A precise measurement method based on optical differential effect

Abstract

The application discloses a kind of precision measurement methods based on optical differential effect, by utilizing the light self-spin hall effect of light beam when reflecting in dielectric interface, make reflected light field complex amplitude proportional to the spatial first-order differential of incident light field, form the double petal reference spot with zero central intensity and two sides symmetric split.When the polarization azimuth or incident angle of the parameter to be measured changes, the symmetry of spot double peak light intensity is destroyed, at this time, by measuring the normalized difference value of the original two peak point intensity, the high-multiplying linear amplification measurement of weak parameter change can be realized.The application has the advantages of low implementation cost, high measurement accuracy, adjustable measurement accuracy and wide application range, and can be widely applied in polarization measurement, angle sensing, phase delay detection and solution concentration measurement, etc.

Description

Technical Field

[0001] This invention relates to the field of optical measurement technology, and in particular to a precision measurement method based on optical differential effects. Background Technology

[0002] Optical measurement utilizes the wave and particle properties of light to obtain geometric quantities (length, angle, shape, displacement), physical quantities (temperature, strain, refractive index), or state information of the measured object by detecting the information carried after light interacts with matter (such as intensity, phase, polarization, wavelength, frequency, etc.). Its core advantages lie in its non-contact, high-speed, high-resolution, and wide dynamic range. Common optical measurement techniques include geometric optics, laser ranging, laser Doppler velocimetry, infrared thermometry, spectral analysis, and machine vision inspection.

[0003] Optical precision measurement is a high-precision branch of optical measurement, aiming to break through the limits of traditional measurement. It relies on precise photophysical mechanisms such as coherent light, polarization manipulation, interferometry, and the Brewster effect to achieve ultra-high resolution detection. Its main applications include precision manufacturing, metrology, semiconductor chip production, materials engineering, biomedicine, and astronomical observation. Core technologies and methods include: interferometry (e.g., for nanometer-scale length, displacement, and three-dimensional surface morphology measurement), diffraction and spectroscopy (e.g., using grating diffraction or Raman spectroscopy to measure minute displacements, angular displacements, or material composition and structure), and polarization and profilometry (using ellipsometers for sub-nanometer-scale thin film thickness measurement, or using laser triangulation for rapid three-dimensional profile scanning).

[0004] However, existing optical precision measurement methods have many shortcomings: high-precision measuring instruments are usually complex and expensive; there is a trade-off between measurement range and resolution, making it difficult to maintain high resolution while maintaining a large measurement range; and they are susceptible to interference from uncertainties such as environmental noise, instrument noise drift, ambient temperature fluctuations, vibration, and sample preparation and alignment errors, which reduce measurement reliability. In recent years, new methods such as weak measurement, optical frequency combs (femtosecond laser frequency combs to achieve absolute distance measurement with meter-level range and nanometer-level resolution), and quantum-enhanced optical measurement (using quantum entangled light sources to push measurement accuracy close to or even break through the standard quantum limit) have been proposed. Although these methods can achieve higher accuracy, they are complex and costly. Therefore, realizing a simple, low-cost, and high-precision optical precision measurement method remains a major challenge in the field of optical measurement. Summary of the Invention

[0005] To address the technical problems of complex device structures, high costs, and insufficient measurement accuracy in current optical precision measurement methods, this invention provides a precision measurement method based on optical differential effects, which can significantly improve the measurement accuracy of minute changes in optical parameters. This method features a simple device, requiring only a single reflection and two polarization elements, eliminating the need for interferometer arms or phase-locked loops, thus significantly reducing system complexity and manufacturing costs. It has a wide range of applications, capable of measuring minute changes in optical parameters such as polarization, phase, propagation direction (angle), and solution concentration. Furthermore, it offers high accuracy, achieving a measurement precision of up to [insert accuracy here]. Metric-level accuracy; adjustable precision, different levels of accuracy can be achieved by changing the incident angle or incident polarization.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A precision measurement method based on optical differential effects includes the following steps:

[0008] Step 1: The polarized incident beam is obliquely incident onto the surface of the reflecting medium at a preset incident angle, and the polarization direction of the incident beam is adjusted to be perpendicular to the incident surface;

[0009] Step 2: After reflection by the reflecting medium, the reflected beam exhibits the optical spin Hall effect. The component of the polarization direction along the horizontal direction is taken as the outgoing light field. The horizontal direction is perpendicular to the polarization direction of the incident beam. At this time, the spatial distribution of the outgoing light field is proportional to the first spatial derivative of the incident light field, forming a pair of symmetrically split light spots. Then, the spatial positions of the points where the intensity of the two light spots is maximum are recorded. and ;

