lens L12, thus recolliding the diverging light beam into parallel light. In this embodiment, the focal length of the telephoto lens L27 is 250 mm. The first CCD camera 8 is positioned behind the telephoto lens L27 and is used to receive and observe the magnified light spot shape. The displacement stage 17 is set on the rear selection optical path guide rail 14 and is used to support the first CCD camera 8 and move it precisely along the optical axis. The second CCD camera 16 is positioned on the reflected light path of the beam splitter 15 and is used to coordinate with the beam splitter 15 to calibrate the zero position of the high-precision rotating stage 4. In this embodiment, the resolution is not less than 1024×1024 pixels.

[0127] Furthermore, the device described in this embodiment also includes a front selection optical path guide 13, a rear selection optical path guide 14, a large circular arc guide 11, and a small circular arc guide 12. The front selection optical path guide 13 is used to support the short focal length lens L12 and the first polarizer P13; the rear selection optical path guide 14 is used to support the second polarizer P26, the long focal length lens L27, the displacement stage 17, and the first CCD camera 8; the large circular arc guide 11 and the small circular arc guide 12 are respectively used to support and adjust the angles of the front selection optical path and the rear selection optical path.

[0128] The components described above are arranged sequentially along the optical path, with the following connection relationship: laser source 1 → beam splitter 15 → short focal length lens L12 → first polarizer P13 → sample under test 5 → second polarizer P26 → long focal length lens L27 → first CCD camera 8. During zero-position calibration, the beam splitter 15 is inserted between the laser source 1 and the short focal length lens L12, and the second CCD camera 16 is positioned on its reflected optical path.

[0129] In this embodiment, the short focal length lens L12, the first polarizer P13, the high-precision rotating stage 4, the second polarizer P26, the long focal length lens L27, and the first CCD camera 8 are respectively a specific implementation of the focusing element, the front polarizer, the rotating stage, the rear polarizer, the transformation imaging element, and the detector in the method of Embodiment 1. The beam-splitting prism 15 and the second CCD camera 16 are respectively a specific implementation of the beam-splitting element and the auxiliary detector in the method of Embodiment 1; The displacement stage 17 is a specific implementation of the displacement stage in the method of Example 1.

[0130] Finally, as an alternative to the above technical solutions, the high-precision rotary stage 4 in this invention can employ an electrically controlled precision goniometer or a piezoelectric ceramic driven angle adjustment platform to achieve higher precision angle feedback; the first CCD camera 8 can employ a CMOS industrial camera or a linear array detector to reduce costs while meeting resolution requirements; the rotation drive of the second polarizer P26 can employ a stepper motor or servo motor in conjunction with an encoder to achieve precise polarization angle control; the laser source 1 can employ a 670 nm semiconductor laser instead of a 632.8 nm helium-neon laser. All of the above alternatives can achieve the technical objectives of this invention.

[0131] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A precise refractive index measurement method based on weak measurement and the optical spin Hall effect, characterized in that, Includes the following steps: The laser beam emitted from the laser source is passed through a pre-selective polarizer to form incident light, thus constructing a pre-selective state for weak measurement; The incident light is incident on the surface of the sample to be tested and reflected, and the reflected light produces a lateral displacement related to the refractive index of the sample to be tested. The reflected light is passed through a post-selective polarization element, the transmission direction of which is nearly orthogonal to the transmission direction of the pre-selective polarizer, to construct a post-selective state, and the lateral displacement is amplified into observable spot splitting through a weak value amplification mechanism. The incident angle of the incident light relative to the surface of the sample to be tested is changed, the polarization element is rotated and the centroid position of the reflected light spot under different polarization angles is obtained. Based on the change range of the centroid position with the polarization angle and the symmetry about the orthogonal position, the characteristic incident angle is determined. At the characteristic incident angle, the beam is symmetrically deflected and the reflected spot image is acquired with the orthogonal position of the post-selected polarization element as a reference. The magnified beam transverse displacement is obtained through differential operation, and the deviation of the post-selected polarization element relative to the orthogonal position is recorded as the post-selection angle. Substituting the characteristic incident angle, the post-selection angle, and the beam lateral shift into the correlation equation, the refractive index of the sample under test is determined.

2. The precision refractive index measurement method based on weak measurement and optical spin Hall effect according to claim 1, characterized in that: The incident light is configured as linearly polarized light with P polarization as the main polarization component and a trace S polarization component. The incident light is focused by a focusing element and then incident on the surface of the sample to be tested. The reflected light is received by a detector after passing through a conversion imaging element. The left-hand circularly polarized component and the right-hand circularly polarized component in the reflected light produce lateral displacements in opposite directions in the direction perpendicular to the incident surface.

