Optical micro-rheological measurement method and device for representing viscoelastic modulus of material

Abstract

The invention discloses a laser speckle micro-rheology method and device for measuring viscoelasticity of a soft substance by using a single-frame image. Coherent light generated by the laser light source is irradiated on a to-be-detected sample in the sample cell after beam expansion, emergent light of the coherent light after multiple scattering in the to-be-detected sample forms a stretched speckle image through the elliptical diaphragm, and the stretched speckle image is collected by the camera and transmitted to the computer. A single-frame image formed when the rolling shutter camera is exposed contains the dynamic change of speckles. Strength self-correlation analysis is carried out between rows of the single-frame image to obtain spatial correlation information containing the average speckle size in the stretching direction and temporal correlation information containing the dynamic change of the speckles. According to the method, the function capable of reflecting the time correlation can be extracted, then the mean square displacement is obtained through the relation between the mean square displacement and the time correlation function, and then the information representing the viscoelastic modulus of the to-be-tested material is obtained through the generalized Stokes-Einstein relation.

Description

TECHNICAL FIELD

[0001] The present application relates to an optical micro-rheological measurement method and device for characterizing the viscoelastic modulus of a material, and in particular to a method and device for measuring the viscoelasticity of biological tissue based on a single-frame laser speckle image. BACKGROUND

[0002] Viscoelasticity is an important mechanical property of a substance, which is used to describe the physical quantity of the substance showing both elastic and viscous characteristics when subjected to force. Specifically, when a viscoelastic material is subjected to external force, its deformation includes not only immediate and reversible elastic deformation, but also gradual and irreversible viscous deformation over time.

[0003] Dynamic measurement of viscoelasticity in biological tissue is of great significance for understanding the biomechanical properties, physiological functions and disease states of the tissue. For example, in disease diagnosis and detection, changes in tissue viscoelasticity can be used as an indicator of disease occurrence and development; in cell behavior research, the viscoelasticity of the extracellular matrix has a significant impact on basic cell processes such as cell diffusion, growth, proliferation, migration and differentiation; in clinical applications, the viscoelastic properties of the cornea are affected by factors such as thickness, intraocular pressure and curvature, and its measurement is helpful for the diagnosis and treatment of ophthalmic diseases.

[0004] Rheometers are the preferred tool for measuring the rheological properties of materials. The principle design of traditional mechanical rheometers measures the viscoelasticity by applying different stress and deformation conditions to the material and measuring its deformation response. Commonly used rheometers include capillary rheometers, rotational rheometers, oscillatory rheometers and torque rheometers. However, rheometers have some limitations and shortcomings when measuring the viscoelasticity of biological tissue, which make them not completely suitable for dynamic measurement of the viscoelasticity of biological tissue at the microscale. Traditional rheometers usually require a relatively large sample size, which may not be met by biological tissue. In the measurement process of the rheometer, the direct contact of the rotor may damage the natural microstructure of the biological tissue, thereby affecting the authenticity of the measurement results. More importantly, rheometers usually use macroscopic mechanical loading methods, which can only obtain the overall mechanical response of the biological tissue and cannot reflect the microstructure of the biological tissue.

[0005] Micro-rheology is an experimental technique that infers the rheological properties of a material by observing the motion of tracer particles at microscopic scales. It can be used to study the viscoelastic properties of materials, especially complex fluids such as biological tissues, cell suspensions, polymer solutions, etc. that cannot be measured by conventional rheometers. Optical micro-rheology usually disperses tracer particles, such as fluorescently labeled microparticles, in the material to be measured, and then tracks the random Brownian motion of these particles over time using dynamic light scattering (DLS) or diffusion wave spectroscopy (DWS) to obtain the motion trajectory. The motion of these microparticles is influenced by the viscoelastic properties of the surrounding medium, so by analyzing the motion trajectory of the particles, such as the mean square displacement, the stress, strain, and time relationship of the material can be calculated, and thus the rheological parameters such as viscoelasticity of the material can be obtained. According to whether an external excitation is applied, it can be divided into active micro-rheology and passive micro-rheology. Passive micro-rheology is a non-contact and non-destructive measurement method because it does not require additional control devices, so it has a wider range of applications and is more suitable for studying the physiological functions and pathological states of biological tissues.

[0006] Currently, Huazhong University of Science and Technology has published a "Device and method for characterizing the viscoelasticity of soft matter by optical micro-rheology" (Application Publication No. CN112748042A). This patent replaces the tracer particles in traditional micro-rheological techniques by tracking one of the characteristic points in the laser speckle, optical vortex, to measure the viscoelastic modulus of the material, and can obtain high-frequency response that cannot be obtained by traditional rheometers. In addition, this technology can distinguish between elastic modulus and viscous modulus, and obtain their responses at wide frequencies respectively. However, when tracking the random motion of optical vortex, this technology needs to calculate the statistical information of the mean square displacement of optical vortex per unit time at different times, resulting in a large amount of calculation of this method, which cannot dynamically track the viscoelasticity in real time.

