Method for regulating and controlling back focus of scattering medium by using positive and negative retina-like transmission matrix

Abstract

The invention relates to the technical field of optical scattering focusing, in particular to a method for regulating and controlling a back focus of a scattering medium by a positive and negative retina-like transmission matrix, which comprises the following steps of: modulating light wavefront on a spatial light modulator (4), collecting intensity speckles by a receiving end (13) after the modulated light passes through the scattering medium (9), firstly, a complex transmission matrix T of a scattering medium is solved based on a forward or inverse retina-like Hadamard modulation basis in combination with a common-path self-reference method, and then an optimized wavefront pattern loaded on the spatial light modulator (4) is solved based on the complex transmission matrix T and a phase conjugation algorithm. The feasibility of the method for regulating and controlling the back focus of the scattering medium by using the positive and negative retina transmission matrixes is proposed and verified for the first time.

Description

Technical Field

[0001] This invention relates to the field of optical scattering and focusing technology. Background Technology

[0002] Optical focusing through scattering media is a fundamental challenge in beam shaping. The inhomogeneity of the refractive index of the scattering medium causes light scattering during propagation, resulting in severe distortion of the original wavefront. Although light scattering is often considered an obstacle to optical imaging and focusing, focusing through scattering media can be achieved by actively manipulating the incident wavefront due to the time-reversal symmetry of Maxwell's equations. This principle is based on the fact that when absorption is negligible, multiple scattered light emitted from a point source can be sent back to its origin. Based on this, various wavefront shaping techniques have been developed, including optical phase conjugation (OPC), iterative feedback, and transfer matrix (TM) methods. Among these, the TM method provides a systematic framework for controlling light propagation in complex media by establishing a deterministic linear relationship between the incident and transmitted wavefronts. Currently, focusing is mainly achieved using conventional real-basis TM or different vector basis matrices; however, how to control the back focal size (SOF) and depth of focus (DOF) of the scattering medium remains an unresolved but crucial problem. Summary of the Invention

[0003] The technical problem to be solved by this invention is: how to control the size of the back focal spot and its depth of focus of the scattering medium.

[0004] The technical solution adopted in this invention is: a method for controlling the focal point of the scattering medium by the positive or negative retinal-like transmission matrix. The light wavefront is modulated on the spatial light modulator (4). After the modulated light passes through the scattering medium (9), the intensity speckle is collected by the receiver (13). First, the complex transmission matrix T of the scattering medium is obtained by combining the positive or negative retinal-like Hadamard modulation basis with the common self-reference method. Then, the optimized wavefront pattern loaded on the spatial light modulator (4) is obtained by solving the complex transmission matrix T and the phase conjugate algorithm.

[0005] Specifically, the steps include the following:

[0006] Step 1: To achieve positive or negative retina-like arrangement of pixels inside the N2-order Hadamard base mask, first generate a (S×N)×(S×N) positive or negative retina-like modulation mask (Cartesian pixel scale magnified by S2 times). Divide this mask into N2 grids, ensuring a constant resolution in the central circular region. The regions outside the central circular region are divided into unequal resolutions based on radius and angle (specifically, for positive retina, the resolution gradually increases towards the outer layer in terms of radius and angle, and the resolution of each grid area gradually increases radially; for negative retina, the resolution gradually decreases towards the outer layer in terms of radius and angle, and the resolution of each grid area gradually decreases radially). After the division is complete, the grids are spirally numbered from the inside out (from 1 to N2). To facilitate the sequential filling of elements from each row of the Hadamard base into the generated positive or negative retina-like mask, the numbering pattern is not limited to the spiral numbering from the inside out mentioned above. It is only necessary to ensure that the filling pattern of a series of row vectors of the Hadamard base is consistent. S and N are both natural numbers, and N is an even number.

[0007] Step 2: Using Matlab software, generate an N2×N2 Hadamard basis (including 1 and -1 values), where each row has a dimension of 1×N2. Sequentially fill the row elements of the Hadamard matrix into the aforementioned positive or negative retinal modulation masks (total degrees of freedom N2) until the mask is full. Then, modulate the light wavefront using the generated series of positive or negative retinal modulation matrices.

