Optical interference measurement device and optical interference measurement method

Abstract

Provided is an optical interference measurement technology that improves the resolution of an intensity characteristic curve in the depth direction without using a broadband light source. The optical interference measurement device (1) comprises: a measurement unit (2) for interfering a reflected wave from a reflection surface of an object to be measured with a reflected wave from a reference surface of an irradiated electromagnetic wave to obtain an interference pattern of the interference waves; and a signal processing unit (8) for performing Fourier transform on the interference pattern to construct an intensity characteristic curve in the depth direction. The signal processing unit (8) comprises: a model parameter estimation unit (201) for estimating parameters of a model equation for an assumed number of surfaces based on a model equation of an interference pattern assuming that the object to be measured is a structure having a predetermined structure; an optimal model selection unit (202) for selecting an optimal model by a statistical method based on the model equation to which the parameters estimated for the assumed number of surfaces are applied; and an intensity characteristic curve reconstruction unit (203) for reconstructing the intensity characteristic curve based on the optimal model.

Description

Technical Field

[0001] The present invention relates to an optical interference measurement device and an optical interference measurement method, and more particularly to a Fourier domain optical interference measurement device and a Fourier domain optical interference measurement method. Background Art

[0002] Optical coherence tomography (OCT) is conventionally known as a technology for imaging the internal structure of an object to be measured at high resolution in a non-contact and non-invasive manner.

[0003] In Fourier-domain OCT (FD-OCT) measurements, the intensity of the interference light is first measured for each spectral component of light. The DC component is then subtracted from the interference light intensity to obtain an intensity distribution known as an interferogram. A fast Fourier transform (FFT) is performed on the interferogram to obtain the intensity spectrum of the reflected light in the depth direction. Patent Document 1 discloses swept-source OCT (SS-OCT) as a device for performing FD-OCT measurements.

[0004] Prior art literature

[0005] Patent Literature

[0006] Patent Document 1: International Publication No. 2015 / 001918 Summary of the Invention

[0007] Problems to be solved by the invention

[0008] The resolution of the depth-direction intensity spectrum of a 3D measurement system using FD-OCT is limited by the frequency bandwidth of the light source. This is because Fast Fourier Transformation is used to reconstruct the interferogram into a depth-direction intensity characteristic curve.

[0009] More specifically, if the object being measured is a layered structure with discrete spacing and the frequency bandwidth of the light source is infinite, the intensity characteristic curve obtained from its Fourier transform should be a delta function sequence. However, in reality, the frequency bandwidth becomes a window function, so the intensity characteristic curve obtained is the convolution of the Fourier transform of the window function and the Fourier transform of the interference pattern.

[0010] Therefore, in order to improve the depth resolution of the intensity characteristic curve, it is necessary to further expand the frequency bandwidth of the light source. However, expanding the frequency of the light source has the problem of increasing the size of the generating device and the cost.

[0011] The present invention has been made in view of such circumstances, and its object is to improve the resolution of the intensity characteristic curve in the depth direction without using a broadband light source in optical interferometry technology.

[0012] Means for solving problems

[0013] In order to achieve the above-mentioned purpose, the optical interference measurement device according to the first embodiment of the present invention comprises: a measuring unit for irradiating an electromagnetic wave onto a measurement object and a reference surface, causing a reflected wave from the reflecting surface of the measurement object and a reflected wave from the reference surface to interfere with each other, thereby obtaining an interference pattern of the interference waves; and a signal processing unit for constructing an intensity characteristic curve in the depth direction by performing Fourier transform on the interference pattern, the signal processing unit comprising: a model parameter estimating unit for estimating parameters of the model formula for each assumed number of surfaces within a specified range of assumed numbers of surfaces based on a model formula of the interference pattern assuming that the measurement object is a layered structure having at least one reflecting surface; an optimal model selecting unit for selecting an optimal model formula by a statistical method based on the model formula to which the parameters estimated for each assumed number of surfaces are applied; and an intensity characteristic curve reconstruction unit for reconstructing the intensity characteristic curve in the depth direction based on the optimal model formula.

[0014] In the above aspect, the model parameter estimating unit preferably estimates the parameters of the model equation based on a model equation of an interference pattern assuming that the object to be measured is a layered structure having a constant refractive index in each layer and at least one reflecting surface.

[0015] Moreover, in the above method, it is preferred that the optimal model selection unit reconstructs the interference pattern using the model formula that applies the parameters estimated for each assumed number of surfaces, calculates the likelihood of the reconstructed interference pattern and the original interference pattern, and selects the optimal model formula based on the information amount criterion obtained by using the assumed number of reflection surfaces as a degree of freedom.

[0016] Furthermore, in the above aspect, it is preferable that the range of the number of assumed faces is determined based on structural characteristics of the object to be measured.

[0017] Furthermore, in the above aspect, it is preferable that the range of the number of the assumed planes is determined based on the number of peaks of the intensity characteristic curve in the depth direction formed by the original interference pattern.

[0018] Moreover, the optical interference measurement method according to the second embodiment of the present invention includes the following steps: irradiating an object to be measured and a reference surface with electromagnetic waves, performing Fourier transform on an interference pattern of interference waves obtained by interfering a reflected wave from the reflecting surface of the object to be measured and a reflected wave from the reference surface, thereby forming an intensity characteristic curve in the depth direction; estimating parameters of the model formula for each assumed number of surfaces within a specified range of assumed numbers of surfaces based on a model formula of the interference pattern assuming that the object to be measured is a layered structure having at least one reflecting surface; selecting an optimal model formula by a statistical method based on the model formula to which the parameters estimated for each assumed number of surfaces are applied; and reconstructing the intensity characteristic curve based on the optimal model formula.