[0007] In addition, Malvern Instruments Limited's "Micro-rheology of complex fluids based on dynamic light scattering by improved single light scattering mode detection" (Application Publication No. CN102575984A) laser speckle micro-rheology. This patent analyzes the mean square displacement of tracer particles <Δr 2 (t)> based on the dynamic light scattering method (DLS) to obtain the autocorrelation function of the electric field, and then through the formula correlate to the viscoelastic modulus G * . This system relies on single scattering, and when the system becomes multiple scattering, this analysis is no longer valid. Therefore, the deficiency of this patent is that it can only measure fluids with very low concentration, and cannot be used to measure fluids that cannot be diluted and are opaque.

[0008] In addition, Shanghai University of Science and Technology discloses a micro-rheological measurement device and method for measuring viscoelastic fluid (application publication number CN103776802A). The patent aims to provide a micro-rheological measurement device and method for directly measuring the viscous modulus and elastic modulus of viscoelastic fluid without diluting the fluid to be measured. The method is based on the diffusion wave spectrum (DWS) to obtain the mean square displacement <Δr 2 (t)> by calculating the self-correlation function g2(t) of the scattered light intensity, and then obtains the viscous modulus and elastic modulus of the viscoelastic fluid according to the mean square displacement. The patent has the following disadvantages: (1) the measurement of weak viscoelastic modulus fluid depends on expensive high-speed cameras; (2) a long time is required for data acquisition to obtain the complete time self-correlation function curve; (3) the process of calculating the time self-correlation function from a large number of speckles is complex and time-consuming, and storing the speckle data also occupies a large amount of hard disk space.

[0009] In summary, the main disadvantages of the traditional mechanical rheological measurement method are complex design and operation, the need for direct contact with the sample to be measured, and the inability to detect viscoelastic modulus at the microscopic scale. The main disadvantages of the optical micro-rheological measurement method based on DLS and DWS are complex calculation, and the lower limit of the range of viscoelastic modulus that can be measured and the high-frequency response depend on the maximum acquisition speed of the camera used. SUMMARY

[0010] The present application aims to overcome the defect of long-time acquisition of time-varying speckle image sequences in existing laser speckle micro-rheological technology, and provides a method for measuring the viscoelastic modulus of fluid based on single-exposure acquisition and a device thereof. The method does not require sample contact, external excitation, sample dilution, tracer particles, or long-time data acquisition by high-speed cameras.

[0011] To solve the above technical problems, the present application adopts the following technical solutions:

[0012] An optical micro-rheological measurement method for characterizing the viscoelastic modulus of a material, comprising the following steps:

[0013] Step 1: divide the sample to be measured into two parts, configure the first part of the sample in a container, place the container in a sample cell, and irradiate it with a laser light source that has passed through a first linear polarizer and a beam expander. The scattered light formed by multiple scattering of the light in the sample forms a speckle pattern, which is then transmitted through a lens, an elliptical diaphragm, an imaging lens, and a second linear polarizer, and then read out by a rolling shutter camera using rolling shutter exposure to obtain a pixel intensity signal, which is transmitted to a computer;

[0014] Step 2: calculate the intensity autocorrelation degree g2(n) between pixel rows separated by n rows in the speckle image by the computer, and the calculation expression is:

[0015]

[0016] where I(i,j) represents the pixel value of the i-th column and j-th row in the speckle image, I(i,j+n) represents the pixel value of the i-th column and j+n-th row in the speckle image, < > represents the average of all values, i = 1, j = 1;

[0017] Step 3, the computer obtains g2(t) according to the established theoretical spatiotemporal intensity autocorrelation function and g2(n) obtained in step 2, and the theoretical spatiotemporal intensity autocorrelation function is:

[0018]

[0019] where β represents a parameter of the system, which is determined by the coherence of the light source and the actual setting, NA represents the numerical aperture in the readout direction of the rolling shutter camera, λ represents the wavelength of the laser, LEDT represents the exposure delay time between the pixel rows in the rolling shutter, r is the product of the pixel row number n and the pixel size in the speckle image read by the rolling shutter camera, jinc 2 (x) is the square of the second-order Bessel function jinc(x), <Δr 2 (nLEDT) represents the mean square displacement, γ and ζ are experimental constants that explain the optical properties of the sample.

[0020] Step 4, according to the calculated g2(t), the mean square displacement <Δr 2 (t) is calculated again using the following formula (3) based on formula (3).

