Method and apparatus for measuring the transfer matrix of scattering media based on phase mask enhancement

Abstract

This invention relates to a method and apparatus for measuring the transmission matrix of a scattering medium based on phase mask enhancement. The method includes: generating a collimated beam and dividing it into multiple sub-beams; applying a desired phase delay to each sub-beam and then merging them into a single beam to apply a phase mask factor; changing the amplitude distribution of the beam and inputting multiple modulation patterns to obtain multiple modulation optical fields; sequentially inputting each modulation optical field into a scattering medium to form multiple speckle patterns and obtaining the amplitude distribution; adjusting the phase mask factor and repeating the above steps; and iteratively calculating the transmission matrix of the scattering medium based on the obtained amplitude distribution. Compared with the prior art, this invention proposes to increase the constraint conditions on the phase by externally implanting a phase mask control module, overcoming the difficulty of accurately measuring the phase dimension information of the transmission matrix in traditional amplitude-type spatial light modulator non-interference scattering medium transmission matrix measurement methods. It has advantages such as high measurement accuracy and fast measurement speed.

Description

Technical Field

[0001] This invention relates to the field of optical field manipulation technology for scattering media, and in particular to a method and apparatus for measuring the transmission matrix of scattering media based on phase mask enhancement. Background Technology

[0002] The uneven refractive index distribution within a strong scattering medium causes multiple deflections in the photon propagation trajectory, resulting in a rapidly dissipating speckle pattern after the light beam is disturbed by the medium. In recent years, researchers have discovered that the light beam does not propagate randomly during scattering, but rather propagates directionally according to the inherent transmission channels within the scattering medium. Utilizing this characteristic, technologies such as bio-antiscattering optical focusing and imaging based on wavefront shaping have been proposed. The inherent transmission channels of the scattering medium are typically represented by a transmission matrix with M×N complex elements, which can accurately quantify the linear coupling relationship between the N input optical field units and the M output optical field units. Therefore, the concept of the transmission matrix has been widely applied since its inception. For example, researchers have achieved breakthroughs in optical imaging resolution, significantly improved the computational power of optical neural networks, and achieved efficient decoupling between the spectral and spatial dimensions of computational spectroscopy by measuring the transmission matrix.

[0003] To accurately describe the propagation process of a light beam through a scattering medium, high-precision measurement of the transmission matrix with large complex elements is required. Currently, transmission matrix measurement methods are mainly divided into three categories: reference arm interferometry, self-reference interferometry, and non-interferometry. The first two methods use orthogonal bases such as Hadamard as input light fields and measure the complex amplitude distribution behind the scattering medium using phase-shifting interferometry of the reference light. The transmission matrix of the scattering medium is then solved through simple matrix transformations, where the reference light can be introduced from an additional reference arm or the same optical path. However, phase-shifting interferometry is susceptible to interference from air disturbances, photon shot noise, mechanical vibrations, etc., resulting in visible jitter during the measurement of the complex amplitude light field, which severely limits the accuracy of the transmission matrix measurement. Non-interferometry only requires controlling a series of input light fields with different amplitude or phase distributions according to a random probability distribution and measuring the scattered light intensity distribution corresponding to each input light field. The transmission matrix can then be calculated using phase retrieval algorithms such as the Gerchberg-Saxton algorithm, variational Bayesian expectation-maximization algorithm, SDP, EKF-MSSM, GAMP, and prVAMP. This type of method has the outstanding advantages of strong noise resistance and high measurement accuracy, and is currently a hot research direction in the field of scattering medium transfer matrix measurement.

[0004] Amplitude-based optical field modulation devices, such as digital micromirror arrays, offer approximately a thousand-fold improvement in modulation speed and possess inherent advantages in spectral width, polarization sensitivity, and stability, playing a crucial role in breakthroughs in the application of scattered optical field modulation technology. However, when these amplitude-based spatial light modulators are applied to interference-free transfer matrix measurement methods, the lack of known constraints on the phase dimension makes the non-convex optimization problem of the phase retrieval algorithm particularly prominent. During iteration, it is prone to convergence to local optima, leading to low measurement accuracy. Therefore, how to achieve accurate measurement of the transfer matrix of a scattering medium using amplitude-based optical field modulation devices remains a pressing challenge in the field of scattering medium optical field modulation technology. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing methods for measuring the transfer matrix of non-interference scattering media in amplitude-type optical field modulators, which suffer from low measurement accuracy due to the lack of known constraints on the phase dimension. This invention provides a method and apparatus for measuring the transfer matrix of scattering media based on phase mask enhancement. By implanting an external phase mask control module, an additional phase mask factor is applied to the optical field modulated by the amplitude-type spatial light modulator. During the iterative optimization algorithm for the scattering media transfer matrix, the difference in speckle pattern values ​​under different phase mask factors is balanced to provide sufficient convergence constraints for the algorithm, guiding it to always converge towards the true value of the transfer matrix, thereby calculating the transfer matrix with high accuracy. This invention significantly improves the measurement accuracy of the scattering media transfer matrix of amplitude-type spatial light modulators.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for measuring the transfer matrix of a scattering medium based on phase mask enhancement includes the following steps:

[0008] Step 1: Generate a collimated beam, divide the collimated beam into L independently propagating sub-beams according to L different spatial regions, apply the required phase delay to L-1 sub-beams, and then combine all sub-beams into a single beam to apply the phase masking factor Φ. 1 ;

[0009] Step 2: Input the beam with applied phase masking factor into the pre-acquired optical field control module, and sequentially input P control patterns into the optical field control module. According to the input control patterns, the amplitude distribution of the beam with applied phase masking factor is changed sequentially to obtain P different control optical fields. Input each control optical field into the scattering medium in sequence. After being disturbed by the scattering medium, P different speckle patterns are formed. Collect the intensity distribution of each speckle pattern and calculate the amplitude distribution of each speckle pattern.

