Patent Publication Number: US-2022221266-A1

Title: Optical interference measuring apparatus and optical interference measuring method

Description:
The present application is a U.S. National Phase of PCT/JP2020/020586 filed on May 25, 2020 claiming priority to Japanese Patent Application No. 2019-100828 filed on May 30, 2019. The disclosure of the PCT Application is hereby incorporated by reference into the present application. 
    
    
     TECHNICAL FIELD 
     The present invention relates to an optical interference measuring apparatus and an optical interference measuring method and, more particularly, to a Fourier domain optical interference measuring apparatus and a Fourier domain optical interference measuring method. 
     BACKGROUND ART 
     Conventionally, optical coherence tomography (OCT) has been known as a technique of imaging the internal structure of a measurement target at high resolution non-contact, non-invasive manner. 
     Fourier domain OCT (FD-OCT) measurement is a method of acquiring the intensity spectrum of reflected light in the depth direction by measuring an interference light intensity for each light spectrum component and performing fast Fourier transform of the obtained interference signal (interferogram). Typical apparatus configurations for FD-OCT measurement include two types, i.e., a spectral domain-OCT (spectral domain-OCT) apparatus and a swept source-OCT (SS-OCT). 
     Patent Literature 1 discloses a technique of removing noise with a synchronous bandpass filter by providing a lock-in amplifier for weak signal detection on the detector side in measuring an interferogram. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: WO 2015/001918 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, depending on measurement sensitivity, the above noise removal alone is sometimes insufficient. 
     The present invention has been made in consideration of the above circumstances and has as its object to reduce noise in an interferogram in optical interference measurement. 
     Solution to Problem 
     In order to achieve the above object, an optical interference measuring apparatus according to the first aspect of the present invention includes a measuring unit configured to acquire an interferogram of an interference wave by irradiating a measurement target and a reference surface with electromagnetic waves and causing a reflected wave from a reflecting surface of the measurement target to interfere with a reflected wave from the reference surface and a signal processing unit configured to configure an intensity profile in a depth direction by performing Fourier transform of the interferogram. The signal processing unit includes a first noise removal unit configured to perform filtering by deleting data in regions other than a pass region which is a region set with reference to a measurement target installation position from the intensity profile and reconfigure an interferogram by performing inverse Fourier transform of an intensity profile after the filtering. 
     In the first aspect, the signal processing unit preferably includes a second noise removal unit configured to generate a diagonal constant matrix D from an interferogram, calculate a singular value diagonal matrix S by performing singular value decomposition of the diagonal constant matrix D, delete a noise component from the singular value diagonal matrix, and reconfigure an interferogram by using a singular value diagonal matrix from which the noise component is deleted. 
     In addition, an optical interference measuring apparatus according to the second aspect of the present invention includes a measuring unit configured to acquire an interferogram of an interference wave by irradiating a measurement target and a reference surface with electromagnetic waves and causing a reflected wave from a reflecting surface of the measurement target to interfere with a reflected wave from the reference surface and a signal processing unit configured to configure an intensity profile in a depth direction by performing Fourier transform of the interferogram. The signal processing unit includes a second noise removal unit configured to generate a diagonal constant matrix from an interferogram, calculate a singular value diagonal matrix by performing singular value decomposition of the diagonal constant matrix, delete a noise component from the singular value diagonal matrix, and reconfigure an interferogram by using a singular value diagonal matrix from which the noise component is deleted. 
     In the first and second aspects, the second noise removal unit preferably sets an evaluation value based on a component of a singular value diagonal matrix, determines whether the evaluation value is smaller than a predetermined threshold, and repeatedly deletes a noise component from the singular value diagonal matrix until the evaluation value becomes smaller than the predetermined threshold. 
     In the first and second aspects, the signal processing unit preferably includes a model parameter estimation unit configured to estimate, based on a model formula of an interferogram when it is assumed that a measurement target is a layered structure having at least one reflecting surface, a parameter for the model formula for each assumed surface count in a predetermined assumed surface count range, an optimal model selection unit configured to select an optimal model formula by a statistical technique from the model formula to which a parameter estimated for each of the assumed surface count is applied, and an intensity profile reconfiguration unit configured to reconfigure an intensity profile in the depth direction based on the optimal model formula. 
     An optical interference measuring method according to the third aspect of the present invention includes a step of acquiring an interferogram by irradiating a measurement target and a reference surface with electromagnetic waves and causing a reflected wave from a reflecting surface of the measurement target to interfere with a reflected wave from the reference surface, a step of configuring an intensity profile in a depth direction by performing Fourier transform of the interferogram, a step of performing filtering by deleting data in regions other than a pass region which is a region set with reference to a measurement target installation position from the intensity profile, and a step of reconfiguring an interferogram by performing inverse Fourier transform of an intensity profile after the filtering. 
     Advantageous Effects of Invention 
     An optical interference measuring apparatus and an optical interference measuring method according to the above configurations can reduce noise in an interferogram. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating the schematic configuration of an optical interference measuring apparatus according to an embodiment of the present invention. 
         FIG. 2  is a schematic configuration view of the measuring unit of the optical interference measuring apparatus. 
         FIG. 3  is a graph illustrating the shape of an interferogram obtained by the optical interference measuring apparatus. 
         FIG. 4  is a functional configuration view of the signal processing unit of the optical interference measuring apparatus. 
         FIG. 5  is a view for explaining the structure of a layered structure. 
         FIG. 6  is a view illustrating graphs for explaining a method of noise removal by a first noise removal unit. 
         FIG. 7  is a graph for explaining noise removed by noise removal using singular value decomposition. 
         FIG. 8  is a flowchart of processing by an optical interference measuring method using the optical interference measuring apparatus. 
         FIG. 9  is a flowchart of noise removal processing in the optical interference measuring method. 
         FIG. 10  is a flowchart of noise removal processing of the noise removal which uses a filter. 
         FIG. 11  is a flowchart of noise removal processing of the noise removal which uses singular value decomposition. 
         FIG. 12  is a flowchart of model parameter estimation processing in the optical interference measuring method. 
         FIG. 13  is a flowchart of optimal model selection processing in the same method. 
         FIG. 14  is a view illustrating graphs for simulation results of intensity profile reconfiguration using the model parameters estimated by the same method. 
         FIG. 15  is a view illustrating graphs for noise removal results using a filter in the same method. 
         FIG. 16  is a view illustrating graphs for noise removal results by singular value decomposition using an interferogram after noise removal using the filter. 
         FIG. 17  is a view illustrating graphs for optimal model selection results using an interferogram after noise removal by the singular value decomposition. 
         FIG. 18  is a functional configuration view of a signal processing unit according to one modification of the optical interference measuring apparatus according to the embodiment. 