[0010] Step 3: When scenario one occurs: the polarization direction of the incident beam is deflected relative to the direction perpendicular to the incident plane in step 1. hour;

[0011] Or, scenario two: When the incident angle changes relative to the preset value in step 1, and the polarization direction of the incident beam is adjusted to have a preset deflection angle relative to the direction perpendicular to the incident plane in step 1. hour;

[0012] Both of these situations cause the symmetrically split light spot to become asymmetrically distributed. At this point, in... and Record the intensity values ​​of the two light spots at the respective locations. and ;

[0013] Step 4: Calculate the normalized intensity difference The Simultaneously satisfying the following formulas:

[0014]

[0015] in, and Let be the reflection coefficients of plane waves parallel and perpendicular to the incident plane, respectively. Let be the beam waist radius of the incident beam. For wave number, The incident angle after the symmetrically split light spot becomes an asymmetrically distributed light spot; This represents a factor related to propagation distance. , For Rayleigh distance, For the reflected beam from the reflecting interface to and The propagation distance at that location;

[0016] Then based on the calculations... Solve for case one Or in scenario two The amount of change relative to the preset value.

[0017] Preferably, in step 1, the reflecting medium is a prism or plate made of a dielectric material with a refractive index of The incident beam is a fundamental Gaussian linearly polarized laser beam.

[0018] Preferably, in step 3, when situation one occurs, if If the normalized intensity difference approaches 0, then... Approximately satisfies:

[0019] .

[0020] Preferably, in step 3, when situation two occurs, if the angle of incidence is at Brewster's angle... minor changes nearby Then the normalized intensity difference Approximately satisfies:

[0021] ;

[0022] in ,pass Solve Change relative to the preset value .

[0023] Preferably, when it is necessary to measure the phase delay, the phase delay to be measured is converted into an equivalent polarization angle change, and then the solution in case one is obtained. This leads to the determination of the phase delay to be measured.

[0024] Preferably, when it is necessary to measure the concentration of a chiral solution, the polarization direction of the incident light beam is changed by allowing the chiral solution to be measured, and then the solution in case one is solved. This allows us to obtain the concentration of the chiral solution to be tested.

[0025] Preferably, in step 3, when situation one occurs, the further the preset value of the incident angle is from the Brewster angle, the more the normalized intensity difference... Follow The greater the linear slope of the change, the higher the sensitivity to the measurement of polarization changes;

[0026] When scenario two occurs, the preset deflection angle is set. The larger the value of the normalized intensity difference, the closer the preset value of the incident angle is to the Brewster angle. Variation with incident angle The greater the linear slope of the change, the higher the sensitivity to the measurement of changes in the incident angle.

[0027] The technical advantages of this invention are as follows:

[0028] (1) The apparatus used to implement the method of the present invention is simple and inexpensive. The present invention utilizes only a single reflection of light on the surface of the reflective medium. The main components are a reflective medium and a pair of polarizers. It does not require complex interferometers, phase-locked loops or quantum light sources, which significantly reduces the complexity and cost of the system.

[0029] (2) High measurement accuracy. This is due to three reasons: (i) When the deflection of the incident polarization relative to the direction perpendicular to the incident plane is close to zero, the intensity difference... The deflection angle is proportional to the polarization direction. It exhibits a linear amplification relationship. Or a small change in the angle of incidence can lead to Significant changes, based on which high-precision measurements can be performed. (ii) By utilizing a common-mode suppression architecture, the difference in intensity between the two light spots is measured, effectively eliminating common-mode noise caused by light source power fluctuations and environmental vibrations, thus achieving high signal-to-noise ratio measurement; (iii) Due to the measurement signal used in this invention... Since the ratio is dimensionless and the intensity of the two light spots responds synchronously to fluctuations in the power of the light source, the measurement results are insensitive to fluctuations in the absolute power of the incident light and are naturally immune to long-term power drift of the incident light source (i.e., they do not depend on the light source for frequency and amplitude stabilization). This fundamentally reduces the system's reliance on high-performance lasers and associated costs. This is the core advantage of this method compared to traditional interferometric methods.

[0030] (3) Measurement accuracy is adjustable. When the incident angle is changed, and the deflection of the incident polarization relative to the direction perpendicular to the incident plane approaches zero, the intensity difference... Follow The slope, which changes linearly, is altered, thus enabling measurements of different accuracy levels.

