A mineral section analysis system and method for an off-axis digital holographic microscope

Abstract

The present application relates to the technical field of mineral section analysis, and particularly provides a mineral section analysis system and method of off-axis digital holographic microscope, the method comprising S1: placing a mineral section in an on-axis digital holographic microscope system and recording a hologram; S2: holographic imaging and reconstruction to obtain an amplitude transmittance distribution and a phase transmittance distribution; and S3: based on the obtained phase distribution, in combination with the thickness and refractive index relationship of the mineral section, inversely calculating the thickness distribution or the refractive index distribution of the mineral section; the present application simultaneously obtains the amplitude transmittance distribution and the phase transmittance distribution through numerical reconstruction; the amplitude transmittance reflects the light absorption and scattering characteristics of the mineral section, and can be used for identifying the mineral boundary, inclusions and opaque regions; the phase transmittance reflects the change of the optical path difference, and then the thickness distribution or the refractive index distribution of the mineral section can be quantitatively inverted.

Description

Technical Field

[0001] This invention relates to the field of mineral section analysis technology, and specifically provides a mineral section analysis system and method using an off-axis digital holographic microscope. Background Technology

[0002] Mineral slice analysis is a fundamental and crucial technique in geological research. By observing the optical properties of thin sections of rocks or minerals, important information such as the composition, structure, texture, and physical properties of minerals can be obtained. Traditional mineral slice analysis methods mainly rely on polarizing microscopes to qualitatively or semi-quantitatively identify minerals by observing their optical characteristics (such as color, pleochroism, interference colors, extinction type, and ductility sign) under single-polarized, crossed-polarized, and conic light systems. However, traditional methods have the following limitations: (1) They rely on human experience and judgment, are highly subjective, lack quantitative analysis capabilities, and are difficult to standardize the measurement of mineral parameters; (2) They are difficult to directly obtain quantitative physical parameters such as the thickness distribution and refractive index changes of samples, which limits the depth of analysis of the correlation between mineral optical properties and physical structure; (3) For mineral samples with low transparency, strong surface scattering, or complex optical properties, traditional transmitted light observation methods are limited by imaging contrast and resolution, resulting in a significant decrease in effectiveness.

[0003] In recent years, quantitative phase imaging (QPI), as a label-free and non-contact optical measurement method, has been increasingly applied in the analysis of transparent and translucent samples. This technique acquires the phase delay distribution caused by the sample, and then inverts physical parameters such as sample thickness and refractive index, providing a new technical approach for the quantitative analysis of mineral slices. Digital holographic microscopy is an important method for achieving QPI. It utilizes optocouplers to record a digital hologram formed by the interference of reference light and object light carrying sample information, and then uses computer numerical simulation of the diffraction propagation process to reconstruct the wavefront, thereby simultaneously obtaining the amplitude and phase distribution information of the sample.

[0004] However, mineral slices typically exhibit low transmittance, uneven surfaces, varying thicknesses, and complex internal structures, significantly differing from the transparent, thin samples commonly found in biological or materials science. Existing digital holographic imaging systems designed for biological samples have not been specifically optimized for the physical characteristics of mineral slices in terms of illumination methods and optical path structures. Therefore, directly applying them to mineral slice analysis often results in problems such as low imaging contrast, large phase reconstruction errors, and inaccurate thickness inversion, failing to meet the practical needs of quantitative geological analysis.

[0005] In summary, there is an urgent need to develop a digital holographic imaging system and analysis method specifically designed for mineral slice analysis. This system should be able to adapt to the optical characteristics of mineral samples and achieve high-precision phase recovery and physical parameter inversion, thereby improving the automation and standardization of quantitative analysis of mineral slices. Summary of the Invention

[0006] Firstly, to address the aforementioned problems, this invention provides a digital holographic imaging system and analysis method specifically designed for mineral slice analysis, adapting to the optical characteristics of mineral samples. The specific system scheme is as follows:

