CN110017776B - Holographic aberration absolute calibration method and system based on shift and polynomial fitting - Google Patents
Holographic aberration absolute calibration method and system based on shift and polynomial fitting Download PDFInfo
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Abstract
The invention relates to a holographic aberration absolute calibration method and a system based on shift and polynomial fitting, belonging to the field of optical measurement and comprising the following steps: after the first hologram is collected, orthogonally moving the sample twice and respectively capturing to obtain three holograms; adjusting the phase of the hologram to obtain three original phase results; performing coordinate transformation on the result to enable the phases of the transformed test objects to be consistent; differential calculation is carried out to obtain phase difference data of the system aberration phase before and after two displacements; calculating Chebyshev polynomial coefficients so as to calculate the system aberration phase; and subtracting the system aberration phase from the obtained original phase result containing the aberration to obtain the phase of the test object. The invention can effectively protect the medium-high frequency information of an object phase, has low requirement on the arrangement of an optical path, and can carry out system aberration compensation on any traditional digital holographic microscope imaging system by only adding an additional three-axis displacement platform.
Description
Technical Field
The invention relates to a digital holographic microscope aberration absolute calibration method and system based on sequential shift and Chebyshev polynomial fitting, and belongs to the technical field of optical measurement.
Background
Digital holographic microscopy is a non-destructive, label-free and interferometric quantitative phase contrast technique that has great impact in many fields of biology, neuroscience, nanoparticle tracking, microfluidics and metrology. Like other conventional interference systems, digital holographic microscopy systems also suffer from system phase distortion, which is mainly introduced by aberrations of the microscope objective and other optical elements themselves and system setup errors. Typically, system phase aberrations are superimposed on the sample phase information, which needs to be compensated for.
Recently, many physical and numerical methods have been proposed to compensate or calibrate for system phase distortion. The use of a telecentric configuration or a tunable lens can introduce phase aberrations into the reference beam that will partially compensate for the low order phase aberrations. The double exposure method requires that the sample be removed from the reference beam in the second exposure and that the total aberration can be accurately compensated. The physical compensation method can well compensate aberration theoretically, but in practical application, the requirements on the accuracy and stability of an optical path are extremely high, so that the method is limited by errors among devices, and an ideal result cannot be obtained due to adjustment errors. In the numerical compensation method, the system phase aberration is described by a spherical function, a parabolic function and a Zernike polynomial. The least squares fit method and the principal component analysis method can be used to obtain the low order parameters of the standard polynomial. In the fitting method, the selection of the non-specimen region needs to be performed before the least square fitting, and the selection of the non-specimen region using the deep learning technique is proposed in recent literature. The phase aberration can also be extracted in a non-linear optimization process, where the phase change of the sample is the subject of optimization. Numerical compensation is an approximation method per se, and the optical path is not required to be too high. The calculation functions and algorithms used are different, the errors of the method are different, the method is applicable to the conditions, namely, the types of aberrations which can be eliminated by the method are different from the preconditions used by the method, even some methods can lose information, for example, the background is required to occupy a proportion which is far greater than that of a test sample by using a background fitting method, and the target object information is inevitably lost by using a filtering method to realize compensation.
In optical surface measurements, the widely used Fizeau and Twyman-Green interferometers use a common quality reference surface (λ/20Peak to Valley) as a test standard, and in order to obtain sub-nanometer scale measurements, the absolute test technique is one of the most important techniques for calibrating the reference surface deviations. Several absolute test methods for optical surface measurement have been proposed, such as the two-sphere method, the random sphere averaging method, and the shift-and-rotate method. In the shift-rotate absolute test method, the position of the reference surface is unchanged during the measurement, and the test surface is tested in both the shifted and rotated positions. Based on the measurement data of the shift and rotation positions, deviations of the test surface can be extracted. The calibration process of the reference surface deviation in the shift-rotation absolute test method provides a new digital holographic microscope absolute calibration possibility for us.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a digital holographic microscope aberration absolute calibration method and system based on sequential shift and Chebyshev polynomial fitting, which can effectively protect medium-high frequency information of an object phase and eliminate various low-order and high-order aberrations even for very complex aberrations.