[0031] (4) Wide applicability, suitable for multi-parameter detection. Through appropriate optical conversion devices or systems, minute changes in the optical parameters to be measured (such as phase, stress, temperature, concentration, etc.) are converted into... This method can be used to achieve high-precision measurements even when the incident angle changes. It provides a single optical path compatible with precision measurements of three types of minute parameters: polarization, angle, and phase. Its multi-parameter compatibility is significantly superior to that of single-function interferometers or ellipsometers. Attached Figure Description

[0032] To more clearly illustrate the technical solutions of the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a schematic diagram of the optical path structure used in an embodiment of the present invention, based on optical differential measurement of the polarization direction or incident light angle change. In the diagram, 1 is a polarizer, 2 is a reflecting medium, 3 is an analyzer, and 4 is a laser beam analyzer.

[0034] Figure 2 This is a diagram of the reflected light spot after the reflected beam passes through the analyzer in an embodiment of the present invention; where a1, a2, and a3 are theoretical results, and b1, b2, and b3 are experimental results; a2 and b2 correspond to The symmetrical splitting of the light spots at time, a1, b1 and a3, b3 respectively correspond to and Asymmetrical light spots at that time.

[0035] Figure 3 Normalized intensity difference in embodiments of the present invention Deflection angle perpendicular to the incident plane Theoretical and experimental results of the changes are shown in the figure; where (a) and (b) correspond to respectively Range of variation and .

[0036] Figure 4 Normalized intensity difference in embodiments of the present invention Theoretical and experimental results as the incident angle changes; where (a) and (b) correspond to the incident angles after the symmetrically split light spot becomes asymmetrically distributed. Range of variation and the angle of incidence at Brewster angle minor changes nearby .

[0037] Figure 5 This is a schematic diagram of the optical path structure based on optical differential measurement of phase delay used in an embodiment of the present invention; wherein 1 is a polarizer, 2 is a reflecting medium, 3 is an analyzer, 4 is a laser beam analyzer, 5 is a phase delayer, 6 is a quarter-wave plate, and 7 is a half-wave plate.

[0038] Figure 6 Normalized intensity difference provided in embodiments of the present invention With phase delay Theoretical and experimental results of the changes are shown in the figure; where (a) and (b) correspond to the range of phase delay variation, respectively. and .

[0039] Figure 7 This is a schematic diagram of the optical path structure for measuring the concentration of chiral solutions based on optical differential measurement, provided in an embodiment of the present invention; wherein 1 is a polarizer, 2 is a reflective medium, 3 is an analyzer, 4 is a laser beam analyzer, and 8 is a cuvette containing a chiral solution.

[0040] Figure 8 Normalized intensity difference provided in embodiments of the present invention Depending on the concentration of glucose and fructose solutions The theoretical curves showing the changes; where (a) and (b) correspond to glucose solution and fructose solution, respectively.

[0041] Figure 9 Normalized intensity difference provided in embodiments of the present invention Depending on the concentration of glucose and fructose solutions The experimental results show the changes. Detailed Implementation

[0042] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0043] To realize the precision measurement method based on optical differential effect provided in this embodiment, the measurement device includes a laser source, a polarizer, a reflective medium, an analyzer, and a laser beam analyzer arranged sequentially along the optical path propagation direction.

[0044] Adjust the transmission axis of the polarizer to make the incident beam linearly polarized (s-polarized) perpendicular to the incident plane. The incident beam is reflected at the interface of the reflecting medium at a preset incident angle. The reflected beam then passes through the analyzer and propagates as horizontally polarized light (p-polarized component) to the laser beam analyzer, where a pair of symmetrical split beams can be detected. The spatial distribution of this output light field is proportional to the spatial differential of the incident light field, forming a null optical balance reference. Determine and record the positions of the two beams with maximum intensity. When the incident polarization changes slightly relative to the vertical direction, the original two split beams will evolve into an asymmetrical distribution. Record the intensity values ​​at the two original positions with the maximum intensity. Calculate the ratio of the difference in intensity at these two points to their sum, which is proportional to the azimuth and incident angle of the incident polarization. This allows measurement of the change in polarization and the magnitude and amount of change in the incident angle.