         FIG. 19  is a flowchart for setting an assumed surface count range by the signal processing unit. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, however, the present invention is not limited to these embodiments. In the description of the following embodiments, the same reference numerals denote the same constituent elements, the same terms mean similar constituent elements, and redundant descriptions will be omitted as appropriate. 
     Embodiment 
     1. Overall Configuration of Optical Interference Measuring Apparatus 
       FIG. 1  is a block diagram illustrating the schematic configuration of an optical interference measuring apparatus  1  according to an embodiment of the present invention. The optical interference measuring apparatus  1  is an SS-OCT, and this apparatus is used for, for example, the inspection of the internal structure of a concrete structure. 
     As illustrated in  FIG. 1 , the optical interference measuring apparatus  1  includes a measuring unit  2 , a control processing unit  3 , an operation unit  4 , a display unit  5 , and a storage unit  6 . 
       FIG. 2  illustrates the schematic configuration of the measuring unit  2 . 
     The measuring unit  2  mainly includes a light source  21 , a beam splitter  22 , an automatic stage  23  for the installation of a measurement target, a reference surface  24 , and a detector  25 . 
     The light source  21  is a variable frequency swept light source. This light source emits an electromagnetic beam while sweeping a wavelength at regular intervals within a predetermined wavelength band. It is possible to use, as the light source  21 , an oscillation source such as an oscillation source using a Gunn diode or Shottkey barrier diode (SBD) which is a semiconductor material, and an oscillation source, based on frequency conversion using nonlinear crystal using a wavelength variable semiconductor laser (LD) as seed light. Alternatively, an oscillation source such as a TUNNET diode, resonance tunnel diode (RTD), or monolithic microwave IC (MMIC) may be used as the light source  21 . 
     The beam splitter  22  is, for example, a beam splitter having a branching ratio of 50:50. The beam splitter  22  splits a light beam B from the light source  21  into measurement light B 1  and reference light B 2 . 
     The automatic stage  23  holds a measurement target and sets a measurement surface. The measurement surface is a surface of a measurement target. The automatic stage  23  is configured such that the surface of the measurement target can move in the directions of two axes, that is, the X-axis and Y-axis, when a plane orthogonal to the optical axis of the measurement light B 1  is assumed to be an XY plane. The automatic stage  23  is driven and controlled by a measurement control unit (to be described later). 
     The reference surface  24  is a mirror and reflects the reference light B 2 . 
     The detector  25  is, for example, a Schottky barrier diode provided with a waveguide and an antenna and detects an interference signal between the reflected light of the reference light B 2  (to be described later) and the reflected light of the measurement light B 1  (to be described later). 
     The light source  21  changes the frequency of the oscillator under the control of a measurement control unit  7 . A lock-in amplifier  31  for detecting weak currents is connected to the detector  25 . A function generator  29  applies On-Off modulation to the light source  21  to provide a reference signal to the lock-in amplifier  31  on the detector  25  side. 
     Light emitted from the light source  21  enters the beam splitter  22  through a collimate lens  26   a  and is split into the measurement light B 1  and the reference light B 2 . The reference light B 2  propagates to the reference surface  24  while being collimated by a collimate lens  26   b  and is reflected by the reference surface  24 . This light then propagates to the detector  25  through the beam splitter  22 . Meanwhile, the measurement light B 1  is shaped in terms of its beam shape by a collimate lens  26   c  and propagates to the measurement target. The light reflected by the reflecting surface of the measurement target then enters the beam splitter  22  again and propagates to the detector  25  through a collimate lens  26   d.    
     Note that in this description, the “reflecting surface” of a measurement target includes the surface and the internal reflecting surface of the measurement target. Accordingly, the first reflecting surface means the surface of the measurement target. 
     According to the principle of SS-OCT, when the frequency of the light source  21  is swept, an interference pattern (interferogram) corresponding to the difference between the optical path length of the measurement light B 1  from the measurement target and the optical path length of the reference light B 2  is generated. The detector  25  detects the interference pattern. A DAQ system (data acquisition system) 32 samples and digitizes the detection signal and outputs the resultant signal as image data. This image data is the interferogram illustrated in  FIG. 3 . 
     Referring back to  FIG. 2 , the control processing unit  3  can refer to an arbitrary electrical circuit (or its part). The electrical circuit includes, for example, arbitrary numbers of electrical parts including resistors, transistors, capacitors, and inductors. This circuit may have an arbitrary form including, for example, an integrated circuit, an aggregate of integrated circuits, a microcontroller, a microprocessor, and an aggregate of electrical parts on a printed board (PCB). The control processing unit  3  may be incorporated in the housing of the optical interference measuring apparatus  1 , a standalone device, or part of a discrete personal computer. 
     The control processing unit  3  includes, as functional units, the measurement control unit  7  that controls measurement by the measuring unit  2 , a signal processing unit  8  that processes a signal acquired by the measuring unit  2 , and an output unit  9 . The functions of the respective functional units including functional units further described in detail below may be implemented by circuits or by executing a program. When these functions are to be implemented by a program, the program may be stored in a recording medium such as a magnetic disk, flexible disk, optical disk, compact disk, Blu-ray (trademark registration) disk, or DVD. 
     The measurement control unit  7  modulates the frequency of the light source  21 . In addition, the measurement control unit  7  controls the driving of the automatic stage  23 . The signal processing unit  8  performs processing for configuring an intensity profile from an interferogram. The signal processing unit  8  will be described in detail later. The output unit  9  displays the intensity profile generated by the signal processing unit  8  on the display unit  5  and stores the profile in the storage unit  6 . 
     The operation unit  4  is a device for allowing a user to input instructions to the optical interference measuring apparatus  1  and includes, for example, a mouse, a touch pad, a keyboard, an operation panel, a joystick, buttons, and switches, etc. 
     The display unit  5  is, for example, a liquid crystal display and displays the intensity profile and other information generated by the signal processing unit  8 . 
     2. Detailed Configuration of Signal Processing Unit 
     Next, the signal processing unit  8  will be described in detail with reference to  FIG. 4 . The signal processing unit  8  includes an FFT analysis unit  10 , a super-resolution analysis unit  20 , and a noise removal unit  30 . 
     The FFT analysis unit  10  reconfigures an intensity profile in the depth direction (hereinafter simply referred to as an “intensity profile”) by performing fast Fourier transform of an interferogram. This method is a known method, and hence an explanation of the method will be omitted. 
     The super-resolution analysis unit  20  includes a model parameter estimation unit  201 , an optimal model selection unit  202 , and an intensity profile reconfiguration unit  203 . 
     The model parameter estimation unit  201  models the interferogram measured by the optical interference measuring apparatus  1  and estimates parameters for the model formula. 
     More specifically, as illustrated in  FIG. 5 , assume a virtual layered structure M without attenuation and dispersion which includes a reflecting surface count L of at least one, with a refraction index n 1  in each layer being constant. 
     Letting E r (κ) be an electric field from the reference surface side and Es(κ) be an electric field from the measurement target side, an interferogram I(κ) obtained by measuring the layered structure M can be expressed as follows. Note that in this case, “reflecting surface” is an interface between air and the layered structure M or between adjacent layers and a surface that reflects or internally reflects measurement light, that is, the surface of the layered structure M is the first reflecting surface. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           I 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         = 
                         
