WO2002075290A1 - Measuring method and device, and imaging method and device - Google Patents

Abstract

An object is caused to transmit a tera-hertz pulse light generated by a generatig unit. The transmitted light is measurated by a sensor to determine the amplitude ransmittance and the phase difference of a predetermined frequency. From a formula representing the relation among the determined values and the complex index of refraction of the object, the complex index of refraction of the object is determined by successive approximation. This formula reflects the multiple reflection of the tera-hertz pulse light inside the object. When a new approximate solution of the complex index of refraction is determined by successive approximation by giving an approximate solution of the complex index of refraction, the transmittance for the light to emerge from the surrounding medium and enter the object, the transmittance for the light to emerge from the object and enter the medium, and a term based on the multiple reflection are handled as known values determined by the given approximate solution.

Description

 Specification

 Measurement Method and Apparatus and Imaging Method and Apparatus This application is based on Japanese Patent Application No. 74551 (filed on Mar. 15, 2001), the contents of which are incorporated herein by reference.

Technical field

 The present invention relates to a measuring method and an apparatus for measuring a complex refractive index or a complex permittivity of an object to be measured, and a method and an apparatus for imaging an object to be measured using the same. Background art

 A substance has a specific refractive index depending on its properties. The refractive index varies depending on the frequency (and therefore the wave number), and the frequency dependence of the refractive index is inherent to the substance. Therefore, it is widely used to optically measure the refractive index of a substance in order to examine the properties of the substance.

 The information obtained when measuring the transmitted or reflected light of a substance by conventional spectroscopy such as Fourier transform infrared spectroscopy (FTIR) was only the energy transmittance or the energy-reflectance. In order to determine the refractive index (generally a complex number) of a substance based on the measurement results, the frequency dependence of the energy transmittance or the energy reflectance is measured, and the measured results are compared with the theoretical equation in a certain frequency range. Were optimized using the nonlinear least squares method.

 Since such a method involves complicated calculations, there were problems such as a long analysis time. Even when only a complex refractive index for a specific frequency is required, complicated procedures such as finding the frequency dependence of the refractive index are required.

Apart from the method described above, a measurement method for measuring the complex refractive index of an object using Terahertz spectroscopy is described in a paper by Lionel Duvillaret, Frederic Garet, and Jean-Louis Coutaz ("AReliable"). Method for Extraction of Material Parameters in Terahertz Time-Domain Spectroscopy ", IEEE Journal of Selected Topics in Quantum Electronics, Vol. 2, No. 3, pp. 739-746 (1996)).

 Terahertz spectroscopy can simultaneously obtain two pieces of information, amplitude information and phase information. The above-mentioned paper discloses an equation showing the relationship between the complex transmittance and the amplitude transmittance and phase difference obtained by measurement. This equation contains two values obtained from the measurement (amplitude transmittance and phase difference) and two unknowns (the real and imaginary parts of the complex index of refraction). It is possible to find the complex refractive index at each frequency by solving a system of binary equations based on the relational equation that contains. Therefore, complicated procedures such as finding the wavelength dependence of the refractive index are not required.

 However, in this case, it is extremely difficult to solve the equations because the system of binary equations has a very complicated form. Therefore, the measurement method disclosed in the above-mentioned paper introduces a non-negative evaluation function (error function) that always becomes 0 when the optimum value is given when ignoring multiple reflections inside the DUT. However, a method of obtaining the complex refractive index by minimizing the evaluation function is adopted. In addition, when considering multiple reflections inside the device under test, an evaluation function is introduced for terms that are not based on multiple reflections, and terms based on multiple reflections are treated as perturbation, and complex A technique for determining the refractive index is also disclosed. In this successive approximation, when an approximate solution of the complex refractive index is given to obtain a new approximate solution of the complex refractive index, only the term based on the multiple reflection is treated as a known number determined by the given approximate solution. A new approximate solution is obtained by minimizing the evaluation function based on the known numbers. In other words, every time a new approximate solution is obtained during successive approximation, the evaluation function is minimized.

The measurement method disclosed in the above-mentioned paper is superior to the case where a complex refractive index is measured by Fourier transform infrared spectroscopy, in that a complicated procedure such as determining the wavelength dependence of the refractive index is not required. ing. Also, in the measurement method disclosed in the above-mentioned paper, when ignoring multiple reflection, the complex refractive index is obtained by using an evaluation function, so that compared with the case of solving using a complicated equation as it is, The amount of calculation is reduced, and the measurement time can be shortened. Furthermore, when multiple reflections are considered, the shadow By treating the sound by successive approximation, the complex refractive index can be obtained stably and accurately.

 However, in the measurement method disclosed in the above-mentioned paper, the calculation for minimizing the evaluation function must be performed each time a new approximate solution is obtained in the successive approximation, and the amount of calculation for measuring the complex refractive index is required. Will be very much.

 As described above, the case where the complex refractive index is measured has been described.Since it is well known that the complex refractive index and the complex permittivity have a fixed relationship, the case where the complex permittivity of the device under test is measured. The same applies to. Disclosure of the invention

 The present invention eliminates the need for complicated procedures such as finding the wavelength dependence of the refractive index, and furthermore, a measurement method capable of reducing the amount of calculation and stably and accurately measuring the complex refractive index or the complex dielectric constant. An object of the present invention is to provide a method and an apparatus for imaging a device under test using the same.

According to the present invention, a measuring method for measuring a complex refractive index or a complex dielectric constant of an object to be measured detects a terahertz pulse light generated from the terahertz pulse light and a terahertz pulse light that reaches the light source via a predetermined optical path. By irradiating the object to be measured with terahertz pulse light in a state where the object to be measured is arranged on the optical path by using the detecting unit, the pulsed light transmitted through the object to be measured and detected by the detecting unit and the measured object Obtaining a measurement time-series waveform that is a time-series waveform of the electric field strength of one of the pulse lights detected by the detection unit by reflecting the object, and replacing the object to be measured on the optical path. Electric field intensity of the pulsed light generated from the generator and detected by the detector in either the state where the predetermined sample is placed and the state where neither the DUT nor the sample is placed on the optical path. Time series waveform of Calculating a complex refractive index or a complex permittivity of the device under test based on a relationship between the reference time-series waveform and the measured time-series waveform. The calculating step includes: (a) obtaining an amplitude rate of a predetermined frequency based on an amplitude of a predetermined frequency obtained from the measured time-series waveform and an amplitude of a predetermined frequency obtained from the reference time-series waveform; The phase of the predetermined frequency obtained from the shape and the phase of the predetermined frequency obtained from the reference time-series waveform (C) a step-by-step approximation based on an equation indicating the relationship between the amplitude ratio at a predetermined frequency and the phase difference at a predetermined frequency and the complex refractive index or complex permittivity at a predetermined frequency of the device under test. Obtaining a complex refractive index or a complex dielectric constant. In the successive approximation, when an approximate solution of the complex refractive index or the complex permittivity is given to obtain a new approximate solution of the complex refractive index or the complex permittivity, at least light is transmitted from a medium around the measured object to the measured object. A new approximate solution is obtained by treating the transmittance at the time of incidence and the transmittance at the time when light exits from the measured object into the medium as known numbers determined by the given approximate solution. The measuring method for measuring the complex refractive index or the complex dielectric constant of an object to be measured according to the present invention is a method for detecting a terahertz pulse light which is generated from a terahertz pulse light and which reaches the light source via a predetermined optical path. When the object to be measured is placed on the optical path by using the terahertz pulse light, the object is irradiated with the terahertz pulsed light, and transmitted through the object to be measured to detect the electric field Acquiring a measurement time-series waveform that is a time-series waveform of intensity, and either a state in which a predetermined sample is arranged on the optical path instead of the object to be measured or a state in which neither the object nor the sample is arranged on the optical path. In this state, the measured light is measured based on the relationship between the reference time-series waveform, which is the time-series waveform of the electric field strength, of the pulse light generated from the generator and detected by the detector, and the measured time-series waveform. Complex refractive index or complex induction And a calculation step of calculating the rate. The calculation step is as follows: (a) An amplitude ratio of a predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier-transforming the measured time-series waveform to an amplitude of a predetermined frequency obtained by Fourier-transforming the reference time-series waveform, is obtained. (B) obtaining a phase difference between a phase of a predetermined frequency obtained by Fourier-transforming the measured time-series waveform and a phase of a predetermined frequency obtained by Fourier-transforming the reference time-series waveform; c) Obtain the complex refractive index or complex permittivity by successive approximation based on the equation showing the relationship between the amplitude rate and the phase difference of the predetermined frequency and the complex refractive index or complex permittivity of the device under test at the predetermined frequency. And steps. The formula neglects the multiple reflection of the terahertz pulse light inside the device under test.In successive approximation, the approximate solution of the complex refractive index or complex permittivity is given to give the complex refractive index or complex permittivity. When obtaining a new approximate solution, the approximate solution given the transmittance when light enters the object from the medium around the object and the transmittance when light exits from the object to the medium. Should be treated as a known number determined by And obtain a new approximate solution.

 The above equation may reflect the multiple reflection of the terahertz pulse light inside the device under test. In this case, in the successive approximation, when an approximate solution of the complex refractive index or the complex permittivity is given to obtain a new approximate solution of the complex refractive index or the complex permittivity, light is transmitted from the medium around the measured object to the measured object. By treating the term based on the transmittance at the time of incidence, the transmittance at the time when light exits from the DUT to the medium, and the multiple reflection as known numbers determined by the given approximate solution, a new approximate solution is obtained. obtain.