[0021] g2(t) = 1 + exp{―2γ[k 2 <Δr 2 (t)>] ζ} (3)

[0022] where t = nLEDT is the product of the pixel row number n in the speckle image read by the rolling shutter camera and the exposure delay time LEDT between the pixel rows in the rolling shutter, is the wave number, λ is the wavelength, n is the refractive index of the sample, γ and ζ are optical parameters of the sample, which are obtained by looking up a table, and the table is derived by Monte Carlo ray tracing on the given optical properties of the sample, and the optical properties of the sample are calculated by fitting the diffusion theory to the speckle diffusion reflection profile (DRP) obtained by time-averaging the speckle time series.

[0023] Step 5, finally, the viscoelastic modulus of the material is calculated through the following generalized Stokes-Einstein relationship.

[0024]

[0025] 1 / ω=t;

[0026] where K B is the Boltzmann constant, T is the absolute temperature, a is the radius of the particles in the fluid, Γ is the gamma function,

[0027] γ and ζ are obtained by the following steps:

[0028] Step 3.1: Use the laser light source passing through the first linear polarizer and beam expander to continuously illuminate the sample for 2-5 seconds, collect the speckle time series images, set the ROI as a circular area with a diameter of 36-75 μm, covering the core area of the diffuse reflection light intensity distribution;

[0029] Step 3.2: Calculate the average intensity of each pixel position in the speckle sequence images in the time series, and obtain the static intensity I avg (x,y) of each pixel position; avg (x,y) is converted to polar coordinates (ρ,θ), and for each radial distance ρ, the average photon flux of all pixels on the circumference is calculated to obtain ψ(ρ);

[0030] Step 3.3: Intensity calibration: Convert the pixel intensity ψ(ρ) to absolute photon flux Φ(ρ);

[0031] The formula is: where ψ bg is the background light intensity;

[0032] Camera response refers to the ability of the camera to respond to unit photon flux;

[0033] Gain refers to the amplification multiple of the signal output by the camera sensor;

[0034] Exposure time refers to the length of time that the camera sensor receives light signals in one shot;

[0035] Step 3.4: According to the linear relationship between Φ(ρ) and μ eff , use nonlinear least squares method to solve μ a and μ s ';

[0036] where μ s ' = μ s (1-g), g is the Mie scattering theory calculation scattering anisotropy factor, ∝ represents linear relationship, μ s ' is the reduced scattering coefficient, μ a is the absorption coefficient, and μ s represents the scattering coefficient;

[0037] Step 3.5: Verify by Monte Carlo simulation, track 10 5 total momentum transfer distribution P(Y), wherein: wherein, θ is the scattering polar angle, k0 is the wave number;

[0038] Y is the total momentum transfer, Y accumulates the momentum transfer effect of all scattering events in the photon path, reflects the interaction intensity of light and scattering structure, P(Y) represents the total momentum transfer distribution of the photon in the sample due to scattering, q is the scattering wave vector, P(Y) is the histogram of Y, describing the statistical distribution of the total momentum transfer of a large number of photons;

[0039] Step 3.6: Laplace transform P(Y) to get L{P(Y)}, and fit to a parameterized function: Obtain γ and ζ, wherein S is the transform parameter.

[0040] An optical micro-rheological measurement device for characterizing the viscoelastic modulus of a material, comprising a laser, a first linear polarizer, a beam expander, a sample cell, a focusing lens, an elliptical diaphragm, an imaging lens, a second linear polarizer, a rolling shutter camera and a computer in the above method; a container containing a sample is arranged in the sample cell;

[0041] The first linear polarizer, the beam expander are arranged in sequence on the first light path of the laser directed to the sample cell, and the focusing lens, the elliptical diaphragm, the imaging lens, the second linear polarizer, the rolling shutter camera are arranged in sequence along the extension light path of the sample cell or arranged in sequence along the reflection direction of the first light path of the sample cell, and the polarization direction of the second linear polarizer is perpendicular to the polarization direction of the first linear polarizer.

[0042] The computer comprises a processor and a memory, and the memory stores instructions executable by the processor to execute the method according to steps 2-5.

[0043] The characteristics are that: the coherent light emitted by the laser passes through the first linear polarizer and the beam expander in sequence and then irradiates onto the sample to be measured in the sample cell. The emergent light of the coherent light after multiple scattering in the sample to be measured forms a stretched speckle image through the elliptical diaphragm, and is finally collected by the rolling shutter camera and transmitted to the computer for processing to obtain viscoelastic information capable of characterizing the sample to be measured.

[0044] The sample cell is used for containing the container, and the sample to be measured is contained in the container, and the sample cell is used for controlling the temperature of the sample during measurement.

[0045] The first linear polarizer is used to modulate the laser into completely linearly polarized light and control the light intensity of the laser.

[0046] The elliptical diaphragm is used to change the numerical aperture of the system in two perpendicular directions to stretch the speckle size in the camera exposure readout direction.

[0047] The polarization direction of the second linear polarizer is perpendicular to the polarization direction of the first linear polarizer, which is used to filter out the direct reflected light without scattering and only keep the speckle field information of a single polarization state, thereby increasing the contrast of the speckle image.