[0007] A mineral section analysis system for an off-axis digital holographic microscope includes: a semiconductor laser; a polarizer, a first half-wave plate, and a polarizing beam splitter arranged sequentially along the output light path of the semiconductor laser, the polarizing beam splitter splitting the incident light into an object beam and a reference beam; a pinhole mirror, a first reflecting mirror, a first microscope objective, a non-polarizing beam splitter, and an image acquisition device connected to a computer arranged sequentially along the propagation direction of the object beam; a second reflecting mirror, a second half-wave plate, and a second microscope objective arranged sequentially along the propagation direction of the reference beam, the output light from the second microscope objective being incident on the non-polarizing beam splitter; the non-polarizing beam splitter combining the object beam and the reference beam before outputting it to the image acquisition device; and a mineral section sample to be tested positioned between the first reflecting mirror and the first microscope objective.

[0008] In this scheme, the linear polarization and controllable beam splitting of the light beam are achieved through the combination of polarizers, half-wave plates, and polarizing beam splitters. This eliminates the adverse effects of the unpolarized components of the light source on the interference contrast, ensures the interference efficiency of the reference and object beams, and improves the signal-to-noise ratio of the hologram. The entire object and reference beam paths are independently controlled, and finally, they are combined by an unpolarized beam splitter to form off-axis interference, allowing complete amplitude and phase information to be recorded in a single image. Imaging and recording mineral slices using this system effectively overcomes the shortcomings of low transmittance and strong light absorption in mineral slices, which makes it difficult to generate effective interference.

[0009] Preferably, both the first and second microscope objectives are spherical wave objectives.

[0010] In this scheme, both the first and second microscope objectives are spherical wave objectives, enabling the object beam and reference beam to form spherical wave interference on the recording surface of the image acquisition unit. The two spherical waves have the same wavefront curvature, and during interference, they cancel each other out spherical phase factors, resulting in a flat interference fringe distribution on the recording surface. This significantly reduces the stringent requirements on the optical element placement distance, achieving large field-of-view and highly stable holographic recording without the need for a precise collimation system. It is particularly suitable for samples with uneven thickness and undulating surfaces, such as mineral slices. Furthermore, spherical wave interference reduces additional phase distortion introduced by sample tilt or defocus, improving the accuracy and repeatability of phase reconstruction.

[0011] Preferably, the polarizing beam splitter is configured such that the polarization direction of the transmitted object beam is parallel to the direction of the emitted light from the semiconductor laser, and the polarization direction of the reflected reference beam is perpendicular to the direction of the emitted light from the semiconductor laser.

[0012] A method for analyzing mineral slices using an off-axis digital holographic microscope includes the following steps: S1, placing the mineral slice in the system described in any one of claims 1 to 3 and recording the hologram; S2, performing holographic imaging and reconstruction to obtain the amplitude transmittance distribution and the phase transmittance distribution; S3, based on the obtained phase distribution and combined with the relationship between the thickness and refractive index of the mineral slice, inverting and calculating the thickness distribution or refractive index distribution of the mineral slice.

[0013] In this scheme, both amplitude transmittance and phase transmittance distributions are obtained simultaneously through numerical reconstruction. Amplitude transmittance reflects the absorption and scattering characteristics of light by the mineral slice and can be used to identify mineral boundaries, inclusions, and opaque areas; phase transmittance reflects changes in optical path difference, and can thus quantitatively invert the thickness or refractive index distribution of the mineral slice. Compared with the qualitative or semi-quantitative identification of traditional polarizing microscopy, this method achieves full-field, high-precision quantitative characterization of mineral composition, providing objective and reproducible data support for petrology, mineral deposit geology, and other fields. This process does not require special labeling or staining of the sample, preserving the original state of the mineral slice and avoiding the damage to the sample structure caused by chemical treatment.

[0014] Preferably, step S1 is followed by step S11: using a checkerboard calibration system and calculating the actual magnification.

[0015] In this step, the actual magnification of the system is measured using a checkerboard calibration plate, and the physical size corresponding to each pixel is calculated, providing a spatial size calibration benchmark for subsequent image reconstruction. This calibration step eliminates magnification uncertainties caused by optical component processing errors, assembly errors, and temperature drift, ensuring the traceability of thickness distribution and refractive index inversion results.

