CN115046469B - Interference fringe envelope extraction method for optical fiber white light interference - Google Patents
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Abstract
The invention discloses an interference fringe envelope extraction method for optical fiber white light interference, which takes interference fringe signals obtained by a white light interference system through low coherence interferometry as a research object to deeply analyze the characteristics and principles of white light interference, and provides an improved envelope peak value extraction algorithm by combining a full width half maximum method, a phase shift method and a Hilbert transform method. The algorithm processes the positioning process of the interference zero-order fringes step by step, thereby not only ensuring the extraction precision of the interference envelope, but also greatly reducing the operation time of the algorithm and optimizing the overall performance of the optical fiber white light interference.
Description
Technical Field
The invention belongs to the technical field of optical detection, and particularly relates to an interference fringe envelope extraction method for optical fiber white light interference.
Background
The optical fiber white light technology is a non-contact and non-invasive imaging technology with micron-scale resolution, which uses the basic principle of a weak coherent light interferometer to detect the back reflection or several scattering signals of the tissue on the incident weak coherent light, and can obtain the two-dimensional or three-dimensional structural image of the tissue through scanning. White light interferometry has a resolution one to two orders of magnitude higher than other imaging techniques, such as ultrasound imaging, magnetic Resonance Imaging (MRI), X-ray Computed Tomography (CT), and so forth, and has found wide application in various fields, particularly in the field of three-dimensional contour measurement in recent years.
The white light interference signal usually presents a cosine curve with a central wavelength as a period, and the envelope amplitude is modulated by the spectral function of a broad spectrum light source, and is characterized by a main maximum, namely the peak value of the zero-order fringes of the interference pattern, corresponding to the zero optical path difference between the reference arm and the sample arm. The zero-order fringe position provides a reliable absolute position reference for the measurement from which the absolute value of the measured phase value (corresponding to the measured physical quantity) can be obtained. White light interferometry is performed by determining the zero path difference position of the acquired white light interferometry signal. In most cases, as noise exists in the white light interference fringes, certain distortion can occur to the signals, and the phase and the amplitude do not necessarily correspond completely during interference, only effective information of zero optical path points is difficult to extract from the characteristics of the interference fringes, so that the positioning of the zero optical path difference position can be converted into the positioning of the interference light intensity peak position, namely the extraction of interference envelope. Along with the application of the white light interference principle technology in the fields of three-dimensional morphology measurement, optical fiber sensing measurement and the like, a plurality of white light interference envelope processing methods are proposed, including a square filtering envelope method, a function fitting method, a Fourier transform method, a wavelet transform method, a Hilbert transform method, a sampling theorem envelope function evaluation method and the like, and the algorithms are thousands of times and mature gradually along with the time. However, although there are many methods for extracting an interference envelope in a white light interference application in the prior art, from the standpoint of the white light interference envelope extraction method alone, there is still a great improvement space in terms of algorithm accuracy, speed, processing efficiency and the like, and there is also a great improvement space in terms of achieving a balance between algorithm accuracy and speed.
Disclosure of Invention
The invention aims at an interference fringe envelope extraction method facing optical fiber white light interference.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: the embodiment of the invention provides an interference fringe envelope extraction method for optical fiber white light interference, which specifically comprises the following steps:
step 1: obtaining interference fringe signals of a sample to be tested through a white light interference system;
step 2: the half-height full-width method is adopted, and the position x of the zero-order stripe is positioned through the midpoint corresponding to the half-height full-width 1 ；
Step 3: solving the fringe contrast of the white light interference signal by adopting a phase shift method, judging the position and the phase of the maximum fringe contrast, and obtaining the interference signalZero optical path difference point position x 2 ；
Step 4: comparing the half-height full-width method coarse positioning position with the phase shift method to solve the zero optical path difference position, if two points are obtained
Judging that the white light phase shift method is accurate in positioning, finishing envelope extraction, and outputting the position of the interference zero-order stripe; otherwise, the position is considered to have errors or is a surface discontinuous point, and the position of the interference zero-order fringe is obtained after Hilbert transformation and filtering.