[0008] Step 3: Perform an i-step phase shift on the reference light, and then superimpose it with a positive or negative retina-like modulation base using a self-referenced pattern to ultimately generate i×N×N modulation patterns. In one embodiment, i is 4; i is a natural number, i≥2, and commonly 3 or 4.

[0009] Step 4: Sequentially load i×N×N modulation patterns onto the spatial light modulator 4. , As the input light field, camera 13 captures the data for each modulation pattern. The corresponding intensity speckle; Step 5: Using the intensity speckle from Step 3, calculate the output light field using the i-step phase shift formula. Using the formula Solve for the complex transmission matrix T of the scattering medium;

[0010] Step 6: Combining the complex transmission matrix T of the scattering medium obtained in Step 4, the optimized wavefront focused at the output target position is calculated using the phase conjugate algorithm, and then loaded onto the spatial light modulator 4 to achieve focusing behind the scattering medium.

[0011] The positive or negative retinal modulation mask is characterized by different distributions of degree-of-freedom density in the central region and the periphery. The positive retinal mask simulates the characteristics of the biological retina, with a high degree-of-freedom density in the central region (i.e., high resolution) and a low degree-of-freedom density in the periphery (i.e., low resolution). The negative retinal mask exhibits the opposite degree-of-freedom density distribution to the positive retinal mask.

[0012] The distribution of the central and surrounding areas is achieved by merging different numbers of pixel units from the original 512×512 pixels to form "superpixels". That is, high-resolution areas use small-sized "superpixels" and low-resolution areas use large-sized "superpixels".

[0013] The apparatus used in the method of adjusting the focal point of the scattering medium by the positive and negative retinal transmission matrix includes a solid-state continuous laser (1), a beam expander (2), a half-wave plate (3), a spatial light modulator (4), a first lens (5), an aperture stop (6), a second lens (7), a first microscope objective (8), a scattering medium (9), a second microscope objective (10), a polarizer (11), a sleeve lens (12), and a camera (13), arranged sequentially on the same optical path. The solid-state continuous laser (1) is a solid-state continuous linearly polarized laser. The laser emitted by it is expanded by the beam expander (2), and then the polarization state of the beam is adjusted by the half-wave plate (3). The light beam is incident on the spatial light modulator (4) at a suitable incident angle and then subjected to wavefront modulation (such as vertical incidence). The light beam modulated by the spatial light modulator (4) passes through the first lens (5), the aperture stop (6), and the second lens (7) in sequence and is then conjugated to the first microscope objective (8). The first microscope objective (8) focuses the light and then irradiates the front surface of the scattering medium (9). The second microscope objective (10) and the sleeve lens (12) work together to image the speckle light field transmitted through the scattering medium (9) onto the receiver (13). The receiver (13) receives the intensity speckle, where the polarizer (11) is used to modulate the polarization state of the speckle in order to obtain the maximum information of the speckle.

[0014] The beneficial effects of this invention are as follows: This invention achieves modulation of the light wavefront by generating positive or negative retinal-like Hadamard modulation bases, and then measures the corresponding positive or negative retinal-like Hadamard transfer matrices to achieve light field focusing. A common-path self-reference strategy is employed, where the signal light and reference light are co-channel superimposed and interfered, realizing the measurement of the complex transfer matrix of the scattering medium and light field focusing. This invention can effectively control the focal size and depth of focus behind the scattering medium simply by changing the degree-of-freedom density distribution of the retinal-like modulation base. The proposed focal size and depth-of-focus control scheme has various potential applications in scattering environments. For example, an enlarged focal size can expand the illumination area of ​​fluorescence imaging, reduce the number of scans, and improve the efficiency of scattering fluorescence imaging; its extended depth of focus helps to image deeper into the scattering medium. Conversely, a reduced focal size and shortened depth of focus can improve spatial resolution.

