CN108309245B - Phase compensation correction method and system for spectral domain optical coherence tomography - Google Patents

Phase compensation correction method and system for spectral domain optical coherence tomography Download PDF

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CN108309245B
CN108309245B CN201810154881.0A CN201810154881A CN108309245B CN 108309245 B CN108309245 B CN 108309245B CN 201810154881 A CN201810154881 A CN 201810154881A CN 108309245 B CN108309245 B CN 108309245B
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周红仙
王毅
马振鹤
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Northeastern University Qinhuangdao Branch
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Abstract

The invention discloses a phase compensation correction method and system for spectral domain optical coherence tomography. The compensation correction method comprises the following steps: acquiring a wrapped phase and an initial non-wrapped phase with larger noise of spectral domain optical coherence tomography; acquiring noise of the initial non-wrapped phase; judging whether the noise of the initial non-wrapped phase is larger than a set threshold value or not, if so, performing low-pass filtering noise reduction processing on the initial non-wrapped phase to obtain a noise-reduced non-wrapped phase; determining wrapping times according to the non-wrapping phase after noise reduction; if not, determining the wrapping times according to the initial non-wrapping phase; the unwrapped phase is determined to be less noisy. The method and the system of the invention have no boundary problem when phase compensation is carried out, and can eliminate the problems of +/-2 pi segmentation error and noise amplification introduced in the segmentation boundary by the current method.

Description

Phase compensation correction method and system for spectral domain optical coherence tomography
Technical Field
The invention relates to the field of phase detection, in particular to a phase compensation correction method and system for spectral domain optical coherence tomography.
Background
In recent years, QPI technology has attracted wide attention in surface contour imaging and cell imaging, and QPI can be used to realize label-free imaging of living cells to obtain three-dimensional size information of cells. Phase contrast microscopy and differential interference microscopy convert phase to intensity, and because phase and intensity are non-linear, these two techniques can only be used for qualitative phase imaging. Phase-shift interferometric imaging, digital holography, fourier phase microscopy and hilbert phase microscopy, developed in recent years, enable quantitative phase imaging with cellular nanometer precision. However, the phase imaging techniques all have the phase wrapping problem, the phase wrapping is the inherent problem of the interference technique, because the interference coupling term is a cosine function, the periodicity of the cosine function can not demodulate the real phase, only the main value part (namely the wrapped phase) located in [ -pi, pi ] can be given, and the difference between the wrapped phase and the real phase is integral multiple of 2 pi. At present, various numerical unwrapping methods are proposed, wherein the numerical unwrapping is to perform corresponding phase compensation on a demodulation result according to the continuity of a sample phase, but when the sample phase changes greatly or the noise is large, an error occurs in the numerical unwrapping, and when the phase difference between two adjacent points is larger than pi, the numerical unwrapping cannot recover the real phase.
Optical Coherence Tomography (OCT) based on low Coherence light interference provides a convenient phase computation method, i.e., phase-resolved OCT, which has the advantage of depth resolution and can be used for phase imaging of multilayer samples. With the development of frequency Domain OCT, particularly, with the development of Spectral Domain Optical Coherence Tomography (SDOCT) based on a spectrometer, the phase stability of the system is greatly improved, and the stability and accuracy of nanometer and sub-nanometer are realized, but similar to other interference methods, the SDOCT also has a phase wrapping problem.
Currently, various methods have been proposed to solve the phase wrapping problem of SDOCT. In the SDOCT, the unwrapping is performed by using a non-wrapped phase with large noise, i.e., a 2 pi segment is performed on the non-wrapped phase, the wrapping frequency is determined, and the wrapping phase with small noise is compensated in a segment manner, wherein the current wrapping frequency calculation formula is [ Floor ((θ)uw+π)/2π)]Floor () represents a rounding down calculation, θuwA non-wrapped phase with a large noise. The method is not limited by the fact that the phase difference between two adjacent points cannot be larger than pi. However, this fractional compensation method amplifies noise when the non-wrapped phase is segmented, when the non-wrapped phase is close to the segment boundary, i.e., θuwClose to (2K pi + pi), where K is an integer, due to the influence of noise, a segmentation error of ± 1 occurs, and accordingly, a compensation error of ± 2 pi occurs, and even with small noise, such a boundary segmentation error occurs, and the small noise is amplified to 2 pi, which causes a phase unwrapping error in the SDOCT.