[0048] The rolling shutter camera refers to a shutter scheme in a CMOS image sensor, in which each frame of image is exposed and read out row by row from top to bottom, and there is a short exposure delay time between rows.

[0049] Further, the exposure delay time can be artificially adjusted by an external trigger circuit to adapt to the measurement of samples with different viscoelastic properties, thereby widening the viscoelastic measurement range of the device.

[0050] An optical micro-rheological measurement device for characterizing the viscoelastic modulus of a material, comprising the following: a laser, a first linear polarizer, a beam expander, a sample cell, a focusing lens, an elliptical diaphragm, an imaging lens, a second linear polarizer, a rolling shutter camera, and a computer; a container containing a sample is arranged in the sample cell;

[0051] The first linear polarizer, the beam expander are arranged in sequence on the first light path of the laser towards the sample cell, and the focusing lens, the elliptical diaphragm, the imaging lens, the second linear polarizer, and the rolling shutter camera are arranged in sequence along the first light path through the extended light path of the sample cell, or arranged in sequence along the reflection direction of the first light path by the sample cell, and the polarization direction of the second linear polarizer is perpendicular to the polarization direction of the first linear polarizer.

[0052] The computer comprises a processor and a memory, the memory stores instructions and mapping relationships in the optical micro-rheological measurement method for characterizing the viscoelastic modulus of a material, and the instructions can be executed by the processor to perform the method of steps 2-5.

[0053] In some embodiments, the speckle image stretched by the elliptical diaphragm is collected by the rolling shutter camera, and the implementation further comprises: placing the imaging light path on the other side of the sample to be measured to collect the scattered light penetrating the sample.

[0054] In the method, the exposure delay time LEDT between rows of the rolling shutter camera can be artificially adjusted, and the adjustment range is 6.6 μs to 100 ms, which is equivalent to a global shutter camera frame rate of 10 fps to 15,151 fps, so that a wide range of viscoelasticity measurement and high-precision measurement of weak viscoelastic samples can be realized.

[0055] The application has the beneficial effects that the application provides a laser speckle micro-rheological detection device and method based on a rolling shutter camera and an elliptical diaphragm, the viscoelastic properties of a sample can be measured by using only a single frame of speckle image, the problems of high storage cost and calculation cost and inability of real-time measurement caused by long-time collection of dynamic speckle images by a high-speed camera in the traditional optical micro-rheological method based on DWS and GSER theory are solved, the measurement system is simple, the data processing method is simple, the measurement range of viscoelastic modulus is wide, the measurement precision is high, and real-time measurement can be realized. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 is a device structure schematic diagram in an embodiment of the application;

[0057] Figure 2 is a method flowchart of an embodiment of the application;

[0058] Figure 3 is a result of change of viscoelastic modulus of a self-made sample obtained by using the method of the application and viscoelastic modulus obtained by a traditional rotary rheometer with respect to frequency. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical scheme and advantages of the application clearer, the application is further described in detail below by combining with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application, and are not used to limit the application.

[0060] As shown in Figure 1 , it is a device for measuring viscoelastic modulus of soft matter by using a single frame of image in an embodiment of the application, which comprises a laser 1, a first linear polarizer 2, a beam expander 3, a sample cell 4, a lens 5, an elliptical diaphragm 6, an imaging lens 7, a second linear polarizer 8, a rolling shutter camera 9 and a computer 10, and a sample to be measured is placed in the sample cell 4 capable of controlling temperature.

[0061] The sample cell is used for containing a container or a glass clamp, the sample to be measured is contained in the container or the glass clamp, and the sample cell is used for controlling the temperature of the sample during measurement. The container or the glass clamp comprises a container or a glass clamp, and the sample to be measured is placed in the container or the glass clamp. When the biological tissue sample is placed in the glass clamp, physiological saline is supplemented around the tissue.

[0062] The laser 1 irradiates laser to the sample cell 4, here, the laser can be a low-power laser harmless to human body, and the wavelength λ of the laser can be determined according to the required speckle pattern of the sample cell 4. The first linear polarizer 2 and the beam expander 3 are arranged in sequence on the light path of the laser 1 irradiating to the sample cell 4.

[0063] The lens 5 collects the multiply scattered light reflected from the sample, at this time, the coherent light emitted by the laser 1 passes through the first linear polarizer 2 and the beam expander 3 in turn, and then irradiates the sample to be measured in the sample cell 4, and has a speckle pattern after experiencing multiple scattering and interference in the sample, the lens 5 can form an image of the speckle pattern representing a plurality of point light sources of the sample. The first linear polarizer is used to modulate the laser to be completely linearly polarized light and control the light intensity of the laser.