[0010] Step 3: Repeat steps 1-2, and adjust the phase mask factor to Φ respectively.2 Φ 3 , ..., Φ K Calculate the amplitude distribution of the corresponding speckle pattern, where L, P, and K are all positive integers;

[0011] Step 4: Based on the amplitude distribution of the modulation pattern and speckle pattern corresponding to each phase mask factor, the scattering medium transfer matrix is ​​solved by an iterative optimization algorithm.

[0012] Furthermore, the process of solving the scattering medium transfer matrix includes the following steps:

[0013] Step a1: Initialize the scattering medium transfer matrix D, which contains M×N randomly distributed complex elements, where M and N are both positive integers;

[0014] Step a2: Adjust the phase mask factor Φ 1 Copy P times row by row to obtain a phase mask matrix Θ of size P×N. 1 Based on the control pattern and the phase mask factor Φ 1 For the corresponding speckle pattern amplitude distribution, define the detection matrix X and the observation matrix Y, where X = [X1, X2, ..., X...]. P ] T The size is P×N, where the symbol T represents transpose; The dimensions are P×M;

[0015] Step a3: Calculate the estimated value of the observation matrix based on the detection matrix X and the initialized scattering medium transmission matrix D. The symbol ° represents dot product, and the symbol H represents the conjugate transpose of a matrix;

[0016] Step a4: Maintain the estimated value of the observation matrix. The phase distribution remains unchanged, and The amplitude distribution of the observed matrix Y is replaced with its amplitude distribution, resulting in... The symbol ∠ represents phase;

[0017] Step a5: From Calculate the scattering medium transfer matrix using the detection matrix X. Among the symbols Represents the pseudo-inverse of a matrix;

[0018] Step a6: Repeat steps a2-a5 sequentially to calculate the phase mask factor Θ. 2 Θ 3 、…、Θ K The corresponding scattering medium transfer matrix D 2 D 3 ... D K ;

[0019] Step a7: Take the average value of each obtained scattering medium transfer matrix to update the scattering medium transfer matrix D, thus completing one iteration calculation;

[0020] Step a8: Repeat steps a2-a7 in sequence to continuously optimize and update the scattering medium transfer matrix D until the number of iterations reaches the preset first iteration threshold, or the difference between the scattering medium transfer matrix D and the result of the previous iteration is less than the preset first difference threshold, then obtain the final scattering medium transfer matrix D.

[0021] Furthermore, the process of solving the scattering medium transfer matrix includes the following steps:

[0022] Step b1: Based on the control pattern and the phase mask factor Φ 1 The corresponding speckle pattern amplitude distribution is used to define the detection matrix X = [X1, X2, ..., X]. P ] T The size is P×N; the observation matrix is ​​set. The dimensions are P×M;

[0023] Step b2: Set initial parameters, including the variance of the value d1 in the first row of the transfer matrix. The initial value of the first row of the transfer matrix D is d1 = [d 1i ] i＝{1,2,…,N} Missing phase in the first column of the observation matrix Y The mean of the posterior distribution is m = [m i ] i＝{1,2,…,N} And variance Δ = [Δ i ] i＝{1,2,…,N} ;

[0024] Step b3: Adjust the phase mask factor Φ 1 Copy P times row by row to obtain a phase mask matrix Θ of size P×N. 1 Take the first column element y from the observation matrix Y. p1 9p = {1, 2, ..., P} form the vector y1;

[0025] Step b4: Calculate the variance of the noise. The variance The calculation expression is:

[0026]

[0027] In the formula, x i and x j These represent the i-th and j-th column vectors in the detection matrix X, respectively. and Representing the phase mask matrix Θ respectively1 The i-th and j-th column vectors in the data, Representative of the actual part;

[0028] Step b5: Calculate the mean and variance of the posterior distribution. The expressions for calculating the mean and variance of the posterior distribution are as follows:

[0029]

[0030]

[0031] In the formula, I1 and I0 represent the zeroth and first-order functions of the first kind of modified Bessel functions, respectively, t={1,2,i-1,i+1,…,N};

[0032] Step b6: Repeat steps b3-b5, respectively, based on the phase mask factor Φ. 1 Φ 2 , ..., Φ K The amplitude distribution of the corresponding control pattern and speckle pattern is calculated. Ultimately As input values ​​for the next iteration of the calculation;

[0033] Step b7: Repeat steps b2-b6 until the number of iterations reaches the preset second iteration threshold or m. i If the difference between the result of the previous iteration and the result of the previous iteration is less than the preset second difference threshold, then the first row value d1 = m in the scattering medium transfer matrix D is obtained.

[0034] Step b8: Repeat steps b2-b7 to solve for the values ​​d2, d3, ..., dm in rows 2, 3, ..., M of the transfer matrix D. M Complete the calculation of all parameters of the scattering medium transfer matrix D.

[0035] The present invention also provides a measuring device for implementing the above-mentioned method for measuring the transmission matrix of a scattering medium based on phase mask enhancement, comprising a collimation and beam expansion module, a phase mask control module, an optical field modulation module, a photoelectric detection module, a data acquisition and control module, and a transmission matrix calculation module, wherein a scattering medium mounting area for mounting the scattering medium is provided between the optical field modulation module and the photoelectric detection module;

[0036] The collimation and beam expanding module is used to convert the received beam into a collimated beam with a certain aperture.

[0037] The data acquisition and control module is used to generate phase mask factors and transmit them to the phase mask control module, and also to generate modulation patterns and transmit them to the light field modulation module.