                           
                              
                             
                               
                                 
                                   E 
                                   r 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   E 
                                   s 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                              
                           
                           2 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                                
                               
                                 
                                   A 
                                   0 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           ⁢ 
                           
                             
                                
                               
                                 1 
                                 + 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       1 
                                     
                                     L 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     
                                       a 
                                       l 
                                     
                                     ⁢ 
                                     
                                       e 
                                       
                                         i 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                         ⁢ 
                                         
                                           
                                              
                                             ⁢ 
                                             kb 
                                           
                                           l 
                                         
                                       
                                     
                                   
                                 
                               
                                
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where |A O (k)| 2  is the intensity of a light source, 
     
       
         
           
             
               a 
               l 
             
             = 
             
               
                 
                   n 
                   
                     l 
                     + 
                     1 
                   
                 
                 - 
                 
                   n 
                   l 
                 
               
               
                 
                   n 
                   
                     l 
                     + 
                     1 
                   
                 
                 + 
                 
                   n 
                   l 
                 
               
             
           
         
       
     
     is the reflection coefficient (Fresnel reflection) between the layers, b l =[Σ p=1   l (z p −z p−1 )n p ] is the optical path length difference (hereinafter referred to as an “optical distance”) from the reference surface to each layer, z is the distance to each layer, 1=1, 2, 3, . . . , L represents reflecting surface numbers up to L, p=1, 2, 3, . . . , l represents reflecting surface numbers up to 1. 
     When the interferogram l(k) is normalized with the intensity |A O (k)| 2  of the light source and there is no multireflection in the sample, the following approximation can be established. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           D 
                           k 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               I 
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             
                               
                                 
                                   | 
                                   
                                     
                                       A 
                                       0 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           1 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                              
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   1 
                                 
                                 L 
                               
                               ⁢ 
                               
                                 
                                   a 
                                   l 
                                 
                                 ⁢ 
                                 
                                   e 
                                   
                                     i 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       
                                         π 
                                         ⁢ 
                                         kb 
                                       
                                       l 
                                     
                                   
                                 
                               
                             
                              
                           
                           2 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   1 
                                 
                               
                               L 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     a 
                                     l 
                                   
                                   ⁢ 
                                   
                                     e 
                                     
                                       i 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         
                                           π 
                                           ⁢ 
                                           b 
                                         
                                         l 
                                       
                                       ⁢ 
                                       k 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       a 
                                       l 
                                     
                                     * 
                                   
                                   ⁢ 
                                   
                                     e 
                                     
                                       
                                         - 
                                         i 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         
                                            
                                           ⁢ 
                                           b 
                                         
                                         l 
                                       
                                       ⁢ 
                                       k 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   1 
                                 
                               
                               L 
                             
                             ⁢ 
                             
                               
                                 
                                   ∑ 
                                   
                                     m 
                                     = 
                                     1 
                                   
                                 
                                 L 
                               
                               ⁢ 
                               
                                 
                                   a 
                                   l 
                                 
                                 ⁢ 
                                 
                                   
                                     a 
                                     m 
                                   
                                   * 
                                 
                                 ⁢ 
                                 
                                   e 
                                   
                                     
                                       - 
                                       i 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       π 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           
                                             b 
                                             m 
                                           
                                           - 
                                           
                                             b 
                                             l 
                                           
                                         
                                         ) 
                                       
                                     
                                     ⁢ 
                                     k 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             D 
                             κ 
                           
                           ∼ 
                           
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   1 
                                 
                               
                               L 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     a 
                                     l 
                                   
                                   ⁢ 
                                   
                                     e 
                                     
                                       i 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         
                                           π 
                                           ⁢ 
                                           b 
                                         
                                         l 
                                       
                                       ⁢ 
                                       
                                         k 
                                         min 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     e 
                                     
                                       i 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         
                                            
                                           ⁢ 
                                           b 
                                         
                                         l 
                                       
                                       ⁢ 
                                       Δ 
                                       ⁢ 
                                       k 
                                       ⁢ 
                                       κ 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       a 
                                       l 
                                     
                                     * 
                                   
                                   ⁢ 
                                   
                                     e 
                                     
                                       
                                         - 
                                         i 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         
                                           π 
                                           ⁢ 
                                           b 
                                         
                                         l 
                                       
                                       ⁢ 
                                       
                                         k 
                                         min 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     e 
                                     
                                       
                                         - 
                                         i 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         
                                           π 
                                           ⁢ 
                                           b 
                                         
                                         l 
                                       
                                       ⁢ 
                                       
                                         Δ 
                                         ⁢ 
                                         k 
                                         ⁢ 
                                         κ 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where k min  is the minimum wavenumber, Δk is a wavenumber interval, and k=0, 1, 2, 3, . . . , K−1 represents a wavenumber. 
     In addition, equation (2) can be simplified as a model formula as follows by setting 
     Accordingly, model formula (3) has three parameters, namely L, A l , and γ l . 
     The reflecting surface count L is assumed based on model formula (3), and the remaining parameters A l  and γ l  are estimated as follows. An assumed reflecting surface count will be hereinafter referred to as an “assumed surface count.” 
     First, the z conversion of a filter p j  is performed as follows. 
     
       
         
           
             
               
                 
                   
                     P 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ∏ 
                         
                           l 
                           = 
                           1 
                         
                         L 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               x 
                               
                                 - 
                                 1 
                               
                             
                             - 
                             
                               
                                 γ 
                                 l 
                               
                               
                                 - 
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               x 
                               
                                 - 
                                 1 
                               
                             
                             - 
                             
                               
                                 γ 
                                 l 
                               
                               
                                 * 
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           2 
                           ⁢ 
                           L 
                         
                       
                       ⁢ 
                       
                         
                           p 
                           j 
                         
                         ⁢ 
                         
                           x 
                           
                             - 
                             j 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Then, the convolution integral between the normalized interferogram and the filter is as follows. 
     
       
         
           
             
               
                 
                   
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           2 
                           ⁢ 
                           L 
                         
                       
                       ⁢ 
                       
                         
                           p 
                           j 
                         
                         ⁢ 
                         
                           D 
                           
                             κ 
                             - 
                             j 
                           
                         
                       
                     
                     = 
                     0 
                   
                   , 
                   
                     κ 
                     = 
                     
                       2 
                       ⁢ 
                       L 
                     
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       L 
                     
                     + 
                     1 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       L 
                     
                     + 
                     2 
                   
                   , 
                   
                     . 
                     
                         
                     
                     . 
                     
                         
                     
                     . 
                   
                   ⁢ 
                   
                       
                   
                   , 
                   
                     K 
                     - 
                     1 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     This equation can be rewritten into a matrix as follows. 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               D 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                           
                             
                               D 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 - 
                                 1 
                               
                             
                           
                           
                             
                               D 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 - 
                                 2 
                               
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               D 
                               2 
                             
                           
                           
                             
                               D 
                               1 
                             
                           
                           
                             
                               D 
                               0 
                             
                           
                         
                         
                           
                             
                               D 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 + 
                                 1 
                               
                             
                           
                           
                             
                               D 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                           
                             
                               D 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 - 
                                 1 
                               
                             
                           
                           
                             
                               . 
                               
                                   
                               
                               . 
                               
                                   
                               
                               . 
                             
                           
                           
                             
                               D 
                               3 
                             
                           
                           
                             
                               D 
                               2 
                             
                           
                           
                             
                               D 
                               1 
                             
                           
                         
                         
                           
                             
                               D 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 + 
                                 2 
                               
                             
                           
                           
                             
                               D 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 + 
                                 1 
                               
                             
                           
                           
                             
                               D 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               D 
                               4 
                             
                           
                           
                             
                               D 
                               3 
                             
                           
                           
                             
                               D 
                               2 
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             ⋮ 
                           
                           
                             
                                 
                             
                           
                           
                             ⋱ 
                           
                           
                             
                                 
                             
                           
                           
                             ⋮ 
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 2 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 3 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 4 
                               
                             
                           
                           
                             
                               . 
                               
                                   
                               
                               . 
                               
                                   
                               
                               . 
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 1 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 2 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                               
                             
                           
                         
                         
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 1 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 2 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 3 
                               
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 + 
                                 1 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                               
                             
                           
                           
                             
                               D 
                               
                                 K 
                                 - 
                                 1 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               p 
                               0 
                             
                           
                         
                         
                           
                             
                               p 
                               1 
                             
                           
                         
                         
                           
                             
                               p 
                               2 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               p 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 - 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               p 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   Dp 
                   = 
                   0 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     At this time, the data count of D needs to satisfy K≥L+1. However, the actual measurement data, that is, the data set of D k    
     
       
      
       {tilde over (D)} 
      
     
     includes noise, and hence p is obtained by solving the following optimization problem. 
     