The invention adopts the following technical scheme:
in one aspect, the invention provides a holographic aberration absolute calibration method based on shift and polynomial fitting, comprising the following steps:
(1) acquiring holograms, and obtaining three holograms containing the phase of a test object and the phase of system aberration by orthogonally moving a sample twice on a vertical plane of an optical axis and respectively capturing the holograms after acquiring a first hologram; the system aberrations include tilt aberrations caused by off-axis angles of off-axis holograms, and other aberrations introduced by imperfect coincidence of optical elements such as microscope objectives through which the reference and object light passes, including: low order and high order aberrations such as defocus, spherical aberration, astigmatism, etc.;
(2) respectively carrying out phase mediation on the three holograms obtained in the step (1), extracting + 1-level information of a frequency spectrum of the three holograms by a phase demodulation method based on Fourier transform, and extracting a phase of a test object from the + 1-level information to obtain three original phase results containing aberration; the original phase result comprises a system aberration phase and a test object phase, the system aberration phase components in the three original phase results are the same, and the test object phase component has corresponding micro displacement, wherein the +1 level information of the frequency spectrum refers to the component of the Fourier frequency spectrum of the hologram corresponding to the real image information of the object;
(3) performing coordinate transformation on the three original phase results containing the aberration obtained in the step (2), so that the phases of the three transformed phase results of the test objects are consistent after transformation, and the aberration phases of the system have micro displacement;
(4) performing differential calculation on the three phase results obtained in the step (3) to obtain phase difference data of the system aberration phase before and after two displacements;
(5) calculating the coefficient of the Chebyshev polynomial of the system aberration phase according to the Chebyshev polynomial and the movement amount corresponding to the displacement of two times of the two phase difference data obtained in the step (4), and bringing the coefficient of the Chebyshev polynomial into the Chebyshev polynomial to calculate the system aberration phase;
(6) and (3) subtracting the system aberration phase obtained in the step (5) from the original phase result containing the aberration obtained in the step (2) to obtain the phase of the test object.
Preferably, in step (2), the original phase result corresponding to the first hologram is as shown in formula (i):
T1(x,y)＝R(x,y)+O(x,y) (Ⅰ)
in formula (i), R (x, y) and O (x, y) are the system aberration phase and the test object phase, respectively, (x, y) are the horizontal and vertical position coordinates of a point on the image, respectively, wherein the system aberration phase R (x, y) can be expressed as shown in formula (ii):
in the formula (II), aiIs the coefficient of the Chebyshev polynomial, Ci(x, y) are terms of the chebyshev polynomial, and n is the number of terms of the chebyshev polynomial;
moving the sample and capturing the hologram for the first time on the vertical plane of the optical axis, wherein the moving direction is set as the x axis, the moving distance is Δ x, then moving the sample and capturing the hologram for the second time on the vertical plane of the optical axis along the y axis perpendicular to the x axis, the moving distance is Δ y, and the corresponding original phase result obtained by the step (2) is shown as the formula (III):
preferably, in the step (3), coordinate transformation is performed on the three original phase results obtained in the step (2), so that the phases of the test objects of the three transformed phase results become consistent, and there is a small displacement between the system aberration phases, as shown in formula (iv):
preferably, the difference calculation of the three phase results obtained in step (3) is performed in step (4), so as to obtain phase difference data Δ T of the system aberration phase before and after two displacements1And Δ T2As shown in formula (V):
in the formula (V), Δ Cix(x, y) and Δ Ciy(x, y) are the differentials of the chebyshev polynomial in the x and y directions, respectively, and equation (v) can be expressed in matrix form as:
CA＝ΔT (Ⅵ)
wherein C, A and Δ T are represented as:
A＝[a1 a2…an]T (Ⅷ)
ΔT＝
[ΔT1(1,1) ΔT1(1,2)…ΔT1(M,N) ΔT2(1,1) ΔT2(1,2)…ΔT2(M,N)]T (Ⅸ)
wherein M and N are the number of rows and columns of the digital hologram, solving equation (VI) to obtain coefficient a of Chebyshev polynomiali。
Preferably, the coefficient a of the chebyshev polynomialiSubstituting formula (II) to calculate the system aberration phase, and adopting the original phase result T containing aberration1And (x, y) subtracting the system aberration phase R (x, y) to obtain the phase of the test object.