[0019] Effects of the Invention

[0020] According to the optical interferometry device or the optical interferometry method having the above-described configuration, the resolution of the intensity characteristic curve in the depth direction can be improved without using a broadband light source. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a block diagram showing a schematic configuration of an optical interferometer measurement device according to an embodiment of the present invention.

[0022] Figure 2 FIG. 1 is a schematic diagram showing the structure of the measuring section of the optical interference measuring device.

[0023] Figure 3 3 is a diagram showing the shape of an interference pattern obtained by the optical interference measurement device.

[0024] Figure 4 FIG. 4 is a functional configuration diagram of the signal processing unit of the optical interferometer measurement device.

[0025] Figure 5 It is a diagram illustrating the structure of a layered structure.

[0026] Figure 6 A diagram illustrating a method of noise removal by the first noise removal unit.

[0027] Figure 7 A diagram illustrating noise removed by noise removal based on singular value decomposition.

[0028] Figure 8 1 is a flowchart of the process of the optical interferometry method using the optical interferometry device.

[0029] Figure 9 This is a flowchart of the noise removal process in the optical interferometry method.

[0030] Figure 10 This is a flowchart of the noise removal process using a filter in the noise removal.

[0031] Figure 11 This is a flowchart of the noise removal process based on singular value decomposition in the noise removal.

[0032] Figure 12 This is a flowchart of the process of estimating model parameters in the optical interferometry method.

[0033] Figure 13 is a flowchart of the process of optimal model selection in this method.

[0034] Figure 14 This is a simulation result of reconstructing the intensity characteristic curve using the model parameters estimated by this method.

[0035] Figure 15 : is a graph showing the result of noise removal by the filter in this method.

[0036] Figure 16 1 and 2 are diagrams showing the results of noise removal by singular value decomposition using the interference pattern after noise removal by the above-mentioned filter.

[0037] Figure 17 3 is a diagram showing the results of selecting the optimal model using the interference pattern after noise removal based on the above-mentioned singular value decomposition.

[0038] Figure 18 This is a functional configuration diagram of a signal processing unit according to a modified example of the optical interferometer measurement device of the present embodiment.

[0039] Figure 19 This is a flowchart of the setting of the range of the assumed number of planes by the signal processing unit. DETAILED DESCRIPTION

[0040] Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings, but the present invention is not limited thereto. In the following description of the embodiments, the same components are denoted by the same reference numerals, and the same components are denoted by the same names, and repeated descriptions are omitted as appropriate.

[0041] [Implementation Method]

[0042] 1. Overall structure of the optical interferometry device

[0043] Figure 1 1 is a block diagram showing a schematic configuration of an optical interferometry device 1 according to an embodiment of the present invention. The optical interferometry device 1 is an SS-OCT, and is used for inspecting the internal structure of a concrete structure, for example.

[0044] like Figure 1As shown, the optical interference measurement device 1 includes a measurement unit 2 , a control processing unit 3 , an operation unit 4 , a display unit 5 , and a storage unit 6 .

[0045] Figure 2 It is a diagram showing a schematic configuration of the measuring unit 2 .

[0046] The measuring unit 2 mainly includes a light source 21 , a beam splitter 22 , an automatic stage 23 for placing a measurement object, a reference surface 24 , and a detector 25 .

[0047] The light source 21 is a variable frequency scanning light source that emits an electromagnetic beam while scanning the wavelength at a fixed period within a predetermined wavelength band. As the light source 21, an oscillation source using a Gunn diode or a Schottky barrier diode (SBD) as a semiconductor material, an oscillation source based on a frequency conversion using a nonlinear crystal using a wavelength-variable semiconductor laser (LD) as a seed light, etc. can be used. Alternatively, as the light source 21, an oscillation source such as a tunneling transit time (TUNNET) diode, a resonant tunnel diode (RTD), or an MMIC (Monolithic Microwave IC) can also be used.

[0048] The beam splitter 22 has a splitting ratio of, for example, 50:50. The beam splitter 22 splits the light beam B from the light source 21 into measurement light B1 and reference light B2.

[0049] The automatic stage 23 holds the object to be measured and defines a measurement plane. The measurement plane is the surface of the object to be measured. The surface of the object to be measured is configured to be movable along two axes, assuming that a plane perpendicular to the optical axis of the measurement light B1 is the XY plane. The automatic stage 23 is driven and controlled by a measurement control unit (described later).

[0050] The reference surface 24 is a reflective mirror and reflects the reference light B2 .

[0051] The detector 25 is, for example, a Schottky barrier diode with a waveguide and an antenna, and detects an interference signal between reflected light of reference light B2 and reflected light of measurement light B1 , which will be described later.

[0052] Light source 21 changes the frequency of the oscillator under control from measurement control unit 7. Lock-in amplifier 31 for detecting weak current is connected to detector 25. Function generator 29 on-off modulates light source 21 and provides a reference signal to lock-in amplifier 31 on the detector 25 side.

[0053] The light emitted from the light source 21 enters the beam splitter 22 via the collimator lens 26a and is split into the measurement light B1 and the reference light B2. The reference light B2 is collimated by the collimator lens 26b and travels toward the reference surface 24. After being reflected by the reference surface 24, it travels through the beam splitter 22 toward the detector 25. Meanwhile, the measurement light B1 is shaped by the collimator lens 26c, travels toward the object being measured, and after being reflected by the object's reflective surface, it again enters the beam splitter 22 and travels through the collimator lens 26d toward the detector 25.

[0054] In this specification, the "reflective surface" of the object to be measured includes both the surface and internal reflective surface of the object to be measured. Therefore, the first reflective surface refers to the surface of the object to be measured.

[0055] According to the principle of SS-OCT, when the frequency of the light source 21 is scanned, an interference pattern (interference figure) corresponding to the difference in optical path length between the measurement light B1 from the measurement object and the reference light B2 is generated. The interference pattern is detected by the detector 25. The detection signal is sampled and digitized by the DAQ system (data acquisition system) 32 and output as image data. This image data is Figure 3 The interference pattern shown.