[0064] The elliptical diaphragm 6 adjusts the amount of light irradiated by the lens 5 after convergence to the imaging lens 7, at this time, the elliptical diaphragm 6 controls the amount of light applied to the imaging lens 7 by adjusting the diameter of the circular opening, in this embodiment, unlike the circular hole provided in the general image acquisition module, the elliptical hole of the elliptical diaphragm 6 is an elliptical hole with a narrow and long shape having a major axis in the first direction, the light collected by the lens 5 passes through the elliptical hole and is applied to the imaging lens 7 through it. The elliptical diaphragm 6 changes the numerical aperture NA in two directions by adjusting the amount of light in the two perpendicular directions of the major and minor axes, so as to achieve the purpose of stretching the speckle. This is to ensure that in the dynamic speckle correlation imaging device using the rolling shutter imaging method in the embodiment, a longer time sampling information can be encoded into the stretched spatial correlation in a single frame speckle image.

[0065] The imaging lens 7 receives the light whose amount is adjusted by the elliptical diaphragm 5, and focuses the light to the rolling shutter camera 9, here, the magnification of the speckle image is controlled by the distance between the sample, the lens 5 and the imaging lens 7, and the size of the region detected in the sample decreases with the increase of the magnification.

[0066] The second linear polarizer 8 is placed on the light path between the imaging lens 7 and the rolling shutter camera 9, and the polarization direction of the second linear polarizer 8 is perpendicular to the polarization direction of the first linear polarizer 2, which is used to filter out the directly reflected light without scattering in the sample, and only keep the speckle field information of a single polarization state, so as to increase the contrast of the speckle image.

[0067] The rolling shutter camera 9 detects the light filtered from the second linear polarizer 8 to obtain a speckle image. The rolling shutter camera refers to a shutter scheme in which each frame of image is exposed and read out row by row from top to bottom in the CMOS image sensor, and there is a short exposure delay time between rows. In the traditional global exposure scheme, after the aperture is opened, the entire photosensitive element of the photosensitive assembly is exposed at the same time. All pixels of the sensor collect light at the same time and are exposed at the same time. Unlike the traditional way, the rolling shutter camera uses rolling shutter exposure, that is, when the CMOS starts to expose, the photosensitive element senses light from the first row, the second row, the third row... in a certain order, until the entire photosensitive assembly is exposed from top to bottom. Each row completes its work, that is, the exposure time of different rows of pixels is different.

[0068] Further, the exposure delay time can be artificially adjusted by an external trigger circuit to the exposure timing of the CMOS sensor to adapt to the measurement of samples with different viscoelastic properties, to broaden the viscoelastic measurement range of the device and to be transmitted to the computer 10.

[0069] In another embodiment, the speckle image stretched by the elliptical diaphragm 6 is collected by the rolling shutter camera 9, and the implementation further includes: placing the imaging light path of the lens 5 to the rolling shutter camera 9 on the other side of the sample to be measured to collect scattered light that penetrates the sample.

[0070] The materials, reagents, etc. used in the examples can be obtained commercially unless otherwise specified. The viscoelastic samples used in the following example embodiments are simulated biological tissue samples, hereinafter referred to as simulated samples, which are used to verify the accuracy of the viscoelasticity detection method of the present embodiment. The simulated samples are prepared as follows: In the present embodiment, the optical properties of the real tissue are simulated by adding titanium dioxide nanoparticles, so the viscoelastic modulus of the real tissue sample can be calculated based on the viscoelastic modulus of the simulated sample.

[0071] The polydimethylsiloxane (PDMS) with appropriate amount of titanium dioxide nanoparticles is used as the viscoelastic simulated biological tissue sample. The main components of PDMS are silicon-based polymer base and crosslinker. The base is a flowable liquid, and the base and the crosslinker are mixed at a ratio of 10:1 to form a transparent elastomer with toughness after solidification. The titanium dioxide nanoparticle powder is added to increase the scattering intensity of the sample.

[0072] Further, during the solidification process of the PDMS, the viscoelastic modulus of the simulated sample changes from tens of pascals before solidification to tens of thousands of pascals after complete solidification, and the solidification speed is uniform. The viscoelastic modulus of the PDMS at different times during the solidification process is measured by the present embodiment, and the viscoelastic modulus of the PDMS with the same ratio is measured synchronously by a conventional rotational rheometer (application publication number US9423333B2) for comparison, which proves that the present embodiment can be used to measure the viscoelastic modulus of the sample to be measured.

[0073] As shown in FIG. 1, a method for measuring the viscoelastic modulus of soft matter using a single frame image according to an embodiment of the present application includes the following steps: Figure 2

[0074] Step 1: Record the single-frame laser speckle image data scattered by the sample at different times by the rolling shutter camera 9. As a reference example, the sample is a viscoelastic material PDMS.

[0075] Step 2: Calculate the intensity autocorrelation function g2(n) between the pixel rows of the single-frame speckle images at different times.