       
         
           
             
               
                 
                   arg 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       min 
                       p 
                     
                     ⁢ 
                     
                       
                          
                         
                           
                             D 
                             ˜ 
                           
                           ⁢ 
                           p 
                         
                          
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     where p is the data set of p j . 
     In this case, however, since there is an obvious solution of p=0, some constraint condition must be provided to avoid such a solution. Equation (6) can be expanded into 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           P 
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         = 
                         
                           
                             
                               ∏ 
                               
                                 l 
                                 = 
                                 1 
                               
                             
                             ˜ 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   x 
                                   
                                     - 
                                     1 
                                   
                                 
                                 - 
                                 
                                   
                                     γ 
                                     l 
                                   
                                   
                                     - 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   x 
                                   
                                     - 
                                     1 
                                   
                                 
                                 - 
                                 
                                   
                                     γ 
                                     l 
                                   
                                   
                                     * 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               0 
                             
                             
                               2 
                               ⁢ 
                               L 
                             
                           
                           ⁢ 
                           
                             
                               p 
                               j 
                             
                             ⁢ 
                             
                               x 
                               
                                 - 
                                 j 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               p 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   - 
                                   2 
                                 
                                 ⁢ 
                                 L 
                               
                             
                           
                           + 
                           
                             
                               p 
                               
                                 
                                   2 
                                   ⁢ 
                                   L 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   
                                     - 
                                     2 
                                   
                                   ⁢ 
                                   L 
                                 
                                 - 
                                 1 
                               
                             
                           
                           + 
                           
                             
                               . 
                               
                                   
                               
                               . 
                               
                                   
                               
                               . 
                               
                                 + 
                                 
                                   p 
                                   1 
                                 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 - 
                                 1 
                               
                             
                           
                           + 
                           
                             
                               p 
                               0 
                             
                             ⁢ 
                             
                               x 
                               0 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Therefore, the following constraint condition is provided: 
     
       
         
           
             
               
                 
                   
                     subject 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       p 
                       
                         2 
                         ⁢ 
                         L 
                       
                     
                   
                   = 
                   
                     
                       p 
                       0 
                     
                     = 
                     1 
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     thus, solving the optimization problem of equation (8). Substituting obtained p into polynomial equation (9) to obtain the solution, results in acquiring γ l  and γ l *. 
     Equation (3) can be rewritten into the following matrix. 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             1 
                           
                           
                             1 
                           
                           
                             
                                 
                             
                           
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             
                               
                                 γ 
                                 1 
                               
                               1 
                             
                           
                           
                             
                               
                                 γ 
                                 1 
                               
                               
                                 * 
                                 1 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               1 
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               
                                 * 
                                 1 
                               
                             
                           
                           
                             
                               . 
                               
                                   
                               
                               . 
                               
                                   
                               
                               . 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               1 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               
                                 * 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                 γ 
                                 1 
                               
                               2 
                             
                           
                           
                             
                               
                                 γ 
                                 1 
                               
                               
                                 * 
                                 2 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               2 
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               
                                 * 
                                 2 
                               
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               2 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               
                                 * 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               
                                 γ 
                                 1 
                               
                               3 
                             
                           
                           
                             
                               
                                 γ 
                                 1 
                               
                               
                                 * 
                                 3 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               3 
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               
                                 * 
                                 3 
                               
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               3 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               
                                 * 
                                 3 
                               
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                           
                             ⋮ 
                           
                           
                             
                                 
                             
                           
                           
                             
                                 
                             
                           
                           
                             ⋱ 
                           
                           
                             ⋮ 
                           
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                               
                                 γ 
                                 1 
                               
                               
                                 ( 
                                 
                                   K 
                                   - 
                                   2 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 1 
                               
                               
                                 * 
                                 
                                   ( 
                                   
                                     K 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               
                                 ( 
                                 
                                   K 
                                   - 
                                   2 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               
                                 * 
                                 
                                   ( 
                                   
                                     K 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               . 
                               
                                   
                               
                               . 
                               
                                   
                               
                               . 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               
                                 ( 
                                 
                                   K 
                                   - 
                                   2 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               
                                 * 
                                 
                                   ( 
                                   
                                     K 
                                     - 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 γ 
                                 1 
                               
                               
                                 ( 
                                 
                                   K 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 1 
                               
                               
                                 * 
                                 
                                   ( 
                                   
                                     K 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               
                                 ( 
                                 
                                   K 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 2 
                               
                               
                                 * 
                                 
                                   ( 
                                   
                                     K 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                                 
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               
                                 ( 
                                 
                                   K 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 γ 
                                 L 
                               
                               
                                 * 
                                 
                                   ( 
                                   
                                     K 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               A 
                               1 
                             
                           
                         
                         
                           
                             
                               
                                 A 
                                 1 
                               
                               * 
                             
                           
                         
                         
                           
                             
                               A 
                               2 
                             
                           
                         
                         
                           
                             
                               
                                 A 
                                 2 
                               
                               * 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               A 
                               L 
                             
                           
                         
                         
                           
                             
                               
                                 A 
                                 L 
                               
                               * 
                             
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             D 
                             0 
                           
                         
                       
                       
                         
                           
                             D 
                             1 
                           
                         
                       
                       
                         
                           
                             D 
                             2 
                           
                         
                       
                       
                         
                           
                             D 
                             3 
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               1 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   Ga 
                   = 
                   d 
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     However, as in the above case, the actual measurement data 
     
       
      
       {tilde over (d)} 
      
     
     includes noise, and hence solving the following optimization problem (or Moore-Penrose pseudoinverse matrix) will obtain 
     ã, that is, (a set of) A l . 
     
       
         
           
             
               
                 
                   
                     a 
                     ~ 
                   
                   = 
                   
                     
                       arg 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           min 
                           a 
                         
                         ⁢ 
                         
                           
                              
                             
                               Ga 
                               - 
                               
                                 d 
                                 ˜ 
                               
                             
                              
                           
                           
                             p 
                             = 
                             2 
                           
                           2 
                         
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               G 
                               T 
                             
                             ⁢ 
                             G 
                           
                           ) 
                         
                         
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         G 
                         T 
                       
                       ⁢ 
                       
                         d 
                         ˜ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where (G T G) −1 G T  is the pseudoinverse matrix of G. 
     In this manner, the model parameter estimation unit  201  estimates the parameters A l  and γ l  in the case of the assumed surface count L. 
     The model parameter estimation unit  201  further calculates a measurement target reflection coefficient a l  and an optical distance b l  from the estimated parameters A l  and γ l . 
     First, a l  is obtained by calculating the absolute value of the obtained parameter A l . 
     
       
         
           
             
               
                 
                   
                     a 
                     l 
                   
                   = 
                   
                     
                       | 
                       
                         A 
                         l 
                       
                       | 
                     
                     = 
                     
                        
                       
                         
                           a 
                           l 
                         
                         ⁢ 
                         
                           e 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             
                               
                                 π 
                                 ⁢ 
                                 b 
                               
                               i 
                             
                             ⁢ 
                             
                               k 
                               min 
                             
                           
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     In addition, b l  is obtained from γ l  by using equation (15). 
     