Disclosure of Invention
The invention aims to provide a phase compensation correction method and a phase compensation correction system for spectral domain optical coherence tomography, so as to eliminate phase wrapping errors in SDOCT.
In order to achieve the purpose, the invention provides the following scheme:
a phase compensation correction method for spectral domain optical coherence tomography, the compensation correction method comprising:
acquiring a wrapping phase of spectral domain optical coherence tomography;
acquiring an initial non-wrapped phase of spectral domain optical coherence tomography;
acquiring noise of the initial non-wrapped phase;
judging whether the noise of the initial non-wrapped phase is larger than a set threshold value or not to obtain a first judgment result;
when the first judgment result shows that the noise of the initial non-wrapped phase is larger than a set threshold value, performing low-pass filtering noise reduction processing on the initial non-wrapped phase to obtain a noise-reduced non-wrapped phase;
using formulas
Figure BDA0001580977180000021
Determining the wrapping times a, wherein theta'uwRepresenting the de-noised unwrapped phase, θwRepresenting the wrapped phase, Round () representing the most recent rounding calculation;
when the first judgment result shows that the noise of the initial non-wrapped phase is not greater than a set threshold value, a formula is used
Figure BDA0001580977180000022
Determining a number of parcels a, where θuwRepresenting an initial non-wrapped phase;
determining unwrapped phase as θw+2aπ。
Optionally, the acquiring an initial non-wrapped phase of spectral domain optical coherence tomography specifically includes:
and obtaining an initial non-wrapping phase of the spectral domain optical coherence tomography by using a synthetic wavelength method or a spectral domain calculation method.
Optionally, the set threshold is pi.
A phase compensation correction system for spectral domain optical coherence tomography, the compensation correction system comprising:
the wrapping phase acquisition module is used for acquiring a wrapping phase of spectral domain optical coherence tomography;
the initial non-wrapped phase acquisition module is used for acquiring an initial non-wrapped phase of spectral domain optical coherence tomography;
the noise acquisition module of the initial non-wrapped phase is used for acquiring the noise of the initial non-wrapped phase;
the first judgment module is used for judging whether the noise of the initial non-wrapped phase is larger than a set threshold value or not to obtain a first judgment result;
the noise reduction processing module is used for performing low-pass filtering noise reduction processing on the initial non-wrapped phase to obtain a noise-reduced non-wrapped phase when the first judgment result shows that the noise of the initial non-wrapped phase is greater than a set threshold;
a wrapping number determination module for using a formula
Figure BDA0001580977180000031
Determining the wrapping times a, wherein theta'uwRepresenting the de-noised unwrapped phase, θwRepresenting the wrapped phase, Round () representing the most recent rounding calculation;
a wrapping number determining module, further configured to utilize a formula when the first determination result indicates that the noise of the initial non-wrapping phase is not greater than a set threshold
Figure BDA0001580977180000032
Determining a number of parcels a, where θuwRepresenting an initial non-wrapped phase;
an unwrapped phase determining module for determining an unwrapped phase as θw+2aπ。
Optionally, the initial non-wrapped phase obtaining module obtains the initial non-wrapped phase of the spectral domain optical coherence tomography by using a wavelength synthesis method or a spectral domain calculation method.
Optionally, the set threshold is pi.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention has no boundary problem when phase compensation is carried out, and can eliminate the problems of +/-2 pi segmentation error and noise amplification introduced into the segmentation boundary by the current method.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a phase compensation correction method for spectral domain optical coherence tomography according to the present invention;
FIG. 2 is a schematic diagram of a phase compensation correction system for spectral domain optical coherence tomography according to the present invention;
FIG. 3 is a diagram illustrating the relationship between optical path difference and phase in an embodiment;
FIG. 4 is a diagram of a wrapping phase in an embodiment;
FIG. 5 is a schematic diagram of an unwrapped phase in accordance with an embodiment;
FIG. 6 is a diagram illustrating phase compensation performed by a current 2 π segmentation-based method according to an embodiment;
FIG. 7 is a schematic diagram of phase compensation using the method of the present invention in an embodiment.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
FIG. 1 is a flow chart of a phase compensation correction method for spectral domain optical coherence tomography according to the present invention. As shown in fig. 1, the compensation correction method includes:
step 100: the wrapped phase of spectral domain optical coherence tomography is acquired. In the reflective SDOCT system, the interference spectrum collected by the spectrometer can be expressed as:
Figure BDA0001580977180000041
in formula (1), k is wavenumber, S (k) is the spectral intensity distribution function of the light source, IsAnd IrN is the reflection light intensity of the sample arm and the reference arm, N is the refractive index, m is an integer, Δ d is the resolution of the frequency domain of fourier transform, Δ d is 1/2N Δ kN, Δ k and N are the wave number sampling interval and the sampling number of the spectrum respectively, N Δ d is determined by the position of the extreme point of the fourier transform amplitude spectrum of formula (1), and the phase of the phase spectrum corresponding to the position of the extreme point of the amplitude spectrum is θ.