Further, the positions of the interference zero-order fringes obtained after Jing Xier Bert transformation and filtering are specifically as follows: solving white light interference signals by using Hilbert transform algorithm and repositioning maximum fringe contrast position x 3 The method comprises the steps of carrying out a first treatment on the surface of the Filtering the interference envelope obtained by the Hilbert transform solution, and compensating the time delay of the interference envelope; maximum stripe contrast position x obtained by Hilbert transform and post-filtering solution 4 And substituting the position of the maximum fringe contrast solved by the phase shift method into the position of the zero optical path difference calculated by the phase shift method, wherein the position of the zero optical path difference is the position of the interference zero-order fringe.
Further, the hilbert transform algorithm is replaced by a fourier transform method, a wavelet transform method, an extremum method or a function fitting method.
Further, the phase shift method is a Care phase shift method.
Further, the step 2 specifically includes: after the maximum value of the interference fringe is found, the point corresponding to the full width at half maximum is determined according to the amplitude value, then the position can be positioned to the midpoint of the connecting line of the two points corresponding to the full width at half maximum, and the position is taken as the zero-order fringe position x of coarse positioning 1 。
Further, the step 3 specifically includes:
the contrast of white light interference signal fringes is solved by adopting a Carre phase shift method, and the steps are introduced as follows:
in the measuring process, the micro-displacement mechanism drives the probe to move along the optical axis direction to set the scanning intervalIs that
The corresponding phase change amount is +.>
When the micro-displacement mechanism moves once, one frame of image is acquired, and the light intensity corresponding to four adjacent frames of images of the same pixel point can be expressed as:
wherein I is 1 、I 2 、I 3 、I 4 Respectively continuously collecting light intensity distribution of four frames of interference fringes, I B For the intensity of the background light,
phase, M is fringe contrast.
Phase distribution at this location
The method comprises the following steps:
the fringe contrast M at this location is:
recording the stripe contrast M of all positions in the scanning process, and obtaining the maximum stripe contrast M P Corresponding phase
The position x corresponding to the zero-order stripe can be obtained according to the following formula 2 ：
Wherein p is the number of frames corresponding to the position of the maximum modulation degree.
Further, the white light interference signal is solved by using a Hilbert transform algorithm, and the position x of the maximum fringe contrast is repositioned 3 The process of (1) is specifically as follows:
the hilbert transform is:
wherein f (t) is a real-valued function;
the analytic signal F (t) may be configured to:
F(t)＝f(t)+iHT{f(t)}
then
Where u (ω) is a step function,
representing the fourier transform +.>
Representing the inverse fourier transform, I (t) representing the real part of the interference signal,/>
Representing an imaginary part of the interference signal; thus, the transformed I (t) generates displacement of-90 degrees; therefore, plural->
Is the envelope signal of white light interference, i.e
The position d of the central stripe can be determined by extracting the maximum of the envelope curve
Calculating the phase corresponding to the maximum contrast obtained by Hilbert transform>
And then->
The following formula is substituted: />
The repositioning maximum stripe contrast position x can be obtained 3 。
Compared with the prior art, the invention has the remarkable advantages that:
based on an optical fiber white light interferometry system built by a traditional Michelson interferometer, the invention divides the process of interference zero-order fringe and envelope extraction into three steps of coarse positioning, a phase shift method and Hilbert transformation from the forming principle and expression of interference fringes, comprehensively considers the phase characteristic and amplitude characteristic of the interference fringes, has the speed and precision of the method, ensures that the peak value error of the extracted envelope is 0.1um level, and further improves the detection precision of white light interference in a mode of improving the positioning precision of the zero-order fringes. The overall performance of the optical fiber white light interference is optimized.
Drawings
FIG. 1 is a schematic diagram of an interference signal and an envelope.
Fig. 2 is a schematic diagram of the full width half maximum method of the present invention.
Fig. 3 is a schematic diagram of the phase shift method of the present invention.
Fig. 4 is a flow chart of an interference fringe envelope extraction method.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The implementation of the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.