 According to the present invention, a measuring method for measuring a complex refractive index or a complex dielectric constant of an object to be measured detects a terahertz pulse light generated from the terahertz pulse light and a terahertz pulse light that reaches the light source via a predetermined optical path. By using the detector and arranging the object on the optical path and irradiating the object with terahertz pulse light, the pulse light detected by the detector is reflected by the object and reflected by the detector. Obtaining a measurement time-series waveform, which is a time-series waveform of the electric field strength, and, with a predetermined sample placed in place of the DUT on the optical path, reflecting the sample generated from the generator to the detector. Calculating a complex refractive index or a complex permittivity of an object to be measured based on a relationship between a reference time-series waveform that is a time-series waveform of the electric field intensity of the pulsed light detected by the method and a measurement time-series waveform. Is provided. The calculation stage is

(a) obtaining an amplitude rate of a predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier transforming the measured time-series waveform to an amplitude of a predetermined frequency obtained by Fourier-transforming the reference time-series waveform; (B) calculating a phase difference between a phase of a predetermined frequency obtained by Fourier transforming the measured time series waveform and a phase of a predetermined frequency obtained by Fourier transforming the reference time series waveform; Obtaining a complex refractive index or a complex permittivity by successive approximation based on an expression indicating a relationship between a frequency amplitude rate and a phase difference of a predetermined frequency and a complex refractive index or a complex permittivity of the device under test at a predetermined frequency. Have. The equation is to ignore the multiple reflection of the terahertz pulse light inside the DUT, and to reflect the light reflected only once on the surface of the DUT on the detector side and on the surface opposite to the detector of the DUT. This reflects the light reflected only once at the time.In the successive approximation, when the approximate solution of the complex refractive index or the complex permittivity is given to obtain a new approximate solution of the complex refractive index or the complex permittivity, the light is affected. The transmittance and reflectance when light enters the object from the medium around the object, and the light A new approximate solution is obtained by treating the transmittance and reflectivity at the time of exiting into the medium as known numbers determined by the given approximate solution.

 The above equation may reflect the multiple reflection of the terahertz pulse light inside the device under test. In this case, in the successive approximation, when an approximate solution of the complex refractive index or the complex permittivity is given to obtain a new approximate solution of the complex refractive index or the complex permittivity, light is transmitted from the medium around the measured object to the measured object. By treating the transmittance and reflectance at the time of incidence, the transmittance and reflectance at the time when light exits from the DUT to the medium, and the term based on multiple reflection as known numbers determined by the given approximate solution , To obtain a new approximate solution. An imaging method according to the present invention is a method of imaging an object to be measured according to a complex refractive index or a complex dielectric constant of the object to be measured or a distribution of physical property values based on any of these. When measuring the complex refractive index or complex permittivity of each part of the specimen, the above-described measurement method is applied.

According to the present invention, a measuring device for measuring a complex refractive index or a complex dielectric constant of an object to be measured detects a terahertz pulse light which is generated from a terahertz pulse light generating portion and reaches through a predetermined optical path and reaches the terahertz pulse light. A Terahertz pulse light is applied to the object under measurement with the object positioned on the optical path, so that the pulsed light transmitted through the object and detected by the detection unit and the measurement A measurement time-series waveform acquisition unit that acquires a measurement time-series waveform that is a time-series waveform of the electric field strength of one of the pulse lights detected by the detection unit by reflecting an object; The electric field intensity of the pulse light generated from the generator and detected by the detector with the specified sample placed in place of the DUT or with the DUT and sample not placed on the optical path Time series waveform A time-series waveform, based on the relationship between the measured time-series waveform, and a calculator for calculating the complex refractive index or the complex permittivity of the object to be measured, the arithmetic unit is determined from _(a) measurement time series waveform An amplitude rate calculator for calculating the amplitude rate of the predetermined frequency based on the amplitude of the predetermined frequency and the amplitude of the predetermined frequency obtained from the reference time series waveform; and (b) the phase of the predetermined frequency obtained from the measurement time series waveform and the reference time series. (C) a phase difference calculator for calculating a phase difference between the phase of the predetermined frequency and the phase difference of the predetermined frequency, which is obtained from the waveform, and a complex refractive index or complex permittivity of the device under test at the predetermined frequency. Based on relational expression And a successive approximation unit for finding a complex refractive index or a complex permittivity by successive approximation. In the successive approximation, when obtaining a new approximate solution of the complex refractive index or the complex permittivity by giving the approximate solution of the complex refractive index or the complex permittivity in the successive approximation, at least light is reflected from a medium around the object to be measured. A new approximate solution is obtained by treating the transmittance when entering the object and the transmittance when light exits the medium from the object to be measured as known numbers determined by the given approximate solution.

The measuring device for measuring the complex refractive index or the complex dielectric constant of an object to be measured according to the present invention includes a generation unit for the terahertz pulse light and a detection device for detecting the terahertz pulse light generated from the generation unit and arriving via a predetermined optical path. Irradiating the object with terahertz pulse light in a state where the object to be measured is placed on the optical path, the electric field intensity of the pulsed light transmitted through the object and detected by the detector A measurement time-series waveform acquisition unit that obtains a measurement time-series waveform that is a time-series waveform, and a state in which a predetermined sample is arranged on the optical path instead of the object to be measured or neither the object nor the sample is arranged on the optical path In this state, based on the relationship between the measured time-series waveform and the reference time-series waveform, which is the time-series waveform of the electric field strength, of the pulsed light generated from the generator and detected by the detector, Complex refractive index or complex permittivity And a calculation unit for calculating. The calculation unit calculates (a) the amplitude ratio of the predetermined frequency, which is the ratio of the amplitude of the predetermined frequency obtained by Fourier transforming the measured time series waveform to the amplitude of the predetermined frequency obtained by Fourier transforming the reference time series waveform. The amplitude ratio calculation unit to be obtained, and (b) a phase difference for obtaining a phase difference between a phase of a predetermined frequency obtained by Fourier transforming the measurement time-series waveform and a phase of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform. An arithmetic unit, and (c) a complex refractive index by successive approximation based on an equation indicating a relationship between an amplitude rate of a predetermined frequency and a phase difference of the predetermined frequency and a complex refractive index or a complex permittivity of a predetermined frequency of the device under test. Or a successive approximation unit for obtaining a complex permittivity. The equation ignores multiple reflections of the terahertz pulse light inside the device under test, and the successive approximation unit gives an approximate solution of the complex refractive index or complex permittivity in the successive approximation to give the complex refractive index. Or, when obtaining a new approximate solution of the complex permittivity, the transmittance when light enters the object from the medium around the object and the transmittance when the light exits from the object to the medium Is treated as a known number determined by the given approximate solution, thereby obtaining a new approximate solution. When calculating the complex refractive index or the complex permittivity, the successive approximation unit can use an expression reflecting multiple reflection of the terahertz pulse light inside the device under test. In this case, in the successive approximation, when the approximate solution of the complex refractive index or the complex permittivity is given in the successive approximation to obtain a new approximate solution of the complex refractive index or the complex permittivity, light is applied to the medium around the object to be measured. By treating the transmittance based on the incident light from the object to the measured object, the transmittance when the light is emitted from the measured object to the medium, and the term based on multiple reflection as known numbers determined by the given approximate solution , Get a new approximate solution.

According to the present invention, a measuring device for measuring a complex refractive index or a complex dielectric constant of an object to be measured detects a terahertz pulse light which is generated from a terahertz pulse light generating portion and reaches through a predetermined optical path and reaches the terahertz pulse light. A Terahertz pulsed light irradiating the DUT with the DUT placed on the optical path, reflecting the DUT and detecting the electric field of the pulsed light detected by the detector. A measurement time-series waveform acquisition unit that acquires a measurement time-series waveform that is a time-series waveform of intensity, and a sample generated from the generation unit and reflected by a predetermined sample placed on the optical path in place of the DUT. Calculates the complex refractive index or complex permittivity of the DUT based on the relationship between the reference time-series waveform, which is the time-series waveform of the electric field strength, of the pulse light detected by the detection unit, and the measured time-series waveform. And an operation unit that performs the operation. The calculation unit includes: ( _a ) a predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier-transforming the measured time-series waveform to an amplitude of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform; (B) the phase of the predetermined frequency obtained by Fourier transforming the measured time series waveform and the phase of the predetermined frequency obtained by Fourier transforming the reference time series waveform; A phase difference calculation unit for calculating a phase difference; and And a successive approximation unit for obtaining a complex refractive index or a complex permittivity by approximation. The formula ignores the multiple reflection of the terahertz pulse light inside the DUT, and reflects the light reflected only once on the surface of the DUT on the detector side and the surface on the opposite side of the detector from the DUT. The successive approximation unit gives a complex refractive index or complex permittivity approximate solution in the successive approximation to provide a new approximate solution of complex refractive index or complex permittivity in the successive approximation. When light is incident on the DUT from the medium around the DUT, A new approximate solution is obtained by treating the transmittance and reflectivity at the time of exposure and the transmittance and reflectivity when light exits from the object to be measured into the medium as known numbers determined by the given approximate solution.

 For the successive approximation unit, an expression reflecting multiple reflection of the terahertz pulse light inside the object to be measured can be used. In this case, in the successive approximation, when giving an approximate solution of the complex refractive index or the complex permittivity to obtain a new approximate solution of the complex refractive index or the complex permittivity in the successive approximation, light is emitted around the object to be measured. The transmittance and reflectivity when light enters the object from the medium, the light transmittance and reflectivity when light exits from the object to the medium, and terms based on multiple reflection are determined by the given approximate solution. A new approximate solution is obtained by treating it as a known number.