[0056] Return to Figure 2 The control processing unit 3 can refer to any circuit (or portion thereof), for example, a circuit comprising any number of electrical components such as resistors, transistors, capacitors, and inductors. This circuit can be in any form, such as an integrated circuit, a collection of integrated circuits, a microcontroller, a microprocessor, or a collection of electrical components on a printed circuit board (PCB). The control processing unit 3 can be incorporated into the housing of the optical interferometry device 1, or it can be independent, or even part of a standalone personal computer.

[0057] The control processing unit 3 includes, as functional units, a measurement control unit 7 for controlling the measurement performed by the measurement unit 2, a signal processing unit 8 for processing the signals acquired by the measurement unit 2, and an output unit 9. The functions of each functional unit, including those described in greater detail below, can be implemented using circuits or by executing a program. When implemented using a program, the program can be stored on a storage medium such as a magnetic disk, floppy disk, optical disk, CD, Bluetooth (registered trademark) optical disk, or DVD.

[0058] The measurement control unit 7 modulates the frequency of the light source 21. Furthermore, the measurement control unit 7 controls the driving of the automatic stage 23. The signal processing unit 8 performs processing to generate an intensity characteristic curve based on the interference pattern. Details of the signal processing unit 8 will be described later. The output unit 9 displays the intensity characteristic curve generated by the signal processing unit 8 on the display unit 5 and stores it in the storage unit 6.

[0059] The operation unit 4 is a device for a user to input instructions to the optical interferometry device 1 , and includes, for example, a mouse, a touch pad, a keyboard, an operation panel, a joystick, buttons, switches, and the like.

[0060] The display unit 5 is, for example, a liquid crystal display, and displays the intensity characteristic curve generated by the signal processing unit 8 and other information.

[0061] 2. Detailed structure of the signal processing unit

[0062] Below, refer to Figure 4 The signal processing unit 8 will be described in detail. The signal processing unit 8 includes an FFT analysis unit 10 , a super-resolution analysis unit 20 , and a noise removal unit 30 .

[0063] The FFT analysis unit 10 reconstructs an intensity characteristic curve in the depth direction (hereinafter also simply referred to as “intensity characteristic curve”) by performing fast Fourier transform on the interference pattern. This method is a well-known method, and therefore its description is omitted.

[0064] The super-resolution analysis unit 20 includes a model parameter estimation unit 201 , an optimal model selection unit 202 , and an intensity characteristic curve reconstruction unit 203 .

[0065] The model parameter estimation unit 201 models the interference pattern measured by the optical interference measurement device 1 and estimates parameters of the model equation.

[0066] Specifically, assuming that Figure 5 The imaginary layered structure M shown has a refractive index n in each layer. l Fixed, with a reflective surface number L of at least one, no attenuation and no dispersion.

[0067] The interference pattern I(κ) obtained by measuring the layered structure M is assumed to be the electric field from the reference surface side. r (κ), the electric field from the object to be measured is E s (κ) is described as follows. In addition, the "reflecting surface" here is the interface between the layered structure M and the air or the interface between adjacent layers, and is a surface that reflects the measurement light or reflects the inner surface. In other words, the surface of the layered structure M is the first reflecting surface.

[0068] [Formula 1]

[0069]

[0070] Where |A0(k)| 2 Indicates the intensity of the light source, Represents the reflection coefficient between layers (Fresnel reflection), It represents the optical path length difference from the reference surface to each layer (hereinafter referred to as "optical distance"), z represents the distance to each layer, l = 1, 2, 3, ..., L represents the reflection surface number up to L, p = 1, 2, 3, ..., l represents the reflection surface number up to l.

[0071] The intensity of the light source |A0(k)| 2 Normalizing the interference pattern I(k) and assuming that there are no multiple reflections in the sample, it can be approximated as follows.

[0072] [Formula 2]

[0073]

[0074] Among them, k min represents the minimum wave number, Δk represents the wave number interval, and κ=0, 1, 2, 3,…, K-1 represents the wave number sequence.

[0075] Furthermore, if in formula (2)

[0076] [Formula 3]

[0077]

[0078] As a model formula, it can be simplified as follows.

[0079] [Formula 4]

[0080]

[0081] Thus, the model formula (3) has L, A l , γ l These three parameters.

[0082] Based on the model formula (3), assuming the number of reflecting surfaces L, the other parameters A are estimated as follows: l , γ l Hereinafter, the assumed number of reflection surfaces will be referred to as the “assumed number of surfaces”.

[0083] First, assume that the filter p j The z-transform is

[0084] [Formula 5]

[0085]

[0086] The convolution of the normalized interference pattern and the filter is

[0087] [Formula 6]

[0088]

[0089] If we rewrite it as a matrix, it becomes

[0090] [Formula 7]

[0091]

[0092] At this time, the number of data in D needs to satisfy K≥2L+1. However, the actual measurement data is the data set of Dκ

[0093] [Formula 8]

[0094]

[0095] Contains noise, so p is obtained by solving the following optimization problem.

[0096] [Formula 9]

[0097]

[0098] Where p is p j dataset.

[0099] However, since there is a zero solution such as p = 0, it is necessary to impose a constraint condition that prevents such a solution from occurring. If equation (6) is expanded, it becomes

[0100] [Formula 10]

[0101]

[0102] Therefore, giving

[0103] [Formula 11]

[0104] subject to p 2L =p0=1 (10)

[0105] This constraint condition solves the optimization problem of equation (8). Substitute the obtained p into polynomial (9) and solve it, thus obtaining γ l and γ l *.

[0106] In addition, if formula (3) is rewritten as a matrix, it becomes

[0107] [Formula 12]

[0108]

[0109] However, as before, the actual measurement data

[0110] [Formula 13]

[0111]

[0112] Contains noise, so by solving the following optimization problem (or Moore-Penrose generalized inverse matrix), we can get

[0113] [Formula 14]

[0114] That is A l (set of).