[0015] This invention proposes and verifies for the first time the feasibility of a method for controlling the focal point behind a scattering medium using positive or negative retina-like transfer matrices. Preliminary studies show that positive or negative retina-like TMs can not only achieve effective focusing behind the scattering medium, but also achieve independent control of the focal point size and depth of field by redistributing its degree-of-freedom density. This method, while achieving focusing, can simultaneously adjust the focal spot size and depth of field, thereby adapting to the spatial scattering characteristics of the medium and providing a new means for manipulating the light field in complex scattering environments. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the device of the present invention;

[0017] Figure 2 (a) to (c) are schematic diagrams of modulation masks with different spatial degrees of freedom density arrangements, namely natural sequence mask, positive retina and negative retina;

[0018] Figure 3 From (a) to (c), these are simulation focusing results obtained from the natural sequence Hadamard modulation basis (HTM), the reticular-like Hadamard modulation basis (RHTM), and the anti-reticular-like Hadamard modulation basis (ARHTM), respectively.

[0019] Among them, 1-solid-state continuous laser, 2-beam expander, 3-half-wave plate, 4-spatial light modulator, 5-first lens, 6-aperture stop, 7-second lens, 8-first microscope objective, 9-scattering medium, 10-second microscope objective, 11-polarizer, 12-sleeve lens, 13-camera. Detailed Implementation

[0020] like Figure 1-3As shown, the method for controlling the focal point of a scattering medium using positive or negative retinal-like transfer matrices involves modulating the wavefront of light on a spatial light modulator 4. The modulated light passes through a scattering medium 9 and is ultimately collected by a receiver 13, which acquires the corresponding intensity speckle pattern. The method is characterized by: firstly, solving for the complex transfer matrix T of the scattering medium based on a positive or negative retinal-like Hadamard modulation basis combined with a self-reference method; and then solving for the optimized wavefront pattern loaded on the spatial light modulator 4 based on the complex transfer matrix T and a phase conjugate algorithm. Specifically, the method includes the following steps:

[0021] Step 1: Generate a (S×N)×(S×N) positive or negative retinal modulation mask, divide this mask into a grid of exactly N2 grids, so that the resolution of the focal circle region is constant, and the region outside the focal circle is divided into different resolutions according to the radius and angle. After the division is completed, the grids are spirally numbered from the inside to the outside (numbered from 1 to N2).

[0022] Step 2: Using Matlab software, generate an N2×N2 Hadamard basis (including 1 and -1 values), where each row has a dimension of 1×N2. Sequentially fill the row elements of the Hadamard matrix into the aforementioned positive or negative retinal modulation masks (total degrees of freedom N2) until the mask is full. Then, modulate the light wavefront using the generated series of positive or negative retinal modulation matrices.

[0023] Step 3: Perform an i-step phase shift on the reference light, and then superimpose it with a positive or negative retina-like modulation base using a self-referenced pattern to ultimately generate i×N×N modulation patterns. In one embodiment, i is 4;

[0024] Step 4: Sequentially load i×N×N modulation patterns onto the spatial light modulator 4. Camera 13 is used to capture each modulation pattern The corresponding intensity speckle; Step 5: Using the intensity speckle from Step 3, calculate the output light field using the i-step phase shift formula. Using the formula Solve for the complex transmission matrix T of the scattering medium;

[0025] Step 6: Combining the complex transmission matrix T of the scattering medium obtained in Step 4, the optimized wavefront focused at the output target position is calculated using the phase conjugate algorithm, and then loaded onto the spatial light modulator 4 to achieve focusing behind the scattering medium.

[0026] In the measurement of the transfer matrix (TM), the Hadamard basis used is orthogonal and consists of binary elements, where "1" represents phase 0 and "-1" represents phase π. This allows for convenient generation and accurate measurement, thus efficiently reconstructing the TM. This invention achieves effective control of the light wavefront by introducing two types of Hadamard basis masks: positive retina-like and negative retina-like. The positive retina-like mask simulates the characteristics of the biological retina, with a high degree-of-freedom density (high resolution) in the central region and a low degree-of-freedom density (low resolution) in the periphery. The negative retina-like mask exhibits the opposite degree-of-freedom density distribution. In this invention, the degree-of-freedom density distribution is achieved by merging different numbers of pixel units from the original 512×512 pixels to form "superpixels." That is, small-sized "superpixels" are used in high-resolution regions, and large-sized "superpixels" are used in low-resolution regions.