 An imaging apparatus according to the present invention is an apparatus for imaging an object to be measured in accordance with a complex refractive index or a complex dielectric constant of the object to be measured or a distribution of physical property values based on either of them. including. BRIEF DESCRIPTION OF THE FIGURES

 FIG. 1 is a schematic configuration diagram schematically illustrating an imaging device according to a first embodiment of the present invention.

 FIG. 2 is a diagram schematically illustrating a state in the vicinity of a measurement site of an object to be measured according to the first embodiment of the present invention.

 FIG. 3 is a schematic flowchart showing the operation of the control / arithmetic processing unit of the imaging device according to the first embodiment of the present invention.

 FIG. 4 is a schematic configuration diagram schematically showing an imaging device according to the second embodiment of the present invention.

 FIG. 5 is a diagram schematically showing a state near a measurement site of an object to be measured in the second embodiment of the present invention.

FIG. 6 is a schematic flowchart showing the operation of the control / arithmetic processing unit of the imaging device according to the second embodiment of the present invention. BEST MODE FOR CARRYING OUT THE INVENTION

 Hereinafter, a measuring method and apparatus, and an imaging method and apparatus according to the present invention will be described with reference to the drawings.

 [First Embodiment]

 FIG. 1 is a schematic configuration diagram schematically illustrating an imaging device according to a first embodiment of the present invention. FIG. 2 is a diagram schematically showing a state near the measurement site of the DUT 20 according to the present embodiment. FIG. 3 is a schematic flowchart showing the operation of the control / arithmetic processing unit 23 of the imaging apparatus according to the present embodiment.

 In the imaging device according to the present embodiment, as shown in FIG. 1, a femtosecond pulse light L 1 radiated from a femtosecond pulse light source 1 composed of a laser light source or the like is converted into two pulse lights L by a beam splitter 2. Divided into 2, L3.

 One of the divided pulse lights L 2 becomes a pump pulse (pulse excitation light) for exciting the terahertz light generator 7 and causing the generator 7 to generate the terahertz pulse light. After being pumped by the chopper 3, the pump pulse L 2 is guided to the terahertz light generator 7 through the plane reflecting mirrors 4, 5 and 6. The other split pulse light L 3 is a probe pulse for determining the timing for detecting terahertz pulse light.

(Sampling pulse light). The probe pulse L3 is guided to the terahertz photodetector 11 through a plane reflecting mirror 8, a movable mirror 9 formed by combining two or three plane reflecting mirrors, and a plane reflecting mirror 10.

 The movable mirror 9 arranged on the optical path of the probe pulse L3 can be moved in the direction of the arrow X by the moving mechanism 12. The moving mechanism 12 is controlled by a control / arithmetic processor 23. The optical path length of the probe pulse L3 changes according to the amount of movement of the movable mirror 9, and the time for the probe pulse L3 to reach the detector 11 is delayed. That is, in the present embodiment, the movable mirror 9 and the moving mechanism 12 constitute a time delay device that changes the time at which the probe pulse L3 reaches the detector 11.

On the other hand, when the generator 7 is excited by the pump pulse L2, the generator 7 emits a terahertz pulse light L4 to the tera. The Rutsuparusu light L 4 to Terra, approximately 0. 1 X 1 0 ¹² from 1 0 0 X 1 0 ¹² optical frequency domain to Hertz is preferable. Terra Hertz The pulsed light L4 is condensed at the condensing position via curved mirrors 13 and 14 such as a parabolic mirror. In the present embodiment, a measurement site of the device under test 20 is arranged at this focusing position. Here, it is assumed that the DUT 20 is a plate-like member having a parallel plate with a known thickness d and is made of a uniform material. However, the DUT 20 is not limited to this.For example, when locally irradiating terahertz pulse light, the thickness d may be different for each measurement site if known. .

 The device under test 20 is arranged such that the optical axis of the terahertz pulse light L4 with respect to the device under test 20 substantially matches the normal to the surface of the device under test 20. To improve the measurement accuracy, it is better for the incident angle distribution to be narrow, so that the smaller the angle 0 between the outermost ray of the terahertz pulse light L4 incident on the DUT 20 and the optical axis is, the better. good. On the other hand, in order to increase the spatial resolution as an image, the larger the angle S, the better. Therefore, it is necessary to determine the angle 0 as necessary.

 If an image is not required, it is not shown in the drawing, but it is better to use an irradiation optical system in which the terahertz pulsed light L4 is incident on the DUT 20 as parallel light. It is more preferable to improve the value. In the following description, a description will be given assuming that the terahertz pulse light is perpendicularly incident on the device under test 20, but the case of oblique incidence can be similarly considered.

 In the present embodiment, the DUT 20 can be two-dimensionally moved in the in-plane direction of the DUT 20 by a moving mechanism 26 such as a stage. Thus, the measurement site of the object 20 can be two-dimensionally scanned along the surface of the object 20.

 The terahertz pulse light L5 transmitted through the device under test 20 passes through curved mirrors 15 and 16 such as a parabolic mirror and is detected by a detector 11. The terahertz pulse light L5 detected by the detector 11 is converted into an electric signal and sent to the amplifier 21.

The repetition period of the femtosecond pulse light L1 emitted from the femtosecond pulse light source 1 is on the order of several KHz to MHz. Therefore, the terahertz pulse light L4 emitted from the generator 7 is also emitted in a repetition on the order of several KHz to MHz. The existing detector 11 instantaneously converts the waveform of this terahertz pulse light into its It is impossible to measure the shape as it is.

 Therefore, in the present embodiment, utilizing the fact that the terahertz pulse light L 4 having the same waveform is radiated in the order of several KHz to MHz repeatedly, the distance between the pump pulse L 2 and the probe pulse L 3 is increased. A method of measuring the waveform of the terahertz pulse light L5 with a time delay, that is, the so-called pump-probe method, is adopted. That is, by delaying the timing for activating the terahertz light detector 11 by a second with respect to the pump pulse L2 for activating the terahertz light generator 7, the terahertz pulse at a point in time delayed by The electric field intensity of the light L5 can be measured by the detector 11. In other words, the probe pulse L 3 gates the terahertz photodetector 11.

 By gradually moving the movable mirror 9, the delay time can be gradually changed. By shifting the timing of applying the gate by the time delay device described above, the electric field strength at each delay time of the repeatedly arriving terahertz pulse light L5 can be sequentially obtained as an electric signal from the detector 11. it can. This makes it possible to measure the time-series waveform E (t) of the electric field intensity of the terahertz pulse light L5. The terahertz photodetector 11 generates an optically excited carrier only when receiving the probe pulse L3. At this time, if an electric field of the terahertz pulse light is applied, a photoconductive current proportional to the electric field flows. The measured current J (te) can be expressed using the electric field E (t) of the terahertz pulse light and the photoconductivity g (t—te) of the photoexcited carrier. That is, J (te) = SE (t) g (t) dt. Since the photoconductivity g (t—te) has a delta function characteristic, the measured current value J (te) should be considered to be proportional to the electric field strength E (t) of the incoming terahertz pulse light L5. Can be. The electric signal sent from the detector 11 to the amplifier 21 is amplified by the amplifier 21 and then A / D converted by the A / D converter 22.

In the present embodiment, when measuring the time-series waveform E (t) indicating the electric field intensity of the terahertz pulse light L5, the control / arithmetic processing unit 23 transmits a control signal to the moving mechanism 12 to delay the signal. While gradually changing the time, the AZD converter 22 The stored data is stored in memory 23A. As a result, the entire data showing the time-series waveform E (t) of the electric field intensity of the terahertz pulsed light L5 transmitted through a certain measurement site of the device under test 20 is stored in the memory 23A. Thereafter, the control / arithmetic processing unit 23 transmits a control signal to the moving mechanism 26 and sequentially scans the measurement site of the device under test 20 two-dimensionally, thereby obtaining a time-series waveform E (t) for each measurement site. ) Is stored in memory 23A.

 In the present embodiment, the device under test 20 is arranged on the optical path between the generator 7 and the detector 11 (in this embodiment, the condensing position of the terahertz pulse light L4 shown in FIG. 1). The time-series waveform E (t) of the electric field intensity of the terahertz pulse light measured in this state is called the measured time-series waveform Es am (t).

As can be understood from the above description, in the present embodiment, the above-described elements 1 to 16, 21, 22, and 26, the function of the control / arithmetic processing unit 23 for controlling the moving mechanisms 12 and 26, and the control The function that the arithmetic processing unit 23 takes in data from the A / D converter 22 constitutes a measurement time series waveform acquisition unit that acquires a measurement time series waveform E _saB (t) for each measurement site. The control / arithmetic processing unit 23 performs an operation shown in FIG. 3 described later, and can be configured using, for example, a convenience store.

Here, a method of obtaining the complex refractive index N (ω) of the DUT 20 based on the measured time-series waveform E _sam (t), which is employed in the present embodiment, will be described.

In a state where the device under test 20 is not placed on the optical path between the generator 7 and the detector 11, the electric field strength of the terahertz pulse light is the same as when measuring the measurement time-series waveform E _S (t). Measure the time series waveform E (t) of degrees in advance. This time-series waveform E (t) is referred to as a reference time-series waveform E _rei (t).

The reference time-series waveform E _ref (t) is subjected to a Fourier transform defined by the following equation (1) to obtain a reference (reference) amplitude IE _ref (ω) I and a phase S _ref (ω) Ask for. The Fourier transform defined by the following equation (1) is performed on the measured time-series waveform E _san (t) to obtain the amplitude IE _sam (ω) I and the phase 6 _S (ω).