[0038] The phase mask control module includes a beam splitter, a phase delay device group, and a beam combiner. The beam splitter is used to divide the collimated beam into L independently propagating sub-beams according to L different spatial regions. The phase delay device group has L-1 phase delay devices, and each phase delay device is individually controlled to apply additional phase constraints to the L-1 sub-beams. Different phase mask factors are applied by changing the phase delay amount. The beam combiner is used to combine the L sub-beams into a single beam according to their original spatial positions in the collimated beam.

[0039] The light field modulation module is used to change the amplitude distribution of the beam output by the phase mask control module according to the applied modulation pattern, thereby generating different modulated light fields.

[0040] The scattering medium is used to create speckle patterns by disturbing various modulated optical fields.

[0041] The photoelectric detection module is controlled by the data acquisition and control module and is used to detect the intensity distribution of speckle.

[0042] The transmission matrix calculation module is used to calculate the transmission matrix of the scattering medium using an iterative optimization algorithm.

[0043] Furthermore, the phase delay device group also includes half-wave plates and knife-edge apertures. The number of half-wave plates is L-1, and the number of knife-edge apertures is L. Each half-wave plate is used to adjust the polarization direction of L-1 sub-beams so that the polarization direction of all sub-beams is consistent. Each knife-edge aperture blocks all sub-beams respectively, and changes the illumination area of ​​the sub-beams on the light field control module by adjusting the position and angle of the knife edge.

[0044] Furthermore, the phase delay device is any one of a liquid crystal phase delayer, an electro-optic modulator, a phase-type liquid crystal spatial light modulator, and a Fresnel phase delayer.

[0045] Furthermore, the light field modulation module includes a spatial light modulator and a filtering optical path. The spatial light modulator is used to modulate the amplitude of the modulation light field, and the filtering optical path is set at the output end of the spatial light modulator to filter out diffracted light of a specific order.

[0046] Furthermore, the spatial light modulator is a digital micromirror array or an amplitude-type liquid crystal spatial light modulator.

[0047] Furthermore, the photoelectric detection module includes an imaging lens and a photoelectric sensor. The imaging lens is used to collect scattered light beams and image them onto the photoelectric sensor. The photoelectric sensor is used to detect the intensity distribution of speckle and convert it into an electrical signal, which is then sent to the transmission matrix calculation module.

[0048] Furthermore, the photoelectric sensor is any one of a CCD image sensor, a CMOS image sensor, a photomultiplier tube, or a photodiode.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] (1) This invention provides additional constraints for the transmission matrix iterative optimization algorithm by adding a phase mask factor to the amplitude-type spatial light modulator, guiding the algorithm to always converge toward the true value of the transmission matrix, which significantly improves the measurement accuracy of the amplitude-type spatial light modulator for the transmission matrix of the scattering medium.

[0051] (2) The present invention adopts a non-interference transmission matrix measurement method, which has strong anti-noise ability, is not easily affected by environmental factors, and has high measurement accuracy.

[0052] (3) This invention utilizes the extremely fast modulation speed of amplitude-type spatial light modulators such as digital micromirror arrays to significantly improve the measurement speed of the scattering medium transmission matrix;

[0053] (4) After the scattering medium transmission matrix is ​​measured, the phase mask control module can be removed without changing the positional relationship between the light field modulation module, the scattering medium, and the photoelectric detection module, so as not to affect the performance of subsequent scattering light field modulation applications. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of a scattering medium transmission matrix measurement device based on phase mask enhancement provided in an embodiment of the present invention;

[0055] Figure 2 This is a flowchart of an algorithm for solving the transfer matrix of a scattering medium provided in an embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram of a scattering medium transfer matrix measurement device based on phase mask enhancement provided in Embodiment 1 of the present invention;

[0057] Figure 4 This is a flowchart of a data acquisition and control process provided in Embodiment 1 of the present invention;

[0058] Figure 5 This is a flowchart of a method for solving the scattering medium transfer matrix using the Gerchberg-Saxton algorithm, as provided in Embodiment 1 of the present invention.

[0059] Figure 6 This is a comparison chart of measurement results of a scattering medium transfer matrix provided in Embodiment 1 of the present invention;

[0060] Figure 7This is a flowchart of a method for solving the transfer matrix of a scattering medium using a variational Bayesian expectation-maximization algorithm, as provided in Embodiment 2 of the present invention.

[0061] Figure 8 This is an image showing the effect of restoring an image through a scattering medium using the solution of the present invention, as provided in Embodiment 5 of the present invention.

[0062] Figure 9 This is an effect diagram of focusing through a scattering medium using the solution of the present invention provided in Embodiment 6 of the present invention, wherein regions a and b are effect diagrams of single-point focusing, and regions c and d are effect diagrams of multi-point focusing;

[0063] Figure 10 This is a schematic diagram of the structure of a beam splitter provided in an embodiment of the present invention;

[0064] In the diagram, 1. Collimation and beam expansion module; 2. Phase mask control module; 3. Optical field modulation module; 4. Scattering medium; 5. Photodetector module; 6. Data acquisition and control module; 7. Transmission matrix calculation module; 8. Beam splitter; 9. Phase delay device group; 10. Beam combiner; 11. First lens; 12. Second lens; 13. Aperture; 14. First half-wave plate; 15. Polarizing beam splitter prism; 16. Second half-wave plate; 17. Liquid crystal phase delayer; 18. First reflector; 19. 20. Second reflecting mirror, 21. First knife-edge aperture, 22. Second knife-edge aperture, 23. Depolarizing beam splitter, 24. Third lens, 25. Third reflecting mirror, 26. Fourth lens, 27. Digital micromirror array, 28. Fifth lens, 29. Fourth reflecting mirror, 30. Sixth lens, 31. Seventh lens, 32. Objective lens, 33. CMOS image sensor, 34. Main control computer, 35. Electro-optic modulator, 36. Phase-type liquid crystal spatial light modulator, 37. Photomultiplier tube. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0066] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0067] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0068] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed during use. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0069] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0070] This invention provides a method for measuring the transfer matrix of a scattering medium based on phase mask enhancement, comprising the following steps:

[0071] Step 1: Generate a collimated beam, divide the collimated beam into L independently propagating sub-beams according to L different spatial regions, apply the required phase delay to L-1 sub-beams, and then combine all sub-beams into a single beam to apply the phase masking factor Φ. 1 ;

[0072] Step 2: Input the beam with applied phase masking factor into the pre-acquired optical field control module, and sequentially input P control patterns into the optical field control module. According to the input control patterns, the amplitude distribution of the beam with applied phase masking factor is changed sequentially to obtain P different control optical fields. Input each control optical field into the scattering medium in sequence. After being disturbed by the scattering medium, P different speckle patterns are formed. Collect the intensity distribution of each speckle pattern and calculate the amplitude distribution of each speckle pattern.

[0073] Step 3: Repeat steps 1-2, and adjust the phase mask factor to Φ each time. 2 Φ 3 , ..., Φ K Calculate the amplitude distribution of the corresponding speckle pattern, where L, P, and K are all positive integers;

[0074] Step 4: Based on the amplitude distribution of the modulation pattern and speckle pattern corresponding to each phase mask factor, the scattering medium transfer matrix is ​​solved by an iterative optimization algorithm.

[0075] The present invention also provides a measuring device for implementing the above-described measuring method, including a collimation and beam expansion module, a phase mask control module, an optical field modulation module, a scattering medium, a photoelectric detection module, a data acquisition and control module, and a transmission matrix calculation module;

[0076] The collimation and beam expansion module is used to convert the received beam into a collimated beam;

[0077] The data acquisition and control module is used to generate phase mask factors and transmit them to the phase mask control module, and also to generate modulation patterns and transmit them to the light field modulation module.

[0078] The phase mask control module includes a beam splitter, a phase delay device group, and a beam combiner. The beam splitter is used to divide the collimated beam into L independently propagating sub-beams according to L different spatial regions. The phase delay device group has a total of L-1 phase delay devices, and each phase delay device is individually controlled to apply the required phase delay to the L-1 sub-beams. The beam combiner is used to combine the L sub-beams into a single beam according to their original spatial positions in the collimated beam, and then apply a phase mask factor to this beam.

[0079] The optical field modulation module is used to change the amplitude distribution of the beam output by the phase mask control module and apply corresponding modulation patterns to generate different modulated optical fields.

[0080] The scattering medium is used to create speckle patterns by disturbing various controlled optical fields.

[0081] The photoelectric detection module is used to detect the intensity distribution of speckle;

[0082] The transmission matrix calculation module is used to calculate the transmission matrix of the scattering medium using an iterative optimization algorithm.

[0083] The present invention can be applied to fields such as biomedical imaging, optical detection, optical communication, and optical computing.

[0084] This invention, by implanting an external phase mask control module, adds constraints on the phase during transfer matrix measurement. It leverages the advantages of amplitude-based optical field modulation devices such as DMDs in terms of modulation speed, spectral width, polarization sensitivity, and stability, while ensuring that the phase retrieval algorithm always converges towards the true value of the transfer matrix. Therefore, this invention overcomes the drawback of traditional amplitude-based optical field modulation devices' non-interference scattering medium transfer matrix measurement methods, which struggle to accurately measure the phase dimension information of the transfer matrix. It effectively improves the measurement accuracy of the transfer matrix, providing a superior solution for achieving high-quality reconstruction of images disturbed by scattering media and for controlling arbitrary optical field distributions at the output.

[0085] Example 1

[0086] This embodiment first provides a non-interference scattering medium transmission matrix measurement device based on phase mask enhancement, including a collimation and beam expansion module 1, a phase mask control module 2, an optical field modulation module 3, a photoelectric detection module 5, a data acquisition and control module 6, and a main control computer 33; the scattering medium 4 is located between the optical field modulation module 3 and the photoelectric detection module 5;

[0087] The working principle of the non-interference scattering medium transmission matrix measurement method based on phase mask enhancement used in this embodiment is as follows: the laser source emits a laser with a wavelength of 532nm. After passing through the collimation and beam expansion module 1 composed of the first lens 11 and the second lens 12, the collimated beam is sequentially input into the phase mask control module 2 and the light field modulation module 3 for modulation to generate a modulated light field. After the light field is disturbed by the scattering medium 4, speckle is formed.

[0088] Optionally, the photoelectric detection module 5 includes an objective lens 31 and a CMOS image sensor 32. The objective lens 31 (20×) is placed in front of the CMOS image sensor 32 to collect the scattered beam and to acquire a speckle image through the CMOS image sensor 32.

[0089] The main control computer 33 is used to control the phase mask control module 2 and the light field modulation module 3 to generate the modulation light field and to accurately calculate the amplitude and phase distribution of the scattering medium transmission matrix from the modulation light field and the speckle distribution detected by the CMOS image sensor 32.