       
         
           
             
               
                 
                   
                     b 
                     l 
                   
                   = 
                   
                     φ 
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       Δ 
                       ⁢ 
                       k 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     where ϕ is the argument of γ l  of a complex number. 
     In this manner, the intensity profiles a l  and b 1  with the assumed surface count L can be obtained. 
     When, however, model formula (3) described above is applied to actual measurement, the reflecting surface count L of the measurement target is unknown. Accordingly, the range of the assumed surface counts L is determined, and the model parameters A l  and γ l  and the intensity profiles a l  and b l  described above are obtained with respect to each assumed surface count within the range. 
     The range of the assumed surface counts L may be determined, for example, based on the structural characteristics of a measurement target. More specifically, a concrete structure such as a tunnel wall surface can be assumed to have a reflecting surface count falling within a predetermined range (for example, the range of 1 to 10) in terms of structure. For this reason, the optical interference measuring apparatus  1  may be configured to allow a user to input or set in advance the range of the assumed surface counts L of measurement targets (a minimum value L min  of L and a maximum value L max  of L) to the apparatus before measurement or computation. 
     The model parameter estimation unit  201  estimates the model parameters A l  and γ l  described above and computes the intensity profiles a l  and b l  with respect to each assumed surface count L within the range of the designated assumed surface counts L (for example, 1, 2, . . . 10). 
     The intensity profile reconfiguration unit  203  reconfigures the intensity profiles a l  and b from equations (15) and (16) obtained by the model parameter estimation unit  201 . 
     The optimal model selection unit  202  calculates the likelihood between the reconfigured interferogram reconfigured by substituting the parameters A l  and γ l  corresponding to each reflecting surface count and estimated by the model parameter estimation unit  201  into model formula (3) and a measured interferogram obtained by measurement. The optimal model selection unit  202  selects an optimal model, i.e., the assumed surface count L constituting the optimal model, by applying the assumed surface count L as the degree of freedom to an information amount criterion based on the degree of freedom and the calculated likelihood. 
     Note that as information amount criteria to be applied, Akaike&#39;s information criteria (AIC), finite correction AIC (AICc), or Bayesian information amount criteria (BIC), etc., can be used, although not specifically limited. Known techniques can be used to calculate a likelihood and can be applied to information amount criteria. 
     The noise removal unit  30  includes a first noise removal unit  301  and a second noise removal unit  302 . 
     First, an interferogram acquired in measurement by the optical interference measuring apparatus  1  theoretically has the shape illustrated in  FIG. 3 . However, in actual measurement, the interferogram includes noise as illustrated in  FIG. 6(A) . Noise includes periodic noise originating from multireflection, etc., in the measurement system and random white Gaussian noise. The first noise removal unit  301  removes periodic noise. The second noise removal unit  302  removes white Gaussian noise. 
     The first noise removal unit  301  will be described. The FFT analysis unit  10  converts an interferogram into an intensity profile by fast Fourier transform (FFT). Converting an interferogram including noise as illustrated in  FIG. 6(A)  into an intensity profile by fast Fourier transform will find peaks, when the surface of a measurement target is set as a measurement target installation position, at positions other than in a region near the measurement target installation position, as illustrated in  FIG. 6(B) . These peaks are periodic noise components. 
     The first noise removal unit  301  multiples an intensity profile by a window function having, as a pass region, a region set with reference to the measurement target installation position at an optical distance in the depth direction of the measurement target and the remaining regions as deletion regions to perform filtering to delete data in the deletion regions.  FIG. 6(C)  illustrates an intensity profile obtained by filtering using a rectangular window. 
     As illustrated in  FIG. 6(B) , a pass region may be set by designating a predetermined range before and after a measurement target installation position as a reference by setting a surface position of the measurement target as a measurement target installation position. If, for example, the thickness of a measurement target is 10 mm and a surface position (measurement target installation position) of the measurement target is 100 mm, a pass region can be set at 50 mm before and after the measurement target installation position, i.e., in the range of 50 mm to 150 mm. As described above, the first noise removal unit  301  functions as a kind of bandpass filter. 
     Alternatively, when the middle position of a measurement target is set as a measurement target installation position, the range obtained by adding a predetermined margin to half of the thickness of the measurement target before and after the measurement target installation position as a reference may be set as a pass region and the remaining regions may be set as deletion regions. 
     In addition, a window function to be used is not limited to a rectangular window illustrated in  FIG. 6(C) , and it is possible to use various types of window functions used for filtering, such as a Gaussian window, a Hann window, and a Hamming window. 
     Next, the first noise removal unit  301  converts the intensity profile obtained by deleting the data in the deletion regions into an interferogram, as illustrated in  FIG. 6(D) , by inverse Fast Fourier transform (IFFT). 
     In this manner, periodic noise can be effectively deleted from an interferogram. 
     The second noise removal unit  302  will be described. 
       FIG. 7  is a graph for explaining white Gaussian noise removed by the second noise removal unit  302 . Referring to  FIG. 7 , the black line indicates a theoretical interferogram, and the gray line indicates an interferogram including white Gaussian noise. The theoretical interferogram and the interferogram including noise almost overlap each other. The envelope of the peaks of the theoretical interferogram has a continuous smooth waveform. In contrast to this, the envelope of the interferogram including white Gaussian noise includes portions protruding randomly as indicated by the arrows and hence is not smoothly continuous. The second noise removal unit  302  deletes such noise in the following manner. 
     (a) The second noise removal unit  302  represents measurement data 
     
       
      
       {tilde over (D)} 
      
     
     in a matrix from the interferogram like equation (8) and generates a constant diagonal matrix with an element count of (K−2L−1)×(2L+1). 
     
       
         
           
             
               
                 
                   ( 
                   
                     
                       
                         
                           
                             D 
                             
                               2 
                               ⁢ 
                               L 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                               + 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                               + 
                               2 
                             
                           
                         
                       
                       
                         
                           
                               
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               1 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             D 
                             
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                               - 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               2 
                               ⁢ 
                               L 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                               + 
                               1 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               3 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               2 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             D 
                             
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                               - 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                               - 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               2 
                               ⁢ 
                               L 
                             
                           
                         
                       
                       
                         
                           
                               
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               4 
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               3 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                               
                           
                         
                       
                       
                         
                           ⋯ 
                         
                       
                       
                         
                           
                               
                           
                         
                       
                       
                         
                           ⋱ 
                         
                       
                       
                         
                           … 
                         
                       
                       
                         
                           
                               
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             D 
                             2 
                           
                         
                       
                       
                         
                           
                             D 
                             3 
                           
                         
                       
                       
                         
                           
                             D 
                             4 
                           
                         
                       
                       
                         
                           
                               
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               + 
                               1 
                               - 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             D 
                             1 
                           
                         
                       
                       
                         
                           
                             D 
                             2 
                           
                         
                       
                       
                         
                           
                             D 
                             3 
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               1 
                               - 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             D 
                             0 
                           
                         
                       
                       
                         
                           
                             D 
                             1 
                           
                         
                       
                       
                         
                           
                             D 
                             2 
                           
                         
                       
                       
                         
                           
                               
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               2 
                               - 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                       
                       
                         
                           
                             D 
                             
                               K 
                               - 
                               1 
                               - 
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                           
                         
                       
                     
                   
                   ) 
                 
               
               
                 
                   ( 
                   
                     1 
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     (b) The second noise removal unit  302  performs singular value decomposition (SVD) of the matrix 
     
       
      
       {tilde over (D)} 
      
     
     according to equation (17). 
     