[0115] [Formula 15]

[0116]

[0117] Among them, (G T G) -1 G T is the generalized inverse matrix of G.

[0118] In this way, the model parameter estimation unit 201 estimates the parameter A when the number of faces is assumed to be L. l and γ l .

[0119] In addition, the model parameter estimation unit 201 uses the estimated parameter A l and γ l , calculate the reflection coefficient a of the measured object l and optical distance b l .

[0120] First, get the obtained A l The absolute value of a l .

[0121] [Formula 16]

[0122]

[0123] And, using formula (15), from γ l Get b l .

[0124] [Formula 17]

[0125]

[0126] in, is the plural number γ l The angle of .

[0127] In this way, the strength characteristic curve a can be obtained when the number of faces L is assumed. l 、b l .

[0128] However, in actual measurement, when the above model formula (3) is applied, the number of reflective surfaces L of the object being measured is unknown. Therefore, the range of the number of assumed surfaces L is determined in advance, and the above model parameter A is calculated for each number of assumed surfaces in the range. l , γ l And strength characteristic curve a l 、b l .

[0129] The range of the assumed number of faces L can be determined, for example, based on the structural characteristics of the object being measured. Specifically, it can be expected that the number of reflection faces of a concrete structure such as a tunnel wall is within a certain range (e.g., a range of 1 to 10). Therefore, the optical interference measurement device 1 can be configured so that the user can input or set the range of the assumed number of faces L of the object being measured (the minimum value L of L) in advance in the device before measurement or calculation. min and the maximum value of L max ).

[0130] The model parameter estimation unit 201 performs the above-mentioned model parameter A for each of the assumed face numbers L within the specified range of the assumed face number L (for example, 1, 2, ..., 10). l , γ l Estimation and strength characteristic curve a l 、b l Operation.

[0131] The intensity characteristic curve reconstruction unit 203 reconstructs the intensity characteristic curve a based on equations (15) and (16) obtained by the model parameter estimation unit 201. l 、b l .

[0132] The optimal model selection unit 202 calculates the parameter A for each number of reflecting surfaces estimated by the model parameter estimation unit 201. l , γ l Substituting the model equation (3) into the reconstructed interferogram and the likelihood of the measured interferogram obtained by measurement. The optimal model selection unit 202 uses the number of assumed faces L as a degree of freedom and selects the optimal model, i.e., the number of assumed faces L constituting the optimal model, based on the degree of freedom and the calculated likelihood, by applying the information criterion.

[0133] The information criterion to be applied is not particularly limited, and Akaike's Information Criterion (AIC), Limited Corrected AIC (AICc), Bayesian Information Criterion (BIC), etc. can be applied. A known method can be used for calculating likelihood and applying the information criterion.

[0134] The noise removal section 30 includes a first noise removal section 301 and a second noise removal section 302 .

[0135] First, in the measurement of the optical interference measurement device 1, the interference pattern obtained is theoretically shown as Figure 3 However, in actual measurement, Figure 6 (A) contains noise. Noise includes periodic noise caused by multiple reflections in the measurement system and random Gaussian white noise. The first noise removal unit 301 removes the periodic noise, and the second noise removal unit 302 removes the Gaussian white noise.

[0136] The first noise removal unit 301 is described. The FFT analysis unit 10 transforms the interference pattern into an intensity characteristic curve by fast Fourier transform (FFT). Figure 6 The noise-containing interference pattern (A) is transformed into an intensity characteristic curve, as shown in Figure 6 As shown in (B), when the surface of the measurement object is set as the measurement object installation position, peaks are also observed in areas other than the vicinity of the measurement object installation position. These are periodic noise components.

[0137] Therefore, the first noise removal unit 301 performs filtering, applies a window function to the intensity characteristic curve, and deletes the data in the deletion area of the window function. The window function uses the area set based on the setting position of the measured object in the optical distance in the depth direction of the measured object as the pass-through area, and uses the other areas as the deletion area. Figure 6 (C) shows the intensity characteristic curve after filtering using a rectangular window.

[0138] As shown in the figure, the pass region can be set by specifying a predetermined range before and after the surface position of the measurement object, using the measurement object installation position as a reference. For example, if the measurement object is 10 mm thick and the surface position (measurement object installation position) is 100 mm, the pass region can be set to 50 mm before and after the measurement object installation position, that is, a range of 50 mm to 150 mm. In this way, the first noise removal unit 301 functions as a bandpass filter.

[0139] Alternatively, the center position of the object to be measured may be used as the object setting position, and the object setting position may be used as a reference. A range of half the thickness of the object to be measured plus a specified margin may be set as a passing area before and after, and the rest may be set as a deletion area.

[0140] Furthermore, the window function is not limited to the rectangular window shown in the figure, and various window functions used in filtering processing, such as a Gaussian window, a Hanning window, and a Hamming window, can be used.

[0141] Then, the first noise removal unit 301 transforms the intensity characteristic curve of the data from which the deletion area is deleted into Figure 6 The interference pattern is as shown in (D).

[0142] In this way, periodic noise can be effectively removed from the interference pattern.

[0143] The second noise removal unit 302 will be described.

[0144] Figure 7 This figure illustrates the Gaussian white noise removed by the second noise removal unit 302. In the figure, the black line represents the theoretical interferogram, and the gray line represents the interferogram containing Gaussian white noise. While the theoretical interferogram and the interferogram containing noise roughly overlap, the peaks of the theoretical interferogram have a smooth, continuous envelope, whereas the envelope of the interferogram containing Gaussian white noise has randomly protruding portions, as indicated by the arrows, and the envelope is not smoothly continuous. The second noise removal unit 302 removes this noise as described below.