[0016] Preferably, the holographic imaging in step S2 includes the following steps: S21, performing a two-dimensional Fourier transform on the hologram to obtain the spectral distribution, extracting the spectral terms carrying sample information and shifting them to the center of the spectrum, and then performing an inverse Fourier transform to obtain the complex amplitude distribution of the object light wave on the recording plane.

[0017] In this step, the hologram is converted to the frequency domain using a two-dimensional Fourier transform, separating the positive (or negative) first-order terms carrying sample information from the zero-order terms in the spectrum. This spectral term is truncated and shifted to the center, then subjected to an inverse Fourier transform to obtain the complex amplitude distribution of the object wave on the recording plane, effectively removing the zero-order and conjugate images. This processing allows for the reliable extraction of even weak phase information from low-transmittance mineral slices, and the reconstructed complex amplitude distribution exhibits a high signal-to-noise ratio, laying the foundation for subsequent focusing and parameter inversion.

[0018] Preferably, step S2 further includes: S22, using a diffraction propagation algorithm to propagate the complex amplitude distribution values ​​of the recording plane to the clear imaging plane to obtain a focused complex amplitude distribution.

[0019] In this step, the diffraction propagation algorithm overcomes the difficulties of unknown mineral slice thickness and the inability to directly locate the precise image plane, achieving digital autofocus without the need for mechanically moving the sample or objective lens. Only after obtaining the focused complex amplitude distribution can subsequent amplitude and phase extraction achieve physical accuracy, avoiding phase distortion and measurement errors caused by defocusing.

[0020] Preferably, step S2 further includes: taking a model of the complex amplitude distribution of the focused light field to obtain the amplitude transmittance distribution of the reconstructed mineral slice.

[0021] Preferably, step S2 further includes: extracting phase information from the focused complex amplitude distribution, and obtaining the true phase transmittance distribution of the mineral slice through phase unwrapping and distortion compensation processing.

[0022] In this step, after extracting the wrapped phase from the focused complex amplitude, a phase unwrapping algorithm is used to restore the continuous phase distribution and eliminate jumps. Distortion compensation removes additional phase distortions introduced by system optical path bending, sample tilt, etc., to obtain the true phase transmittance distribution of the mineral slice. The true phase distribution is directly related to the thickness and refractive index of the mineral slice; the thickness can be inverted by combining the known refractive index, or vice versa. This information can be used to identify mineral species, quantitatively analyze the degree of mineral alteration (such as refractive index changes), and reconstruct three-dimensional morphology. The combined application of phase unwrapping and distortion compensation significantly improves the accuracy and robustness of quantitative inversion, upgrading mineral slice analysis from traditional "color analysis" to "phase measurement and property calculation."

[0023] The beneficial effects of this invention are:

[0024] This invention addresses the limitations of traditional polarizing microscopes, which suffer from high subjectivity and insufficient quantitative capabilities, as well as the difficulty of conventional digital holographic microscopes in adapting to the low transmittance, uneven thickness, and complex surface characteristics of mineral sections. It proposes a dedicated off-axis digital holographic microscopy analysis system and method. By optimizing the optical path structure (including polarization control, spherical wave objective matching, spatial filtering collimation, and off-axis interference design), the system significantly improves the ability to record high-contrast holograms of mineral samples. Combined with digital reconstruction processes such as holographic spectral filtering, automatic focusing of angular diffraction, phase unwrapping, and distortion compensation, the system can simultaneously obtain the amplitude transmittance distribution and the true phase transmittance distribution of mineral sections, thereby retrieving key quantitative parameters such as thickness and refractive index. Attached Figure Description

[0025] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the system of the present invention;

[0027] Figure 2 This is a schematic flowchart of the method of the present invention;

[0028] Figure 3 This is an off-axis digital hologram of the Helan stone sample recorded in this invention;

[0029] Figure 4 This is a diagram showing the chessboard grid markings of the present invention.