[Equation 1] Ε {ω) =… (1)

Next, the complex amplitude transmittance t (ω) of the device under test 20 is determined by the following equation (2). That is, while obtaining the amplitude transmittance Τ (ω) which is the ratio between the amplitude 1 E _S (ω) I and the amplitude IE _ref (ω) |, the phase difference between the phase 0 _S (ω) and the phase S _ref (ω) Obtain φ (ω). [Equation 2]

(2)

 The complex amplitude transmittance t (ω) of a substance (the DUT 20) can be represented by the complex refractive index Ν (ω) of the substance. Here, t 1 (ω) and r 1 (ω) are the complex transmittance and the complex reflectance when light enters the substance from the medium, respectively, and the complex transmittance and complex reflection when the light exits from the substance to the medium. Let the rates be t 2 (ω) and r 2 (ω), respectively. These values t 1 (ω), r 1 (ω), t 2 (ω), and r 2 (ω) are expressed by the complex refractive index 物質 ( ω). However, in the present embodiment, the refractive index η of the medium on both sides of the DUT 20 is assumed assuming that the DUT 20 is in the air or in a vacuum. Is 1. Note that the refractive index η. It can be considered in the same way even when the value is other than 1, and it is not necessary that the mediums on the entrance side and the exit side are the same.

 [Equation 3]

 Two

 (3)

 Ν {ω) + 1

[Equation 4]

 1-Ν {ω)

 (Four)

 1 + Ν {ω)

[Equation 5]

 , 2Ν (ω)

 ( Five)

 2 'Ν {ω) + 1

[Equation 6] (6)

Ν {ω) +1 The complex refractive index Ν (ω) of the device under test 20 is expressed by the following equation (7), where η _Ε (ω), η, (ω) are real numbers.

 [Equation 7]

Ν (ω) = n _R (ω) + in _x (ω)

 The terahertz pulse light transmitted through the device under test 20 includes various patterns of transmitted light shown in FIGS. 2 (a) to 2 (d). Fig. 2 (a) shows the light that is transmitted without being reflected inside the DUT 20 (transmitted light that is not multiple reflection), and Fig. 2 (b) is the light that is reflected twice inside the DUT 20. Fig. 2 (c) shows the light that is reflected and transmitted four times inside the DUT 20 (light that has been multiply reflected), and Fig. 2 (d) ) Indicate light that is reflected and transmitted 2 k times inside the DUT 20 (light that has been k-times reflected multiple times). Here, k is an integer of 0 or more.

 Considering multiple reflections up to m times, the complex amplitude transmittance t (ω) is given by the following equation (8), where ω is the angular frequency of light, d is the thickness of the DUT 20 and c is the speed of light. expressed. However, A in equation (8) was placed as shown in the following equation (9).

 8 (ω) = t, (ω) -ίΛωγ exp ί {Ν {ω) -ί}

 exp ω)

 c

[Equation 9]

A = ίΛω} (ω) χ A \ · exp (/ arg A) (9)

By substituting the equations (2) and (7) into the equation (8), the following equation (10) is obtained. Equation (10) is an equation showing the relationship between the amplitude transmittance Τ (ω) and the phase difference φ (ω) and the complex refractive index Ν (ω) = n _R (ω) + i 11 [(ω). . Equation (10) is an equation that ignores multiple reflections when m = 0, and an equation that reflects multiple reflections when m≥1. In the present embodiment, the measurement of E (t) is terminated at the maximum delay time determined by the length of the moving mechanism 12. At this time, if the thickness d and the approximate refractive index of the DUT 20 are known, the number of possible multiple reflections within the maximum delay time can be known. In some cases, the number of multiple reflections can be determined directly from the measured time-series waveform. In order to further improve the measurement accuracy of the complex refractive index, it is preferable that m in the equation (10) is matched with the actual number of multiple reflections. In the present embodiment, however, any integer of m ≥ 0 Should be set to. That is, multiple reflections may be ignored or taken into account. If m = 0, then A = tl (ω) · t2 (ω).

 [Equation 10]

Τ {ω) ε ^{ίφ [ω]} = exp ί {η „\ ω) + irij (ω) -ΐ) − d χ \ A \-exp (i arg A) (1 0)

 c

 Taking the logarithm of both sides of equation (10) gives the following equation (11).

[Equation 1 1]

 For the real part and the imaginary part of the equation (11), the relations of the following equations (12) and (13) hold, respectively.

[Equation 1 2]

[Equation 1 3]

η _Ε (ω) is expressed by the following equation (1 4) from the following equation (1 3), and (ω) is expressed by the following equation (1 5) from the equation (1 2).

[Equation 1 4] n _R {ω) = ― {φ {ω)-arg} + 1… (1 4)

do) [Equation 1 5]

In Equations (14) and (15), the amplitude transmittance Τ (ω) and the phase difference φ (ω) are values obtained from the measured values as described above. However, the parameter Α included in Equations (14) and (15) depends on n _R (ω) and (ω) (Equations (9), (3), (5) to (5) (7)), it is very difficult to solve equations (14) and (15) simultaneously.

The inventor of the present invention obtains the following successive approximation for the first time by deriving the equations (14) and (15) from the equation (10) with the parameter 一 as shown in the equation (9). It was found that the complex refractive indices ( _nR ( _ω ) and η 【(ω)) were _obtained by extremely simple calculations. That is, unlike the measurement method disclosed in the above-mentioned paper, the amount of calculation can be reduced and the complex refractive index can be stably and accurately obtained without using an evaluation function.

First, appropriate initial values are given as approximate solutions for n _R (ω) and _ηι (ω). For example, since the approximate value of the complex refractive index of the device under test 20 is generally known, this value can be used as an initial value. Substitute the approximate solution into equation (9) to calculate Α (ie, IAI and arg A). Equation (3) and Equations (5) to (7) are used when calculating A. Treat the calculated A as a known number determined by the given approximate solution, and substitute it into Equations (14) and (15) to calculate the values of n _R (ω) and (ω). By using the calculated n _R (ω) and (ω) as new approximate solutions and repeating the same calculation until the values of η _κ (ω) and (ω) converge, the complex refractive index Ν (ω) = n _R (ω) + i nj (ω) can be obtained.

As described above, in the successive approximation, when an approximate solution of the complex refractive index is given to obtain a new approximate solution of the complex refractive index, Α is treated as a known number determined by the given approximate solution. Get a solution. That is, when m = 0 (that is, when the multiple reflection is ignored), the transmittance tl and the light when the light enters the device 20 from the medium around the device 20 are measured. Transmittance t 2 when exiting from 0 to the medium By treating as a known number determined by the given approximate solution, a new approximate solution is obtained. When m≥l (ie, when multiple reflections are considered), an approximation given by the terms based on the transmittance tl, the transmittance t2, and the multiple reflection (the term ∑ in equation (9)) A new approximate solution is obtained by treating it as a known number determined by the solution.

 Referring to FIG. 1 again, the control / calculation processing unit 23 obtains the complex refractive index for each measurement site of the DUT 20 by the above-described calculation. The image processing unit 24 generates image data indicating the distribution of the complex refractive index of the device under test 20 obtained by the control / arithmetic processing unit 23. The generated image is displayed on a display unit 25 such as a CRT.

 An example of the operation of the control / arithmetic processing unit 23 in the present embodiment will be described with reference to FIG. When the control and arithmetic processing unit 23 starts operation, it measures the reference time-series waveform E ref (t) (step S1), performs a Fourier transform on the measured reference time-series waveform Eref (t), and performs amplitude I Eref (ω) | and the phase Θ ref (ω) are obtained (step S2). Next, the control / arithmetic processing unit 23 measures the measurement time series waveform Esam (t) for each measurement site of the DUT 20 (step S3), and converts the measured measurement time series waveform Esam (t). Fourier transform is performed to find amplitude I Esam (ω) | and phase 0sam (co) (step S4). Then, using the amplitude I Eref (ω) | and the phase 0 ref (ω) obtained in step S 2 and the amplitude I Esam (ω) | and the phase S sam (ω) obtained in step S 4, The transmittance Τ (ω) and the phase difference φ (ω) are calculated (step S5).

Subsequently, the control / arithmetic processing unit 23 performs the processing of steps S6 to S10 described below for each measurement site of the DUT 20. That is, for a certain measurement site, initial approximation n _R (ω), η, set the (omega) (Step S 6), the approximate value currently set _{η Β (ω), η,} (ω) Then, the parameter Α is calculated by the method described above (step S 7).

The control / arithmetic processing unit 23 calculates A, the latest calculated in step S7, and the amplitude transmittance T (ω) and the phase difference φ (ω) calculated in step S5 for the measurement site, using the formula ( 14) and by substituting the equation (1 5), a new approximate solution n _R (omega) 'eta, calculates the (omega) (step S 8). Next, the control / arithmetic processing unit 23 determines whether or not the approximate solution _ηκ (ω), η, (ω) obtained most recently in step S8 has converged (step S8). 9). This determination is made, for example, by comparing the approximate solution η _κ (ω), η, (ω) obtained most recently in step S8 with the approximate solution n _R (ω), (ω) obtained in the previous calculation. This can be performed based on whether the difference (absolute value) is equal to or less than a predetermined value.

If it is determined not to be converged in the step S 9, the approximate solution obtained to date in step _{S 8 n R (ω),} η, set the (omega) as a new approximate value (Step S 1 0) Return to step S7.

On the other hand, if it is determined that the convergence has been achieved in step S9, the control / calculation processing section 23 ends the calculation for the measurement site. Thereafter, the control / arithmetic processing unit 23 controls the moving mechanism 26, and repeats the processing of steps S6 to S10 for the remaining measurement sites. If it is determined that the approximate solutions η _κ (ω), η, (ω) have converged for all the measurement sites, the converged approximate solutions n _R (ω), η, (ω) (that is, The complex refractive index of the measurement site) is supplied to the image processing unit 24. The image processing unit 24 displays an image indicating the distribution of the complex refractive index on the display unit 25 (Step S11), and ends the operation.