[0090] In this embodiment, the phase mask control module 2 applies phase constraints by loading the required phase mask factor onto the input collimated beam. Optionally, the specific method is as follows: the collimated and expanded beam is split into two beams of equal intensity by the first half-wave plate 14 and the polarizing beam splitter 15. The phase delay of one beam is changed using the liquid crystal phase retarder 17; the polarization direction of the other beam is adjusted using the second half-wave plate 16 so that the polarization directions of the two beams are consistent; the two beams are blocked by the first knife-edge aperture 20 and the second knife-edge aperture 21 respectively, and the positions and angles of the first knife-edge aperture 20 and the second knife-edge aperture 21 are adjusted so that the two beams have the same illumination area on the digital micromirror array 26, and the boundary line between the two beams is parallel to the short side of the digital micromirror array 26; finally, the two beams are combined into one beam by the depolarizing beam splitter 22, thereby applying a specific phase mask factor to the light field.

[0091] It should be noted that the beam splitter in this embodiment includes a first half-wave plate 14 and a polarizing beam splitter prism 15, which splits the collimated and expanded beam into two beams of equal intensity. In practical use, the beam splitter can be a combination of multiple sets of half-wave plates and polarizing beam splitters to split the collimated and expanded beam into L independently propagating sub-beams and output them; for example... Figure 10 As shown, the collimated and expanded beam is input from the left into a combination of multiple half-wave plates and polarizing beam splitters, split into multiple independently propagating sub-beams, and finally output through the right side.

[0092] The collimated and expanded beam is split into two beams of equal intensity by the first half-wave plate 14 and the polarizing beam splitter 15.

[0093] Preferably, a 4f optical system and a third reflector 24 can be set after the phase mask control module 2 to input the phase-modulated beam into the light field control module 3, wherein the 4f optical system consists of a third lens 23 and a fourth lens 25.

[0094] The light field modulation module includes a spatial light modulator and a filter optical path. The spatial light modulator is a digital micromirror array or an amplitude-type liquid crystal spatial light modulator.

[0095] In this embodiment, the light field modulation module 3 modulates the input light through the digital micromirror array 26. Specifically, the digital micromirror device 26 includes 1024×768 micromirrors. 768×768 micromirrors located in the central region are selected as the effective modulation area. The remaining micromirrors are always turned off during modulation. 24×24 micromirrors are combined into one modulation unit, resulting in a total of 32×32 modulation units. The main control computer 33 generates a modulation pattern with 32×32 units and controls the digital field through the data acquisition and control module 6. The micromirror array 26 effectively controls the binary intensity of the micromirrors in the control area to turn them on and off, thereby achieving amplitude control of the corresponding point in the control light field. A filter optical path is set after the digital micromirror array 26. The filter optical path includes a 4f optical system and a fourth reflector 28. The 4f optical system consists of a fifth lens 27 and a sixth lens 29. The two lenses are placed one in front of the other along the light propagation direction, and the focal planes of the two lenses coincide to filter out the zero-order diffracted light. The zero-order diffracted light is converged by the seventh lens 30 and input into the scattering medium 4.

[0096] like Figure 4 As shown, the specific workflow of the main control computer 33 controlling the data acquisition control module 6 in this embodiment is as follows:

[0097] Step c1: The main control computer 33 generates 2048 control patterns X1, X2, ..., X based on a two-dimensional normal distribution, each containing 1024 control units. 2048 ;

[0098] Step c2: The data acquisition and control module 6 sets the phase delay of the liquid crystal phase delay unit 17 to 0 in order to apply a phase mask factor to the beam after passing through the collimation and beam expansion module 1.

[0099] Step c3: The data acquisition and control module 6 arranges the control pattern X1, which contains 1024 control units, into a 32×32 unit pattern by row arrangement. Then, it expands the value of each control unit by 24×24 and adds zero matrices of size 768×128 on both sides of the matrix to generate a control signal of size 768×1024, which is then loaded into the digital micromirror array 26. This changes the amplitude distribution of the light field with applied phase masking factor according to the control pattern X1, filters out the zero-order diffracted light, and then focuses it through the seventh lens 30 before inputting it into the scattering medium 4. The data acquisition and control module 6 controls the CMOS image sensor 32 to acquire the intensity distribution of the speckle pattern. The speckle pattern contains a total of 65,536 pixels;

[0100] Step c4: Repeat step c3, sequentially adjusting patterns X2, X3, ..., X... 2048 The data is loaded into the digital micromirror array 26, and the speckle distribution corresponding to each control pattern is acquired sequentially.

[0101] Step c5: The data acquisition and control module 6 sets the phase delay of the liquid crystal phase delay unit 17 to π / 2, and repeats steps c3-c4, sequentially adjusting the control patterns X1, X2, ..., X... 2048 The data is loaded into the digital micromirror array 26, and the amplitude distribution of the speckle pattern corresponding to each control pattern is acquired sequentially.

[0102] Step c6: The data acquired by the data acquisition and control module 6 is input into the main control computer 33, and the main control computer 33 calculates the amplitude distribution of the speckle pattern. And solve for the transfer matrix.

[0103] like Figure 5 As shown, in this embodiment, the Gerchberg-Saxton iterative optimization algorithm is used to solve for the transfer matrix of the scattering medium. The specific steps are as follows:

[0104] Step d1: Initialize the scattering medium transfer matrix D, which contains 65536×1024 randomly distributed complex elements;

[0105] Step d2: Set the phase mask factor Φ 1 Given a matrix containing 1024 elements, each with a value of exp(j0); set the phase mask factor Φ 1 This is copied row-by-row 2048 times, resulting in a phase mask matrix Θ of size 2048×1024. 1 Based on the control pattern and the phase mask factor Φ 1 For the corresponding speckle pattern amplitude distribution, define the detection matrix X and the observation matrix Y, where X = [X1, X2, ..., X...]. 2048 ] T The dimensions are 2048×1024, where the symbol T indicates transpose; The dimensions are 2048×65536;

[0106] Step d3: Calculate the estimated value of the observation matrix based on the detection matrix X and the initialized scattering medium transmission matrix D.