[0030] Figure 5 A two-dimensional Fourier transform was performed on the Helan stone slice hologram of this invention to obtain the spectral distribution of the hologram;

[0031] Figure 6 In this invention Figure 5 A diagram illustrating the movement of the captured spectrum to the center of the spectrum;

[0032] Figure 7 This is the amplitude transmittance distribution diagram of the Helan stone slice reconstructed by the present invention;

[0033] Figure 8 This is a reconstructed phase distribution map of a Helan stone slice containing inclusions and distortions, as presented in this invention.

[0034] Figure 9 For the present invention Figure 8 Phase curve at the dashed line;

[0035] Figure 10 For the present invention Figure 8Reconstructed phase distribution map without phase distortion;

[0036] Figure 11 For the present invention Figure 10 Phase curve at the dashed line;

[0037] Figure 12 For the present invention Figure 8 Phase distribution map after removing phase wrapping and distortion;

[0038] Figure 13 For the present invention Figure 12 Phase curve at the dashed line;

[0039] Figure 14 This invention provides a three-dimensional topological mapping of the phase field.

[0040] In the above figures, the corresponding reference numerals are as follows:

[0041] 1-Semiconductor laser, 2-Polarizer, 3-First half-wave plate, 4-Polarizing beam splitter, 5-Pinhole mirror, 6-First reflecting mirror, 7-Second reflecting mirror, 8-Second half-wave plate, 9-First microscope objective, 10-Second microscope objective, 11-Unpolarizing beam splitter, 12-Sample to be tested, 13-Image acquisition device CCD, 14-Computer. Detailed Implementation

[0042] The technical solution of the present invention will be clearly and completely described in conjunction with the accompanying drawings and through specific implementation methods of the embodiments of the present invention.

[0043] Example 1:

[0044] This embodiment provides an off-axis digital holographic optical system applicable to mineral slices, the system as follows: Figure 1 As shown, the system includes: a semiconductor laser; a polarizer, a first half-wave plate, and a polarizing beam splitter arranged sequentially along the output light path of the semiconductor laser; the polarizing beam splitter splits the incident light into an object beam and a reference beam; a pinhole mirror, a first reflecting mirror, a first microscope objective, a non-polarizing beam splitter, and an image acquisition device arranged sequentially along the propagation direction of the object beam; a second reflecting mirror, a second half-wave plate, and a second microscope objective arranged sequentially along the propagation direction of the reference beam, wherein the output light from the second microscope objective is incident on the non-polarizing beam splitter; the non-polarizing beam splitter combines the object beam and the reference beam and outputs them to the image acquisition device; and a mineral slice sample to be tested is placed between the first reflecting mirror and the first microscope objective.

[0045] Along the main optical path of the semiconductor laser, a polarizer, a first half-wave plate, and a polarizing beam splitter are sequentially arranged. The polarizing beam splitter divides the incident light into two paths: one is the object beam, which propagates along the original main optical path; the other is the reference beam, which is perpendicular to the main optical path. A pinhole mirror and a first reflecting mirror are sequentially arranged along the object beam path. The pinhole mirror, located between the polarizing beam splitter and the first reflecting mirror, is used to expand, filter, and collimate the object beam. The first reflecting mirror adjusts the collimated object beam direction to be parallel to the reference beam. Along the adjusted object beam path, a first microscope objective, a non-polarizing beam splitter, and an image acquisition device (preferably a CCD image sensor in this embodiment) are sequentially arranged. The mineral slice sample to be tested is arranged between the first reflecting mirror and the first microscope objective, near the front focal plane of the first microscope objective. Along the reference beam path, a second reflecting mirror, a second half-wave plate, and a second microscope objective are sequentially arranged. The second reflecting mirror adjusts the reference beam direction to be parallel to the object beam, the second half-wave plate adjusts the polarization direction of the reference light, and the second microscope objective matches the magnification and wavefront curvature of the object beam. The adjusted reference beam is then incident on the unpolarized beam splitter, where it is combined with the object beam that has passed through the mineral slice and the first microscope objective. The combined object beam and reference beam interfere at a small angle (off-axis interference angle) on the CCD photosensitive target surface, forming a digital hologram. The CCD is connected to a computer via an image acquisition card to record the hologram and transmit it to the computer for numerical reconstruction.