 Steps S 1 and S 2 need not be performed each time the complex refractive index of the device under test 20 is measured, but may be performed at an appropriate frequency. For example, it may be performed only once at the time of product shipment.

 According to the present embodiment, unlike the measurement method disclosed in the above-mentioned paper, the amount of calculation is reduced, and the complex refractive index or the complex dielectric constant is accurately measured without using an evaluation function. Can be.

 In the measurement method described above, when measuring the reference time-series waveform Eref (t), neither the DUT 20 nor any other sample was placed on the optical path of the terahertz light. However, in a state where a sample having a known complex refractive index and a known thickness is arranged on the optical path instead of the DUT 20, the measured time-series waveform E (t) is changed to the reference time-series waveform Eref (t ) May be used.

Also, in many cases, the magnetic permeability can be regarded as 1, and therefore, there is a relationship between the complex refractive index N (ω) and the complex permittivity ε (ω) as expressed by the following equation (16). Therefore, by substituting the complex index of refraction Ν (ω) obtained by the above method into Eq. (16), The electric power ε (ω) can be obtained. If Equation (16) is substituted into Equations (3) through (15), the complex index Ν (ω) can be found without finding the complex index Ν (ω). It is also possible to determine the complex permittivity ε (ω).

 [Equation 1 6]

ε {ω) = Ν (ω) ² … (1 6)

 [Second embodiment]

 FIG. 4 is a schematic configuration diagram schematically showing an imaging device according to the second embodiment of the present invention. FIG. 5 is a diagram schematically showing a state near the measurement site of the DUT 20 according to the present embodiment. FIG. 6 is a schematic flowchart showing the operation of the control-arithmetic processing unit 23 of the imaging device according to the present embodiment.

 In FIG. 4, the same or corresponding elements as those in FIG. 1 are denoted by the same reference numerals, and the description thereof will not be repeated.

 The difference between the imaging device according to the present embodiment and the first embodiment described above is as follows. That is, in the first embodiment, the transmitted light of the DUT 20 is detected by the detector 11, whereas in the present embodiment, the reflected light of the DUT 20 is detected by the detector 11 1 And the operation of the control / arithmetic processing unit 23.

 In the above-described first embodiment, the measurement time-series waveform Esam (t) regarding the transmitted light is acquired for each measurement site of the DUT 20. In the present embodiment, a similar method is used. As a result, a measurement time-series waveform Esam '(t) related to reflected light is acquired for each measurement site of the DUT 20.

 Here, a method of obtaining the complex refractive index N (ω) of the device under test 20 based on the measurement time-series waveform Esam ′ (t), which is employed in the present embodiment, will be described.

On the optical path between the generator 7 and the detector 11, a sample having a known complex refractive index and a known thickness is placed instead of the device under test 20. The reflectivity of this sample is preferably about 100%. In this state, the time-series waveform E (t) of the electric field intensity of the terahertz pulse light related to the reflected light is measured in advance, as in the case of acquiring the measurement time-series waveform Esam '(t). This time-series waveform E (t) is called a reference time-series waveform Erei '(t). By performing a Fourier transform on the reference time-series waveform Eref '(t) as defined by equation (1), the reference (reference) amplitude I Eref' (ω) I and the phase 0 ref (ω) is calculated. The amplitude l Esam '(ω) | and the phase Ssani' (ω) are calculated by performing a Fourier transform as defined by equation (1) on the measured time-series waveform E sanT (t). I do.

 Further, the complex amplitude reflectance r (ω) of the device under test 20 is obtained by the following equation (17). That is, while calculating the amplitude reflectance R (ω), which is the ratio of the amplitude I Esam '(ω) | to the amplitude | Eref' (ω) |, the phase SsanT (ω) and the phase Sref '(ω) Calculate the phase difference (ω).

[Equation 1 7]

 The complex amplitude reflectance r (ω) of a substance (the device under test 20) can also be expressed using the complex refractive index Ν (ω) of the substance.

 The terahertz pulse light reflected by the device under test 20 includes various patterns of reflected light shown in FIGS. 5 (a) to 5 (d). FIG. 5 (a) shows light reflected only on the incident surface (the surface on the detection unit 11 side) of the device under test 20 (reflected light that is not reflected once and is not a multiple reflection inside). (b) is light that is reflected only once on the surface of the DUT 20 opposite to the detection unit 11 (reflected light that is reflected once inside but is not multiple reflection), and FIG. The light reflected three times inside the object 20 (light reflected multiple times). Figure 5 (d) shows the light reflected (2 k-1) times inside the object 20 ((k-1) ). Here, for convenience, let k be an integer greater than or equal to 0, and refer to the light shown in Fig. 5 (b) as light multiply reflected 0 times, and the light shown in Fig. 5 (a) as light multiply reflected once. To In FIG. 5, the number of reflections indicates the number of reflections inside the DUT 20.

Considering multiple reflections (m,> 0) up to (m '-1) times, the complex amplitude reflectance r (ω) is expressed as follows: ω is the angular frequency of light, and d is the thickness of the DUT 20 , C as the speed of light, is expressed by the following equation (18). However, the parameter B in equation (18) is calculated by the following equation (19) Indicated by In Equation (18), as in the case of the first embodiment, the complex transmittance and the complex reflectance when light enters a substance from a medium are t 1 (ω) and r 1 (ω), respectively. And the complex transmittance and the complex reflectivity when emitted from a substance into a medium are t2 (ω) and r2 (ω), respectively. Further, assuming that the DUT 20 is in the air or in a vacuum, the refractive index η of the medium on both sides of the DUT 20. Is 1. However, the refractive index η. Is the same even when the value is other than 1, and the medium on the incident side and the medium on the exit side do not need to be the same.

 In the present embodiment, a mirror is used as the above-mentioned sample, like many spectroscopes. The signal for reference uses the spectrum of the light reflected by the mirror, and the ratio between the signal and the spectrum reflected by the device under test 20 is defined as the amplitude reflectance. Therefore, in Equation (18), the whole is multiplied by –1 in consideration of the phase inversion when the light is reflected by the mirror.

 [Equation 18]

[Equation 19]

B = ~ t _x (ω) r- \ ω) t ₂ (ω) χ (ω 'exp i \ 2k-N co) .- d

 N-= ο. (19)

= | β |. exp (i arg B) By substituting equation (17) into equation (18) and rearranging, the following equation (20) is obtained. Equation (20) is an equation showing the relationship between the amplitude reflectance R (ω) and the phase difference φ ′ (ω) and the complex refractive index Ν (ω) = η _R (ω) + in, (ω). In Equation (20), if m ′ = 0 or 1, multiple reflection is ignored, and if m ′ = 1, the light reflected only once on the surface of the DUT 20 on the detection unit 11 side and the measured light Reflects light reflected only once on the surface opposite to the detector 11 of object 20 and multiple reflections when m '≥ 2. Will be reflected. In order to further improve the measurement accuracy of the complex refractive index, it is preferable that m ′ ≧ 2. However, in the present embodiment, multiple reflections may be ignored or taken into consideration, and may be set to an arbitrary integer of m ′ ≧ 1. If m ′ = 0, B = 0.

 [Equation 2 0]

2; {n _R (ω) + in, (ω)} ― dx \ B \ · exp (i arg B) (20)

 c

 When the left side of the equation (20) is placed as shown in the following equation (21), and the equation (21) is substituted into the equation (20), the following equation (22) is obtained.

 [Equation 2 1]

 ω (2 1)

 [Equation 2 2]

R '() e ίΦ') = exp] 2i {n _R (ω) + in, (ω) \-ά LBLBexpf? Arg B) (2 2)

 c

 Taking the logarithm of both sides of equation (2 2) gives the following equation (2 3).

 [Equation 2 3]

ΙηΚ '(ω) + ίφ "(ω) = 2ί {η _κ (ω) + + iaigB (2 3)

 Based on the relationship between the imaginary part and the real part on both sides of equation (23), ηκ (ω) is expressed by the following equation (24), and η, (ω) is expressed by the following equation (25) You.

 [Equation 2 4]

{φ "(ω)-^ Β} (2 4)

 2άω

[Equation 2 5]

In Equations (2 4) and (2 5), the amplitude reflectance R ′ (ω) and the phase difference φ ″ (ω) are values obtained from the measured values as described above. However, when the parameter Β is η _κ (ω) And _eta depending on _iota (omega) (Formula (1 9), Equation (3), equation (5) to Formula (7)), R '(omega) and the phase difference phi "(omega) is eta _kappa (omega ) And (ω) (Equation (2 1), Eq. (4), Eq. (7)), it is very difficult to solve Eqs. (24) and (25) as they are. .

The present inventor sets the parameter の as shown in equation (19) and derives equations (24) and (25) from equation (20) for the first time. by performing the approximation, by a very simple calculation, it was found that for obtaining a stable accurately birefringence element refractive index with a relatively small amount of calculations _{(n R} (ω) and _{ηι (ω)).}

First, appropriate initial values of n _R (ω) and (ω) are given as approximate solutions. For example, since the approximate value of the complex refractive index of the device under test 20 is generally known, this value may be used as the initial value. The approximate solution given the initial value is substituted into equation (19) to calculate Β (that is, 1 Β I and arg B). Equation (3) and Equations (5) to (7) are used in the calculation of parameter B. Also, the amplitude reflectance R ′ (ω) and the phase difference φ ″ (ω) are calculated by substituting the approximate solution described above into the equation (21). In this calculation, the equations (4) and (4) are used. (7) The 反射, the amplitude reflectance R ′ (ω) and the phase difference Φ ″ (ω) calculated in this way are treated as known numbers determined by the given approximate solution, and the equations (24) and (24) are used. Substituting into equation (25), the values of n _R (ω) and (ω) are calculated. By using n _R (ω) and (ω) obtained as a new approximate solution and repeating the same procedure until the values of n _R (ω) and η, (ω) converge, complex refraction is obtained. The ratio Ν (ω) = n _R (ω) + i η, (ω) can be obtained.