[0107] Step d4: Maintain the estimated value of the observation matrix. The phase distribution remains unchanged, and The amplitude distribution of the observed matrix Y is replaced with its amplitude distribution, resulting in...

[0108] Step d5, from Calculate the scattering medium transfer matrix using the detection matrix X. Among the symbols Represents the pseudo-inverse of a matrix;

[0109] Step d6: Repeat steps d2-d5 to set the phase mask factor Φ. 2 Given a matrix containing 1024 elements, where the first 512 elements have values ​​of exp(j0) and the last 512 elements have values ​​of exp(jπ / 2); set the phase mask factor Φ 2 This is copied row-by-row 2048 times, resulting in a phase mask matrix Θ of size 2048×1024. 2 And set the observation matrix Y as Then solve for the scattering medium transfer matrix D. 2 ;

[0110] Step d7: Calculate the scattering medium transfer matrix D. 1 and D 2 The average value is used to update the scattering medium transfer matrix D, i.e. This completes one iteration of the calculation;

[0111] Step d8: Repeat steps d2-d7 to continuously optimize and update the scattering medium transfer matrix D until the number of iterations reaches the preset first iteration threshold, or the difference between the scattering medium transfer matrix D and the result of the previous iteration is less than the preset first difference threshold. Then, the final scattering medium transfer matrix D is obtained.

[0112] Figure 6 The results of estimating the speckle distribution using the measured transfer matrix are shown. Under the same control pattern, Figure 6 (a) shows the actual speckle distribution captured by a CMOS image sensor. Figure 6 (b) The speckle distribution estimated using the measured transmission matrix. Figure 6 (c) To estimate the error of the speckle distribution compared to the true speckle distribution.

[0113] Example 2

[0114] This embodiment is largely the same as Embodiment 1, except that in this embodiment, the variational Bayesian expectation-maximization algorithm is used to solve for the transfer matrix of the scattering medium, such as... Figure 7 As shown, the specific steps are as follows:

[0115] Step e1: Set the phase mask factor Φ 1 It is a matrix containing 1024 elements, each with a value of exp(j0); based on the control pattern and the phase mask factor Φ 1 The corresponding speckle pattern amplitude distribution is used to define the detection matrix X = [X1, X2, ..., X]. 2048 ] T The size is 2048×1024; the observation matrix is ​​set. The dimensions are 2048×65536;

[0116] Step e2: Set initial parameters, including the variance of the value d1 in the first row of the transfer matrix. The initial value of the first row of the transfer matrix D is d1 = [d 1i ] i＝{1,2,…,1024} Missing phase in the first column of the observation matrix Y The mean of the posterior distribution is m = [m i ] i＝{1,2,…,1024} And variance Δ = [Δ i ] i＝{1,2,…,1024} ;

[0117] Step e3: Adjust the phase mask factor Φ 1 This is copied row-by-row 2048 times, resulting in a phase mask matrix Θ of size 2048×1024. 1 Take the first column element y from the observation matrix Y. p1 (p = {1, 2, ..., 2048}) form vector y1;

[0118] Step e4: Calculate the variance of the noise. The variance The calculation expression is:

[0119]

[0120] Step e5: Calculate the mean and variance of the posterior distribution. The expressions for calculating the mean and variance of the posterior distribution are as follows:

[0121]

[0122]

[0123] In the formula, I1 and I0 represent the zeroth and first-order functions of the first kind of modified Bessel function, respectively, t={1,2,i-1,i+1,…,1024};

[0124] Step e6: Repeat steps e3-e5 to set the phase mask factor Φ. 2 Given a matrix containing 1024 elements, where the first 512 elements have values ​​of exp(j0) and the last 512 elements have values ​​of exp(jπ / 2); set the phase mask factor Φ 2 This is copied row-by-row 2048 times, resulting in a phase mask matrix Θ of size 2048×1024. 2 And set the observation matrix Y as Then solve for the scattering medium transfer matrix D. 2 According to the phase mask factor Φ 2The amplitude distribution of the corresponding control pattern and speckle pattern is calculated. Ultimately As input values ​​for the next iteration of the calculation;

[0125] Step e7: Repeat steps e2-e6 until the number of iterations reaches the preset second iteration threshold or m. i If the difference between the result of the previous iteration and the result of the previous iteration is less than the preset second difference threshold, then the first row value d1 = m in the scattering medium transfer matrix D is obtained.

[0126] Step e8: Repeat steps e2-e7 to solve for the values ​​d2, d3, ..., d65536 of the transfer matrix D in sequence. 65536 Complete the calculation of all parameters of the scattering medium transfer matrix D.

[0127] Example 3

[0128] This embodiment is largely the same as Embodiment 1, except that in this embodiment, the phase mask control module 2 changes the phase delay of the light beam through the electro-optic modulator 34. Specifically, the data acquisition control module 6 applies an external voltage to the electro-optic modulator 34 to change the transmission characteristics of the input light in the electro-optic modulator 34, thereby changing the phase delay of the light beam.

[0129] Example 4

[0130] This embodiment is largely the same as Embodiment 1, except that in this embodiment, the phase mask control module 2 changes the phase delay of the light beam through a phase-type liquid crystal spatial light modulator 35. Specifically, the phase-type liquid crystal spatial light modulator 35 is controlled by a binary modulation pattern randomly generated by the main control computer 33. By changing the voltage applied to the liquid crystal pixel molecules, different angles are generated between the liquid crystal molecules and the electric field, thereby changing the effective refractive index of the liquid crystal and thus changing the phase delay of the light beam.