[0046] Specifically, the semiconductor laser emits a 635nm unpolarized collimated laser beam, eliminating the need for an additional beam expander and collimator system. Both the first and second microscope objectives are spherical wave objectives, ensuring that the plane light waves received by the microscope objectives are output as spherical light waves. The laser beam output from the semiconductor laser first passes through a polarizer to convert it into linearly polarized light, eliminating the adverse effects of the unpolarized components of the light source on interference contrast. Subsequently, the linearly polarized light passes through a first half-wave plate, adjusting its polarization direction to form a preset angle with the transmission or reflection axis of the polarizing beam splitter, thereby controlling the splitting ratio between the object beam and the reference beam. The polarizing beam splitter splits the incident light into two orthogonally linearly polarized beams: the transmitted object beam (polarization direction parallel to the incident plane) and the reflected reference beam (polarization direction perpendicular to the incident plane). The object beam undergoes spatial filtering and collimation through a pinhole mirror (usually composed of a microscope objective and a pinhole), eliminating high-frequency noise and expanding the beam aperture to accommodate the uneven thickness and low transmittance regions of the mineral slices. After collimation, the object beam is deflected by the first reflecting mirror and transmitted perpendicularly or nearly perpendicularly through the mineral slice sample. It is then magnified by the first microscope objective and enters the unpolarized beam splitter as a spherical wave (object beam). The reference beam is deflected by the second reflecting mirror and passes sequentially through the second half-wave plate and the second microscope objective. It then enters the unpolarized beam splitter as a spherical wave (reference beam) through the second microscope objective. The second half-wave plate rotates the polarization direction of the reference beam to be the same as that of the object beam, ensuring that both beams have the same polarization state, thus obtaining high-contrast interference fringes. The parameters of the second microscope objective are matched with those of the first microscope objective to ensure that the wavefront curvature of the reference beam matches that of the object beam, avoiding the introduction of additional phase distortion. The object beam and reference beam are combined within the unpolarized beam splitter and exit at an off-axis angle, forming an off-axis hologram on the CCD recording surface. The off-axis angle is determined by the CCD sampling interval, preferably between 3-5°; and the pixel size of the image acquisition device is preferably 3.45 × 3.45 μm. 2 The overall off-axis design separates the zero-order terms from the positive and negative first-order terms in the spectrum, making it easy to achieve phase recovery with a single hologram, which is extremely suitable for dynamic or static quantitative analysis of mineral slices.

[0047] Through the above optical path design, this system can form stable interference fringes on the recording surface for mineral slices with low transmittance and complex optical properties, and can provide high-contrast, low-noise, and polarization-controllable holographic recording for mineral samples with low transmittance.

[0048] Example 2:

[0049] The system based on Example 1 can obtain a holographic record of the mineral slice to be tested. Based on this, the complete analysis of the mineral slice includes the following steps:

[0050] S1. Place the mineral slice to be tested in a dual-spherical off-axis digital holographic microscope system and record the hologram;

[0051] S2. Holographic imaging and reconstruction yield amplitude transmittance distribution and phase transmittance distribution.

[0052] S3. Quantitative mineral parameter inversion: Based on the obtained phase distribution and combined with the relationship between the thickness and refractive index of the mineral slice, the thickness distribution or refractive index distribution of the mineral slice is calculated by inversion, so as to realize the quantitative characterization of mineral composition.

[0053] In step S1, the mineral slice to be tested needs to be selected from ore blanks with uniform texture and no obvious cracks. The slices are coarsely ground into a preset thickness by diamond cutting, and then finely polished by coarse and fine abrasive grinding and polishing paste to remove cutting marks and scratches. Finally, the slices are cleaned and dried with anhydrous ethanol, and the thickness uniformity and flatness are checked before use.