The zero-order fringe peak value of the white light interference signal corresponds to the position of the zero-path difference of two arms of the interferometer, and the position is used as the reference point of absolute measurement and is the characteristic of the white light interference signal and is also the key point of signal identification and processing. Unlike the constant-amplitude cosine interference curve obtained by a narrow-band laser light source, the interference fringes obtained by a wide-band light source with a certain spectral width have the following obvious characteristics: the interference signal is in the form of an equal periodic cosine oscillation, but as the optical path difference increases, the envelope of the interference signal decays rapidly, only until there is no intensity fluctuation, and the interference signal curve within the envelope has one main maximum, i.e. the zero-order fringes of the interference pattern. In particular, when a michelson interferometer is driven by a light source with a gaussian spectral distribution, the white light interference signal can be expressed as:
wherein I is 0 Is the intensity of a broad spectrum light source; g (x) is the envelope function of the interference signal, k 0 Wavenumber, x, being the center wavelength of a broad spectrum light source 0 The position of the optical path corresponding to the envelope peak value of the white light interference signal;
and x is the optical path difference of the white light interference system, which is the initial phase caused by the reflection phase shift.
From the wiener-Xin Qin theorem, G (x) and the light source power spectral density function G (k) are a pair of fourier transform pairs:
where G (k) is a normalized light source power spectral density function and k is the wavenumber distributed along the path difference. For gaussian light sources:
wherein, the liquid crystal display device comprises a liquid crystal display device,
λ 0 is the center wavelength of the light source, delta lambda is the full width at half maximum of the light source, L c The coherence length of the light source, ζ is the spectral coefficient of the light source, which is a certain value, and the values (1) and (2) are substituted into (3) to obtain
As can be seen from the white light interference pattern described by equation (4), when x=x 0 When corresponding to the optical path 2k 0 x 0 Obtaining extreme points of interference fringe envelope when the optical path is
And obtaining extreme points of the interference fringes. First phase->
When the interference signal peak coincides with the peak of its envelope. It can be seen that the amplitude and phase of the interference fringes are the main information for extracting the zero optical path point.
As shown in fig. 4, the invention provides an interference fringe envelope extraction method for optical fiber white light interference, which comprises the following steps:
step 1: and obtaining interference fringe signals of the tested sample through a white light interference system.
Step 2: the half-height full-width method is adopted, and the position of the zero-order stripe is positioned through the midpoint corresponding to the half-height full-width methodx 1 。
Step 3: solving the fringe contrast of the white light interference signal by adopting a phase shift method, judging the position and the phase of the maximum fringe contrast, and obtaining the position x of the zero optical path difference point of the interference signal 2 。
Step 4: comparing the half-height full-width method coarse positioning position with the phase shift method to solve the zero optical path difference position, if two points are obtained
Judging that the white light phase shift method is accurate in positioning, finishing envelope extraction, and outputting the position of the interference zero-order stripe; otherwise, the positioning is considered to be an error or a surface discontinuity. The position of the interference zero-order stripe is obtained after Hilbert transformation and filtering.
Further, the Jing Xier Bert transform and filtering process to obtain the position of the interference zero-order fringe specifically comprises the following steps: solving white light interference signals by Hilbert transform and repositioning maximum fringe contrast position x 3 . And filtering the interference envelope obtained by the Hilbert transform solution and compensating the time delay of the interference envelope. Maximum stripe contrast position x obtained by Hilbert transform and post-filtering solution 4 And substituting the position of the maximum fringe contrast solved by the phase shift method into a phase shift method formula to calculate the position of the zero optical path difference, wherein the position is the position of the interference zero-order fringe.