[0076] ​Step 3, the computer calculates g2(t) according to the established theoretical spatiotemporal intensity autocorrelation function and g2(n) obtained in step 2;

[0077] Step 4, according to the calculated g2(t), the mean square displacement <Δr 2 (t)> is calculated.

[0078] Step 5, finally, the viscoelastic modulus of the material is obtained through the generalized Stokes-Einstein equation.

[0079] In step 1 of the embodiment, the exposure delay time between pixel rows of the rolling shutter camera 9 can be adjusted, and the adjustment range is 6.6 μs to 100 ms, which is equivalent to a global shutter camera frame rate of 10 fps to 15,151 fps.

[0080] In step 2 of the embodiment, the formula for calculating the intensity autocorrelation function between pixel rows is specifically:

[0081]

[0082] wherein I(i,j) represents the pixel value of the i-th column and the j-th row in the speckle image, I(i,j+n) represents the pixel value of the i-th column and the j+n-th row in the speckle image, <> represents averaging all values; i=1, j=1.

[0083] Formula (1) describes the second-order intensity autocorrelation function in the speckle image, g2(n) represents the autocorrelation degree of the pixel values separated by n rows in the horizontal direction, the numerator represents the average value of the product of the pixel values separated by n rows in the horizontal direction, which reflects the correlation of the pixel values in the horizontal direction, and the denominator is the product of the average values of the two pixel values, to obtain the spatiotemporal intensity autocorrelation information. In the field of optics and image processing, the second-order intensity autocorrelation function can help analyze the texture, structure and dynamic characteristics in the image.

[0084] In step 3 of the embodiment, the formula of the theoretically derived spatiotemporal intensity autocorrelation function is specifically:

[0085]

[0086] wherein β represents a parameter of the system, which is determined by the coherence of the light source and the actual setting, β=0.5-1, NA represents the numerical aperture of the system in the readout direction of the rolling shutter camera, which is related to the resolution and focal length of the system, λ represents the wavelength of the laser, r is the pixel spacing considered in the speckle image, which is equivalent to the product of the number of rows n of the rolling shutter camera and the pixel size, which is related to the size and distribution of the speckle, jinc 2is the square of the second-order Jinc function. The Jinc function is often used to describe the transverse intensity distribution of a Gaussian beam, and is used to describe the spatial autocorrelation of a speckle field, jinc(x) = 2J1(x) / x, J1(x) is the first-order Bessel function. exp{―2γ[k 2 <Δr 2 (nLEDT) ζ represents the relationship between the mean square displacement and g2(t), LEDT represents the Line Exposure Delay Time which is the exposure delay time between pixel rows in a rolling shutter, and n is the interval of pixel rows in the autocorrelation function. Equation (2) is composed of the normalized temporal intensity autocorrelation function g2(t) and the spatial intensity autocorrelation function g2(r), and is specifically:

[0087] g2(t) = 1 + exp{―2γ[k 2 <Δr 2 (t) ζ} (3)

[0088]

[0089] In a viscoelastic sample, due to Brownian motion, the phase of scattered light changes randomly, so the intensity of scattered light fluctuates over time, and the temporal intensity autocorrelation function g2(t) quantifies these light intensity fluctuations. It is calculated by comparing the light intensity at different time points, thereby obtaining a correlation function describing the change of light intensity over time.

[0090] t in equation (3) represents the real time, i.e. n*LEDT in equation (2) is equivalent to the real time t used for exposure of n rows, according to the characteristics of equation (4), the spatial intensity autocorrelation function g2(r) is only determined by the numerical aperture NA of the system and the wavelength λ of the laser used, and does not change with the viscoelastic properties of the sample to be measured, which can be measured by the completely cured PDMS or other steady-state scattering medium in the embodiment.

[0091] γ and ζ in equation (3) are optical parameters of the sample, which are obtained according to the polarization-sensitive correlation transfer-Monte Carlo ray tracing algorithm (PSCT-MCRT) method 1 、2、 3] comprising the following steps.

[0092] Step 3.1: continuously illuminate the sample for 2-5 seconds using the laser 1 of the device for measuring the viscoelastic modulus of soft matter with a single frame image, and collect a speckle time sequence image, the ROI is set as a circular area with a diameter of 36-75 μm, covering the core area of the diffuse reflection light intensity distribution.

[0093] Step 3.2: Time-averaging the speckle sequence images to generate the static diffuse reflectance profile DRP.

[0094] Time-averaging the speckle sequence images refers to calculating the average intensity of each pixel position in the time sequence of speckle sequence images, which is used to obtain the average photon flux of each pixel position, eliminate the fluctuation of speckle intensity of each pixel over time, and obtain the static intensity I avg (x, y). Convert I avg (x, y) to polar coordinates (p, q) and, for each radial distance p, count the average photon flux of all pixels on the circumference to obtain p

[0095] DRP refers to "radial diffuse reflectance profile", which is measured by measuring the surface of biological tissue or scattering medium after laser irradiation, and the diffuse reflectance intensity at different radial distances.