[0054] When using the system provided in Embodiment 1, the object-reference light intensity ratio can be adjusted by a polarization ratio adjuster composed of a first half-wave plate and a polarizing beam splitter. Since all polarization components of the light wave incident on the polarizing beam splitter are reflected, it can be approximated that all polarization components are transmitted. Rotating the first half-wave plate changes the polarization direction of the linearly polarized light wave between the first half-wave plate and the polarizing beam splitter, thereby adjusting the intensity ratio of the object beam and the reference beam on the recording plane. The second half-wave plate is used to adjust the polarization direction of the reference beam on the recording plane. The polarization orientation of the light wave between the polarizing beam splitter and the second half-wave plate is approximately horizontal; rotating the second half-wave plate directly adjusts the polarization direction of the reference beam on the recording plane. Finally, a single frame of off-axis digital hologram is recorded using an image acquisition device (such as a CCD image sensor).

[0055] Specifically, after step S1, step S11 is required: calibrate the hologram using a checkerboard pattern and calculate the actual magnification.

[0056] In a dual-spherical off-axis digital holographic microscope system, the reference beam is blocked in the optical path, allowing only the object beam to pass through the system. A checkerboard target of known physical size is placed on the system's clear imaging plane, ensuring its image is clearly focused on the image acquisition unit. The intensity distribution image of the checkerboard target is recorded by the image acquisition unit. Based on the number of pixels occupied by each square in the recorded checkerboard image, combined with the known actual physical width of the checkerboard squares and the physical size of a single pixel in the image acquisition unit, the actual magnification of the system is calculated. This magnification serves as a benchmark for subsequent spatial size calibration of the reconstructed image, providing a reliable basis for obtaining sample amplitude and phase distribution information. For example, if a pore is found on a mineral slice, calculating the actual size of the pore using the magnification is more accurate than calculating it directly based on pixel size. The formula is expressed as follows:

[0057] M=(N×∆x) / W(1)

[0058] In the formula, W represents the actual physical width of a single square in the chessboard, N represents the number of pixels occupied by that square in the recorded image, ∆x represents the physical size of a single pixel of the image acquisition unit, and M represents the actual magnification of the system.

[0059] In specific step S3, holographic imaging and reconstruction also include the following steps:

[0060] S21, Spectrum separation and complex amplitude reconstruction; S22, Adaptive focusing reconstruction; S23, Amplitude information extraction; and S24, Phase information extraction.

[0061] In step S21, a two-dimensional Fourier transform is performed on the hologram to obtain the spectral distribution. The spectral term carrying sample information is extracted and shifted to the center of the spectrum to remove the spatial carrier. An inverse Fourier transform is then performed to obtain the complex amplitude distribution U(x,y) of the object wave on the recording plane. The complex amplitude distribution of the object wave obtained in this step contains the amplitude and phase information of the mineral slice.

[0062] In S22, since the thickness distribution of the mineral slice sample is unknown and the precise image plane position is difficult to determine directly, a diffraction propagation algorithm (such as angular spectrum diffraction propagation algorithm, Fresnel diffraction integral method, etc.) is used to propagate the complex amplitude distribution value of the recording plane to the clear imaging plane to obtain the focused complex amplitude distribution.

[0063] In S23, the amplitude transmittance distribution of the reconstructed mineral slice can be obtained by taking the modulus of the complex amplitude distribution of the focused light field. The amplitude transmittance distribution reflects the light absorption and scattering characteristics of the mineral slice. The reconstruction formula is as follows:

[0064] (2)

[0065] in, This represents the reconstructed sample amplitude transmittance distribution.

[0066] In step S24, phase information is extracted from the complex amplitude distribution in step S2. After phase unwrapping and distortion compensation processing, the true phase transmittance distribution of the mineral slice is obtained.

[0067] Specifically, the recorded complex amplitude distribution of the light field is proportional to or equal to the complex amplitude transmittance distribution of the sample light field, i.e., U(x,y)∝U0(x0,y0). The arctangent of the imaginary part of the complex amplitude distribution U(x,y) divided by the real part yields the reconstructed sample phase transmittance distribution, including phase wrapping and distortion. The calculation process is expressed by the following formula:

[0068] (3)

[0069] Where Im() and Re() represent taking the imaginary and real parts of the complex distribution, respectively. This represents the phase transmittance distribution of the sample.