In equation (1), the distance d to be measured is expressed in two parts, d ═ m Δ d +, ═ θ/4 π kcn，kcFor the central wavenumber of the interference spectrum, Δ d is determined by the source bandwidth, usually a few microns, representing distances less than Δ d, with accuracies up to nanometers and sub-nanometers. The SDOCT uses two scales to express the depth, can realize the detection with wide range and high precision, but the wrapping phase theta of theta is obtained by Fourier transformationwIn the range of only [ - π, π]And thus the range is only [ - λ [ ]c/4,λc/4]Much smaller than Δ d, λcRepresenting the center wavelength of the spectrum.
Step 200: an initial unwrapped phase of spectral domain optical coherence tomography is acquired. And obtaining an initial non-wrapping phase of the spectral domain optical coherence tomography by using a synthetic wavelength method or a spectral domain calculation method. The initial unwrapped phase is θuw＝θc0+2a π + Δ θ', where θc0The true value of the phase principal value, a is an integer, i.e., the wrapping times, and Δ θ' is the noise of the initial unwrapped phase.
Step 100: fourier transformed wrapped phase θ according to equation (1)w＝θc0+ Δ θ, Δ θ is the noise that wraps the phase, Δ θ' is much larger than Δ θ. ThetauwAnd thetawSubtracting, because Δ θ' is much larger than Δ θ, neglecting Δ θ, yields
θuw-θw＝2aπ+Δθ'， (2)
As can be seen from equation (2), is represented by (θ'uw-θw) And the wrapping times a are calculated, so that the boundary problem does not occur.
Step 300: and acquiring the noise of the initial non-wrapped phase.
Step 400: and judging whether the noise of the initial non-wrapped phase is larger than a set threshold value, wherein the set threshold value is pi, and obtaining a first judgment result. If so, step 500 is performed, and if not, step 700 is performed.
Step 500: and carrying out low-pass filtering noise reduction treatment on the initial non-wrapped phase to obtain a noise-reduced non-wrapped phase.
Step 600: and determining the wrapping times according to the non-wrapping phase after noise reduction. Using formulas
Figure BDA0001580977180000051
Determining the wrapping times a, wherein theta'uwRepresenting the de-noised unwrapped phase, θwRepresenting the wrapped phase, Round () representing the most recent rounding calculation;
step 700: and determining the wrapping times according to the initial non-wrapping phase. Using formulas
Figure BDA0001580977180000061
Determining a number of parcels a, where θuwIndicating the initial unwrapped phase. Since the initial non-wrapped phase has a large noise, the wrapping times are calculated in step 600 or step 700, and then the wrapping phase θ is wrapped according to the wrapping timeswThe unwrapped phase noise resulting from the compensation correction is small.
Step 800: determining unwrapped phase as θw+2aπ
FIG. 2 is a schematic structural diagram of a phase compensation correction system for spectral domain optical coherence tomography according to the present invention. As shown in fig. 2, the compensation correction system includes:
a wrapped phase acquisition module 201, configured to acquire a wrapped phase of spectral domain optical coherence tomography;
initial unwrapped phaseAn acquisition module 202 for acquiring an initial unwrapped phase of spectral domain optical coherence tomography. The initial unwrapped phase acquisition module 202 obtains the initial unwrapped phase of the spectral domain optical coherence tomography using a wavelength synthesis method or a spectral domain calculation method. The initial unwrapped phase is θuw＝θc0+2a π + Δ θ', where θc0Wrapping the phase as theta for the true value of the phase principal valuew＝θc0+ Δ θ, Δ θ is the noise of the wrapped phase, and Δ θ' is the noise of the original unwrapped phase.