[0027] like Figure 1 As shown, the device for controlling the back focus of a scattering medium using a positive and negative retinal-like transmission matrix includes a solid-state continuous laser 1, a beam expander 2, a half-wave plate 3, a spatial light modulator 4, a first lens 5, an aperture stop 6, a second lens 7, a first microscope objective 8, a scattering medium 9, a second microscope objective 10, a polarizer 11, a sleeve lens 12, and a camera 13, arranged sequentially on the same optical path.

[0028] The laser emitted by the solid-state continuous linear polarization laser 1 is expanded by the beam expander 2, and then the polarization state of the beam is adjusted by the half-wave plate 3. The beam is then irradiated onto the spatial light modulator 4 at a suitable incident angle for wavefront modulation. The beam modulated by the spatial light modulator 4 passes sequentially through the first lens 5, the aperture stop 6, and the second lens 7 before being conjugated to the first microscope objective 8. The first microscope objective 8 focuses the light and irradiates it onto the front surface of the scattering medium 9. The second microscope objective 10 and the sleeve lens 12 work together to image the speckle light field transmitted through the scattering medium 9 onto the receiver 13. The receiver 13 receives the intensity speckle, where the polarizer 11 is used to modulate the polarization state of the speckle to obtain the maximum speckle information.

[0029] Generate either a positive or negative retinal-like modulation mask, fill the mask with elements from the Hadamard basis matrix (total degrees of freedom N²), and then modulate the light wavefront using a series of generated positive or negative retinal-like Hadamard modulation matrices. First, apply an i-step phase shift to the reference light, then superimpose it with the positive or negative retinal-like Hadamard modulation basis using a self-referenced pattern, ultimately generating i×N×N modulation patterns. The PC controls the spatial light modulator 4 to sequentially load i×N×N modulation patterns. At receiver 13, intensity speckle patterns corresponding to each modulation pattern are acquired; the output optical field can be calculated using the acquired intensity speckle patterns and the i-step phase shift formula. ; through formula The complex transfer matrix T of the scattering medium can be solved. Based on the complex transfer matrix T and the phase conjugate algorithm, the optimized wavefront pattern for focusing at the output target position can be solved. The solved optimized wavefront mask is loaded onto the spatial light modulator 4 and projected to finally achieve focusing behind the scattering medium, such as... Figure 3 As shown.

[0030] In one embodiment: the scattering medium 9 is frosted glass, ZnO, or multimode optical fiber.

[0031] In one embodiment: the receiver 13 is a CCD camera or an sCMOS camera.

[0032] In one embodiment: as Figure 2 As shown, from (a) to (c), the masks represent the distribution of a conventional natural sequence mask, a retina-like mask, and an anti-retina-like mask, respectively. In the mask shown in Figure (a), the degrees of freedom are naturally distributed, meaning the degree-of-freedom density is constant. As shown in Figure (b), for the positive retina modulation mask, the distribution characteristic is a high degree-of-freedom density in the central region, gradually decreasing radially; that is, while keeping the total number of degrees of freedom constant, the degrees of freedom are concentrated as much as possible in the central region. For the anti-retina mask, as shown in Figure (c), the distribution characteristic is a high degree-of-freedom density in the surrounding region, gradually increasing radially; that is, while keeping the total number of degrees of freedom constant, the degrees of freedom are distributed as much as possible in the surrounding region. It should be noted that... Figure 2 The paper only presents two special cases of retina-like structures and generates various distribution masks with different spatial distribution states. Based on this, Hadamard elements are sequentially filled into the above masks to generate a series of different positive or negative retina-like Hadamard modulation bases, which can achieve wavefront modulation of light, thereby measuring the corresponding complex transmission matrix T and achieving focusing after passing through the scattering medium. Figure 3 (a)-3(c) show the simulation results of focusing using the transmission matrices measured by the conventional Hadamard modulation base, the positive retinal Hadamard modulation base, and the negative retinal Hadamard modulation base, respectively. The curves show the normalized intensity profile of the focal point. Clearly, compared to the conventional Hadamard base transmission matrix (full width at half maximum of 1.58µm), the positive retinal Hadamard modulation base transmission matrix produces a larger focal point (full width at half maximum of 2.23µm), while the negative retinal Hadamard modulation base transmission matrix produces a smaller focal point (full width at half maximum of 1.28µm). Furthermore, there is a direct proportional relationship between the depth of focus and the focal size. It is easy to deduce that effective control of the focal size and depth of focus can be achieved through positive or negative retinal mask modulation.