The interference signal in step 1 is typically a gaussian signal generated by the interference of a single gaussian light source or a multimodal signal generated by a combined light source, such a signal typically having a main maximum. However, due to noise and signal distortion in the detection process, the main maximum value of the interference fringe is often not the position of the zero-order fringe, so that the influence of the phase and the amplitude of the interference fringe needs to be comprehensively considered. The half-width method is first used because of the angle at which the interference fringes are usually symmetrical. The concept of full width at half maximum is the optical path difference between two points corresponding to half of the main maximum amplitude of the interference fringe, so when the interference fringe is symmetrical, the midpoint corresponding to the full width at half maximum is the position of the interference zero-order fringe. Although white light interference fringes exist in the actual detection processAt a certain distortion, the basic symmetry does not change in principle due to noise. However, in most cases, the full width at half maximum is used for positioning, and the error exceeds
It is therefore necessary to introduce a phase shift method. />
White light phase shift methods were originally derived from monochromatic light phase shift interferometry. In white light interferometry, fringe contrast extremum of the interference fringes occurs at the zero optical path difference point, but measurement errors are often generated due to the fact that the variability of the samples cannot be fully taken to the zero optical path difference point. Therefore, referring to the thought of monochromatic light phase-shift interferometry, the white light phase-shift interferometry combines phase information while analyzing the contrast of interference signal fringes, so that the white light phase-shift interferometry obtains the calculation accuracy of monochromatic light phase-shift interferometry.
The white light phase shift method first finds the maximum fringe contrast position p (p=1, 2,..once., N), which is out of phase with the zero-order interference fringe by the phase difference
Thereby obtaining the position x of the zero optical path difference point calculated by the sampling point 2 。
In the embodiment of the invention, for balancing the speed and the precision, a Care phase shift method is adopted.
The phase shift method can calculate the position of the zero-order stripe when the light rays of different wavelengths participating in interference are overlapped, namely, the position of the phase is 0. By introducing the concept of fringe contrast, fringe contrast can be used as an objective function to provide a reference for envelope extraction and calculation.
However, the carre phase shift method is unfavorable for realizing high-precision anti-interference because the problem of error positioning of the maximum fringe contrast easily occurs, so that an algorithm with higher precision is necessary to be introduced.
The hilbert algorithm is a very well established signal processing algorithm and is widely used in envelope extraction. Compared with other algorithms, the Hilbert algorithm has the advantages of simple operation, high stability and output resultThe reliability is high. Although the operation amount is larger than that of the phase shift method, the method is that and only that
The hilbert algorithm needs to be called when the method is used, and the hilbert algorithm has strong interference resistance to signal extraction in a small range because coarse positioning is realized. The interference envelope obtained by Hilbert transformation is filtered and smoothed, and the time delay generated by the signal is compensated based on the parameters of the filter, so that high positioning accuracy can be obtained.
Note that: the Hilbert transform is only an algorithm with higher precision after the phase shift method is adopted in the invention, and the algorithm can also be a Fourier transform method, a wavelet transform method, an extremum method, a function fitting method and the like, and the Hilbert transform method is only one of algorithms for explaining the detection process of the invention and has no specificity.
Because the Hilbert transform takes longer time and has higher requirements on the quality of interference fringes, if the Hilbert transform is directly used for extracting zero-order fringes of interference signals, the efficiency of an algorithm can be reduced, and the integral precision of the algorithm can be greatly influenced.
Typically, the light source used for white light interferometry is a gaussian distribution spectrum light source. According to the interference principle of light, the white light interference signal is also a cosine modulated gaussian signal curve, and the interference fringes and the envelope of the white light interference signal are shown in fig. 1. The interference fringes are solid lines in the form of periodic cosine oscillations in the figure, and comprise all optical signals; while the interference envelope is a dashed line tangent to the interference fringes and wrapping thereabove. The envelope of the interference fringes provides important information for the extraction of the zero optical path point, and is also the most intuitive method for determining the accurate position of the zero-level fringes.
