CN118444545A - Automatic phase distortion removing method applied to digital holographic microscopy - Google Patents
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Abstract
The invention discloses an automatic phase distortion removing method, which is applied to digital holographic microscopy and relates to the field of computational imaging. In digital holographic microscopy, phase aberrations are typically caused by imperfect components of the optical system and by non-telecentric configurations, severely affecting the visualization and quantitative measurement of phase contrast imaging. To solve these problems, a purely numerical and automatic method is proposed to compensate for the phase distortion. Without a manual selection of samples without background, the compensation is modeled as a surface fitting problem, where the distorted surface is approximated by creating an inverse problem. By using the l1 norm as the loss function and minimizing an objective function, the distortion can be accurately fitted and eliminated numerically. Accurate estimation of the aberration surface is achieved and a high quality, aberration-free quantitative phase contrast image is recovered. The effectiveness of the method relative to the least square method is demonstrated by synthesis and experimental results.
Description
Technical Field
The invention belongs to the field of computational optics, and particularly relates to an automatic phase distortion removing method applied to digital holographic microscopy.
Background
Digital Holographic Microscopy (DHM) is a powerful technique that can measure microstructures such as MEMS circuits and biological samples in real time because it can record the entire wavefront of a three-dimensional scene in a non-invasive and label-free manner. By using a detector such as a CCD or CMOS, an interference pattern between the object wave and the reference wave is recorded and stored digitally. With two-dimensional holograms, the amplitude and quantitative phase distribution of an object can be reconstructed using appropriate algorithmic values, thereby being verified in applications such as tomography, three-dimensional imaging, and extended focus imaging. However, digital holographic microscopy presents a serious distortion problem in quantitative phase contrast imaging. In one aspect, the illumination of the object and reference beams onto the detector in an off-axis optical path produces constant tilt aberrations, resulting in a reconstructed phase tilt. On the other hand, if the Microscope Objective (MO) does not add additional components to form a telecentric arrangement, it is necessary to introduce a second phase distortion to the extracted phase. Furthermore, high order aberrations such as astigmatism and coma may also be present in the final image due to manufacturing imperfections of the system and alignment of the components. These aberrations present in the phase map not only distort the visual effect of the object, but also seriously hamper the quantitative measurement of the true thickness or height of the object.
In order to eliminate aberrations in the reconstructed phase map, various methods are proposed. In general, they can be divided into two groups: physical compensation of the optical recording stage and numerical compensation of the reconstruction stage. The former requires additional optical components or aberration cancellation by multiple recordings. For example, by adding a sleeve lens, a telecentric lens is formed to physically compensate for parabolic phase. Further, the tilt phase is deleted from the phase map by spatial filtering. The double exposure method in the multiple recording scheme can eliminate all aberrations, but must capture a second object-free reference hologram. In some cases, even two more holograms that move laterally have to be collected. Therefore, these methods are applicable only to static scenes. In summary, physical compensation strategies complicate and make holographic recording more cumbersome.
Numerical compensation methods are roughly based on fitting numerical methods involving the use of different polynomials, such as standard polynomials, digital phase masks and Zernike polynomials. By solving the least square problem or the phase change minimization problem, an aberration curved surface can be fitted and subtracted from the phase diagram, and finally, the pure object phase is obtained. Numerical methods have flexibility but still require manual selection of a flat area as a reference surface. Notably, the polynomial-based method is a semi-automatic method in that it requires background information to find a phase residual, which is detected by manually cropping flat background areas. Furthermore, manual filtering and centering operations are inevitably involved in spectrum-based analysis, or assumptions on thin phase objects, whereas self-hologram rotation is only applicable for tilt aberration compensation. Learning-based methods require a large amount of data and extensive computation to perform network training.