[0145] (a) The second noise removal unit 302 expresses the measurement data in a matrix based on the interference pattern in the same manner as in equation (8):

[0146] [Formula 18]

[0147]

[0148] Generate a diagonal matrix with (K-2L-1)×(2L+1) elements

[0149] [Formula 19]

[0150]

[0151] (b) The second noise removal unit 302 performs the matrix

[0152] [Formula 20]

[0153]

[0154] Perform singular value decomposition (SVD) according to formula (17).

[0155] [Formula 21]

[0156]

[0157] (Here, U represents a unitary matrix (complex number, UU*=U*U=I) with (K-2L-1)×(2L+1) elements, S represents a diagonal matrix with (2L+1)×(2L+1) elements, and V represents a unitary matrix with (2L+1)×(2L+1) elements.)

[0158] (c) Then, the second noise removal unit 302 calculates the diagonal matrix S of the singular values according to equation (18).

[0159] [Formula 22]

[0160]

[0161] (where the singular value σ n yes The square root of the eigenvalue of .)

[0162] (d) Then, the second noise removal unit 302 calculates the evaluation value V based on the diagonal matrix S of the singular values. e About the evaluation value V e , for example, the value σ of the (2L+1)th element of the diagonal matrix S can be 2L+1 Considered as a noise component, the value of the 2Lth element σ 2L It is regarded as a signal component and is set according to formula (19).

[0163] [Formula 23]

[0164]

[0165] (e) Then, the second noise removal unit 302 removes at least the smallest singular value σ from the obtained diagonal matrix S of singular values as a noise element. 2L+1 Delete and construct the diagonal matrix S' according to formula (20).

[0166] [Formula 24]

[0167]

[0168] Furthermore, it is not necessary to delete only the smallest singular value, and all the singular values of components considered unnecessary may be deleted.

[0169] (f) Furthermore, based on the calculated diagonal matrix S', the interference pattern is reconstructed according to formula (21)

[0170] [Formula 25]

[0171]

[0172] [Formula 26]

[0173]

[0174] in, Indicates that The least squares approximation of The square error of each element becomes the minimum.

[0175] Noise-removed

[0176] [Formula 27]

[0177]

[0178] does not necessarily become a constant diagonal matrix. Therefore,

[0179] Use along The average value of the diagonal of , reconstructed into a constant diagonal matrix

[0180] [Formula 28]

[0181]

[0182] (g) Using the reconstructed constant diagonal matrix

[0183] [Formula 29]

[0184]

[0185] Repeat steps (b) to (f) until the evaluation value V e Until the evaluation value V e Interference pattern less than the specified threshold Th

[0186] [Formula 30]

[0187]

[0188] Reconstruct the interference pattern after noise removal.

[0189] Regarding the removal of the first noise component and the removal of the second noise component based on singular value decomposition, for example, when it is determined that the influence of the first noise component is greater and the influence of the second noise component is less, only the first noise component is removed; when it is determined that the influence of the second noise component is greater and the influence of the first noise component is less, only the second noise component is removed. Only one of the two may be performed.

[0190] In addition, when both the first noise component and the second noise component are removed, the order of removal is not particularly limited. However, it is preferred that, when the influence of the first noise component is considered to be greater and the influence of the second noise component is less, the first noise component be removed first; and when the influence of the second noise component is considered to be greater and the influence of the first noise component is less, the second noise component be removed first.

[0191] 3. Optical interferometry method

[0192] Below, refer to Figures 8 to 13 The optical interferometry method using the optical interferometry device 1 is described. Parameters, interference patterns, intensity characteristic curves, etc. obtained in the following steps are stored in a storage unit as needed and read in subsequent steps, and their description is omitted.

[0193] Figure 8 This is a flowchart schematically illustrating the processing of this optical interferometry method. First, when the process begins, in step S101, the noise removal unit 30 removes noise from the measured interferogram. Then, in step S102, the model parameter estimation unit 201 estimates model parameters using the noise-removed interferogram. Then, in step S103, the optimal model selection unit 202 selects the optimal model. Then, in step S104, the intensity characteristic curve reconstruction unit 203 reconstructs the intensity characteristic curve in the depth direction. The specific processing of each step is described below.

[0194] Figure 9 This is a flowchart of detailed processing related to noise removal in step S101.

[0195] When noise removal starts, in step S201, the first noise removal unit 301 removes noise using a filter, and in step S202, the second noise removal unit 302 removes noise using singular value decomposition (SVD).

[0196] Figure 10 This is a detailed flowchart of noise removal by the filter in step S201.

[0197] When noise removal by the filter starts, in step S301 , the FFT analysis unit 10 converts the measured interference pattern into an intensity characteristic curve by fast Fourier transform.

[0198] Then, in step S302 , the first noise removal unit 301 defines an area of the intensity characteristic curve based on the installation position of the measurement object as a pass-through area and defines other areas as deletion areas, and performs filtering to delete data in the deletion areas.

[0199] Then, in step S303, the first noise removal unit 301 transforms the intensity characteristic curve obtained after filtering in step S302 into an interference pattern by inverse fast Fourier transform, and the process ends. Then, the process proceeds to step S202.

[0200] Figure 11 This is a flowchart of the detailed process of noise removal based on singular value decomposition in step S202 .

[0201] When the noise removal based on the singular value decomposition is started, in step S401 , the second noise removal unit 302 generates a constant diagonal matrix D based on the interference pattern.

[0202] Then, in step S402, the second noise removal unit 302 performs singular value decomposition on the matrix D and calculates a diagonal matrix S of singular values (Formula (18)).

[0203] Then, in step S403, the second noise removal unit 302 calculates the evaluation value V according to the singular value S. e (Formula (19)).

[0204] Then, in step S404, the second noise removal unit 302 compares the evaluation value V e and the prescribed threshold Th, the evaluation value V e Is it less than the threshold Th?