[0131] Example 5

[0132] This embodiment is largely the same as Embodiment 1, except that it applies the phase mask-enhanced method and apparatus for measuring the transmission matrix of a scattering medium proposed in this invention to image restoration of a transmitted scattering medium. The specific steps include:

[0133] Step f1: Using the scattering medium transfer matrix measurement method and device based on phase mask enhancement proposed in this invention, the scattering medium transfer matrix D with a size of 65536×1024 was measured;

[0134] Step f2: After measuring the scattering medium transfer matrix D, remove all devices except the first reflector 18 in the phase mask control module 2;

[0135] Step f3: Set the number of pixels of the pattern to be transmitted to 32×32, then expand each pixel by a factor of 24×24 and add zero matrices of size 768×128 on both sides of the matrix to generate a control signal of size 768×1024 and load it into the digital micromirror array 26 to generate control light; after the control light is disturbed by the scattering medium 4, it forms a speckle pattern on the CMOS image acquisition unit 32, and the data acquisition control module 6 controls the CMOS image acquisition unit 32 to acquire the intensity distribution I of the speckle pattern. t ;

[0136] Step f4: Based on the intensity distribution of the speckle pattern I t The transmission pattern is recovered from the solved scattering medium transmission matrix D. in This represents the Moore-Penrose pseudo-reversal.

[0137] Figure 9 The method described in this embodiment is used to restore numbers, smiley faces, "SJTU" patterns, and random binary images, and the results are shown after binarizing the restored images with 50% grayscale.

[0138] Example 6

[0139] This embodiment is largely the same as Embodiment 1, except that it applies the phase mask-enhanced method and apparatus for measuring the transmission matrix of a scattering medium proposed in this invention to focusing through a scattering medium. The specific steps include:

[0140] Step g1: Set the number of control units of the digital micromirror array 26 and the number of pixels of the CMOS image sensor 32 to 4096; Using the scattering medium transfer matrix measurement method and device based on phase mask enhancement proposed in this invention, the scattering medium transfer matrix D with a size of 4096×4096 was measured.

[0141] Step g2: Remove all devices except the first reflector 18 in the phase mask control module 2;

[0142] Step g3: Based on the target focusing pattern I f Given the scattering medium transfer matrix D, calculate the modulation pattern of the digital micromirror array 26. Where B(*) represents binarization;

[0143] Step g4: Arrange the control pattern T in rows to form a 64×64 unit pattern, then expand the value of each control unit by 12×12 times and add zero matrices of size 768×128 on both sides of the matrix to generate a control signal of size 768×1024 and load it into the digital micromirror array 26, thereby changing the amplitude distribution of the beam according to the control pattern T.

[0144] Step g5: After the beam passes through the scattering medium 4, it forms a focused pattern on the CMOS image acquisition unit 32. The data acquisition control module 6 controls the CMOS image acquisition unit 32 to acquire the intensity distribution of the focused pattern.

[0145] Figure 9 This demonstrates the specific effect of focusing through the scattering medium in this embodiment. Figure 9 (a) and (b) show the light intensity distribution map and the focal intensity profile map of a single-point focus, respectively. Figure 9 (c) and (d) show the light intensity distribution map with 9 focal points and the light intensity profile map with 4 focal points, respectively.

[0146] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for measuring the transfer matrix of a scattering medium based on phase mask enhancement, characterized in that, Includes the following steps: Step 1: Generate a collimated beam, and then... L The different spatial regions are divided into L Each independently propagating sub-beam, for L- One sub-beam is given the desired phase delay, and then all sub-beams are combined into a single beam to apply the phase masking factor. ; Step 2: Input the beam with the applied phase mask factor into the pre-acquired optical field manipulation module, and then input the following into the optical field manipulation module sequentially. P A control pattern is used to sequentially change the amplitude distribution of the beam to which a phase mask factor has been applied, based on the input control pattern, to obtain... P Each of the different modulated light fields is sequentially input into the scattering medium, and after being disturbed by the scattering medium, it forms... P Collect the intensity distribution of each speckle pattern and calculate the amplitude distribution of each speckle pattern. Step 3: Repeat steps 1-2, and adjust the phase mask factor to the specified values. , … Calculate the corresponding speckle pattern amplitude distribution, the L , P and K All are positive integers; Step 4: Based on the amplitude distribution of the modulation pattern and speckle pattern corresponding to each phase mask factor, the scattering medium transfer matrix is ​​solved by an iterative optimization algorithm.

2. The method for measuring the transmission matrix of a scattering medium based on phase mask enhancement according to claim 1, characterized in that, The process of solving the scattering medium transfer matrix includes the following steps: Step a1: Initialize the scattering medium transfer matrix D The scattering medium transfer matrix D Includes M × N A random distribution of complex elements, the M , N All are positive integers; Step a2: Adjust the phase mask factor Copy line by line P Next, it becomes the size of P × N phase mask matrix Based on the control pattern and phase mask factor The corresponding speckle pattern amplitude distribution is used to set the detection matrix. and observation matrix ,in, The size is P × N , where the symbol T Indicates transpose; The size is P × M ; Step a3: Based on the detection matrix and initialization of the scattering medium transfer matrix D Calculate the estimated value of the observation matrix , where the symbol Dot product, symbol Represents the conjugate transpose of a matrix; Step a4: Maintain the estimated value of the observation matrix. The phase distribution remains unchanged, and The amplitude distribution is replaced by the observation matrix. The amplitude distribution was obtained. , where the symbol Represents phase; Step a5: From and detection matrix Calculate the transmission matrix of the scattering medium , where the symbol Represents the pseudo-inverse of a matrix; Step a6: Repeat steps a2-a5 sequentially to calculate the phase mask factor. , … Corresponding scattering medium transfer matrix , … ; Step a7: Calculate the average value of each obtained scattering medium transfer matrix to update the scattering medium transfer matrix. D This completes one iteration of calculation; Step a8: Repeat steps a2-a7 sequentially, continuously adjusting the scattering medium transfer matrix. D Optimize and update until the number of iterations reaches the preset first iteration threshold, or the scattering medium transfer matrix... D If the difference between the result and the previous iteration is less than a preset first difference threshold, then the final scattering medium transfer matrix is ​​obtained. D .