[0096] Step 3.3: Intensity calibration: convert pixel intensity p

[0097] The formula is: where p bg is the background light intensity.

[0098] Camera response refers to the ability of a camera to respond to unit photon flux, usually expressed in electron counts (e - ) or grayscale values. It reflects the efficiency of the camera in converting the received optical signal into an electrical signal.

[0099] Gain refers to the amplification factor of the signal output by the camera sensor.

[0100] Exposure time refers to the length of time the camera sensor receives light signals in one shot.

[0101] Step 3.4: According to the linear relationship between radial diffuse reflectance profile DRP and m eff , use nonlinear least squares method to solve m a and m s ';

[0102] where m s ' = m s (1-g), g is the Mie scattering theory calculation scattering anisotropy factor, a represents a linear relationship, m s ' is the reduced scattering coefficient, m a is the absorption coefficient, and m s represents the scattering coefficient.

[0103] Step 3.5: Verification by Monte Carlo simulation, tracking 10 5The total momentum transfer distribution P(Y) is calculated, where: where θ is the scattering polar angle and k0 is the wave number.

[0104] Y is the total momentum transfer, Y accumulates the momentum transfer effect of all scattering events in the photon path, reflects the interaction strength of light and scattering structure, P(Y) represents the total momentum transfer distribution of photons in the sample due to scattering, q is the scattering wave vector, P(Y) is the probability distribution function of Y, describes the statistical distribution of the total momentum transfer of a large number of photons, the histogram of Y, that is, P(Y).

[0105] Step 3.6: Laplace transform P(Y) to get L{P(Y)}, and fit it to a parameterized function: Obtain γ and ζ, where S is the transform parameter;

[0106] Since the fitting expression Therefore, γ and ζ in L{P(Y)} are the same as γ and ζ in equation (3).

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[0110] In step 4 of this embodiment, the calculated Using equation (3), the mean square displacement <Δr 2 (t)> is calculated.

[0111] In step 5 of the present embodiment, substituting t = 1 / ω into <Δr 2 (t)> gives Finally, the viscoelastic modulus of the material is obtained by the following generalized Stokes-Einstein equation.

[0112]

[0113] where K B is the Boltzmann constant, T is the absolute temperature, a is the radius of the particles in the fluid, Γ is the gamma function, ω represents the angular frequency, which represents the phase change amount of the system per unit time, and is often used to describe the frequency-dependent physical quantities such as viscoelastic modulus, speckle fluctuation, etc.

[0114] As shown in Figure 3 , the viscoelastic modulus of PDMS obtained by the method of the present application and the viscoelastic modulus obtained by the conventional rotational rheometer (application publication number US9423333B2) at the same time are plotted against frequency. It can be seen from the figure that the viscoelastic modulus obtained by the two methods shows the same trend at different frequencies.

[0115] It should be understood that those skilled in the art can make improvements or changes according to the above description, such as changing the direction of the camera capturing the scattered light, etc., and all these improvements and changes shall fall within the protection scope of the appended claims of the present application.

Claims

1. An optical microrheological measurement method for characterizing the viscoelastic modulus of a material, comprising the following steps: Step 1: The sample to be tested is divided into two parts. The first part of the sample is placed in a container, which is placed in the sample cell and irradiated by a laser light source that has passed through a first linear polarizer and a beam expander. The speckle pattern formed by the scattered light after multiple scattering in the sample is then passed through a lens, an elliptical aperture, an imaging lens, and a second linear polarizer. The speckle image is then read out by a rolling shutter camera using a rolling shutter exposure method to obtain the pixel intensity signal and transmit it to the computer. Step 2: The computer calculates the intensity autocorrelation g2(n) between pixel rows spaced n apart in the speckle image. The expression for this calculation is: In the formula, I(i,j) represents the pixel value in the i-th column and j-th row of the speckle image, I(i,j+n) represents the pixel value in the i-th column and j+n-th row of the speckle image, and <> represents the average of all values, i=1, j=1; Step 3: The computer obtains g2(t) based on the established theoretical spatiotemporal intensity autocorrelation function and g2(n) obtained in Step 2. The theoretical spatiotemporal intensity autocorrelation function is: In the formula, β represents the system parameters, determined by the coherence and actual settings of the light source; NA represents the numerical aperture in the readout direction of the rolling shutter camera; λ represents the wavelength of the laser; LEDT represents the exposure delay time between pixel rows in the rolling shutter; r is the product of the number of pixel rows n and the pixel size in the speckle image read by the rolling shutter camera; and jinc 2 (x) is the square of the second-order Jensen function jinc(x). Where n is the wave number and n is the sample refractive index, <Δr 2 (nLEDT)> represents the mean square displacement, and γ and ζ are experimental constants that explain the optical properties of the sample; Step 4, calculate according to formula (2) Using formula (3), the mean square displacement < Δr is calculated. 2 ((t)>; g2(t)=1+exp{―2γ[k 2 <Δr 2 (t)>] ζ } (3) In the formula, t = nLEDT is the product of the number of pixel rows n in the speckle image read by the rolling shutter camera and the exposure delay time LEDT between pixel rows in the rolling shutter. Step 5: Finally, the viscoelastic modulus of the material is obtained using the following generalized Stokes-Einstein formula. 1 / ω = t; In the formula, K B Let be the Boltzmann constant, T be the absolute temperature, a be the radius of the particle in the fluid, and Γ be the gamma function.