Thus, the conventional compensation method has disadvantages: 1. the recording light path is complex and more cumbersome; 2. the method is only suitable for static scenes; 3. manual selection and manipulation is required; 4. additional background information is required. Drawbacks of learning-based methods: 1. the data set construction cost is high; 2. the calculation cost is high; 3. there is a lack of interpretability. Aiming at the problems, an automatic removing method of the phase distortion, which meets the actual use scene and the requirements and has lower cost, is necessary.
Disclosure of Invention
The invention provides an automatic phase distortion removing method applied to digital holographic microscopy, which takes diffraction patterns under different diffraction distances as the input of a neural network. By formulating a surface fit as an inverse problem and by solving based onThe optimization of the norms allows accurate estimation of the aberration surface and then recovery of a high quality aberration-free quantitative phase difference image.
The specific technical scheme of the invention is as follows:
the automatic phase distortion removing method applied to digital holographic microscopy is characterized by comprising the following steps of:
S1, using a digital holographic microscopic imaging system to obtain an original holographic image, and assuming that the target phase is a small disturbance compared with the aberration;
S2, utilizing The norm loss function is combined with a least square method of a regularization technology to obtain aberration phi abe corresponding to the original holographic image;
S3, obtaining an unwrapped phase phi corresponding to the original hologram by using a reconstruction algorithm, and calculating the difference between the unwrapped phase and the aberration to obtain an object phase phi obj.
The digital holographic microscopic imaging system of the step S1 is a reflective off-axis Mach-Zehnder interferometer. The laser beam is split by a polarizing beam splitter and enters the interferometer along two paths. The reference beam directly enters the detector after passing through the reflector, and the other beam is focused on the sample through the microscope objective after being reflected, so that the sample is illuminated. The object beam reflected by the sample is then returned to the detector. The two beams interfere with each other to form a hologram.
The digital holographic microscopic imaging system design of the step S1 changes the polarization state cooperatively through a polarization beam splitter and two half-wave plates, thereby causing the interference of two light beams and the adjustment of the contrast of an interference pattern.
The sample phase of step S1 is far less than the aberration, and may specifically be a groove etched on an optical wafer and a microcircuit etched on a sapphire wafer.
A second order fitting model is used in said step S2, which can successfully compensate for common aberrations in digital holographic microscopy imaging, such as tilt, astigmatism and parabolic aberrations. If higher order aberrations need to be removed, the fitting model is extended to higher order fitting models. By means of a fitting model, its coefficients can be estimated, thus determining the aberrations.
The step S2 regards the solution of the aberration coefficient as an inverse problem, and uses a least square method for the solution. By means ofThe norm loss function minimizes the difference between the actual value and the model predicted value and incorporates additional information in conjunction with regularization techniques to prevent overfitting.
The reconstructing algorithm step of the step S3 specifically includes performing fourier transform on the original hologram to obtain a spectrum of the original hologram, extracting a spectrum of a +1-level image from the spectrum of the original hologram, performing inverse fourier transform to obtain a wrapped phase, and obtaining a corresponding unwrapped phase through a least square unwrapped algorithm.
The invention has the beneficial effects of providing an automatic removal method for phase distortion in digital holographic microscopy, which is applied to the actual use requirement of digital holographic microscopy. The method can recover a true object phase image for visualization and quantitative measurement by subtracting the estimated aberration plane from the original phase image. Simulation and experimental results verify the effectiveness of the method in quantitative relative imaging. No manual selection and manipulation and additional background information is required compared to conventional compensation methods. Compared with a data-driven neural network method, the method has the advantages that clear real phases are not required to be obtained for supervision and optimization, and the calculation cost is low.