An initial non-wrapped phase noise obtaining module 203, configured to obtain noise of the initial non-wrapped phase;
a first determining module 204, configured to determine whether the noise of the initial non-wrapped phase is greater than a set threshold, where the set threshold is pi, and obtain a first determination result;
a denoising module 205, configured to perform low-pass filtering denoising on the initial non-wrapped phase to obtain a denoised non-wrapped phase when the first determination result indicates that the noise of the initial non-wrapped phase is greater than a set threshold;
a package number determination module 206 for utilizing the formula
Figure BDA0001580977180000062
Determining the wrapping times a, wherein theta'uwRepresenting the de-noised unwrapped phase, θwRepresenting the wrapped phase, Round () representing the most recent rounding calculation;
the wrapping number determining module 206 is further configured to utilize a formula when the first determination result indicates that the noise of the initial non-wrapping phase is not greater than a set threshold
Figure BDA0001580977180000063
Determining a number of parcels a, where θuwRepresenting an initial non-wrapped phase;
and an unwrapped phase determining module 207 for determining an unwrapped phase. Determining the wrapping times according to the initial non-wrapping phase with larger noise, and obtaining the unwrapping phase with low noise according to the determined wrapping timesθw+2aπ。
The following describes a specific embodiment of the present invention.
Fig. 3 is a diagram illustrating the relationship between the optical path difference and the phase in the embodiment, in which the abscissa represents the optical path difference between the reference arm and the detection arm, and the ordinate represents the corresponding phase.
Fig. 4 is a diagram of a wrapping phase in an embodiment. As shown in fig. 4, fourier transform is performed on the interference spectrum collected by the spectrometer to obtain the wrapped phase.
For the calculation of the non-wrapped phase, the current method is to calculate a non-wrapped phase with larger noise by using a wavelength synthesis method or a spectral domain method, and then correct the wrapped phase with smaller noise by using the non-wrapped phase with larger noise to obtain the non-wrapped phase with smaller noise. Assume that the unwrapped phase with the larger noise is θuwWith a small noise wrapped phase of thetawThen use the existing compensation method to pair thetauwPerforming 2 pi segmentation, with phase compensation amount of 2 pi [ Floor ((theta))uw+π)/2π)]Floor () represents a round-down calculation. However, when the phase of the synthesized wavelength is close to the boundary of the 2 pi segment, an error of ± 1 occurs in the order of the segment due to the influence of noise, an error of ± 2 pi occurs in the correction for a single wavelength, and even a small noise may cause such an error of the segment to occur.
In order to solve the error problem of segmented unwrapping, the method firstly subtracts a main value part from a non-wrapped phase, and then calculates wrapping times so as to eliminate boundary segmentation errors. The measured wrapped phase may be expressed as θw＝θc0+Δθ，θc0Δ θ represents the noise, which is the true value of the phase principal value.
Measured non-wrapped phase θuwCan be expressed as:
θuw＝θc0+2aπ+Δθ′， (3)
in equation (3), a is an integer, i.e., the wrapping number, Δ θ 'is noise, and since Δ θ' is much larger than Δ θ (the unwrapped phase θ is therefore larger than Δ θ)uwCan only be used for calculating the wrapping times and has less noise on the wrapping phase thetawPerforming phase compensation). ThetauwAnd thetawSubtracting, because Δ θ' is much larger than Δ θ, ignoring Δ θ, yields,
θuw-θw＝2aπ+Δθ′， (4)
as can be seen from equation (4), using θuw-θwThe wrapping times a are calculated, no boundary problem occurs, and therefore, the low-noise unwrapping phase thetauwCan be expressed as:
Figure BDA0001580977180000071
in formula (5), Round () represents the most recent rounding calculation. As can be seen from the formulas (4) and (5), the compensation method has no boundary problem, is only influenced by the noise delta theta ', and only leads to the calculation error of the wrapping times a when the absolute value delta theta' | is larger than pi, and when the noise is too large, the theta needs to be firstly calculateduwFiltering and denoising to obtain denoised theta'uw。
For high noise non-wrapped phase thetauwCarrying out low-pass filtering noise reduction pretreatment;
from theta 'after noise reduction pretreatment'uwCalculating the wrapping times, for the wrapping phase theta with less noisewPerforming phase compensation according to the formula
Figure BDA0001580977180000081
The wrapping times a are obtained by calculation, and the unwrapping phase of the low noise is thetaw+2aπ。
Compared with the existing phase unwrapping method, the method has the following advantages: the invention has no boundary problem when phase compensation is carried out, and can eliminate the problems of +/-2 pi segmentation error and noise amplification introduced into the segmentation boundary by the current method.