[0033] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for controlling the focal point of a scattering medium using a positive and negative retinal-like transmission matrix, wherein the light wavefront is modulated on a spatial light modulator (4), and the modulated light passes through a scattering medium (9), and the intensity speckle is collected by a receiver (13), characterized in that: First, the complex transmission matrix T of the scattering medium is obtained by combining the positive or negative retinal Hadamard modulation basis with the common self-reference method. Then, the optimized wavefront pattern loaded on the spatial light modulator (4) is obtained by solving the complex transmission matrix T and the phase conjugate algorithm. Specifically, the steps include the following: Step 1: To achieve positive or negative retina-like arrangement of pixels inside the N2-order Hadamard base mask, first generate a (S×N)×(S×N) positive or negative retina-like modulation mask. Divide this mask into N2 grids, ensuring a constant resolution in the central circular region. Divide the regions outside the central circular region into different resolutions based on radius and angle. After the division, spirally number the grids from the inside out. Numbering is to facilitate the sequential filling of elements from each row of the Hadamard base into the generated positive or negative retina-like mask. The numbering pattern is not limited to the spiral numbering from the inside out mentioned above; it is sufficient to ensure that the filling pattern of the series of row vectors of the Hadamard base is consistent. S and N are both natural numbers, and N is an even number. Step 2: Using Matlab software, generate an N2×N2 Hadamard basis, where each row has a dimension of 1×N2. Sequentially fill the row elements of the Hadamard matrix into the aforementioned positive or negative retinal modulation mask until it is full. Then, modulate the light wavefront using the generated series of positive or negative retinal Hadamard matrices. Step 3: Perform an i-step phase shift on the reference light, and then superimpose it onto a positive or negative retinal-like Hadamard modulation base using a self-referenced pattern to ultimately generate i×N×N modulation patterns. ; Step 4: Sequentially load i×N×N modulation patterns onto the spatial light modulator 4. , As the input light field, camera 13 captures the data for each modulation pattern. The corresponding intensity speckle; Step 5: Using the intensity speckle from Step 3, calculate the output light field using the i-step phase shift formula. Using the formula Solve for the complex transmission matrix T of the scattering medium; Step 6: Combining the complex transmission matrix T of the scattering medium obtained in Step 4, the optimized wavefront focused at the output target position is calculated using the phase conjugate algorithm, and then loaded onto the spatial light modulator 4 to achieve focusing behind the scattering medium.

2. The method according to claim 1, characterized in that: The positive or negative retinal mask is characterized by different distributions of degree-of-freedom density in the central region and the periphery. The positive retinal mask simulates the characteristics of the biological retina, with a high degree-of-freedom density in the central region (i.e., high resolution) and a low degree-of-freedom density in the periphery (i.e., low resolution). The negative retinal mask exhibits the opposite degree-of-freedom density distribution to the positive retinal mask.

3. The method according to claim 2, characterized in that: The distribution of the central and peripheral areas is achieved by merging different numbers of pixel units from the original 512×512 pixels to form "superpixels". That is, high-resolution areas use small-sized "superpixels" and low-resolution areas use large-sized "superpixels".

Images