[0045] Suppose that linearly polarized light is reflected at the interface between air and the reflecting medium, and the polarization direction of the incident beam makes an angle with the perpendicular direction. The angle of incidence is The refractive index of the reflecting medium is The incident light field distribution can be expressed as... ,in and These are the two orthogonal polarization components of the incident light field in the horizontal and vertical directions, respectively. and These are the horizontal and vertical coordinates within the incident plane, respectively; This represents the Gaussian complex amplitude distribution of the incident beam. The beam here is selected based on the fundamental Gaussian mode distribution. ,in, Represents the Rayleigh distance of a Gaussian beam. It is the waist radius of the Gaussian beam. The imaginary unit, For wave number, , Let be the wavelength of a Gaussian beam in a vacuum. and Let the horizontal spatial coordinates be the origin of the waistband center. Let be the axial coordinates along the direction of beam propagation. This represents the natural exponential function.

[0046] When a linearly polarized light beam is reflected at the surface of a reflecting medium, the reflected beam will undergo the Spin Hall Effect of Light (SHEL) due to spin-orbit interaction, resulting in transverse spin splitting of the left and right spin components. Specifically, along the wave vector... The incident plane wave component in the direction of reflection, after reflection, produces the following reflected light field distribution:

[0047] (1)

[0048] in, The horizontal component of the spatial spectrum of the reflected beam. Represents the vertical component of the spatial spectrum of the reflected beam. Let be the wave vector of the incident plane wave. and These represent the wave vector in the horizontal direction, i.e. Direction and perpendicular direction directional components, and These are unit vectors in the horizontal and vertical directions, respectively; and Let represent the reflection coefficients of plane waves parallel to and perpendicular to the incident plane, respectively. yes Spatial spectrum and These are the horizontal and vertical components of the spatial spectrum of the incident beam, respectively. and These are the horizontal and vertical components of the incident light field, respectively.

[0049] If the reflected light passes through an analyzer and its transmission direction is horizontal, then the spectrum of the emitted light is:

[0050] (2)

[0051] After inverse Fourier transform, the spatial distribution of the emitted light is obtained. .

[0052] When the polarization direction of the incident beam is set to be perpendicular, that is... At this time, the emitted light is

[0053] (3)

[0054] in This represents the horizontal coordinates within the cross-section of the reflected beam. Represents the vertical coordinates within the cross-section of the reflected beam. This represents the Gaussian complex amplitude distribution of the reflected beam. The symbol represents the partial derivative. This expression indicates that the outgoing light field is proportional to the spatial first differential of the incident light field, and its corresponding intensity distribution is a pair of symmetrically split light spots, forming a measurement reference. Calculating the cross-sectional intensity reveals the location where the intensity of the two spots is maximum (where the derivative of the intensity with respect to spatial coordinates is zero). .

[0055] Next, let No longer equal to 0, according to equation (2), the emitted light is: Compared to equation (3), An additional term is added to the differential. The interference results in an asymmetrical intensity distribution, instead exhibiting a two-spot distribution with one strong and one weak light spot. The two spots at the aforementioned two positions are then calculated. Intensity value at And define normalized intensity difference The ratio of the difference between these two intensities to their sum:

[0056]

[0057] Bundle and Substituting into the above formula, we get:

[0058]

[0059] in It is a factor related to the propagation distance.

[0060] When the incident polarization deflection angle Very small ( In the case of ), formula Approximately

[0061]

[0062] Mode This indicates that the normalized intensity difference signal The small amount of deflection relative to the incident polarization angle They exhibit a linear proportional relationship. Tiny changes can lead to The significant change is due to the angular magnification effect brought about by optical differential, which can be used for precise measurement. The changes.

[0063] Additionally, when the angle of incidence is very close to Brewster's angle... In the case where the angle of incidence is minor changes nearby When, the above formula It can be approximated as

[0064]

[0065] in The equation represents the incident angle after the symmetrically split light spot becomes asymmetrically distributed. This indicates that near Cape Brewster, It is extremely sensitive to changes in the angle of incidence, making and The relationship is linear. Note: At this point... Although small, it follows The rate of change is large, which is the fundamental reason for its high sensitivity. Even a small change in the incident angle near Brewster's angle can lead to... The significant change can be used to accurately measure changes in the angle of incidence. It should be noted that the formula... The approximate condition for the validity of is and It is fixed to a non-zero constant value (e.g., 1°, 2°, and 5° as used in Example 2). In the actual measurement of the incident angle, As pre-defined system parameters, they do not participate in the changes being measured, and therefore will not cause divergence. If If the value is too large, the full form of equation (5) should be used directly for numerical inversion.

[0066] The specific measurement steps are as follows:

[0067] (1) Rotate the transmission direction of the polarizer to the vertical direction so that the polarization state of the beam after passing through is perpendicular to the incident plane (i.e., the p polarization component is zero and the s polarization state is zero).