In one aspect, the invention provides a system for implementing the digital holographic microscope aberration absolute calibration method based on sequential shift and chebyshev polynomial fitting, which comprises a three-axis displacement platform, wherein an object to be measured is positioned on the three-axis displacement platform.
For a standard digital holographic microscope optical path arrangement, the aberration compensation of the system can be carried out only by adding an additional three-axis displacement platform, and the compensation of any traditional digital holographic microscope optical system can be realized.
Preferably, the system further comprises a polarization laser, a first half-wave plate, a spatial filter and a polarization beam splitter prism which are sequentially arranged, light is divided into two paths after passing through the polarization beam splitter prism, one path is provided with a second half-wave plate, the light is reflected by a second reflecting mirror after passing through the second half-wave plate and then irradiates on the CCD detector through the non-polarization beam splitter prism, the other path is reflected by the first reflecting mirror and then irradiates on an object to be detected positioned on the three-axis displacement platform and irradiates on the CCD detector through the first microscope objective and the non-polarization beam splitter prism.
Further preferably, the polarized laser is a polarized helium-neon laser.
After the first hologram is collected, the sample is orthogonally moved twice on the vertical plane of the optical axis and the holograms are respectively captured, and the key point of the invention is to obtain the system aberration phase parameters of the Chebyshev polynomial from the three holograms, wherein the system aberration phase can be represented by a series of Chebyshev polynomials. The calculated system phase aberration is then subtracted from the phase distribution of the object wave to achieve quantitative phase imaging. The main advantage of this absolute calibration method is that it can effectively protect the medium and high frequency information of the object phase, eliminating various low and high order aberrations even for very complex aberrations.
The invention can realize the compensation of system aberration for any traditional digital holographic microscope optical system so as to obtain clear and accurate test object phase.
The present invention is not described in detail, and the prior art can be adopted.
The invention has the beneficial effects that:
1) compared with the prior art, the method calculates the system aberration phase from three specific holograms captured twice by orthogonally moving the sample on the vertical plane of the optical axis through the Chebyshev polynomial, thereby effectively realizing aberration compensation on the result and obtaining the correct phase of the test object.
2) The invention has low requirement on the light path setting of the experimental system, and can carry out system aberration compensation on any traditional digital holographic microscope experimental system by only adding an additional three-axis displacement platform.
3) The invention has better compensation effect on background aberration, can effectively protect medium-high frequency information of the phase of a tested object, and can simultaneously compensate various low-order and high-order aberrations of an experimental system even for very complex aberration instead of compensating only low-order oblique aberration and defocusing aberration.
Drawings
Fig. 1 is a schematic structural diagram of an implementation system of an absolute aberration calibration method for a digital holographic microscope based on sequential shift and chebyshev polynomial fitting according to an embodiment of the present invention, where 1, a polarized he-ne laser, 2, a first half-wave plate, 3, a spatial filter, 4, a polarized beam splitter prism, 5, a first reflector, 6, a test sample, 7, a first microscope objective, 8, a second half-wave plate, 9, a second reflector, 10, a second microscope objective, 11, an unpolarized beam splitter prism, 12, a three-axis shift stage, 13, and a CCD detector;
FIG. 2 is a flow chart of the absolute calibration method of aberration of a digital holographic microscope based on sequential shift and Chebyshev polynomial fitting according to the present invention;
FIG. 3 is a schematic diagram of orthogonal shift of a digital holographic microscopic aberration absolute calibration method based on sequential shift and Chebyshev polynomial fitting according to the present invention;
FIG. 4(a), FIG. 4(b), and FIG. 4(c) are three holograms collected by the present invention, respectively;
FIG. 5(a), FIG. 5(b), and FIG. 5(c) are the original phase results of the phase modulation of the three holograms in FIG. 3, respectively;
FIG. 6(a) is a system aberration phase result obtained by the method of the present invention;
FIG. 6(b) is a phase diagram of a test object obtained after aberration compensation according to the method of the present invention;
FIG. 7(a) is a phase diagram of a test object after aberration compensation in comparative example 1 using a conventional principal component analysis-based method;
FIG. 7(b) is a phase diagram of a test object after aberration compensation using the method of the present invention;
FIG. 8(a) is an enlarged view of the white frame mark portion in FIG. 7 (a);
FIG. 8(b) is an enlarged view of the white frame mark portion in FIG. 7 (b);
FIG. 9 is a cross-sectional outline comparison display of the solid white line in FIGS. 8(a) and 8 (b).