[0070] After obtaining the sample's phase transmittance distribution, it is unwrapped using traditional phase image unwrapping methods (such as path-tracking unwrapping algorithms and unwrapping algorithms based on solving the minimum norm). Phase distortion compensation methods (such as the least squares method) are then used to compensate for the phase transmittance distribution of the mineral slices. The distortion is mainly low-order, such as first-order and second-order phase distortion, which exists as low-frequency information in the reconstructed image. Therefore, by fitting the distortion surface and subtracting the fitted surface from the distorted phase distribution, the true sample phase transmittance distribution reconstructed based on the fundamental principles of off-axis holographic imaging and digital image processing can be obtained. After unwrapping the phase and compensating for distortion, the reconstructed phase distribution is finally obtained.

[0071] Meanwhile, to achieve a more intuitive analysis of mineral morphology and composition, the phase information can be used to uniquely characterize the refractive index distribution of the mineral itself by fixing the thickness of the mineral slice, thereby inverting the main components of the mineral slice.

[0072] Furthermore, to visually represent the phase distribution characteristics within a mineral, conventional three-dimensional topological mapping can be performed on the phase field.

[0073] In step S3, when the thickness of the mineral slice is known, the refractive index distribution is inverted from the phase distribution to characterize the mineral composition; and when the mineral composition is uniform, the thickness distribution is inverted from the phase distribution to characterize the mineral morphology.

[0074] Experimental Example 1:

[0075] This experimental example uses Helan stone ore.

[0076] S1. Place the Helan stone ore slice in a dual-spherical off-axis digital holographic microscope system. The objective beam passes through the area of ​​the Helan stone sample to be recorded. The CCD photosensitive target surface records the hologram, which is then transferred to the computer for storage and numerical reconstruction, completing the holographic recording. The off-axis angle is selected as 4.0654°. The resulting off-axis digital hologram is shown below. Figure 3 As shown.

[0077] S11, perform checkerboard calibration on the holographic record and calculate the actual magnification of the system, such as... Figure 4 As shown, the checkerboard target used has a single square of 0.1 mm, and each square occupies 713 pixels. The image acquisition device uses a CCD sensor with a pixel size of 3.45 × 3.45 μm. 2 The actual magnification of the off-axis digital holographic imaging system with a magnification of 40x can be calculated using equation (1) to be 25x.

[0078] S2, Holographic Imaging and Reconstruction: S21, Perform a two-dimensional Fourier transform on the acquired hologram to obtain its spectral distribution, such as... Figure 5 As shown; the spectrum of the signal term or conjugate term is truncated with an appropriate filtering range, and then the truncated spectrum is moved to the center of the spectrum, as shown. Figure 6 As shown, the high-frequency spatial carrier contained in this item can be removed, and then a two-dimensional inverse Fourier transform can be performed to obtain the complex amplitude distribution of the object light wave on the recording plane.

[0079] S22 uses an angular spectrum propagation algorithm to propagate the reconstructed complex amplitude distribution to the clear imaging location.

[0080] S23, by taking the modulus of the obtained complex amplitude distribution of the light field, the reconstructed amplitude transmittance distribution of the Helan stone slice can be obtained. The amplitude transmittance distribution is as follows: Figure 7 As shown.

[0081] S24, the reconstructed phase distribution map containing wrapping and distortion obtained through equations (2) and (3), as shown in... Figure 8 As shown, for the conversion Figure 8 The conversion at the middle dashed line is as follows: Figure 9 The phase curve shown includes encapsulation and distortion, from Figure 9 It is clear that the phase is confined to between -π and π, failing to display the true thickness and refractive index distribution. Phase distortion compensation is achieved using the least squares method. Since the distortion in the off-axis holographic reconstruction phase distribution is mainly low-order distortion, such as first-order and second-order phase distortion, it exists in the reconstructed image as low-frequency information. Therefore, by fitting the distortion surface and subtracting the fitted surface from the distorted phase distribution, a reconstructed phase distribution map containing no phase distortion is obtained, as shown below. Figure 10 As shown, the position of the dashed line remains unchanged, and the corresponding phase curve is as follows. Figure 11 As shown. Subsequently, the path-tracking unwrapping algorithm was used to finally obtain the phase transmittance distribution of the real Helan stone slice reconstructed based on the fundamental principles of off-axis holographic imaging and digital image processing, as shown. Figure 12 As shown, the reconstructed phase distribution curve of the Helan stone slice after removing phase wrapping and distortion is... Figure 13 As shown. From Figure 13 As can be clearly seen, the method described in the above embodiments can yield a clear phase transmittance distribution of the Helan stone slice.