[0068] (2) The light beam is incident obliquely onto the surface of the reflecting medium at a predetermined angle, and spin-orbit interaction occurs during reflection. The analyzer is rotated to a horizontal position so that the reflected light passes through the analyzer, and the horizontal polarization component of the light propagates to the laser beam analyzer for observation. At this time, the light intensity is symmetrically distributed and splits into two equally sized spots along the direction perpendicular to the incident plane. The spatial positions of the intensity peaks of the two spots are recorded. .

[0069] (3) Rotate the transmission direction of the polarizer from the vertical direction by a small angle, so that the polarization of the incident light changes slightly relative to the original vertical direction. .

[0070] (4) Keeping the polarizer's transmission direction unchanged, the reflected light propagates to the laser beam analyzer after passing through the polarizer. At this time, it is observed that the two originally symmetrically distributed light spots have evolved into an asymmetrical distribution, at the specified position. Record its intensity value at the location. .

[0071] (5) Put Substitution of values calculate Then substitute the result into the formula or Calculate the minute change in the incident polarization direction .

[0072] (6) In the above steps, if fixed To cause the angle of incidence to change near Brewster's angle, it is done by measuring... calculate reuse or The formula yields the changed incident angle and its change.

[0073] Example 1.

[0074] See Figure 1 This embodiment is used to measure minute changes in polarization direction. The apparatus used includes: a polarizer 1, a reflecting medium 2, an analyzer 3, and a laser beam analyzer 4. The incident light source here is a He-Ne laser (wavelength...). ,power Waist radius The reflecting medium is a glass prism with a refractive index of [missing information]. The surface is smooth and it is placed on a precision rotating stage. The polarizer and analyzer use Glan laser polarizers.

[0075] The specific experimental steps are as follows:

[0076] (1) Rotate the polarizer to make the polarization direction of the incident beam perpendicular to the incident surface. The beam is transmitted to the surface of the glass block. Adjust the turntable to select and determine the incident angle. In this embodiment, the preset incident angle selected is... .

[0077] (2) After the beam is reflected at the air-glass interface, it passes through the analyzer (transmission direction is horizontal), achieving optical spatial differentiation. The reflected light is observed using a laser beam analyzer; its central intensity is zero, and two symmetrically split beams are visible. Figure 2 (a2 and b2 in the diagram) record the positions of the symmetrical double-lobed light spot at the two maximum intensity points in the direction perpendicular to the incident plane. and .

[0078] (3) Adjust the polarizer to change the polarization direction of the incident light by a small angle. Meanwhile, the analyzer remains stationary. At this point, the reflected light is observed to become two asymmetrical spots, one strong and one weak. Figure 2 (a1, b1 or a3, b3), record the position at this time. and Strength at the point and .

[0079] (4) Combine the two strengths and Substitute the value into the expression calculate Then substitute the result into the formula or Solve for the polarization change .

[0080] (5) Change the incident angle to a value further away from Brewster's angle, here we choose 30° and 15° respectively, repeat the above steps, and record. and The value, then substitute into the formula , Calculate the corresponding change in polarization direction. .

[0081] like Figure 2 As shown, the incident polarization angles are given respectively. The intensity distribution of the reflected beam after passing through the analyzer is observed by a laser beam analyzer. The first line shows the theoretical result, and the second line shows the experimental result. The experimental observation results are in perfect agreement with the theoretical simulation, verifying the physical realization of the spatial differential effect described in this invention. Figure 2 As can be seen from a2 or b2, the incident Gaussian light intensity distribution, after reflection from the interface and passing through the orthogonal analyzer, splits into two symmetrical light spots. This corresponds precisely to the optical spatial differential result of the incident Gaussian electric field distribution. Figure 2 As can be seen from a1, b1, or a3, b3, after the incident polarization changes, the original two split light spots become asymmetrical. and The intensity difference at the point is significantly correlated with the incident polarization.

[0082] like Figure 3 As shown in (a), the normalized intensity difference is given for three incident angles (15°, 30°, and 45°). With the incident light polarization angle Theoretical and experimental results of the changes. It can be seen that: (i) the experimental points and theoretical curves are in high agreement, verifying the accuracy of this method. The residuals between the experimental points and theoretical curves are mainly caused by shot noise from the laser beam analyzer, verifying that the noise limit of this method is limited by quantum shot noise, rather than system drift. (ii) In Within a small angle range close to 0°, and (iii) Comparing the slopes of the curves at different incident angles reveals that the further the incident angle is from the Brewster angle (e.g., 15°), the steeper the slope, indicating higher measurement sensitivity. This is because in regions far from the Brewster angle, the reflectivity of p-polarized light is... Larger, making The term is significantly enhanced, thereby increasing the interference effect with the differential term, resulting in a more significant intensity difference between the two light spots, and the normalized intensity difference... For small polarization angles They are more sensitive to changes.