As described above, in the successive approximation to obtain a new approximate solution of the complex refractive index by giving the approximate solution of the complex refractive index, the parameter Β, the amplitude reflectance R ′ (ω), and the phase difference φ ″ (ω) Is treated as a known number determined by the given approximate solution, a new approximate solution is obtained: In the case of m '= 1 (ie, multiple reflections are ignored and the entrance surface of the DUT 20) (In the case where light reflected only on the surface of the detection unit 11 is reflected), the transmittance t 1 when light enters the device 20 from the medium around the device 20, and the reflection By treating the transmittance rl and the transmittance t2 and the reflectance r2 when light exits from the device under test 20 into the medium as known numbers determined by the given approximate solution, a new Obtain an approximate solution. When m≥2 (that is, when multiple reflection is considered), the transmittance t1, the reflectance r1, the transmittance t2, the reflectance r2, and the term based on the multiple reflection (equation 1 9) The new approximate solution is obtained by treating 項 in the above) as a known number determined by the given approximate solution.

 Next, an example of the operation of the control / arithmetic processing unit 23 in the present embodiment will be described with reference to FIG. When the operation starts, the control / arithmetic processing unit 23 measures the reference time-series waveform Erei '(t) (step S21), Fourier-transforms the reference time-series waveform Eref' (t), and outputs an amplitude. I Erei '(ω) | and phase 0 rei' (ω) are obtained (step S22). Next, the control / arithmetic processing unit 23 measures the measurement time-series waveform Esam '(t) for each measurement site of the DUT 20 (step S23), and the measurement time-series waveform Esam' (t) ) Is Fourier-transformed to obtain an amplitude 1 Esam '(ω) | and a phase Θ sam' (ω) (step S24). Then, the amplitude I Erei '(ω) 1 and the phase S ref' (ω) obtained in step S 22, and the amplitude I EsanT (ω) | and the phase θ sam '(ω) obtained in step S 24 Is used to calculate the step amplitude reflectance R (ω) and the phase difference φ ′ (ω) (step S25).

Subsequently, the control / arithmetic processing unit 23 performs the processing of steps S26 to S31 described later for each measurement site of the DUT 20. In step S 2 6, for a measurement site, the initial approximation n _R (ω), η, sets the (omega). In the next step S 2 7, approximate value n _R (omega) which is currently set to calculate the Β in the manner previously described in accordance with n _r (ω). In step S 28 following step S 27, R ′ (ω) and φ ″ (ω) are calculated. In step S 28, the amplitude reflection calculated in step S 25 for the measurement site concerned The ratio R (ω) and the phase difference φ ′ (ω) are used.

In step S 29, the control / arithmetic processing unit 23 calculates the に newly calculated in step S 27 and the R ′ (ω) and ぴ ″ (ω) calculated latest in step S 28. ) Is substituted into Equations (2 4) and (2 5) to calculate a new approximate solution n _R (ω), η, (ω) In the next step S 30, step S 29 It is determined whether or not the approximate solution n _R (ω), η, (ω) obtained most recently has converged. This determination is made, for example, by the approximate solution n _R ( ω), η, (ω) and the neighborhood obtained by the previous calculation. Nikai eta _kappa (omega), the difference between n _t (omega) (absolute value) on the basis of or less than a predetermined value, can be performed.

If it is determined in step S30 that convergence has not occurred, in step S31, the approximate solution η _κ (ω), η, (ω) obtained most recently in step S29 is _replaced with a new approximate value. And return to step S27.

On the other hand, if it is determined that the convergence has been achieved in step S30, the control / calculation processing section 23 ends the calculation for the measurement site. Thereafter, control, arithmetic processing unit 23 controls the moving mechanism 26 repeats the processing of steps S 26~S 3 1 for the rest of the measurement site, for every measurement site, approximate solution eta _kappa When it is determined that (ω), η, (ω) have converged, the converged approximate solution n _R (ω), η _Γ (ω) (that is, the complex refractive index of the measurement site) for each measurement site is calculated. Supply to 24 to the image processing unit. The image processing unit 24 displays an image showing the distribution of the complex refractive index on the display unit 25 (step S32), and ends the operation.

 In steps S21 and S22, it is not necessary to perform the measurement every time the complex refractive index of the device under test 20 is measured, but may be performed at an appropriate frequency. For example, it may be performed only once at the time of product shipment.

 According to the present embodiment, the complex refractive index or complex permittivity can be measured stably and accurately with a relatively small amount of calculation.

 The complex permittivity ε (ω) can be obtained by substituting the complex refractive index Ν (ω) obtained by the method described above into equation (16). By substituting Equation (16) into Equations (3) to (7) and Equations (18) to (25), the complex refractive index Ν (ω) can be obtained without calculating the complex refractive index Ν (ω). As in the case of Ν (ω), it is also possible to obtain the complex permittivity ε (ω).

 The embodiments of the present invention have been described above, but the present invention is not limited to these embodiments.

For example, in the above-described first and second embodiments, the complex refractive index of each measurement site of the DUT 20 is measured and its distribution is imaged. It is sufficient to measure only the complex refractive index or complex permittivity of only 20 measurement sites. No. Further, if no image is required and it is desired to measure the average complex refractive index or complex permittivity of a certain range of the device under test 20, the terahertz pulse light L4 is applied to the device under test 20 as described above. In the above embodiments, the complex refractive index was obtained as a final measurement result, but other physical property values may be used. In the case of obtaining a final measurement result, the present invention can also be applied to a case where a complex refractive index or a complex permittivity is obtained as an intermediate step for obtaining the physical property value. For example, if the frequency dependence of the complex refractive index can be theoretically determined, such as when the device under test 20 is a semiconductor, etc. (Eg, carrier density and mobility of semiconductors) can be obtained. If you want to find the carrier density and mobility of a semiconductor, you can do so immediately based on the complex index of refraction at a single frequency. In this case, if it is desired to obtain these values with higher accuracy, it is effective to calculate by the least squares method using the frequency dependence of the complex refractive index. A similar calculation can be made by optimizing the parameters to minimize the difference between the measured transmission and reflection spectra and the theoretical value, but the computational complexity is relatively high. Become. Therefore, as described above, the amount of calculation is reduced by calculating the complex refractive index based on the measurement result and optimizing the parameters while comparing the calculation result with the theoretical formula. Therefore, the present invention is also effective as preprocessing for parameter optimization.

 The inventor obtained a complex refractive index using an n-type silicon wafer as the object 20 according to the measurement method employed in the first embodiment described above.

The amplitude transmittance Τ (ω) and the phase difference φ (ω) at the frequency 0.6 THz (up to 20 cm- ') obtained in step S5 of the flowchart shown in FIG. 3 are Τ (ω) = 0.6 10 The phase difference φ (ω) was 5.78. Based on this result, the complex refractive index Ν (ω) finally obtained by the above-described method was n _R (ω) = 3.44 and η, (ω) = 0.0027. This value is the value known as the complex refractive index of a silicon wafer, η _κ (ω) = 3.41 and (ω) = 0.0024 (“Basic physical properties chart” Eto Keiei (Kyoritsu Shuppan, (1 972), p. 254)). As described above, it was actually confirmed that the present invention is useful in obtaining a complex refractive index. As described above, according to the present embodiment, a complicated procedure for determining the wavelength dependence of the refractive index is not required. As a result, it is possible to provide a measuring method and an apparatus capable of reducing the amount of calculation and stably and accurately measuring the complex refractive index or the complex dielectric constant, and an imaging method and an apparatus for an object to be measured using the same. be able to. Industrial applicability

 The measuring method and measuring device according to the present invention can be applied to a method and a device for obtaining a complex refractive index or a complex dielectric constant of a substance. Further, the present invention can be applied to a method and an apparatus for imaging an object to be measured according to the complex refractive index or the complex dielectric constant of the object to be measured or the distribution of physical property values of any of these.