The specific implementation mode is as follows:
in order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific examples, but not limited thereto, and the present invention is not described in detail and is in accordance with the conventional techniques in the art.
Example 1:
a method for absolute calibration of aberration of a digital holographic microscope based on sequential shift and Chebyshev polynomial fitting can compensate system aberration of any conventional digital holographic microscope optical system to obtain clear and accurate phase of a test sample, as shown in FIG. 2, and comprises the following steps:
(1) collecting the holograms to obtain three holograms containing the phase of the test object and the system aberration, namely, after collecting the first hologram, orthogonally moving the sample twice on the vertical plane of the optical axis and respectively capturing the holograms; the system aberrations include tilt aberrations caused by off-axis angles of off-axis holograms, and other aberrations introduced by imperfect coincidence of optical elements such as microscope objectives through which the reference and object light passes, including: low order and high order aberrations such as defocus, spherical aberration, astigmatism, etc.;
(2) respectively carrying out phase demodulation on the three holograms obtained in the step (1), extracting + 1-level information of frequency spectrums of the three holograms by a phase demodulation method based on Fourier transform, and extracting phases of test objects from the + 1-level information to obtain original phase results containing aberrations, wherein system aberration phase components in the three original phase results are the same, and the phase components of the objects have corresponding micro displacement, wherein the + 1-level information of the frequency spectrums refers to components corresponding to real image information of the objects in the Fourier frequency spectrums of the holograms;
in step (2), the original phase result corresponding to the first hologram may be as shown in formula (i):
T1(x,y)＝R(x,y)+O(x,y) (Ⅰ)
in formula (I), R (x, y) and O (x, y) are the system aberration phase and the test sample phase, respectively, and (x, y) are the horizontal and vertical position coordinates of a point on the image, respectively. Wherein the system aberration phase R (x, y) can be represented as shown in formula (II):
in the formula (II), aiIs the coefficient of the Chebyshev polynomial, Ci(x, y) are terms of the chebyshev polynomial, and n is the number of terms of the chebyshev polynomial;
moving the sample and capturing the hologram for the first time on the vertical plane of the optical axis, wherein the moving direction is set as x-axis, the moving distance is Δ x, then moving the sample and capturing the hologram for the second time on the vertical plane of the optical axis along the y-axis perpendicular to the x-axis, wherein the moving distance is Δ y, as shown in fig. 3, and the corresponding original phase result obtained by the step (2) is shown in formula (iii):
(3) and (3) carrying out coordinate transformation on the three original phase results obtained in the step (2), so that the phase components of the objects of the three transformed phase results become consistent, and the phase components of the system aberration have micro displacement, as shown in the formula (IV):
(4) for the three phase nodes obtained in the step (3)If the difference is calculated, phase difference data delta T of the system aberration before and after two displacements is obtained1And Δ T2As shown in formula (V):
in the formula (V), Δ Cix(x, y) and Δ Ciy(x, y) are the differentials of the chebyshev polynomial in the x and y directions, respectively, and equation (v) can be expressed in matrix form as:
CA＝ΔT (Ⅵ)
wherein C, A and Δ T are represented as:
A＝[a1 a2…an]T (Ⅷ)
ΔT＝
[ΔT1(1,1) ΔT1(1,2)…ΔT1(M,N) ΔT2(1,1) ΔT2(1,2)…ΔT2(M,N)]T (Ⅸ)
wherein M and N are the number of rows and columns of the digital hologram;
(5) solving the equation (VI) according to the two differential data obtained in the step (4) and the displacement corresponding to the Chebyshev polynomial and the 2 nd displacement, and obtaining the Chebyshev polynomial coefficient a of the system aberrationiThe system aberration R (x, y) of the digital holographic microscope can be calculated by substituting the coefficients into equation (II);
(6) and (3) the original phase result containing the system aberration obtained in the step (2) comprises the phase of the test object and the phase of the system aberration, and the phase of the test object is obtained by subtracting the phase of the system aberration obtained in the step (5) from the original phase result containing the system aberration.