       
         
           
             
               
                 
                   
                     D 
                     ˜ 
                   
                   = 
                   
                     USV 
                     T 
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     (where 
     U is a unitary matrix (complex numbers: UU*=U*U=I) with an element count of (K−2L−1)×(2L+1), 
     S is a diagonal matrix with an element count of (2L+1)×(2L+1), and 
     V is a unitary matrix with an element count of (2L+1)×(2L+1).) 
     (c) Next, the second noise removal unit  302  obtains the singular value diagonal matrix S according to equation (18). 
     
       
         
           
             
               
                 
                   S 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             σ 
                             1 
                           
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           ⋱ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           0 
                         
                         
                           … 
                         
                         
                           
                             σ 
                             
                               2 
                               ⁢ 
                               L 
                               + 
                               1 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     (where a singular value σ n  is the square root of the eigenvalue of {tilde over (D)}{tilde over (D)} T .) 
     (d) Next, the second noise removal unit  302  calculates an evaluation value V e  from the singular value diagonal matrix S. For example, the evaluation value V e  may be set like equation (19) by regarding a value σ 2L+1  of the (2L+1)th element of the diagonal matrix S as a noise component and also regarding a value σ 2L  of the 2Lth element as a signal component. 
     
       
         
           
             
               
                 
                   
                     V 
                     e 
                   
                   = 
                   
                     
                       σ 
                       
                         
                           2 
                           ⁢ 
                           L 
                         
                         + 
                         1 
                       
                     
                     
                       σ 
                       
                         2 
                         ⁢ 
                         L 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     (e) Next, the second noise removal unit  302  constructs a diagonal matrix S′ according to equation (20) by deleting at least a minimum singular value σ 2L+1  as a noise element from the obtained singular value diagonal matrix S. 
     
       
         
           
             
               
                 
                   
                     S 
                     ′ 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             σ 
                             1 
                           
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           ⋱ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           0 
                         
                         
                           ⋯ 
                         
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Note that the second noise removal unit  302  need not always delete only a minimum singular value but may delete all singular values of components deemed unnecessary. 
     (f) In addition, an interferogram 
     
       
      
       {tilde over (D)}′ 
      
     
     is reconfigured from the calculated diagonal matrix S′ according to equation (21). 
     
       
         
           
             
               
                 
                   
                     
                       US 
                       ′ 
                     
                     ⁢ 
                     
                       V 
                       T 
                     
                   
                   = 
                   
                     
                       D 
                       ~ 
                     
                     ′ 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     where {tilde over (D)}′ is least squares approximation with respect to {tilde over (D)}. That is, the square error of each element of {tilde over (D)}−{tilde over (D)}′ is the minimum. 
     
       
      
       {tilde over (D)}′ 
      
     
     to which noise is removed is not always a diagonal matrix. Accordingly, a diagonal constant matrix {tilde over (D)}′ ave  is obtained by using average values along the diagonals of {tilde over (D)}′. 
     (g) The operations in (b) to (f) are repeated until the evaluation value V e  becomes smaller than a predetermined threshold Th by using the reconfigured diagonal constant matrix {tilde over (D)}′ ave . 
     The interferogram 
     
       
      
       {tilde over (D)}′ 
       ave  
      
     
     with the evaluation value V e  being smaller than the predetermined threshold Th is reconfigured as an interferogram after the noise removal. 
     Only the removal of a first noise component or the removal of a first noise component by singular value decomposition may be separately performed as follows. When, for example, the influence of the first noise component is deemed to be larger and the influence of the second noise component is deemed to be smaller, only the removal of the first noise component is performed. When the influence of the second noise component is deemed to be larger and the influence of the first noise component is deemed to be smaller, only the removal of the second noise component is performed. 
     When both the removal of the first noise component and the removal of the second noise component are performed, removal operations are preferably executed in the following manner, although the execution order is not specifically limited. When the influence of the first noise component is deemed to be larger and the influence of the second noise component is deemed to be smaller, the removal of the first noise component is performed first. When the influence of the second noise component is deemed to be larger and the influence of the first noise component is deemed to be smaller, the removal of the second noise component is performed first. 
     3. Optical Interference Measuring Method 
     An optical interference measuring method using the optical interference measuring apparatus  1  will be described below with reference to  FIGS. 8 to 13 . Assume that in each step described below, obtained parameters, interferograms, intensity profiles, etc., are stored in the storage unit as needed and are read out in subsequent steps. Therefore, an explanation of this operation will be omitted. 
       FIG. 8  is a schematic flowchart for processing by the optical interference measuring method. First, when the processing starts, the noise removal unit  30  removes noise from a measurement interferogram in step S 101 . Next, in step S 102 , the model parameter estimation unit  201  estimates parameters for a model by using the interferogram from which noise has been removed. Next, in step S 103 , the optimal model selection unit  202  selects an optimal model. Next, in step S 104 , the intensity profile reconfiguration unit  203  reconfigures an intensity profile in the depth direction. Processing in each step will be described in detail below. 
       FIG. 9  is a flowchart for detailed processing associated with the noise removal in step S 101 . 
     When noise removal starts, the first noise removal unit  301  removes noise by using a filter in step S 201 . In step S 202 , the second noise removal unit  302  removes noise by singular value decomposition (SVD). Subsequently, the process shifts to step S 102 . 
       FIG. 10  is a detailed flowchart for noise removal by the filter in step S 201 . 
     When noise removal using the filter starts, the FFT analysis unit  10  converts a measurement interferogram into an intensity profile by fast Fourier transform in step S 301 . 
     Next, in step S 302 , the first noise removal unit  301  sets, as a pass region, a region of the intensity profile with reference to a measurement target installation position, and also sets the remaining regions as deletion regions to perform filtering to delete data in the deletion regions. 
     Next, in step S 303 , the first noise removal unit  301  converts the intensity profile after the filtering, which is obtained in step S 302 , into an interferogram by inverse fast Fourier transform and terminates the processing. Subsequently, the process shifts to step S 202 . 
       FIG. 11  is a flowchart for detailed processing for noise removal by singular value decomposition in step S 202 . 
     When noise removal by singular value decomposition starts, the second noise removal unit  302  creates a diagonal constant matrix D from the interferogram in step S 401 . 
     Next, in step S 402 , the second noise removal unit  302  calculates a singular value diagonal matrix S (equation (18)) by performing singular value decomposition of the matrix D. 
     Next, in step S 403 , the second noise removal unit  302  calculates an evaluation value V (equation (19)) from the singular value S. 
     Next, in step S 404 , the second noise removal unit  302  compares the evaluation value V e  with the predetermined threshold Th to determine whether the evaluation value V e  is smaller than the threshold Th. 
     If the evaluation value V e  is equal to or more than the threshold Th (No), the second noise removal unit  302  calculates a singular value S′ by deleting a noise element from the singular value matrix S in step S 405  (equation (20)). 
     Next, in step S 406 , the interferogram matrix 
     
       
      
       {tilde over (D)}′ 
      
     
     is reconfigured by using the singular value decomposition S′. 
     Next, in step S 407 , the diagonal components of the matrix 
     
       
      
       {tilde over (D)}′ 
      
     
     are averaged to obtain the diagonal constant matrix 
     
       
      
       {tilde over (D)}′ 
       ave  
      
     
     so as to establish 
     
       
         
           
             
               D 
               ~ 
             
             = 
             
               
                 
                   D 
                   ~ 
                 
                 ′ 
               
               ave 
             
           
         