[0205] In the evaluation value V e If it is equal to or greater than the threshold value Th (No), in step S405, the second noise removal unit 302 deletes the noise elements from the matrix S of the singular values and calculates the singular values S' (Formula (20)).

[0206] Then, in step S406, the singular value S' is used to reconstruct the matrix of the interference pattern

[0207] [Formula 31]

[0208]

[0209] Then, in step S407, the matrix

[0210] [Formula 32]

[0211]

[0212] The diagonal components of are averaged, as a constant diagonal matrix

[0213] [Formula 33]

[0214]

[0215] In step S408, set

[0216] [Formula 34]

[0217]

[0218] Return to step S402 and repeat steps S402 to S404.

[0219] On the other hand, in step S404, the evaluation value V e If it is smaller than the threshold value Th ("Yes"), the interference pattern D is regarded as the interference pattern after noise removal, and the processing is terminated and the processing proceeds to step S102.

[0220] Alternatively, instead of setting a threshold and repeatedly deleting noise components until the evaluation value satisfies the threshold, the number of repetitions may be set in advance and the process may be repeated until the number of repetitions is satisfied.

[0221] Figure 12 This is a detailed flowchart of the estimation of the model parameters in step S102. When the setting of the model parameters starts, in step S501, the model parameter estimation unit 201 sets the range of the number of assumed faces L (i.e., the minimum value L) based on the user input. min and maximum value L max ).

[0222] Then, in step S502, the model parameter estimation unit 201 assumes that the number of faces L is L=L min And initialize it.

[0223] Then, in step S503, the model parameter estimation unit 201 assumes the number of faces L min Next, the parameter γ of the model formula (3) is calculated by the calculation of the above formulas (4) to (12). l .

[0224] Then, in step S504, the model parameter estimation unit 201 uses equation (16) to calculate the parameter γ obtained in step S503. l Calculate the optical distance b l .

[0225] Then, in step S505, the model parameter estimation unit 201 calculates the interference pattern and the parameter γ according to equations (12) to (14). l Calculation parameter A l .

[0226] Then, in step S506, the model parameter estimation unit 201 uses equation (15) according to the parameter A l Calculate the reflection coefficient a l .

[0227] Then, in step S507, the model parameter estimation unit 201 determines whether the assumed number of faces L is L max In the above, it is determined whether or not the analysis of each of the assumed numbers L within the range of the assumed number L set in step S501 has been completed.

[0228] In L for L maxIn the above case ("Yes"), the process ends and proceeds to step S104. max In the case of ("No"), in step S508, the model parameter estimation unit 201 increases the number of assumed faces L to set L = L + 1, and returns to step S501, and repeats steps S501 to S507 until the number of assumed faces L reaches L max That’s all.

[0229] Figure 13 This is a detailed flowchart regarding the selection of the optimal model in step S103.

[0230] When the process starts, the optimal model selection unit 202 sets the range of the number of assumed faces L set in step S501 (ie, the minimum value L min and maximum value L max ).

[0231] Then, in step S602, the optimal model selection unit 202 sets the number of assumed faces L to be L=L min , for initialization.

[0232] Then, in step S603, the model parameter estimation unit 201 uses the optimal model selection unit 202 in the case where the number of assumed faces L=L min The estimated parameter A l , γ l Reconstruct the interference pattern.

[0233] Next, in step S604 , the optimal model selection unit 202 calculates the likelihood between the measured interferogram from which noise has been removed in step S101 and the reconstructed interferogram in step S603 .

[0234] Then, in step S605 , the optimal model selection unit 202 calculates the information amount criterion of the number of assumed faces L using the likelihood obtained in step S604 , assuming the number of assumed faces L as a degree of freedom.

[0235] Then, in step S606, the optimal model selection unit 202 determines whether the assumed number of faces L is L max In other words, it is determined whether or not the analysis of all the assumed numbers L of faces within the range of the assumed number L of faces set in step S501 is completed.

[0236] In L for L max In the above case ("Yes"), in step S607, the optimal model selection unit 202 compares the information criterion values of all the assumed number of faces L, selects the model with the assumed number of faces L having the smallest information criterion value as the optimal model, and ends the processing.

[0237] On the other hand, in step S606, L is less than L maxIn the case of ("No"), in step S608, the optimal model selection unit 202 increases the number of assumed faces L to set L = L + 1, and returns to step S603, and repeats steps S603 to S606 until the number of assumed faces L reaches L max That’s all.

[0238] The number of assumed faces associated with the optimal model thus selected is provided to the reconstruction of the intensity characteristic curve by the intensity characteristic curve reconstruction unit 203 in step S104 .

[0239] The reconstructed intensity characteristic curve can be used not only to analyze the intensity characteristic curve in the depth direction but also to construct a three-dimensional image by solving the interference pattern measured by scanning the two X and Y axes.

[0240] 4. Examples

[0241] 4-1 Example 1: Simulation results based on the estimation of model parameters

[0242] Figure 14 These are the results of a simulated intensity characteristic curve obtained when light source 21 is frequency-modulated at 600 to 665 GHz using optical interferometry apparatus 1. The measured object was set to have an optical distance of 80 mm at its surface (first reflecting surface). The upper, middle, and lower graphs represent the results for samples having the structures shown in Table 1 and a fixed refractive index of 1.53.

[0243] [Table 1]

[0244] Table 1 Simulation conditions of Example 1

[0245]

[0246] In the figure, the black line indicates that the model parameter γ is estimated based on the model formula (3) assuming that the number of faces L = 2 in this embodiment. l 、A l , according to the inferred model parameter γ l 、A l The reconstructed intensity characteristic curve a l 、b l In addition, the gray line shows the result of converting the same interference pattern into an intensity characteristic curve only by fast Fourier transformation for comparison.