Claims

The scope of the claims  1. The measurement method for measuring the complex refractive index or complex permittivity of the DUT  Using a terahertz pulse light generating section and a detecting section for detecting the terahertz pulse light generated from the generating section and arriving via a predetermined optical path, the object to be measured is arranged on the optical path. By irradiating the object to be measured with the terahertz pulse light, a pulse light transmitted through the object to be measured and detected by the detection unit and a pulse reflected by the object to be detected by the detection unit are reflected. Obtaining a measurement time-series waveform that is a time-series waveform of the electric field strength of one of the pulse lights;  In one of a state in which a predetermined sample is arranged in place of the object to be measured on the optical path and a state in which neither the object nor the sample is arranged on the optical path, the state is generated by the generator. Based on a relationship between a reference time-series waveform that is a time-series waveform of the electric field intensity of the pulsed light detected by the detection unit and the measurement time-series waveform, the complex refractive index or the complex dielectric constant of the object to be measured. And a calculation step of calculating  (A) obtaining an amplitude rate of the predetermined frequency based on an amplitude of a predetermined frequency obtained from the measured time-series waveform and an amplitude of the predetermined frequency obtained from the reference time-series waveform; and (b) Calculating a phase difference between a phase of the predetermined frequency obtained from the measurement time-series waveform and a phase of the predetermined frequency obtained from the reference time-series waveform; (c) the amplitude rate of the predetermined frequency and the predetermined frequency; Obtaining the complex refractive index or the complex dielectric constant by successive approximation based on an equation indicating the relationship between the phase difference and the complex refractive index or the complex dielectric constant of the device under test at the predetermined frequency. In the successive approximation, when an approximate solution of the complex refractive index or the complex permittivity is given to obtain a new approximate solution of the complex refractive index or the complex permittivity, at least light is a medium around the object to be measured. By treating the transmittance when the light enters the device under test and the transmittance when light exits from the device under test into the medium as a known number determined by the given approximate solution, a new approximate solution is obtained. obtain.  2. The measurement method for measuring the complex refractive index or complex permittivity of the DUT is as follows: Using a generation unit of the terahertz pulse light and a detection unit that detects the terahertz pulse light that is generated from the generation unit and reaches through a predetermined optical path, the device under test is placed on the optical path. The time-series waveform of the electric field intensity of the pulse light that is transmitted through the object to be measured and is detected by the detection unit by irradiating the object to be measured with the terahertz pulse light in a state where is arranged. Obtaining a measurement time-series waveform;  In one of a state in which a predetermined sample is arranged in place of the object to be measured on the optical path and a state in which neither the object nor the sample is arranged on the optical path, the state is generated by the generator. Based on a relationship between a reference time-series waveform that is a time-series waveform of the electric field intensity of the pulsed light detected by the detection unit and the measurement time-series waveform, the complex refractive index or the complex dielectric constant of the object to be measured. And a calculation step of calculating  The calculation step includes: (a) a ratio of an amplitude of a predetermined frequency obtained by Fourier-transforming the measured time-series waveform and an amplitude of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform. Determining the amplitude rate of the given frequency; and (b) the phase of the given frequency obtained by Fourier transforming the measured time series waveform and the given frequency obtained by Fourier transforming the reference time series waveform. (C) determining the relationship between the amplitude rate at the predetermined frequency and the phase difference at the predetermined frequency and the complex refractive index or complex permittivity at the predetermined frequency of the device under test. Obtaining the complex refractive index or the complex permittivity by successive approximation based on the following equation:  The above equation ignores multiple reflection of the terahertz pulse light inside the device under test,  In the successive approximation, when an approximate solution of a complex refractive index or a complex permittivity is given to obtain a new approximate solution of a complex refractive index or a complex permittivity, light is transmitted from a medium around the measured object to the measured object. A new approximate solution is obtained by treating the transmittance at the time of incidence and the transmittance at the time when light exits from the object to be measured into the medium as known numbers determined by the given approximate solution.  3. The measurement method for measuring the complex refractive index or complex permittivity of the DUT is Using a terahertz pulse light generating section and a detecting section for detecting the terahertz pulse light generated from the generating section and arriving via a predetermined optical path, the object to be measured is arranged on the optical path. Irradiating the object to be measured with the terahertz pulsed light and transmitting the object to be measured and detecting the electric field intensity of the pulsed light detected by the detection unit; Obtaining a measured time-series waveform that is a time-series waveform;  In a state where a predetermined sample is arranged in place of the object to be measured on the optical path, or in a state where neither the object to be measured nor the sample is arranged on the optical path, the light is generated by the generation unit and detected by the detection unit. A calculating step of calculating a complex refractive index or a complex dielectric constant of the device under test based on a relationship between a reference time-series waveform that is a time-series waveform of an electric field intensity of the pulsed light to be measured and the measurement time-series waveform. With  The calculating step includes: (a) calculating the measured time-series waveform Obtaining an amplitude ratio of the predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier transform and an amplitude of the predetermined frequency obtained by Fourier transforming the reference time-series waveform; Obtaining a phase difference between the phase of the predetermined frequency obtained by Fourier transforming the series waveform and the phase of the predetermined frequency obtained by Fourier transforming the reference time series waveform; The complex refractive index or the complex is successively approximated based on an equation indicating a relationship between the amplitude rate and the phase difference of the predetermined frequency and the complex refractive index or the complex dielectric constant of the predetermined frequency of the device under test. Obtaining a dielectric constant; and  The expression reflects multiple reflection of the terahertz pulse light inside the device under test,  In the successive approximation, when an approximate solution of a complex refractive index or a complex permittivity is given to obtain a new approximate solution of a complex refractive index or a complex permittivity, light is transmitted from a medium around the measured object to the measured object. By treating the transmittance based upon incidence, the transmittance based on which light is emitted from the DUT to the medium, and the term based on the multiple reflection as known numbers determined by the given approximate solution. , Get a new approximate solution. 4. The measurement method for measuring the complex refractive index or complex permittivity of the DUT is as follows. Using a terahertz pulse light generating section and a detecting section for detecting the terahertz pulse light generated from the generating section and arriving via a predetermined optical path, the object to be measured is arranged on the optical path. By irradiating the object to be measured with the terahertz pulsed light, the pulsed light reflected by the object to be measured and detected by the detection unit is converted into a measurement time-series waveform that is a time-series waveform of the electric field intensity. Acquisition stage, In a state where a predetermined sample is arranged on the optical path instead of the object to be measured, a time series of electric field intensity of pulsed light generated from the generation unit, reflected by the sample, and detected by the detection unit. A calculating step of calculating a complex refractive index or a complex permittivity of the device under test based on a relationship between a reference time-series waveform that is a waveform and the measurement time-series waveform, wherein the calculating step includes: (a) Obtaining an amplitude ratio of the predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier-transforming the measured time-series waveform and an amplitude of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform. (B) obtaining a phase difference between the phase of the predetermined frequency obtained by Fourier transforming the measured time series waveform and the phase of the predetermined frequency obtained by Fourier transforming the reference time series waveform; (C) the amplitude rate of the predetermined frequency And calculating the complex refractive index or the complex permittivity by successive approximation based on an expression indicating the relationship between the phase difference at the predetermined frequency and the complex refractive index or the complex permittivity of the device under test at the predetermined frequency. Has,  The above equation ignores the multiple reflection of the terahertz pulse light inside the device under test, and reflects the light reflected only once on the surface of the device under test on the detection unit side and the light of the device under test. Reflects light reflected only once on the surface opposite to the detection unit.In the successive approximation, a new approximation of complex refractive index or complex permittivity is given by giving an approximate solution of complex refractive index or complex permittivity. In obtaining the solution, the transmittance and reflectance when light enters the object from the medium around the object, and the transmittance and light when light exits from the object to the medium. A new approximate solution is obtained by treating the reflectance as a known number determined by the given approximate solution. 5. The measurement method for measuring the complex refractive index or complex permittivity of the DUT is as follows:  Using a terahertz pulse light generating section and a detecting section for detecting the terahertz pulse light generated from the generating section and arriving via a predetermined optical path, the object to be measured is arranged on the optical path. A measurement time-series waveform that is a time-series waveform of the electric field intensity of the pulse light that is reflected by the object to be measured by irradiating the object with the terahertz pulse light and detected by the detection unit. Obtaining the In a state in which a predetermined sample is arranged in place of the object to be measured on the optical path, the electric field strength of the pulse light generated by the generation unit and reflected by the sample and detected by the detection unit, A reference time-series waveform that is a time-series waveform of a degree, and a calculation step of calculating a complex refractive index or a complex dielectric constant of the device under test based on a relationship between the measurement time-series waveform and the measurement time-series waveform. , obtained by Fourier transform of _(a) the measurement time series waveform Obtaining an amplitude ratio of the predetermined frequency which is a ratio of an amplitude of a predetermined frequency to an amplitude of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform; and (b) Fourier transforming the measurement time-series waveform. Obtaining a phase difference between the phase of the predetermined frequency obtained by performing the Fourier transform and the phase of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform; and (c) determining the amplitude ratio and the amplitude of the predetermined frequency. Obtaining the complex refractive index or the complex dielectric constant by successive approximation based on an expression indicating the relationship between the phase difference at a predetermined frequency and the complex refractive index or the complex dielectric constant of the device under test at the predetermined frequency. And  The expression reflects multiple reflection of the terahertz pulse light inside the device under test,  In the successive approximation, when an approximate solution of a complex refractive index or a complex permittivity is given to obtain a new approximate solution of a complex refractive index or a complex permittivity, light is transmitted from a medium around the measured object to the measured object. The transmittance and the reflectance at the time of incidence, the transmittance and the reflectance at the time when light exits from the measured object to the medium, and the term based on the multiple reflection, a known number determined by an approximate solution given , A new approximate solution is obtained. 6. The imaging method of imaging the DUT according to the complex refractive index or the complex permittivity of the DUT or the distribution of physical property values based on any of the complex refractive indices or the complex dielectric constants may include the complexities of individual portions of the DUT. The measurement method according to any one of claims 1 to 5 is applied to the measurement of the refractive index or the complex dielectric constant.  