[0082] A three-dimensional topological mapping was performed on the phase field, and the result is as follows: Figure 11 As shown.

[0083] S3. Based on the obtained phase distribution, combined with the relationship between the thickness and refractive index of the mineral slice, the thickness distribution or refractive index distribution of the mineral slice is calculated by inversion, so as to realize the quantitative characterization of mineral composition.

[0084] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of protection claimed by the present invention.

Claims

1. A mineral section analysis system for an off-axis digital holographic microscope, characterized in that, Including semiconductor lasers; A polarizer, a first half-wave plate, and a polarizing beam splitter are sequentially arranged along the output optical path of the semiconductor laser. The polarizing beam splitter splits the incident light into an object beam and a reference beam. The components arranged sequentially along the propagation direction of the object beam are a pinhole mirror, a first reflecting mirror, a first microscope objective, a non-polarizing beam splitter, and an image acquisition device connected to a computer for communication. A second reflecting mirror, a second half-wave plate, and a second microscope objective are sequentially arranged along the propagation direction of the reference beam. The light emitted from the second microscope objective is incident on the unpolarized beam splitter. The unpolarized beam splitter combines the object beam and the reference beam and then emits the beam to the image acquisition device. The mineral slice sample to be tested is placed between the first reflecting mirror and the first microscope objective.

2. The mineral section analysis system for an off-axis digital holographic microscope according to claim 1, characterized in that, Both the first and second microscope objectives are spherical wave objectives.

3. The mineral section analysis system for an off-axis digital holographic microscope according to claim 1, characterized in that, The polarizing beam splitter is configured such that the polarization direction of the transmitted object beam is parallel to the direction of the emitted light from the semiconductor laser, and the polarization direction of the reflected reference beam is perpendicular to the direction of the emitted light from the semiconductor laser.

4. A method for mineral section analysis using an off-axis digital holographic microscope, characterized in that, Includes the following steps: S1. Place the mineral slice in the system described in any one of claims 1 to 3 and record a hologram; S2. Holographic imaging and reconstruction yield amplitude transmittance distribution and phase transmittance distribution; S3. Based on the obtained phase distribution, and combined with the relationship between the thickness and refractive index of the mineral slice, the thickness distribution or refractive index distribution of the mineral slice is calculated by inversion.

5. The method according to claim 4, characterized in that, The step S1 is followed by step S11: using a checkerboard calibration system and calculating the actual magnification.

6. The method according to claim 4, characterized in that, The holographic imaging in step S2 includes the following steps: S21. Perform a two-dimensional Fourier transform on the hologram to obtain the spectral distribution, extract the spectral term carrying the sample information and shift it to the center of the spectrum, and then perform an inverse Fourier transform to obtain the complex amplitude distribution of the object light wave on the recording plane.

7. The method according to claim 6, characterized in that, Step S2 further includes: S22. The complex amplitude distribution values ​​of the recording plane are propagated to the clear imaging plane using a diffraction propagation algorithm to obtain the focused complex amplitude distribution.

8. The method according to claim 7, characterized in that, Step S2 further includes: taking a model of the complex amplitude distribution of the focused light field to obtain the amplitude transmittance distribution of the reconstructed mineral slice.

9. The method according to claim 7, characterized in that, Step S2 further includes: extracting phase information from the focused complex amplitude distribution, and obtaining the true phase transmittance distribution of the mineral slice through phase unwrapping and distortion compensation processing.

Images