In this embodiment, the acquired 3 holograms and the corresponding phase-demodulated original phase results are shown in fig. 4(a), 4(b), and 4(c) and fig. 5(a), 5(b), and 5(c), respectively, the obtained system aberration phase is shown in fig. 6(a), the aberration-compensated phase is shown in fig. 6(b), and in fig. 5 and 6, the abscissa and the ordinate are the position coordinates on the picture, respectively.
Example 2:
the system for realizing the digital holographic microscope aberration absolute calibration method based on sequential shift and Chebyshev polynomial fitting comprises a three-axis displacement platform, wherein an object to be measured is positioned on the three-axis displacement platform.
For a standard digital holographic microscope optical path arrangement, the aberration compensation of the system can be carried out only by adding an additional three-axis displacement platform, and the compensation of any traditional digital holographic microscope optical system can be realized.
Example 3:
the system also comprises a polarized helium-neon laser, a first half-wave plate, a spatial filter and a polarized beam splitter prism which are sequentially arranged, light is divided into two paths after passing through the polarized beam splitter prism, one path is provided with a second half-wave plate, the light is reflected by a second half-wave plate and then irradiates on a CCD detector through a non-polarized beam splitter prism, the other path irradiates on an object to be detected positioned on a three-axis displacement platform after being reflected by a first reflector, and the object to be detected irradiates on the CCD detector through a first microscope objective and the non-polarized beam splitter prism.
Comparative example 1:
a aberration compensation method based on principal component analysis, the method is as described in embodiment 1, and the difference is that only for the first hologram collected in step (1), the method of shifting the positive primary spectrum is directly used to eliminate the tilt aberration, and the method based on principal component analysis is used to eliminate the spherical aberration; the phase after aberration compensation is shown in fig. 7(a), the white frame marks in fig. 7(a) and 7(b) are shown in fig. 8(a) and 8(b) in an enlarged manner, fig. 9 is a cross-sectional outline contrast display diagram of the positions of the white solid lines in fig. 8(a) and 8(b), in fig. 9, the abscissa represents the coordinates of different positions along the white lines in fig. 8(a) and 8(b), and the ordinate represents the phase value.
As can be seen from a comparison of fig. 7(a), 7(b), 8(a), 8(b) and 9, the results of the conventional methods based on principal component analysis are relatively fuzzy, the contour lines thereof are smoother, and some peaks have smaller values or are merged with adjacent peaks. This illustrates that the method based on principal component analysis has a problem that may cause loss of sample detail phase information, which is mainly due to that the method based on principal component analysis extracts and compensates for aberrations by filtering in the frequency domain, which inevitably causes a little loss of sample detail phase information.