Firstly, coarse positioning is carried out on zero-order fringes of interference fringes by adopting a half-height full-width method. As shown in FIG. 2, interference fringes in the actual detection process often exist due to noise and the influence of the detection modeA certain distortion is present when the position corresponding to the main maxima of the interference fringes will not be the position where the phase of the interference fringes is 0. The concept of full width at half maximum is therefore employed to locate the zero order stripe in the middle of the stripe. The half-height full-width method is adopted, and the position x of the zero-order stripe is positioned through the midpoint corresponding to the half-height full-width 1 The optical path difference between two points corresponding to half of the maximum amplitude of the main value of the interference fringe is obtained, after the maximum value of the interference fringe is found, the point corresponding to the full width at half maximum is determined according to the amplitude, then the position can be positioned to the midpoint of the connecting line of the two points corresponding to the full width at half maximum, and the position is taken as the zero-order fringe position x of coarse positioning 1 。
The Care phase shift method is adopted to solve the contrast of white light interference signal fringes, and the basic principle is shown in figure 3. Adopts a discrete measurement mode, and the phase difference of two adjacent discrete points is
Thus every four measurement intervals corresponds to 2 pi, i.e. one wavelength. Each discrete point corresponds to one light intensity, and the discrete points are smoothly connected to obtain interference fringes. The Care phase shift method is to continuously calculate the contrast of the stripe corresponding to the light intensity of each four adjacent points to determine the position of the zero-order stripe. The steps are as follows:
in the measuring process, the micro-displacement mechanism drives the probe to move along the optical axis direction, and the scanning interval is set as
The corresponding phase change amount is +.>
When the micro-displacement mechanism moves once, the image acquisition system acquires one frame of image, and the light intensity corresponding to four adjacent frames of images of the same pixel point can be expressed as:
wherein I is 1 、I 2 、I 3 、I 4 Respectively continuously collecting light intensity distribution of four frames of interference fringes, I B For the intensity of the background light,
phase, M is fringe contrast.
From equation (6), the phase distribution at this position
The method comprises the following steps:
the fringe contrast M at this location is:
recording the stripe contrast M of all positions in the scanning process, and obtaining the maximum stripe contrast M P Corresponding phase
The position x corresponding to the zero-order stripe can be obtained 2 。
Wherein p is the number of frames corresponding to the position of the maximum modulation degree.
Comparing the half-height full-width method coarse positioning position with the phase shift method to solve the zero optical path difference position, if two points are obtained
Judging that the white light phase shift method is accurate in positioning, finishing envelope extraction, and outputting the position of the interference zero-order stripe; otherwise, the positioning is considered to have errors or is a surface discontinuous point, and the Hilbert transformation is adopted to precisely position the zero optical path point.The principle of the hilbert transform is as follows:
defining the hilbert transform as:
where f (t) is a real-valued function, the Hilbert transform is a function of the real signal f (t) and
and (5) performing convolution.
Then the resolved signal F (t) may be constructed as:
F(t)＝f(t)+iHT{f(t)} (10)
then
Where u (ω) is a step function,
representing the fourier transform +.>
Representing the inverse fourier transform, I (t) representing the real part of the interference signal,/>
Representing the imaginary part of the interference signal. Thus, the transformed I (t) is shifted by-90 degrees. Therefore, plural->
Is the envelope signal of white light interference, i.e
The mode of the function is the envelope signal of white light interference, and the extraction packageThe maximum value of the complex curve can determine the position d of the central stripe by
The phase corresponding to the maximum contrast obtained by Hilbert transform can be calculated>
And then will be
Substituting into the formula (8) to obtain the relocation maximum stripe contrast position x 3 。
Since the hilbert transform extracts each peak of the interference fringe, and the obtained interference fringe envelope contains information of each peak, the interference fringe envelope is usually not smooth, and difficulty is brought to extraction of the main maxima, so that smooth filtering is required for the interference envelope. A certain delay may occur in smoothing the filtered interference envelope. The time delay is compensated by the parameter calculation of the filter. Maximum stripe contrast position x obtained by Hilbert transform and filtering compensation time delay solution 4 Is the position of the interference zero-order fringes.