7. The measuring device that measures the complex refractive index or complex permittivity of the DUT A generating section for generating the terahertz pulse light, and a detecting section for detecting the terahertz pulse light generated from the generating section and arriving through a predetermined optical path, wherein the object to be measured is arranged on the optical path. By irradiating the object to be measured with terahertz pulse light, the pulse light transmitted through the object to be measured and detected by the detection unit and the pulse light reflected by the object to be detected and detected by the detection unit Measurement time-series waveform that obtains the measurement time-series waveform that is the time-series waveform of the electric field strength of either one of the pulse lights An acquisition unit;  In a state where a predetermined sample is arranged in place of the object to be measured on the optical path, or in a state where neither the object to be measured nor the sample is arranged on the optical path, the light is generated by the generation unit and detected by the detection unit. A calculating unit that calculates a complex refractive index or a complex dielectric constant of the DUT based on a relationship between a reference time-series waveform that is a time-series waveform of an electric field intensity of the pulsed light to be measured and the measurement time-series waveform. With The calculation unit includes: ( _a ) an amplitude ratio calculation unit that calculates an amplitude ratio of the predetermined frequency based on an amplitude of a predetermined frequency obtained from the measurement time-series waveform and an amplitude of the predetermined frequency obtained from the reference time-series waveform. (B) a phase difference calculator for calculating a phase difference between a phase of the predetermined frequency obtained from the measured time series waveform and a phase of the predetermined frequency obtained from the reference time series waveform; and (c) the predetermined frequency. The complex refractive index or the complex dielectric constant is obtained by successive approximation based on an expression indicating the relationship between the amplitude rate and the phase difference of the predetermined frequency and the complex refractive index or the complex dielectric constant of the device under test at the predetermined frequency. And a successive approximation part for calculating the rate.  The successive approximation unit may be configured such that, in the successive approximation, when a new approximate solution of a complex refractive index or a complex permittivity is obtained by giving an approximate solution of a complex refractive index or a complex permittivity, at least light around the device under test is By treating the transmittance when the light enters the device under test from the medium and the transmittance when the light exits from the device under test into the medium as a known number determined by the given approximate solution, a new Obtain an approximate solution. 8. The measuring device that measures the complex refractive index or complex permittivity of the DUT  A terahertz pulse light generator, and a detector for detecting terahertz pulse light that is generated from the generator and arrives via a predetermined optical path, and wherein the device under test is arranged on the optical path, A measurement time series that acquires a measurement time series waveform that is a time series waveform of electric field intensity of pulse light that is transmitted through the object to be measured and detected by the detection unit by irradiating the object to be measured with a Hertz pulse light. A waveform acquisition unit; In a state where a predetermined sample is arranged in place of the object to be measured on the optical path, or in a state where neither the object to be measured nor the sample is arranged on the optical path, the light is generated by the generator and detected by the detector. Reference time system, which is the time series waveform of the electric field strength of the pulsed light A column waveform, and a calculation unit that calculates a complex refractive index or a complex dielectric constant of the device under test based on a relationship between the measurement time-series waveforms,  The arithmetic unit includes: (a) a ratio of an amplitude of a predetermined frequency obtained by Fourier-transforming the measured time-series waveform to an amplitude of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform; (B) a phase of the predetermined frequency obtained by performing a Fourier transform on the measured time-series waveform and a Fourier transform of the reference time-series waveform. A phase difference calculating unit for calculating a phase difference between the phase of the predetermined frequency and the phase difference of the predetermined frequency; and (c) the complex refractive index or complex of the predetermined frequency of the device under test and the phase difference of the predetermined frequency. A successive approximation unit for calculating the complex refractive index or the complex permittivity by successive approximation based on an expression indicating a relationship with the dielectric constant, wherein the expression includes: inside the device under test of the terahertz pulse light. Neglecting the multiple reflection of  The successive approximation unit may be configured such that, in the successive approximation, when an approximate solution of a complex refractive index or a complex permittivity is given to obtain a new approximate solution of a complex refractive index or a complex permittivity, light is emitted from a medium around the object to be measured. By treating the transmittance when the light enters the device under test and the transmittance when light exits from the device into the medium from the device as a known number determined by the given approximate solution, a new Obtain an approximate solution.  9. The measuring device that measures the complex refractive index or complex permittivity of the DUT  A detector for detecting a terahertz pulse light generated from the generator and reaching the terahertz pulse light via a predetermined optical path, wherein the object to be measured is arranged on the optical path; By irradiating the object to be measured with the terahertz pulsed light, the pulsed light transmitted through the object to be measured and detected by the detection unit acquires a measurement time-series waveform that is a time-series waveform of the electric field intensity. A time-series waveform acquisition unit, In a state where a predetermined sample is arranged in place of the object to be measured on the optical path, or in a state where neither the object to be measured nor the sample is arranged on the optical path, the light is generated by the generator and detected by the detector. A calculating unit that calculates a complex refractive index or a complex dielectric constant of the DUT based on a relationship between a reference time-series waveform that is a time-series waveform of an electric field intensity of the pulsed light to be measured and the measurement time-series waveform. With The arithmetic unit includes: ( _a ) the predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier-transforming the measured time-series waveform and an amplitude of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform. (B) the predetermined frequency obtained by performing a Fourier transform on the phase of the predetermined frequency obtained by Fourier-transforming the measured time-series waveform and the predetermined frequency obtained by performing a Fourier transform on the reference time-series waveform. (C) a complex refractive index or complex permittivity of the predetermined frequency of the device under test and the amplitude rate of the predetermined frequency and the phase difference of the predetermined frequency; And a successive approximation unit for calculating the complex refractive index or the complex permittivity by successive approximation based on an equation indicating the relationship between the Terahertz pulse light and the multiplexed light inside the device under test. It reflects the reflection,  The successive approximation unit may be configured such that, in the successive approximation, when an approximate solution of a complex refractive index or a complex permittivity is given to obtain a new approximate solution of a complex refractive index or a complex permittivity, light is emitted from a medium around the object to be measured. , The transmittance when light enters the device under test, the transmittance when light exits from the device under test to the medium, and the term based on the multiple reflection as known numbers determined by the given approximate solution. A new approximate solution is obtained by handling. 10. The measuring device that measures the complex refractive index or complex permittivity of the DUT  A detector for detecting a terahertz pulse light generated from the generator and reaching the terahertz pulse light via a predetermined optical path, wherein the object to be measured is arranged on the optical path; By irradiating the object to be measured with the terahertz pulse light, a measurement time-series waveform that is a time-series waveform of the electric field intensity of the pulse light detected by the detection unit by reflecting the object to be measured is acquired. A time-series waveform acquisition unit, In a state where a predetermined sample is arranged on the optical path instead of the object to be measured, a time series of electric field intensity of pulsed light generated from the generation unit, reflected by the sample, and detected by the detection unit. A calculation unit that calculates a complex refractive index or a complex dielectric constant of the device under test based on a relationship between the reference time-series waveform that is a waveform and the measurement time-series waveform, wherein the calculation unit includes: An amplitude for obtaining an amplitude ratio of the predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier transforming the measured time series waveform and an amplitude of the predetermined frequency obtained by Fourier transforming the reference time series waveform. (B) the measurement time-series wave A phase difference calculator for calculating a phase difference between a phase of the predetermined frequency obtained by Fourier-transforming the shape and a phase of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform; (C) the predetermined frequency The complex refractive index or the complex permittivity is successively approximated based on an expression indicating the relationship between the amplitude rate and the phase difference of the predetermined frequency and the complex refractive index or the complex permittivity of the predetermined frequency of the device under test. And a successive approximation unit for  The formula ignores multiple reflection of the terahertz pulse light inside the device under test, and reflects light reflected only once on the surface of the device under test on the detection unit side and the light of the device under test. The successive approximation unit reflects light reflected only once on the surface on the side opposite to the detection unit. When obtaining a new approximate solution of the dielectric constant, the transmittance and the reflectance when light is incident on the device under test from the medium around the device under test, and light is transmitted from the device under test to the medium. A new approximate solution is obtained by treating the transmittance and reflectivity at the time of emission as known numbers determined by the given approximate solution. 1 1. The measuring device that measures the complex refractive index or complex permittivity of the DUT  A detector for detecting a terahertz pulse light generated from the generator and reaching the terahertz pulse light via a predetermined optical path, wherein the object to be measured is arranged on the optical path; By irradiating the object to be measured with the terahertz pulse light, a measurement time-series waveform that is a time-series waveform of the electric field intensity of the pulse light detected by the detection unit by reflecting the object to be measured is acquired. A time-series waveform acquisition unit, In a state where a predetermined sample is arranged on the optical path instead of the object to be measured, a time series of electric field intensity of pulsed light generated from the generation unit, reflected by the sample, and detected by the detection unit. A calculation unit that calculates a complex refractive index or a complex dielectric constant of the device under test based on a relationship between the reference time-series waveform that is a waveform and the measurement time-series waveform, wherein the calculation unit includes: An amplitude for obtaining an amplitude ratio of the predetermined frequency, which is a ratio of an amplitude of a predetermined frequency obtained by Fourier transforming the measured time series waveform and an amplitude of the predetermined frequency obtained by Fourier transforming the reference time series waveform. (B) calculating a phase difference between a phase of the predetermined frequency obtained by Fourier-transforming the measured time-series waveform and a phase of the predetermined frequency obtained by Fourier-transforming the reference time-series waveform. The phase difference calculation unit to be obtained; (c) Based on an equation showing the relationship between the amplitude rate of the predetermined frequency and the phase difference of the predetermined frequency and the complex refractive index or complex permittivity of the predetermined frequency of the device under test, the complex refractive index or A successive approximation unit for determining a complex permittivity, wherein the expression reflects multiple reflections of the terahertz pulsed light inside the device under test,  The successive approximation unit may be configured such that, in the successive approximation, when an approximate solution of a complex refractive index or a complex permittivity is given to obtain a new approximate solution of a complex refractive index or a complex permittivity, light is emitted from a medium around the object to be measured. , The transmittance and the reflectance when the light enters the object to be measured, the transmittance and the reflectance when the light exits from the object to the medium, and the terms based on the multiple reflections. A new approximate solution is obtained by treating it as a known number determined by the solution.  12. The imaging device for imaging the DUT according to the complex refractive index or the complex dielectric constant of the DUT or a distribution of physical property values based on either of them, wherein Includes the described measuring device.