The absolute calibration method of aberration of a digital holographic microscope based on sequential shift and Chebyshev polynomial fitting of the present invention is to first separate the phase and aberration of an object by shifting a sample twice, and then calculate the aberration phase using the Chebyshev polynomial. Due to the superiority of the Chebyshev polynomial in representing the aberration of the square aperture, the absolute calibration method can better save the object information and provide a relatively clearer phase image result.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (6)
1. A holographic aberration absolute calibration method based on shift and polynomial fitting is characterized by comprising the following steps:
(1) acquiring holograms, and obtaining three holograms containing the phase of a test object and the phase of system aberration by orthogonally moving a sample twice on a vertical plane of an optical axis and respectively capturing the holograms after acquiring a first hologram;
(2) respectively carrying out phase mediation on the three holograms obtained in the step (1), extracting + 1-level information of a frequency spectrum of the three holograms by a phase demodulation method based on Fourier transform, and extracting a phase of a test object from the + 1-level information to obtain three original phase results containing aberration;
(3) performing coordinate transformation on the three original phase results containing the aberration obtained in the step (2), so that the phases of the three transformed phase results of the test objects are consistent after transformation, and the aberration phases of the system have micro displacement;
(4) performing differential calculation on the three phase results obtained in the step (3) to obtain phase difference data of the system aberration phase before and after two displacements;
(5) calculating the coefficient of the Chebyshev polynomial of the system aberration phase according to the Chebyshev polynomial and the movement amount corresponding to the displacement of two times of the two phase difference data obtained in the step (4), and bringing the coefficient of the Chebyshev polynomial into the Chebyshev polynomial to calculate the system aberration phase;
(6) and (3) subtracting the system aberration phase obtained in the step (5) from the original phase result containing the aberration obtained in the step (2) to obtain the phase of the test object.
2. The method for absolute calibration of holographic aberration based on shift and polynomial fitting according to claim 1, wherein in step (2), the original phase result corresponding to the first hologram is shown as formula (i):
T1(x,y)＝R(x,y)+O(x,y) (Ⅰ)
in formula (i), R (x, y) and O (x, y) are the system aberration phase and the test object phase, respectively, (x, y) are the horizontal and vertical position coordinates of a point on the image, respectively, wherein the system aberration phase R (x, y) is represented by formula (ii):
in the formula (II), aiIs the coefficient of the Chebyshev polynomial, Ci(x, y) are terms of the chebyshev polynomial, and n is the number of terms of the chebyshev polynomial;
moving the sample and capturing the hologram for the first time on the vertical plane of the optical axis, wherein the moving direction is set as the x axis, the moving distance is Δ x, then moving the sample and capturing the hologram for the second time on the vertical plane of the optical axis along the y axis perpendicular to the x axis, the moving distance is Δ y, and the corresponding original phase result obtained by the step (2) is shown as the formula (III):
3. the method for absolute calibration of holographic aberration based on shift and polynomial fitting according to claim 2, characterized in that in step (3), the three original phase results obtained in step (2) are coordinate transformed, so that the test object phases of the transformed three phase results become consistent, and there is a slight shift between the system aberration phases, as shown in formula (iv):
4. the method for absolute calibration of holographic aberration based on shift and polynomial fitting according to claim 3, characterized in that the difference calculation of the three phase results obtained in step (3) is performed in step (4) to obtain the phase difference data Δ T of the system aberration phase before and after two shifts1And Δ T2As shown in formula (V):
in the formula (V), Δ Cix(x, y) and Δ Ciy(x, y) are the differentials of the chebyshev polynomial in the x and y directions, respectively, and equation (v) can be expressed in matrix form as:
CA＝ΔT (Ⅵ)
wherein C, A and Δ T are represented as:
A＝[a1 a2 … an]T (Ⅷ)
ΔT＝[ΔT1(1,1) ΔT1(1,2) … ΔT1(M,N) ΔT2(1,1) ΔT2(1,2) … ΔT2(M,N)]T(Ⅸ)
wherein M and N are the number of rows and columns of the digital hologram, solving equation (VI) to obtain coefficient a of Chebyshev polynomiali。
5. The method of absolute calibration of holographic aberrations based on shift and polynomial fitting of claim 4, characterized in that the coefficients a of Chebyshev polynomials areiSubstituting formula (II) to calculate the system aberration phase, and adopting the original phase result T containing aberration1And (x, y) subtracting the system aberration phase R (x, y) to obtain the phase of the test object.
6. The system for implementing a holographic aberration absolute calibration method based on shift and polynomial fitting of claim 1, comprising a three-axis displacement platform on which the object to be measured is located.
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| Phase aberration compensation of digital holographic microscopy based on least squares surface fitting;Di Jianglei等;《Optics Communications》;20091231;第282卷(第19期);3873-3877 * |
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