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The accompanying drawings, which are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:
FIG. 1 is a flow chart of an automatic phase aberration removal method applied to digital holographic microscopy according to an embodiment of the present invention;
FIG. 2 is a synthetic object phase diagram in an embodiment of the invention, wherein subgraphs (a), (b), (c), and (d) are respectively phase diagrams of 256X 256 dimensions in two-dimensional and three-dimensional visualizations showing computer-generated on a planar background, aberration distortion phase resulting from the addition of the synthetic phase aberration, object phase, and aberration using the first 6 terms of the Zernike polynomial;
FIG. 3 is a comparison of the simulation results of the automatic phase aberration removing method and the conventional least square method according to the embodiment of the present invention, wherein the sub-graphs (a), (b), (c), (d), and (e) are respectively the compensation results of the automatic phase aberration removing method and the conventional least square method, and the comparison results of the corresponding error map and the phase profile on the center line;
FIG. 4 shows the compensation results of higher-order aberrations in the embodiment of the invention, wherein sub-graphs (a), (b), and (c) are respectively the compensation results of the automatic removal method of higher-order aberrations and phase distortions generated by simulation and the conventional least square method;
FIG. 5 is a schematic diagram of an experimental light path and a sample in an embodiment of the present invention, wherein subgraphs (a), (b), and (c) are respectively a digital holographic microscopic light path, a groove sample, and a microcircuit sample;
FIG. 6 shows experimental results of oblique aberration removal of a groove sample in the embodiment of the present invention, wherein subgraphs (a), (b), (c), (d), and (e) are respectively groove holograms, real groove phases obtained by different digital holographic microscopic optical paths, groove phases with oblique aberration, phase compensation results, and comparison results of phase profiles on diagonal lines;
FIG. 7 shows experimental results of tilt aberration removal of a microcircuit sample in an embodiment of the present invention, wherein the sub-graphs (a), (b), (c), (d), and (e) are respectively microcircuit holograms, real microcircuit phases obtained with different digital holographic microscopic optical paths, microcircuit phases with tilt aberration, phase compensation results, and comparison results of phase profiles on diagonal lines;
FIG. 8 shows experimental phase reconstruction results of secondary aberration removal of a groove sample in an embodiment of the present invention, wherein sub-graphs (a), (b), and (c) are respectively the groove phase with the secondary aberration, the phase compensation result, and the comparison result of the phase profile on the diagonal;
FIG. 9 shows experimental complex amplitude reconstruction results of secondary aberration removal of a groove sample in the embodiment of the present invention, wherein sub-graphs (a), (b), (c), and (d) are respectively groove amplitude reconstruction, groove phase with secondary aberration, phase compensation results, and comparison results of phase profiles on diagonal lines;
Fig. 10 shows experimental complex amplitude reconstruction results of secondary aberration removal of a microcircuit sample according to an embodiment of the present invention, wherein sub-graphs (a), (b), (c), and (d) are respectively the microcircuit amplitude reconstruction, the microcircuit phase with secondary aberration, the phase compensation result, and the comparison result of the phase profile on the diagonal.
Detailed Description
The present invention will be described in more detail with reference to the following examples and drawings, in order to make the objects, technical solutions and advantages of the present invention more apparent, and the exemplary embodiments of the present invention and the descriptions thereof are only for explaining the present invention and are not limited thereto.
The automatic phase distortion removing method applied to digital holographic microscopy is characterized by comprising the following steps of:
S1, using a digital holographic microscopic imaging system to obtain an original holographic image, and assuming that the target phase is a small disturbance compared with the aberration;
S2, utilizing The norm loss function is combined with a least square method of a regularization technology to obtain aberration phi abe corresponding to the original holographic image;
S3, obtaining an unwrapped phase phi corresponding to the original hologram by using a reconstruction algorithm, and calculating the difference between the unwrapped phase and the aberration to obtain an object phase phi obj.
The digital holographic microscopic imaging system of the step S1 is a reflective off-axis Mach-Zehnder interferometer. The laser beam is split by a polarizing beam splitter and enters the interferometer along two paths. The reference beam directly enters the detector after passing through the reflector, and the other beam is focused on the sample through the microscope objective after being reflected, so that the sample is illuminated. The object beam reflected by the sample is then returned to the detector. The two beams interfere with each other to form a hologram.