       
     
     in step S 408 . The process then returns to step S 402  to repeat steps S 402  to S 404 . 
     On the other hand, if it is determined in step S 404  that the evaluation value V e  is smaller than the threshold Th (YES), the interferogram D is set as an interferogram after the noise removal, and the processing is terminated. The process shifts to step S 102 . 
     Alternatively, instead of providing a threshold and repeating the deletion of a noise component until an evaluation value satisfies the threshold, a repetition count may be set in advance and noise component removal may be repeated until the set count is satisfied. 
       FIG. 12  is a detailed flowchart associated with the estimation of parameters for a model in step S 102 . When model parameter setting starts, the model parameter estimation unit  201  sets the range of the assumed surface counts L (that is, the minimum value L min  and the maximum value L max ) based on user input, etc., in step S 501 . 
     Next, in step S 502 , the model parameter estimation unit  201  initializes the assumed surface count L into L=L min . 
     Next, in step S 503 , the model parameter estimation unit  201  calculates the parameter γ l  for model formula (3) by calculating equations (4) to (12) under the condition of the assumed surface count L min . 
     Next, in step S 504 , the model parameter estimation unit  201  calculates the optical distance b l  from the parameter γ l  obtained in step S 503  by using equation (16). 
     Next, in step S 505 , the model parameter estimation unit  201  calculates the parameter A l  from the interferogram and the parameter γ l  by calculating equations (12) to (14). 
     Next, in step S 506 , the model parameter estimation unit  201  calculates the reflection coefficient a l  from the parameter A l  by using equation (15). 
     Next, in step S 507 , the model parameter estimation unit  201  determines whether the assumed surface count L is equal to or more than L max , that is, analysis with each assumed surface count L within the range of the assumed surface counts L set in step S 501  is thoroughly completed. 
     If L is equal to or more than L max  (Yes), the processing is terminated, and the process shifts to step S 104 . If L is smaller than L max  (No), the model parameter estimation unit  201  increments the assumed surface count L to set L=L+1 in step S 508 . The process then returns to step S 501  to repeat steps S 501  to S 507  until the assumed surface count L becomes equal to or more than L max . 
       FIG. 13  is a detailed flowchart associated with the selection of an optimal model in step S 103 . 
     When the processing starts, the optimal model selection unit  202  sets the range of the assumed surface counts L (that is, the minimum value L min  and the maximum value L max ) set in step S 501 . 
     Next, in step S 602 , the optimal model selection unit  202  initializes the assumed surface count L into L=L min . 
     Next, in step S 603 , the optimal model selection unit  202  reconfigures an interferogram by using the parameters A l  and γ l  estimated by the model parameter estimation unit  201  with assumed surface count L min . 
     Next, in step S 604 , the optimal model selection unit  202  calculates the likelihood between the measured interferogram from which noise has been removed in step S 101  and the reconfigured interferogram in step S 603 . 
     Next, in step S 605 , the optimal model selection unit  202  calculates an information amount criterion with respect to the assumed surface count L by setting the assumed surface count L as the degree of freedom and using the likelihood obtained in step S 604 . 
     Next, in step S 606 , the optimal model selection unit  202  determines whether the assumed surface count L is equal to or more than L max , that is, analysis with all the assumed surface counts L within the range of the assumed surface counts L set in step S 501  is completed. 
     If L is equal to or more than L max  (Yes), the optimal model selection unit  202  compares information amount criterion values corresponding to all the assumed surface counts L with each other to select a model with the assumed surface count L corresponding to the minimum information amount criterion value as an optimal model in step S 607 . The processing is then terminated. 
     On the other hand, if it is determined in step S 606  that L is smaller than L max  (No), the optimal model selection unit  202  increments the assumed surface count to set L=L+1 in step S 608 . The process then returns to step S 603  to repeat steps S 603  to S 606  until the assumed surface count L becomes equal to or more than L max . 
     In this manner, in step S 104 , the assumed surface count corresponding to the selected optimal model is provided for the reconfiguration of an intensity profile by the intensity profile reconfiguration unit  203 . 
     The intensity profile reconfigured in this manner can be used for the analysis of the intensity profile in the depth direction. In addition, interferograms measured by scanning along the two axes, i.e., the X-axis and the Y-axis, can be used for the configuration of a three-dimensional image. 
     4. Examples 
     4-1. Example 1: Simulation Results Based on Estimation of Model Parameters 
       FIG. 14  illustrates the results of simulations of intensity profiles by the optical interference measuring apparatus  1  when the light source  21  is frequency-modulated with 600 GHz to 665 GHz. A measurement target was set such that the optical distance of the surface (first reflecting surface) was 80 mm. The upper, intermediate, and lower graphs each illustrate a result obtained when a sample had the structure illustrated in Table 1 and a constant refractive index of 1.53. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Table 1 Simulation Conditions in Example 1 
               
            
           
           
               
               
               
            
               
                   
                   
                 Sample Structure 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Reflecting 
                 Thickness  
               
               
                   
                 FIG. 14 
                 Surface Count 
                 (mm) 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Upper 
                 2 
                 10 
               
               
                   
                 Intermediate 
                 2 
                 5 
               
               
                   
                 Lower 
                 2 
                 1 
               
               
                   
                   
               
            
           
         
       
     
     Referring to  FIG. 14 , in this embodiment, the black lines indicate intensity profiles a l  and b l  reconfigured based on the model parameters γ l  and A l  estimated from equation (3) upon setting assumed surface count L=2. In comparison with the black lines, the gray lines each indicate the results of converting the same interferogram into an intensity profile only by fast Fourier transform. 
     Each gray line appears as having a broad peak, whereas each black line appears as having a sharp peak. According to the intensity profiles based on fast Fourier transform, the peak on the first surface and the peak on the second surface are separated from each other in the case of a thickness of 10 mm, overlap each other in the case of a thickness of 5 mm, and are not separated at all in the case of a thickness of 1 mm. In contrast to this, according to the intensity profiles reconfigured based on the estimation of model parameters in this embodiment, the peaks on the first and second surfaces are separated from each other at any thickness. 
     This indicates that an intensity profile in the depth direction which is reconfigured based on estimated model parameters obtained by model parameter estimation by using model formula (3) allows measurement with higher resolution than that based on a technique using general Fourier transform. 
     4-2 Example 2: Actual Measurement Experiment 
     (1) Noise Removal by Filter 
     Next, an actual measurement experiment using the optical interference measuring apparatus  1  was performed. Plastic flat plates having the structures indicated by Table 2 and a constant refractive index were used as measurement targets (samples). Measurement was performed such that the measurement target was placed, with the optical distance of the surface (first reflecting surface) being 80 mm, and a light source was frequency-modulated in the range of 600 GHz to 665 GHz.  FIG. 15  illustrates results of noise removal by filter in step S 201  using actually measured interferograms. The upper, intermediate, and lower graphs respectively indicate the results of experiments conducted under the conditions indicated in Table 2. Pass regions were set at −34 mm to +57 mm with reference to the position (80 mm) of a sample surface (that is, the optical distances were 46 mm to 137 mm). 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Table 2 Actual Measurement Experiment Conditions 
               
            
           
           
               
               
               
            
               
                   
                   
                 Sample Structure 
               
            
           
           
               
               
               
               
               
            
               
                   
                 FIGS. 
                 Reflecting  
                 Thickness 
                   
               
               
                   
                 15 to 17 
                 Surface Count 
                 (mm) 
                 Material 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Upper 
                 2 
                 10 
                 polyethylene 
               
               
                   
                 Intermediate 
                 2 
                 5 
                 polyethylene 
               