3. The precision refractive index measurement method based on weak measurement and optical spin Hall effect according to claim 2, characterized in that: Before constructing the pre-selected state for weak measurement, the process includes moving the detector along the optical axis and acquiring spot images at multiple locations. After extracting the spot radius at each location using a Gaussian model, the beam waist radius is obtained by fitting the Gaussian beam propagation formula.

4. The precision refractive index measurement method based on weak measurement and optical spin Hall effect according to claim 1, characterized in that: The angle between the transmission direction of the post-selected polarizing element and the transmission direction of the pre-selected polarizing plate is . or ,in .

5. The precision refractive index measurement method based on weak measurement and optical spin Hall effect according to claim 1, characterized in that: Changing the incident angle of the incident light relative to the surface of the sample to be tested includes: gradually changing the incident angle in steps over a wide angle range, determining a rough range based on the change of the reflected light spot from a single peak to a concave shape and splitting into two peaks, and gradually changing the incident angle in steps over a second range within the rough range, wherein the first step length is greater than the second step length.

6. The precision refractive index measurement method based on weak measurement and optical spin Hall effect according to claim 1, characterized in that: The process of rotating the post-selected polarization element and obtaining the centroid position of the reflected light spot includes: at each incident angle, rotating the post-selected polarization element to change its transmission direction to multiple polarization angles near the orthogonal position; acquiring multiple frames of reflected light spot images at each polarization angle using a detector; calculating the global centroid ordinate of the reflected light spot at each polarization angle; obtaining the peak-to-peak value of the centroid ordinate as a function of the polarization angle; when the peak-to-peak value exceeds a preset threshold and the centroid ordinate is antisymmetric about the orthogonal position, determining the corresponding incident angle as a candidate incident angle; and determining the candidate incident angle with the largest peak-to-peak value as the characteristic incident angle, wherein the angle corresponding to the orthogonal position is the post-selection reference angle.

7. The precision refractive index measurement method based on weak measurement and optical spin Hall effect according to claim 6, characterized in that: At the characteristic incident angle, using the post-selection reference angle as a reference, the post-selection polarization element is rotated to a position deviating from the orthogonal position by a small angle on both sides. The two angular positions, the smaller angle ; Multiple frames of reflected light spot images were continuously acquired at each angular position, and the average centroid coordinates were calculated. The amplified beam lateral displacement is obtained by subtracting the average values ​​of the two centroid coordinates and dividing by 2. Half of the sum of the average values ​​of the two centroid coordinates is taken as the dynamic reference zero point. The beam lateral displacement per pixel is converted into physical length, and the optical path stability is verified based on the drift of the dynamic reference zero.

8. The precision refractive index measurement method based on weak measurement and optical spin Hall effect according to claim 1, characterized in that: A correlation equation is established with the refractive index as the unknown quantity. The theoretical beam lateral displacement is set to be equal to the measured beam lateral displacement. The theoretical beam lateral displacement is related to the characteristic incident angle, the back selection angle, the wavelength of the incident light, the beam waist radius, and the transmission distance. The correlation equation is solved by a numerical iterative algorithm until the absolute error criterion or the relative change criterion is satisfied. The obtained refractive index is then substituted back into the correlation equation for verification. When the difference between the theoretical beam lateral displacement and the measured beam lateral displacement is less than the experimental measurement uncertainty, the measured refractive index value is output.

9. A precision refractive index measurement device based on weak measurement and optical spin Hall effect, used to perform a precision refractive index measurement method based on weak measurement and optical spin Hall effect as described in any one of claims 1 to 8, characterized in that, include: Laser source; A focusing element is disposed on the output light path of the laser source; A pre-selection polarizer is positioned after the focusing element to establish a pre-selection state; A rotary table is used to hold the sample to be tested and to adjust the incident angle. A subsequent polarization element is placed in the reflected light path of the sample under test, and its transmission direction is configured to be approximately orthogonal to the transmission direction of the preceding polarization element. The imaging element is transformed and positioned after the post-selective polarization element; A detector, positioned after the transformation imaging element, is used to receive and observe the shape of the reflected light spot; A displacement stage is used to support the detector and move it precisely along the optical axis.

10. A precision refractive index measuring device based on weak measurement and optical spin Hall effect according to claim 9, characterized in that: The focusing element is a short focal length lens, the transforming imaging element is a long focal length lens, and the short focal length lens and the long focal length lens are configured in a confocal configuration. It also includes a beam splitter and an auxiliary detector. The beam splitter is detachably disposed between the laser source and the focusing element, and the auxiliary detector is disposed on the reflected light path of the beam splitter to calibrate the zero position of the rotating stage.

Images