The digital holographic microscopic imaging system design of the step S1 changes the polarization state cooperatively through a polarization beam splitter and two half-wave plates, thereby causing the interference of two light beams and the adjustment of the contrast of an interference pattern.
The sample phase of step S1 is far less than the aberration, and may specifically be a groove etched on an optical wafer and a microcircuit etched on a sapphire wafer.
A second order fitting model is used in said step S2, which can successfully compensate for common aberrations in digital holographic microscopy imaging, such as tilt, astigmatism and parabolic aberrations. If higher order aberrations need to be removed, the fitting model is extended to higher order fitting models. By means of a fitting model, its coefficients can be estimated, thus determining the aberrations.
The step S2 regards the solution of the aberration coefficient as an inverse problem, and uses a least square method for the solution. By means ofThe norm loss function minimizes the difference between the actual value and the model predicted value and incorporates additional information in conjunction with regularization techniques to prevent overfitting.
The reconstructing algorithm step of the step S3 specifically includes performing fourier transform on the original hologram to obtain a spectrum of the original hologram, extracting a spectrum of a +1-level image from the spectrum of the original hologram, performing inverse fourier transform to obtain a wrapped phase, and obtaining a corresponding unwrapped phase through a least square unwrapped algorithm.
Example 1: the working flow of the automatic phase distortion removing method applied to digital holographic microscopy is as follows:
The observed object is imaged by a digital holographic microscopy imaging system to obtain a corresponding off-axis hologram, as described in step S1 of fig. 1.
As described in step S2 in fig. 1, the solution of the aberration coefficient is regarded as an inverse problem, and the solution is performed using the least square method. By means ofThe norm loss function minimizes the difference between the actual value and the model predicted value and incorporates additional information in conjunction with regularization techniques to prevent overfitting. The minimized objective function can be written as
Wherein A is a polynomial matrix corresponding to the fitting model,Representing the fitting coefficients of the theoretical fitting model estimates,Representing phase, |·| 1 representsNorm, λ is the regularization parameter.
A second order fitting model is used for the image difference produced in the digital holographic microscopy imaging system that can successfully compensate for common aberrations in digital holographic microscopy imaging, such as tilt, astigmatism, and parabolic aberrations. If higher order aberrations need to be removed, the fitting model is extended to higher order fitting models. By means of a fitting model, its coefficients can be estimated, thus determining the aberrations.
And (3) performing Fourier transform on the original hologram to obtain a frequency spectrum of the original hologram, extracting a frequency spectrum of a +1-level image from the frequency spectrum of the original hologram, performing inverse Fourier transform to obtain a wrapped phase, obtaining a corresponding unwrapped phase through a least square unwrapped algorithm, and calculating a difference between the unwrapped phase and the aberration to obtain an object phase phi obj.
The method according to the invention is implemented on a PC of 3.70GHz and 64GB RAM of Intel Xeon W-2145.
To further demonstrate the practical performance of the automatic phase aberration removal method of the present invention applied to digital holographic microscopy, first the object phase is synthesized, and fig. 2 (a) and fig. 2 (b) show computer-generated 256 x 256-dimensional phase diagrams on a planar background through two-dimensional and three-dimensional visualization, respectively. In fig. 2 (c), the first 6 terms of the Zernike polynomials are used to generate synthetic phase aberrations, resulting in oblique aberrations of the x-axis and y-axis, astigmatism of 0 ° and 45 °, and defocus. By adding the object phase and the aberration, an aberration distortion phase is obtained as shown in fig. 2 (d). The simulation verification results are shown in fig. 3. As can be seen from fig. 3, the automatic phase distortion removal method is based onThe optimization of the norm completely eliminates the aberration, the restored target phase is identical to the original target, and the traditional method gives an inaccurate compensation background. This can be further observed by quantitative comparison of the phase profile on the centerline. To illustrate the ability of the proposed method to remove higher order aberrations, we use the same phase object in fig. 2 (b) to generate higher order aberrations with the first 16 zernike terms, as shown in fig. 4 (a). Assuming that a fourth-order fitting model is adopted, based on the model, a model based onThe norm method and the least square method compensate. The results are shown in FIG. 4 (b) and FIG. 4 (c), respectively. It can be clearly seen that in this case, the conventional method works basically. However, the bottom plane is not flat and contains fluctuations, which will introduce errors in calculating the target phase. While the proposed method gives a fairly flat bottom plane and accurate compensation results. The comprehensive results intuitively illustrate the convenience of generalizing the method to higher order aberration compensation.