               
                   
                 Lower 
                 2 
                 1 
                 polystyrene 
               
               
                   
                   
               
            
           
         
       
     
     Referring to  FIG. 15(A) , the gray line indicates an interferogram before filtering. The gray line in  FIG. 15(B)  indicates the intensity profile obtained by fast Fourier transform of the interferogram before filtering. In addition, the black line in  FIG. 15(B)  indicates an intensity profile after the filtering. The black line in  FIG. 15(A)  indicates the interferogram obtained by inverse fast Fourier transform of the intensity profile after the filtering. 
     As illustrated in  FIG. 15(B) , noise not originating from the samples is accurately deleted by filtering upon setting pass regions with reference to the positions of the sample surfaces, that is, the sample installation positions, for samples of any thickness. In addition, periodic noise is deleted from the interferograms obtained by inverse fast Fourier transform of the intensity profiles after filtering. 
     As described above, periodic noise can be removed from an interferogram in the following manner. The interferogram is Fourier transformed to configure an intensity profile. A pass region is set in the intensity profile with reference to the sample installation position to delete data in regions other than the pass region, thus filtering the intensity profile. Inverse Fourier transform is applied to the intensity profile after the filtering. 
     (2) Noise Removal by Singular Value Decomposition (SVD) 
       FIG. 16  indicates the results obtained by noise removal based on singular value decomposition using an interferogram after noise removal by the above filter. 
     Referring to  FIG. 16 , each gray line indicates an interferogram before noise removal by singular value decomposition, and each black line indicates an interferogram after the noise removal by singular value decomposition. At any thickness, portions protruding from the envelopes before the noise removal are removed to obtain smoothly continuous envelopes, as is obviously indicated by the portions of the interferograms after the noise removal which are indicated by the arrows, in particular. 
     As described above, random white Gaussian noise can be removed from an interferogram by generating a diagonal constant matrix from the interferogram, calculating a singular value diagonal matrix by performing singular value decomposition of the diagonal constant matrix, and deleting noise components from the singular value diagonal matrix. 
     (3) Reconfiguration of Intensity Profile by Optimal Model 
     Next, model parameters were estimated at each assumed surface count by using an interferogram after noise removal by singular value decomposition in the above actual measurement experiment and setting the range of the assumed surface counts L to 1 to 10. In addition, an interferogram was reconfigured at each assumed surface count by using the model parameters. The likelihood between the interferogram after the noise removal and the reconfigured interferogram was calculated, and an AIC value at each assumed surface count was obtained by setting the assumed surface count as the degree of freedom, thereby selecting a model exhibiting the minimum AIC value as an optimal model. The assumed surface counts L corresponding to the minimum AIC values were 7, 7, and 6 with thicknesses of 10 mm, 5 mm, and 1 mm, respectively. 
       FIG. 17(A)  illustrates intensity profiles. Each gray line indicates the intensity profile obtained by Fourier transform of an interferogram after noise removal by the singular value decomposition described above. Each black line indicates the intensity profile reconfigured based on the selected optimal model. 
       FIG. 17(B)  illustrates interferograms. Each gray line indicates the interferogram after noise removal by the singular value decomposition described above. Each black line indicates the interferogram reconfigured based on an optimal model. 
     As is obvious from  FIG. 17(A) , at any thickness, the intensity profile reconfigured based on an optimal model can be observed with higher resolution than the intensity profile generated by Fourier transform. At a thickness of 1 mm, peaks on the first and second reflecting surfaces can be separated from each other. 
     Next, as is obvious from  FIG. 17(B) , at any thickness, the interferogram reconfigured from an optimal model can almost reproduce the interferogram after the noise removal as input data. 
     As described above, an interferogram is reconfigured by using a model formula to which the parameters estimated with respect to each assumed surface count are applied, the likelihood between the reconfigured interferogram and the original interferogram is calculated, and an optimal model formula is selected based on the information amount criterion obtained by setting an assumed surface count as the degree of freedom, thereby reconfiguring an intensity profile by using the optimal model formula. As a result, an intensity profile in the depth direction can be measured with higher resolution than that based on a technique using general Fourier transform. 
     Examples described above each indicate the results of simulations and actual measurement experiments for samples, each with the reflecting surface count L of 2. However, similar results were obtained in the case in which the reflecting surface count L is 1 and 3 or more. 
     As described above, the optical interference measuring method according to this embodiment includes a noise removal method of removing noise and a super-resolution analysis method of reconfiguring an intensity profile based on an optimal model upon estimating model parameters and selecting the optimal model. In addition, the noise removal method includes a noise removal method using a filter and a noise removal method based on singular value decomposition. As is obvious from the above experiment results, these methods each can independently produce an effect and only the noise removal operation may be performed for the purpose of noise removal. Alternatively, only the super-resolution analysis method may be performed for the purpose of improving the resolution. Executing together the noise removal method and the super-resolution analysis method will noticeably improve the resolution, thus providing an advantageous effect. 
     5. Modification 
     One modification of this embodiment may be configured such that steps S 501  and S 601  are automatically set.  FIG. 18  is a functional configuration view of a signal processing unit  8   a  of an optical interference measuring apparatus  1   a  according to this modification. The optical interference measuring apparatus  1   a  has a configuration almost similar to that of the optical interference measuring apparatus  1  but differs from the optical interference measuring apparatus  1  in that the signal processing unit  8   a  includes a model parameter estimation unit  201   a  and an optimal model selection unit  202   a  instead of the model parameter estimation unit  201  and the optimal model selection unit  202 , respectively. 
     The model parameter estimation unit  201   a  performs the processing illustrated in  FIG. 19  instead of step S 501  in estimating model parameters. That is, when the setting of the range of the assumed surface counts L starts, the model parameter estimation unit  201   a  refers to the intensity profile obtained by Fourier transform of an interferogram by the FFT analysis unit  10  (for example, in step S 301 , etc.) to determine an assumed surface count based on a peak count in step S 701 . More specifically, when two peaks are confirmed as indicated by the gray line in  FIG. 14 , the range of peak counts of 2±5 (note, however, that the assumed surface count L is a natural number) is set, and the range of the assumed surface counts is determined as 1 to 7. 
     Next, in step S 702 , the range of the assumed surface counts L (that is, the minimum value L min  and the maximum value L max ) is set based on the above determination, and the processing is terminated. The process then shifts to step S 502 . 
     The optimal model selection unit  202   a  also has a configuration similar to that described above. 
     This configuration makes it possible to automatically set a proper range of the assumed surface counts L, thereby facilitating a measuring operation. 
     Note that the present invention is not limited to the above embodiment and may include various changes. The above embodiment has been described in detail for a better understanding of the present invention. However, the present invention is not limited to an apparatus including all the configurations described above. For example, the above description concerns the optical interference measuring apparatus which is an SS-OCT. However, the present invention is not limited to this and can be applied to an optical interference measuring apparatus such as an SD-OCT configured to obtain an intensity profile in the depth direction by Fourier transform. In addition, with regard to some components of each Example, other components may be added, deleted, or replaced. 
     REFERENCE SIGNS LIST 
     
         
           1 ,  1   a : Optical interference measuring apparatus 
           8 ,  8   a : Signal processing unit 
           20 : Super-resolution analysis unit 
           201 ,  201   a : Model parameter estimation unit 
           202 ,  202   a : Optimal model selection unit 
           203 : Intensity profile reconfiguration unit 
           30 : Noise removal unit 
           301 : First noise removal unit 
           302 : Second noise removal unit