[0083] use When smaller Follow The linear relationship of change is used for precise measurement. For example... Figure 3 As shown in (b) above, the three incident angles are given. exist Within the range, normalized intensity difference Theoretical and experimental results showing the effect of incident light polarization angle. Follow linearly increasing slope The values ​​corresponding to incident angles of 15°, 30°, and 45° are 23.06 / 9.57 / 3.75 / If the laser beam analyzer used has a grayscale depth of 12 bits and a signal-to-noise ratio of 62 dB, then... The uncertainty is Therefore, the smallest resolvable polarization change can be obtained. The results are as follows: , , It is evident that the greater the distance from Brewster's angle, the higher the measurement accuracy of polarization changes. Therefore, adjustable measurement accuracy can be achieved by adjusting the incident angle.

[0084] Example 2.

[0085] This embodiment is used to measure minute changes in angle, employing... Figure 1 The same apparatus. The specific steps are as follows:

[0086] (1) Select the incident angle and repeat steps (1)-(3) in Example 1.

[0087] (2) The two strengths and Substitution of values calculate Then substitute the result into the formula or The angle of incidence at this point, when the two light spots become asymmetrical, can be calculated. The value of .

[0088] (3) Change the incident angle. Here, we select a range of 30° to 80°, which covers the Brewster angle. The nearby region is used to verify the linear amplification range of equation (7). The angle of deflection of the incident polarization relative to the vertical direction is fixed. Repeat the above steps and record. and The value, then substitute into the formula , Find the corresponding .

[0089] like Figure 4 As shown in (a), three incident polarization angles are given. , , At that time, normalized intensity difference Theoretical curves and experimental results showing the effect of incident angle. It can be seen that: (i) The change with the incident angle is generally nonlinear, but when the incident angle approaches Brewster's angle... hour, and The relationship is approximately linear, making it suitable for precision measurement. (ii) Deflection angle The larger, the more The larger the value.

[0090] Approaching Brewster's angle using the angle of incidence hour Values ​​varying with incident angle Precise measurements are performed on the linear relationship. For example... Figure 4 As shown in (b), the above three incident polarization angles are given. exist Within the range, normalized intensity difference With the angle of incidence The theoretical curve of change and experimental results. Based on the formula... Or (7) to obtain Follow linearly increasing slope They are 0.346 / 0.693 / 1.735 / If the laser beam analyzer used has a grayscale depth of 12 bits and a signal-to-noise ratio of 62 dB, then, The uncertainty is Therefore, the smallest resolvable angular change can be determined. The results are as follows: , , .visible, The larger, Follow Changing linear slope The larger the angle of incidence, the higher the measurement accuracy of the change in the incident angle. Note that this rule holds true within the approximate range of equation (7), and is actually verified by the complete numerical calculation of equation (5). Therefore, by adjusting the incident polarization angle, the measurement accuracy of the change in the incident direction can be adjusted.

[0091] Example 3.

[0092] This embodiment is used to measure minute phase delays. Figure 5 This is a schematic diagram of the experimental setup for measuring phase delay based on optical differential measurement provided in this embodiment. The setup includes: a polarizer 1, a reflecting medium 2 (glass prism), an analyzer 3, a laser beam analyzer 4, a phase delayer 5, a quarter-wave plate 6, and a half-wave plate 7.

[0093] use Figure 5 The experimental setup shown is described, and the specific experimental steps are as follows:

[0094] (1) Determining zero phase delay based on optical differential: First, the polarizer sets the polarization direction of the incident light to be perpendicular to the horizontal plane. Angle. Through a quarter-wave plate (fast axis along) After passing through a half-wave plate (within the direction), the linear polarization state remains unchanged. After the direction is determined, the polarization direction is rotated using a half-wave plate (the rotation angle is twice the angle between the incident polarization and the fast axis), turning the linear polarization azimuth angle perpendicular to the horizontal plane (i.e., along the direction perpendicular to the incident plane). Then, the beam travels to the glass prism surface at a preset incident angle. After the reflected light passes through the horizontal analyzer, the horizontal polarization component of the vertically polarized incident light is allowed to pass. A laser beam analyzer is used to observe the two symmetrically split beams to determine the positions of the two beams at their maximum intensity. and .