[0247] Gray lines show broad peaks, while black lines show sharp peaks. The intensity characteristic curve based on fast Fourier transform (FFT) is separated into peaks for the first and second surfaces at a thickness of 10 mm. However, the peaks overlap at a thickness of 5 mm, and there is no separation at all at a thickness of 1 mm. On the other hand, the intensity characteristic curve reconstructed using the estimated model parameters of this embodiment shows separation into peaks for the first and second surfaces regardless of thickness.

[0248] It can be seen from this that by estimating model parameters using model formula (3) and reconstructing the intensity characteristic curve based on the estimated model parameters, the intensity characteristic curve in the depth direction can be measured with a higher resolution than the method based on the conventional Fourier transform.

[0249] 4-2 Example 2: Actual Measurement Experiment

[0250] (1) Noise removal by filters

[0251] Next, a measurement experiment was conducted using the optical interference measurement apparatus 1. A plastic flat plate with a constant refractive index and the structure shown in Table 2 was used as the measurement object (sample). The object was set so that the optical distance of its surface (first reflecting surface) was 80 mm, and the light source was frequency-modulated in the range of 600 to 665 GHz for measurement. Figure 15 The results of noise removal by the filter in S201 were obtained using the measured interferogram. The upper, middle, and lower graphs represent the experimental results under the conditions shown in Table 2. The passband was set to -34 mm to +57 mm (i.e., an optical distance of 46 to 137 mm) relative to the sample surface position (80 mm).

[0252] [Table 2]

[0253] Table 2 Experimental conditions

[0254]

[0255] And, in Figure 15 In (A), the gray line represents the interference pattern before filtering, and the intensity characteristic curve obtained by fast Fourier transform is Figure 15 The gray line of (B). And, Figure 15 The black line in (B) represents the intensity characteristic curve after filtering, and the interference pattern obtained by inverse fast Fourier transform is Figure 15 The black line of (A).

[0256] like Figure 15As shown in (B), regardless of sample thickness, by setting the pass-through area based on the sample surface position (i.e., the sample placement position) and performing filtering, noise not caused by the sample can be reliably removed. Furthermore, the interference pattern obtained by inverse fast Fourier transforming the filtered intensity characteristic curve demonstrates that periodic noise has been removed.

[0257] In this way, an intensity characteristic curve is formed by performing Fourier transform on the interference pattern. In the intensity characteristic curve, the passing area is set based on the sample setting position, and the data of the area outside the passing area is deleted, thereby filtering the intensity characteristic curve. By performing inverse Fourier transform on the filtered intensity characteristic curve, periodic noise can be removed from the interference pattern.

[0258] (2) Noise removal based on singular value decomposition (SVD)

[0259] Figure 16 The result of noise removal by singular value decomposition using the interference pattern after noise removal by the above-mentioned filter is shown.

[0260] exist Figure 16 In the figure, the gray line represents the interferogram before noise removal using singular value decomposition, and the black line represents the interferogram after noise removal using singular value decomposition. It can be seen that, regardless of thickness, the interferogram after noise removal removes the protruding portions of the envelope before noise removal, and the envelope becomes smoothly connected, which is particularly noticeable in the area indicated by the arrow.

[0261] In this way, a constant diagonal matrix is generated from the interference pattern, singular value decomposition is performed on the constant diagonal matrix to calculate the diagonal matrix of singular values, and noise components are deleted based on the diagonal matrix of singular values, thereby removing random Gaussian white noise from the interference pattern.

[0262] (3) Reconstruction of the intensity characteristic curve based on the optimal model

[0263] Next, using the interferograms from the aforementioned field measurements after noise removal using singular value decomposition, we estimated model parameters for each assumed number of facets, L, ranging from 1 to 10. We then reconstructed the interferograms for each assumed number of facets using these model parameters, calculated the likelihood between the noise-removed interferograms and the reconstructed interferograms, and determined the AIC value for each assumed number of facets, using the assumed number of facets as the degree of freedom. The model with the lowest AIC value was selected as the optimal model. The lowest AIC values were obtained for the assumed number of facets, L, of 7, 7, and 6 for thicknesses of 10 mm, 5 mm, and 1 mm, respectively.

[0264] Figure 17(A) represents the intensity characteristic curve, the gray line represents the intensity characteristic curve obtained by Fourier transforming the interference pattern after noise removal based on the above-mentioned singular value decomposition, and the black line represents the intensity characteristic curve reconstructed based on the selected optimal model.

[0265] in addition, Figure 17 (B) represents the interference pattern, the gray line represents the interference pattern after noise removal based on the above-mentioned singular value decomposition, and the black line represents the interference pattern reconstructed according to the optimal model.

[0266] according to Figure 17 As can be seen from (A), regardless of the thickness, the intensity characteristic curve reconstructed according to the optimal model can be observed with a higher resolution than the intensity characteristic curve generated by Fourier transform, and even when the thickness is 1 mm, the peaks of the first reflection surface and the second reflection surface can be separated.

[0267] Then, according to Figure 17 As can be seen from (B), regardless of the thickness, the interferogram reconstructed based on the optimal model can roughly reproduce the input data, that is, the interferogram after noise removal.

[0268] In this way, the interference pattern is reconstructed using a model formula that applies parameters estimated for each assumed number of surfaces, the likelihood of the reconstructed interference pattern and the original interference pattern is calculated, and the optimal model formula is selected based on the information quantity criterion obtained by assuming the assumed number of surfaces as a degree of freedom. Thus, the intensity characteristic curve can be reconstructed using the optimal model formula. As a result, the intensity characteristic curve in the depth direction can be measured with a higher resolution than the method based on the conventional Fourier transform.

[0269] Furthermore, in the above embodiments, the results of simulations and actual measurements on a sample with two reflective surfaces L are shown. However, similar results can be obtained when the number of reflective surfaces L is one or three or more.