In summary, the actual performance of the automatic phase distortion removing method applied to digital holographic microscopy provided by the invention can be realized by only acquiring a single off-axis hologram of a corresponding sample under the application scene of imaging an observation target by a digital holographic microscopy imaging system, and calculating the phase difference phi abe and the unwrapped phase phi through the algorithm and the reconstruction algorithm respectively, and calculating the difference between the unwrapped phase and the aberration to obtain the object phase phi obj. Experiments prove that the method can remove two kinds of aberration common in DHM, namely oblique aberration and secondary aberration. The method provided by the invention has stable effect in simulation and experiment. By subtracting the estimated aberration plane from the original phase image, the true object phase image can be restored for visualization and quantitative measurement.
Claims (7)
1. The automatic phase distortion removing method applied to digital holographic microscopy is characterized by comprising the following steps of:
S1, using a digital holographic microscopic imaging system to obtain an original holographic image, and assuming that the target phase is a small disturbance compared with the aberration;
S2, utilizing The norm loss function is combined with a least square method of a regularization technology to obtain aberration phi abe corresponding to the original holographic image;
S3, obtaining an unwrapped phase phi corresponding to the original hologram by using a reconstruction algorithm, and calculating the difference between the unwrapped phase and the aberration to obtain an object phase phi obj.
2. The method according to claim 1, wherein the digital holographic microscopy imaging system of step S1 is a reflective off-axis Mach-Zehnder interferometer. The laser beam is split by a polarizing beam splitter and enters the interferometer along two paths. The reference beam directly enters the detector after passing through the reflector, and the other beam is focused on the sample through the microscope objective after being reflected, so that the sample is illuminated. The object beam reflected by the sample is then returned to the detector. The two beams interfere with each other to form a hologram.
3. The method according to claim 1, wherein the digital holographic microscopy imaging system of step S1 is configured to cooperatively change the polarization state by means of a polarization beam splitter and two half-wave plates, thereby resulting in interference of the two beams and adjustment of contrast of the interferogram.
4. The method according to claim 1, wherein the sample phase of step S1 is much smaller than the aberration, specifically the grooves etched on the optical wafer and the microcircuits etched on the sapphire wafer.
5. An automatic phase aberration removing method according to claim 1, wherein in step S2, a second order fitting model is used, which successfully compensates for common aberrations in digital holographic microscopy imaging, such as tilt, astigmatism and parabolic aberrations. If higher order aberrations need to be removed, the fitting model is extended to higher order fitting models. By means of a fitting model, its coefficients can be estimated, thus determining the aberrations.
6. The method according to claim 1, wherein the step S2 regards the solution of the aberration coefficients as an inverse problem, and uses a least square method for the solution. By means ofThe norm loss function minimizes the difference between the actual value and the model predicted value and incorporates additional information in conjunction with regularization techniques to prevent overfitting.
7. The method for automatically removing phase distortion in digital holographic microscopy according to claim 1, wherein the step of the reconstruction algorithm in step S3 specifically comprises performing fourier transform on the original hologram to obtain a spectrum of the original hologram, extracting a spectrum of a +1 level image from the spectrum of the original hologram, performing inverse fourier transform to obtain a wrapped phase, and obtaining a corresponding unwrapped phase through a least square unwrapped algorithm.
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