3. The method for measuring the transmission matrix of a scattering medium based on phase mask enhancement according to claim 1, characterized in that, The process of solving the scattering medium transfer matrix includes the following steps: Step b1: Based on the modulation pattern and phase mask factor The corresponding speckle pattern amplitude distribution is used to set the detection matrix. The size is P × N Set the observation matrix The size is P × M ; Step b2: Set initial parameters, including the values ​​in the first row of the transfer matrix. variance Transmission Matrix D The initial value of the first row Observation matrix Y Missing phase in column 1 mean of the posterior distribution and variance ; Step b3: Adjust the phase mask factor Copy line by line P Next, it becomes the size of P × N phase mask matrix Take the observation matrix The first column of elements Composition vector ; Step b4: Calculate the variance of the noise. The variance value The calculation expression is: In the formula, and Representing the detection matrix respectively The Middle i and j Column vector, and These respectively represent the phase mask matrix The first in i and j Column vector, Representative of the actual part; Step b5: Calculate the mean and variance of the posterior distribution. The expressions for calculating the mean and variance of the posterior distribution are as follows: In the formula, , , , and These represent the zeroth and first-order functions of the first kind of modified Bessel functions, respectively. t ={1,2, i -1, i +1,…, N }; Step b6: Repeat steps b3-b5, respectively, based on the phase mask factor. , … The amplitude distribution of the corresponding control pattern and speckle pattern is calculated. , … Ultimately As input values ​​for the next iteration of the calculation; Step b7: Repeat steps b2-b6 until the number of iterations reaches the preset second iteration threshold or When the difference between the result of the previous iteration and the result of the previous iteration is less than the preset second difference threshold, the scattering medium transfer matrix is ​​obtained. D The first row of values ; Step b8: Repeat steps b2-b7 to solve for the transfer matrix in sequence. No. 2,3,…, M row value , … Complete the scattering medium transfer matrix D Calculation of all parameters.

4. A measuring apparatus for implementing the scattering medium transfer matrix measurement method based on phase mask enhancement as described in any one of claims 1-3, characterized in that, It includes a collimation and beam expansion module, a phase mask control module, an optical field modulation module, a photoelectric detection module, a data acquisition and control module, and a transmission matrix calculation module. A scattering medium mounting area for mounting a scattering medium is provided between the optical field modulation module and the photoelectric detection module. The collimation and beam expanding module is used to convert the received beam into a collimated beam with a certain aperture. The data acquisition and control module is used to generate phase mask factors and transmit them to the phase mask control module, and also to generate modulation patterns and transmit them to the light field modulation module. The phase mask control module includes a beam splitter, a phase delay device group, and a beam combiner. The beam splitter is used to split the collimated beam according to... L The different spatial regions are divided into L Each independently propagating sub-beam; the phase delay device group has a total of L- One phase delay device, and each phase delay device is individually controlled to... L- An additional phase constraint is imposed on a sub-beam, and different phase masking factors are applied by changing the phase delay amount; The beam combiner is used to combine L The individual beams are merged into one beam according to their original spatial positions in the collimated beam; The light field modulation module is used to change the amplitude distribution of the beam output by the phase mask control module according to the applied modulation pattern, thereby generating different modulated light fields. The scattering medium is used to create speckle patterns by disturbing various modulated optical fields. The photoelectric detection module is controlled by the data acquisition and control module and is used to detect the intensity distribution of speckle. The transmission matrix calculation module is used to calculate the transmission matrix of the scattering medium using an iterative optimization algorithm.

5. The apparatus according to claim 4, characterized in that, The phase delay device group also includes half-wave plates and knife-edge apertures, the number of which is: L- 1, the number of the knife-edge apertures is L Each half-wave plate is used for... L- The polarization direction of one sub-beam is adjusted to make the polarization direction of all sub-beams consistent; each of the knife-edge apertures blocks all sub-beams respectively, and the illumination area of ​​the sub-beams on the light field control module is changed by adjusting the position and angle of the knife-edge.

6. The apparatus according to claim 4, characterized in that, The phase delay device is any one of a liquid crystal phase delayer, an electro-optic modulator, a phase-type liquid crystal spatial light modulator, and a Fresnel phase delayer.

7. The apparatus according to claim 4, characterized in that, The light field modulation module includes a spatial light modulator and a filter optical path. The spatial light modulator is used to modulate the amplitude of the modulation light field, and the filter optical path is set at the output end of the spatial light modulator to filter out diffracted light of a specific order.

8. The apparatus according to claim 7, characterized in that, The spatial light modulator is a digital micromirror array or an amplitude-type liquid crystal spatial light modulator.

9. The apparatus according to claim 4, characterized in that, The photoelectric detection module includes an imaging lens and a photoelectric sensor. The imaging lens is used to collect scattered light beams and image them onto the photoelectric sensor. The photoelectric sensor is used to detect the intensity distribution of speckle and convert it into an electrical signal, which is then sent to the transmission matrix calculation module.

10. The apparatus according to claim 9, characterized in that, The photoelectric sensor is any one of a CCD image sensor, a CMOS image sensor, a photomultiplier tube, or a photodiode.

Images