[0270] As described above, the optical interferometry method according to this embodiment includes a noise removal method for removing noise, and a super-resolution analysis method for estimating model parameters, selecting an optimal model, and reconstructing an intensity characteristic curve based on the optimal model. Furthermore, the noise removal method includes a filter-based noise removal method and a singular value decomposition-based noise removal method. However, as demonstrated by the experimental results above, each of these methods is effective independently. For noise removal, only noise removal can be performed, while for resolution improvement, only super-resolution analysis can be performed. Combining the noise removal method and super-resolution analysis method can significantly improve resolution, which is advantageous.

[0271] 5.Deformation method

[0272] As a variation of this embodiment, steps S501 and S601 may be automatically set. Figure 18 This is a functional configuration diagram of the signal processing unit 8a of the optical interferometer measurement device 1a related to this modified embodiment. The optical interferometer measurement device 1a has substantially the same configuration as the optical interferometer measurement device 1, but differs in that the signal processing unit 8a includes a model parameter estimation unit 201a and an optimal model selection unit 202a, replacing the model parameter estimation unit 201 and the optimal model selection unit 202, respectively.

[0273] The model parameter estimation unit 201a performs the following steps in place of step S501 in estimating the model parameters: Figure 19 That is, once the range of the assumed number of faces L is set, in step S701, the model parameter estimation unit 201a (e.g., in step S301) refers to the intensity characteristic curve obtained by Fourier transforming the interference pattern by the FFT analysis unit 10 and determines the assumed number of faces based on the number of peaks. Specifically, after confirming that Figure 14 In the case of two peaks as shown by the middle gray line, the range of the number of peaks is set to 2±5 (where the number of assumed planes L is a natural number), and the range of the number of assumed planes L is determined to be 1-7.

[0274] Then, in step S702, the range of the assumed number of faces L (ie, the minimum value L) is set according to the above determination. min , maximum value L max ), end the processing and enter step S502.

[0275] The same applies to the optimal model selection unit 202a.

[0276] Such a configuration can automatically set the appropriate range of the number of assumed surfaces L, and thus the measurement operation can be easily performed.

[0277] The present invention is not limited to the above-described embodiments and may include various modifications. Furthermore, the above-described embodiments have been described in detail to facilitate a better understanding of the present invention, and the present invention is not limited to all of the described configurations. For example, while the above description describes the optical interferometry device as an SS-OCT, this is not limiting. The present invention can also be applied to optical interferometry devices such as SD-OCT, which use Fourier transform to obtain a depth-direction intensity characteristic curve. Furthermore, portions of the configurations of each embodiment may be supplemented, deleted, or replaced with other configurations.

[0278] Description of the label

[0279] 1.1a Optical interferometry device

[0280] 8.8a Signal processing unit

[0281] 20 Super Resolution Analysis Department

[0282] 201, 201a Model parameter estimation unit

[0283] 202, 202a Best Model Selection Department

[0284] 203 Strength Characteristic Curve Reconstruction Department

Claims

1. An optical interference measurement device, characterized in that have: a measuring unit that irradiates an electromagnetic wave toward a measurement object and a reference surface, causes a reflected wave from the reflection surface of the measurement object and a reflected wave from the reference surface to interfere with each other, and obtains an interference pattern of the interference waves; and The signal processing unit performs Fourier transform on the interference pattern to form an intensity characteristic curve in the depth direction. The signal processing unit includes: a model parameter estimating unit that estimates parameters of the model equation for each of the assumed numbers of surfaces within a predetermined range of the assumed number of surfaces, based on a model equation of an interference pattern assuming that the object to be measured is a layered structure having at least one reflecting surface; an optimal model selection unit that selects an optimal model formula by a statistical method based on the model formula to which the parameters estimated for each of the assumed numbers of faces are applied; and an intensity characteristic curve reconstruction unit, configured to reconstruct an intensity characteristic curve in a depth direction based on the optimal model formula; The optimal model selection unit reconstructs an interferogram using the model formula using the parameters estimated for each of the assumed numbers of surfaces, calculates the likelihood between the reconstructed interferogram and the original interferogram, and selects the optimal model formula based on an information quantity criterion obtained using the assumed number of surfaces as a degree of freedom.

2. The optical interference measurement device according to claim 1, wherein The model parameter estimating unit estimates parameters of the model equation based on a model equation of an interference pattern when the object to be measured is a layered structure having a constant refractive index in each layer and at least one reflecting surface.

3. The optical interference measurement device according to claim 1 or 2, characterized in that The range of the assumed number of faces is determined based on the structural characteristics of the object to be measured.

4. The optical interference measurement device according to claim 1 or 2, characterized in that The range of the number of assumed planes is determined based on the number of peaks of the intensity characteristic curve in the depth direction formed by the original interference pattern.

5. A method for optical interference measurement, characterized in that: The following steps are involved: irradiating an object to be measured and a reference surface with electromagnetic waves, and performing Fourier transform on an interference pattern of interference waves obtained by interfering a reflected wave from the reflection surface of the object to be measured with a reflected wave from the reference surface, thereby forming an intensity characteristic curve in the depth direction; A step of estimating parameters of the model equation for each of the assumed numbers of surfaces within a predetermined range of the assumed number of surfaces, based on a model equation of an interference pattern when assuming that the object to be measured is a layered structure having at least one number of reflection surfaces; a step of selecting an optimal model formula by a statistical method based on the model formula to which the parameters estimated for each of the assumed numbers of faces are applied; and The step of reconstructing the intensity characteristic curve based on the optimal model formula; In the step of selecting the optimal model formula, the interference pattern is reconstructed using the model formula that applies the parameters estimated for each assumed number of surfaces, the likelihood of the reconstructed interference pattern and the original interference pattern is calculated, and the optimal model formula is selected based on the information amount criterion obtained with the assumed number of surfaces as the degree of freedom.

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