[0095] (2) Introduce the phase delay to be measured: let the incident polarized light in step (1) pass through the phase delayer, so that The directional vibration component obtains a small phase delay The polarization state becomes elliptically polarized, and its ellipticity is... ,and .

[0096] (3) Conversion from phase delay to polarization change: Passing the beam through the quarter-wave plate in (1), the polarization ellipse becomes linear polarization, denoted as . Then, the beam is passed through the half-wave plate in step (1), and the linear polarization direction is turned to... Direction (i.e., the superimposed small angle perpendicular to the incident plane) ).

[0097] (4) After the beam is reflected by the surface of the reflecting medium, the reflected light passes through the analyzer and is detected and observed by the laser beam analyzer. Record the aforementioned position at this time. and Strength at the point and .

[0098] (5) Put and Substitution , Find and the corresponding change in polarization direction Value. Repeat the above steps, changing the phase delay, to finally obtain... Substitute the expression back into the relation. Calculate the corresponding phase delay. .

[0099] like Figure 6 As shown in (a), the normalized intensity difference is given for three incident angles. With phase delay The changing theoretical curves and experimental results. It can be seen that: (i) intensity difference Always more than phase delay Much larger, indicating that optical differentiation has an amplifying effect on minute phase delays. (ii) Follow The change is generally nonlinear, but when When the values ​​are small, the two are approximately linearly related.

[0100] according to When smaller Follow The linear variation law can be used to determine the phase. Precision measurement. For example... Figure 6 As shown in (b), the cases with incident angles of 30°, 40°, and 50° are given. exist Within the range, Follow The theoretical curves and experimental results show the changes. Follow linearly increasing slope The corresponding incident angles are 4.79 / 2.72 / 1.08 / If the laser beam analyzer has a grayscale depth of 12 bits and a signal-to-noise ratio of 62 dB, then, The uncertainty is Therefore, the smallest resolvable phase change can be obtained: The results are as follows: , , It is evident that the further away from Brewster's angle, the higher the measurement accuracy of phase changes. Furthermore, adjustable accuracy measurements can be achieved by adjusting the incident angle.

[0101] Example 4.

[0102] This example is used to measure the concentration of chiral solutions. Figure 7 This is a schematic diagram of the experimental apparatus for measuring the concentration of chiral solutions based on optical differential methods, as provided in this embodiment. The apparatus includes: a polarizer 1, a reflecting medium 2 (glass prism), an analyzer 3, a laser beam analyzer 4, and a cuvette 8 containing the chiral solution.

[0103] The specific experimental steps are as follows:

[0104] (1) First, without placing the cuvette in the light path, the experimental setup is as follows: Figure 1 As shown, select the incident angle and repeat steps (1)-(2) in Example 1.

[0105] (2) Place the cuvette containing the chiral solution into the light path, as shown in the experimental setup. Figure 7 As shown, repeat steps (3)-(4) in Example 1, and measure the deflection angle of the incident beam relative to the direction perpendicular to the incident surface caused by placing it in the solution. .

[0106] (3) After the incident beam passes through the chiral solution, optical rotation occurs, causing a change in polarization, namely the deflection angle. satisfy: ,in It is the specific rotation of a chiral solution. The thickness of the cuvette containing the solution. This represents the solution concentration. (From...) The solution concentration can be obtained as follows: .

[0107] like Figure 8 As shown, when selecting typical chiral substances—glucose and fructose solutions—the normalized intensity difference is... Concentration of the solution The theoretical curve of change. Glucose and fructose molecules are a pair of isomers, and their aqueous solutions are dextrorotatory and levorotatory, respectively, at ambient temperature. Next pair of wavelengths The specific rotations of the lasers are as follows: and The theoretical curve is... Substituting into equation (5) yields and The relationship was plotted. The figure shows the solution concentrations at incident angles of 15°, 30°, and 45°. exist Within the range, normalized intensity difference Follow The theoretical results of change. It is evident that, in In relatively small cases, Follow The changes are approximately linear. This indicates that... To precisely measure concentration According to the formula and get Follow linearly increasing slope , Figure 8 The glucose solution shown in (a) corresponds to three incident angles. , , , Figure 8 The fructose solution shown in (b) corresponds to three incident angles. , , If the laser beam analyzer used has a grayscale depth of 12 bits and a signal-to-noise ratio of 62dB, then... The uncertainty is Therefore, the smallest resolvable polarization change can be obtained. The glucose solution corresponds to three incident angles as follows: , , The fructose solution corresponds to three incident angles as follows: , , It is evident that the greater the distance from Brewster's angle, the higher the accuracy of solution concentration measurement. Therefore, adjustable measurement accuracy can be achieved by adjusting the incident angle.