FIG. 5 is a schematic diagram of a non-wrapped phase in an embodiment, wherein the upper and lower curves respectively show the non-wrapped phase θ in the embodimentuwAnd wrapped phase thetawSchematic illustration of。
FIG. 6 is a schematic diagram of phase compensation performed by the current 2 π segmentation method according to the present embodiment, wherein the upper curve is a phase compensated by the current 2 π segmentation method, and the lower curve is a wrapped phase θwSchematic representation of (a). In comparison with fig. 5, it can be seen that there is a significant ± 2 pi compensation error at the boundary of the 2 pi segment.
FIG. 7 is a schematic diagram of phase compensation using the method of the present invention in an embodiment, where the upper curve is the phase compensated using the method of the present invention, and the lower curve is the wrapped phase θwSchematic representation of (a). In comparison to FIG. 5, it can be seen that the wrapped phase θ is made using the method of the present applicationwCorrect compensation is obtained, the boundary problem does not exist, and the problems of +/-2 pi segmentation errors and noise amplification introduced into the segmentation boundary by the conventional method can be solved.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (2)

1. A phase compensation correction method for spectral domain optical coherence tomography, the compensation correction method comprising:
acquiring a wrapping phase of spectral domain optical coherence tomography;
acquiring an initial non-wrapped phase of spectral domain optical coherence tomography;
acquiring noise of the initial non-wrapped phase;
judging whether the noise of the initial non-wrapped phase is larger than a set threshold value or not to obtain a first judgment result;
when the first judgment result shows that the noise of the initial non-wrapped phase is larger than a set threshold value, performing low-pass filtering noise reduction processing on the initial non-wrapped phase to obtain a noise-reduced non-wrapped phase;
using formulas
Figure FDA0002637475170000011
Determining the wrapping times a, wherein theta'uwRepresenting the de-noised unwrapped phase, θwRepresenting the wrapped phase, Round () representing the most recent rounding calculation;
when the first judgment result shows that the noise of the initial non-wrapped phase is not greater than a set threshold value, a formula is used
Figure FDA0002637475170000012
Determining a number of parcels a, where θuwRepresenting an initial non-wrapped phase;
determining unwrapped phase as θw+2aπ；
The acquiring of the initial non-wrapped phase of the spectral domain optical coherence tomography specifically includes:
obtaining an initial non-wrapping phase of the spectral domain optical coherence tomography by using a synthetic wavelength method or a spectral domain calculation method;
the set threshold is pi.
2. A phase compensation correction system for spectral domain optical coherence tomography, the compensation correction system comprising:
the wrapping phase acquisition module is used for acquiring a wrapping phase of spectral domain optical coherence tomography;
the initial non-wrapped phase acquisition module is used for acquiring an initial non-wrapped phase of spectral domain optical coherence tomography;
the noise acquisition module of the initial non-wrapped phase is used for acquiring the noise of the initial non-wrapped phase;
the first judgment module is used for judging whether the noise of the initial non-wrapped phase is larger than a set threshold value or not to obtain a first judgment result;
the noise reduction processing module is used for performing low-pass filtering noise reduction processing on the initial non-wrapped phase to obtain a noise-reduced non-wrapped phase when the first judgment result shows that the noise of the initial non-wrapped phase is greater than a set threshold;
a wrapping number determination module for using a formula
Figure FDA0002637475170000021
Determining the wrapping times a, wherein theta'uwRepresenting the de-noised unwrapped phase, θwRepresenting the wrapped phase, Round () representing the most recent rounding calculation;
a wrapping number determining module, further configured to utilize a formula when the first determination result indicates that the noise of the initial non-wrapping phase is not greater than a set threshold
Figure FDA0002637475170000022
Determining a number of parcels a, where θuwRepresenting an initial non-wrapped phase;
an unwrapped phase determining module for determining an unwrapped phase as θw+2aπ；
The initial non-wrapped phase acquisition module acquires an initial non-wrapped phase of the spectral domain optical coherence tomography by using a wavelength synthesis method or a spectral domain calculation method;
the set threshold is pi.
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CN105939652A (en) * 2014-02-04 2016-09-14 南加利福尼亚大学 Optical coherence tomography (OCT) system with phase-sensitive B-scan registration
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