The foregoing has outlined and described the basic principles, features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. The interference fringe envelope extraction method for the optical fiber white light interference is characterized by comprising the following steps of:
step 1: obtaining interference fringe signals of a sample to be tested through a white light interference system;
step 2: by half-height and full-heightThe position x of the zero-order stripe is positioned by the midpoint corresponding to the full width at half maximum 1 ；
Step 3: solving the fringe contrast of the white light interference signal by adopting a phase shift method, judging the position of the maximum fringe contrast and the phase of the position of the maximum fringe contrast, and obtaining the position x of the zero optical path difference point of the interference signal 2 ；
The step 3 specifically comprises the following steps:
the contrast of white light interference signal fringes is solved by adopting a Carre phase shift method, and the steps are introduced as follows:
in the measuring process, the micro-displacement mechanism drives the probe to move along the optical axis direction, and the scanning interval is set as
The corresponding phase change amount is +.>
When the micro-displacement mechanism moves once, one frame of image is acquired, and the light intensity corresponding to four adjacent frames of images of the same pixel point can be expressed as:
wherein I is 1 、I 2 、I 3 、I 4 Respectively continuously collecting light intensity distribution of four frames of interference fringes, I B For the intensity of the background light,
phase, M is fringe contrast;
phase distribution at this location
The method comprises the following steps:
the fringe contrast M at this location is:
recording the stripe contrast M of all positions in the scanning process, and obtaining the maximum stripe contrast M P Corresponding phase
The position x corresponding to the zero-order stripe can be obtained according to the following formula 2 ：
Wherein, p is the number of frames corresponding to the position of the maximum modulation degree;
step 4: comparing the half-height full-width method coarse positioning position with the phase shift method to solve the zero optical path difference position, if two points are obtained
Judging that the white light phase shift method is accurate in positioning, finishing envelope extraction, and outputting the position of the interference zero-order stripe; otherwise, the position of the interference zero-order stripe is obtained after Hilbert transformation and filtering, wherein the error occurs in the positioning or the surface discontinuity point;
the position of the interference zero-order stripe obtained after Jing Xier Bert transformation and filtering is specifically as follows: solving the white light interference signal by using a Hilbert transform algorithm, and repositioning the first maximum fringe contrast position x 3 The method comprises the steps of carrying out a first treatment on the surface of the Filtering the interference envelope obtained by the Hilbert transform solution, and compensating the time delay of the interference envelope; second maximum stripe contrast position x obtained by Hilbert transform and filtered solution 4 And substituting the position of the maximum fringe contrast solved by the phase shift method into the position of the zero optical path difference calculated by the phase shift method, wherein the position of the zero optical path difference is the position of the interference zero-order fringe.
2. The method for extracting an interference fringe envelope for optical fiber white light interference according to claim 1, wherein the hilbert transform algorithm is replaced by a fourier transform method, a wavelet transform method, an extremum method or a function fitting method.
3. The method for extracting an interference fringe envelope for optical fiber white light interference as claimed in claim 1, wherein said phase shift method is a carre phase shift method.
4. The method for extracting the interference fringe envelope of the white light interference oriented to the optical fiber according to claim 1, wherein the step 2 is specifically: after the maximum value of the interference fringe is found, the point corresponding to the full width at half maximum is determined according to the amplitude value, then the position can be positioned to the midpoint of the connecting line of the two points corresponding to the full width at half maximum, and the position is taken as the zero-order fringe position x of coarse positioning 1 。
5. The method for extracting interference fringe envelope for optical fiber white light interference as recited in claim 1, wherein said method uses Hilbert transform algorithm to solve said white light interference signal, and relocates the position x of maximum fringe contrast 3 The process of (1) is specifically as follows:
the hilbert transform is:
wherein f (t) is a real-valued function;
the analytic signal F (t) may be configured to:
F(t)＝f(t)+iHT{f(t)}
then
Where u (ω) is a step function,
representing the fourier transform +.>
Representing the inverse fourier transform, I (t) representing the real part of the interference signal,/>
Representing an imaginary part of the interference signal; thus, the transformed I (t) generates displacement of-90 degrees; therefore, plural->
Is the envelope signal of white light interference, i.e +.>
The position d of the central stripe can be determined by extracting the maximum of the envelope curve
Calculating the phase corresponding to the maximum contrast obtained by Hilbert transform>
And then->
The following formula is substituted:
repositioning the first maximum stripe contrast position x can be obtained 3 。
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