[0108] Approaching Brewster's angle using the angle of incidence hour Follow It exhibits a linear relationship and offers higher resolution, enabling precise measurement of solution concentration. For example... Figure 9 As shown, select the angle of incidence. Experimental measurements were performed on glucose and fructose solutions to obtain normalized intensity differences. Concentration of the solution The theoretical curve and experimental results show that: (i) the experimental results agree very well with the theoretical curve, proving the effectiveness of the method. (ii) In In relatively small cases, Follow The changes are approximately linear. This confirms that it can be used... To precisely measure concentration According to the formula and get Follow linearly increasing slope For: glucose ,fructose If the laser beam analyzer used has a grayscale depth of 12 bits and a signal-to-noise ratio of 62 dB, then, The uncertainty is Therefore, the smallest resolvable concentration change can be determined. The results were as follows: glucose ,fructose .

[0109] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A precision measurement method based on optical differential effect, characterized in that, Includes the following steps: Step 1: The polarized incident beam is obliquely incident onto the surface of the reflecting medium at a preset incident angle, and the polarization direction of the incident beam is adjusted to be perpendicular to the incident surface; Step 2: After reflection by the reflecting medium, the reflected beam exhibits the optical spin Hall effect. The component of the polarization direction along the horizontal direction is taken as the outgoing light field. The horizontal direction is perpendicular to the polarization direction of the incident beam. At this time, the spatial distribution of the outgoing light field is proportional to the first spatial derivative of the incident light field, forming a pair of symmetrically split light spots. Then, the spatial positions of the points where the intensity of the two light spots is maximum are recorded. and ; Step 3: When scenario one occurs: the polarization direction of the incident beam is deflected relative to the direction perpendicular to the incident plane in step 1. hour; Or, scenario two: When the incident angle changes relative to the preset value in step 1, and the polarization direction of the incident beam is adjusted to have a preset deflection angle relative to the direction perpendicular to the incident plane in step 1. hour; Both of these situations cause the symmetrically split light spot to become asymmetrically distributed, at which point... and Record the intensity values ​​of the two light spots at the respective locations. and ; Step 4: Calculate the normalized intensity difference The Simultaneously satisfying the following formulas: in, and Let be the reflection coefficients of plane waves parallel and perpendicular to the incident plane, respectively. Let be the beam waist radius of the incident beam. For wave number, The incident angle after the symmetrically split light spot becomes an asymmetrically distributed light spot; This represents a factor related to propagation distance. , For Rayleigh distance, For the reflected beam from the reflecting interface to and The propagation distance at that location; Then based on the calculations... Solve for case one Or in scenario two The amount of change relative to the preset value.

2. The method according to claim 1, characterized in that, In step 1, the reflecting medium is a prism or plate made of a dielectric material with a refractive index of The incident beam is a fundamental Gaussian linearly polarized laser beam.

3. The method according to claim 1, characterized in that, In step 3, when situation one occurs, if If the normalized intensity difference approaches 0, then... Approximately satisfies: 。 4. The method according to claim 2, characterized in that, In step 3, when situation two occurs, if the angle of incidence is at Brewster's angle... minor changes nearby Then the normalized intensity difference Approximately satisfies: ； in ,pass Solve Change relative to the preset value .

5. The method according to claim 1, characterized in that, When it is necessary to measure the phase delay, the phase delay to be measured is converted into an equivalent polarization direction change, and then the solution in case one is obtained. This leads to the determination of the phase delay to be measured.

6. The method according to claim 1, characterized in that, When it is necessary to measure the concentration of a chiral solution, the polarization direction of the incident light beam is changed by causing the chiral solution to be measured, and then the solution in case one is solved. This allows us to obtain the concentration of the chiral solution to be tested.

7. The method according to claim 1, characterized in that, In step 3, when situation one occurs, the further the preset value of the incident angle is from the Brewster angle, the more the normalized intensity difference... Follow The greater the linear slope of the change, the higher the sensitivity to the measurement of polarization changes; When scenario two occurs, the preset deflection angle is set. The larger the value of the normalized intensity difference, the closer the preset value of the incident angle is to the Brewster angle. Variation with incident angle The greater the linear slope of the change, the higher the sensitivity to the measurement of changes in the incident angle.

Images