2. The measurement method according to claim 1, characterized in that, γ and ζ are obtained using the following steps: Step 3.1: Illuminate the sample continuously for 2–5 seconds using a laser source that has passed through the first linear polarizer and beam expander, and acquire speckle time series images. Set the ROI to a circular area with a diameter of 36–75 μm, covering the core area of ​​diffuse reflection intensity distribution. Step 3.2: Calculate the average intensity of each pixel location in the speckle sequence image over time to obtain the static intensity I at each pixel location. avg (x,y), with the laser incident point as the center, I avg (x,y) is converted to polar coordinates (ρ,θ). For each radial distance ρ, the average photon flux of all pixels on the circumference is calculated to obtain ψ(ρ). Step 3.3: Light intensity calibration: Convert pixel intensity ψ(ρ) into absolute photon flux Φ(ρ); The formula is: Where ψ bg Background light intensity; Camera responsivity refers to a camera's ability to respond to a unit of photon flux; Gain refers to the factor by which a camera amplifies the signal output from the sensor; Exposure time refers to the length of time a camera sensor receives light signals during a single shot; Step 3.4: Based on Φ(ρ) and μ eff The linear relationship is solved using the nonlinear least squares method to obtain μ. a and μ s '; Where μ s ′=μ s (1―g), where g is the scattering anisotropy factor calculated by Mie scattering theory, ∝ represents a linear relationship, and μ s ′ is the reduced scattering coefficient, μ a μ is the absorption coefficient. s Represents the scattering coefficient; Step 3.5: Verify through Monte Carlo simulation, tracking 10 5 For each photon path, calculate the total momentum transfer distribution P(Y), where: Where θ is the scattering polar angle and k0 is the wavenumber; Y represents the total momentum transfer, which sums the momentum transfer effects of all scattering events in the photon path and reflects the interaction strength between light and the scattering structure. P(Y) represents the distribution of the total momentum transfer caused by scattering when a photon propagates in the sample. q is the scattering wave vector. P(Y) is the histogram of Y, which describes the statistical distribution of the total momentum transfer of a large number of photons. Step 3.6: Perform a Laplace transform on P(Y) to obtain L{P(Y)}, and fit it as a parameterized function: Obtain γ and ζ, where S is the transformation parameter.

3. An optical microrheological measurement device for characterizing the viscoelasticity of materials, characterized in that, Includes the components described in claim 1: a laser, a first linear polarizer, a beam expander, a sample cell, a focusing lens, an elliptical aperture, an imaging lens, a second linear polarizer, a rolling shutter camera, and a computer; the sample cell contains a container for holding the sample. The first linear polarizer and the beam expander are arranged sequentially on the first optical path from the laser to the sample cell. The focusing lens, the elliptical aperture, the imaging lens, the second linear polarizer, and the rolling shutter camera are arranged sequentially along the extended optical path of the first optical path through the sample cell, or sequentially along the reflection direction of the sample cell to the first optical path. The polarization direction of the second linear polarizer is perpendicular to the polarization direction of the first linear polarizer. The computer includes a processor and a memory, the memory storing instructions that can be executed by the processor to perform the method described in steps 2 to 5 of claim 1.

4. An optical microrheological measuring device for characterizing the viscoelastic modulus of a material, characterized in that, Includes the components described in claim 1: a laser, a first linear polarizer, a beam expander, a sample cell, a focusing lens, an elliptical aperture, an imaging lens, a second linear polarizer, a rolling shutter camera, and a computer; the sample cell contains a container for holding the sample. The first linear polarizer and the beam expander are arranged sequentially on the first optical path from the laser to the sample cell. The focusing lens, the elliptical aperture, the imaging lens, the second linear polarizer, and the rolling shutter camera are arranged sequentially along the extended optical path of the first optical path through the sample cell, or sequentially along the reflection direction of the sample cell to the first optical path. The polarization direction of the second linear polarizer is perpendicular to the polarization direction of the first linear polarizer. The computer includes a processor and a memory, the memory storing instructions and the mapping relationship as described in claim 1, the instructions being executable by the processor to perform the method described in steps 2 to 5 of claim 1.

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