₂, detection signal values are acquired in the order of a reference signal value x2, a signal value y2 of the specimen, and a noise signal value z2. This is repeated n times until the measurement end frequency f_nso as to acquire a reference signal value xi, a signal value yi of the specimen, and a noise signal value zi (i=1 to n) at each frequency. As shown in [Math. 3], “n” indicates the number of acquired data of detection signal values and is determined by the measurement start frequency f₁, the measurement end frequency f_n, and the frequency interval Δ for measurement.

$\begin{matrix} n = 1 + (fn - f_{1}) / Δ & [Math . 3] \end{matrix}$

With respect to a series of detection signal sequences (n-order vector data) obtained as above, a sequence of signals xi acquired in a state where no specimen is present on the terahertz optical path is defined as a reference spectrum (x₁, x₂, . . . , x_n). A sequence of signal values yi acquired via the specimen is defined as a specimen spectrum (y₁, y₂, . . . , y_n). A sequence of signal values zi acquired by shielding the terahertz optical path is defined as a noise spectrum (n₁, n₂, . . . , n_n).

There is light generated from the non-linear optical crystal 221b resulting from only the pump light. The influence of such light generated without depending on the terahertz light in the non-linear optical crystal 221 is included in the noise spectrum.

The reference spectrum, the specimen spectrum, and the noise spectrum are stored in the control unit 226 and transmitted to the spectrum processing unit 230. Operations of the pump light source 211, the light source (the seed light source) 213, the optical element (galvanometer mirror) 214, the movable stage RM, the detector 225, the dry air inflow control unit 228 can be controlled by the control unit 226.

In the spectrum processing unit 230, an absorption spectrum of the specimen is calculated based on the reference spectrum, the specimen spectrum, and the noise spectrum. The absorption spectrum can be calculated by comparing the specimen spectrum with the reference spectrum to determine how much the specimen spectrum has been attenuated at which wavelength. It should be noted that the far-infrared spectroscopic apparatus of the embodiment is configured to detect terahertz light transmitted through a specimen, but can also be configured to detect reflected light.

A configuration of the spectrum processing unit 230 is illustrated in FIG. 2A. Specifically, the spectrum processing unit 230 includes a noise processing unit 240, a water vapor absorption peak frequency determination unit 250, a spectrum elimination and interpolation unit 260, and an absorption spectrum computation unit 270. As illustrated in FIG. 2A, the water vapor absorption peak frequency determination unit 250 further includes a water vapor absorption peak half-value width input unit 160, a difference interval calculation unit 165, a difference calculation unit 170, a threshold processing unit 180, and a frequency list storage unit 190. The spectrum elimination and interpolation unit 260 includes spectrum elimination units 261a and 261b and interpolation units 265a and 265b. Processing by each unit will be described.

The noise processing unit 240 has a function of acquiring a spectrum on which threshold processing can be performed by subtracting the noise spectrum from each of the reference spectrum and the specimen spectrum (blocks 140a and 140b).

The water vapor absorption peak frequency determination unit 250 has a function of determining a frequency at which the influence of a water vapor absorption peak is caused by calculating a difference between two spectrum intensity values x_jand x_kof the reference spectrum, and performing the threshold processing with a threshold value t.

The spectrum elimination and interpolation unit 260 has a function of eliminating the spectrum at the frequency extracted by a water vapor absorption peak frequency determination unit 250a from the output from the noise processing unit 240 with the spectrum elimination units 261a and 261b, and performing interpolation processing in the interpolation units 265a and 265b.

The absorption spectrum computation unit 270 has a function of computing an absorption spectrum based on the reference spectrum and the specimen spectrum on which spectrum elimination and interpolation processing has been performed by the spectrum elimination and interpolation unit 260.

The dry air supply unit 227 is connected to the sealed chamber 229 and supplies dry air to the interior of the sealed chamber 229. The inflow of dry air is controlled by the dry air inflow control unit 228, whereby the sealed chamber can be kept in humid to dry conditions.

A detailed configuration of the spectrum processing unit 230 and a procedure to output an absorption spectrum derived from a specimen under a humid condition will be described with reference to FIG. 2A.

A reference spectrum, a specimen spectrum, and a noise spectrum are acquired while sequentially switching the measurement frequency f to the measurement start frequency f₁[THz], the measurement end frequency f_n[THz], and frequencies determined by the frequency interval Δ [THz] (f=(f₁, f₂, . . . , f_n)). That is, a reference spectrum I₀=(x₁, x₂, . . . , x_n) obtained in a state where no specimen is present on the terahertz optical path is regarded as 110, and a noise spectrum N=(n₁, n₂, . . . , n_n) obtained by performing a measurement in a state where the terahertz optical path is shielded is regarded as 120, and each of 110 and 120 is input to the noise processing unit 240. In addition, a specimen spectrum I₁=(y₁, y₂, . . . , y_n) obtained by placing a specimen on the terahertz optical path and causing terahertz light to transmit through or to be reflected at the specimen is regarded as 130 and input to the noise processing unit 240.

The noise processing unit 240 subtracts the noise spectrum N from each of the reference spectrum I₀and the specimen spectrum I₁in the blocks 140a and 140b so as to obtain spectra R₀=(r₁, r₂, . . . , r_n) and r₁=(r′₁, r′₂, . . . , r′_n) as shown in [Math. 4] and [Math. 5].

$\begin{matrix} r_{k} = x_{k} - n_{k} & [Math . 4] \end{matrix}$

$\begin{matrix} r_{k}^{'} = y_{k} - n_{k} & [Math . 5] \end{matrix}$

The spectrum R₀obtained by subtracting the noise spectrum N from the reference spectrum I₀is input to the water vapor absorption peak frequency determination unit 250, and then processing of determining (selection processing) a frequency of an absorption peak due to water vapor is executed, and processing of storing the determined frequency is executed.

The water vapor absorption peak half-value width input unit 160 is a portion for inputting the full width at half maximum δ_wof the observed water vapor absorption peak. The difference interval calculation unit 165 calculates a difference interval δ (frequency interval) for computing a difference with respect to the spectrum R₀. As an example, the difference interval δ can be calculated based on the full width at half maximum δ_wof the water vapor absorption peak. For example, the difference interval δ can be calculated as an integer such that δ×Δ approximates the value of twice the full width at half maximum δ_w. The threshold processing unit 180 determines whether the difference value is larger or smaller than the threshold value t, and stores a specific frequency in the frequency list storage unit 190 in accordance with the determination result. The details of the processing described above will be described below.

Next, the spectrum elimination and interpolation processing executed in the spectrum elimination and interpolation unit 260 will be described. As described above, all spectrum intensity values acquired at the frequencies stored in the frequency list storage unit 190 are discarded (eliminated) from the spectrum R₀and the spectrum R₁so as to be put into an uninput state. The discarded spectrum intensity values are restored by applying linear interpolation to spectrum intensity values at frequencies remaining before and after uninput portions (portions where data is eliminated). This enables restoration of a spectrum with reduced influence of water vapor.

A specific example of this spectrum elimination and interpolation processing will be described with reference to FIG. 2B. In FIG. 2B, it is assumed that plots of black circles are spectrum intensity values acquired at the frequencies stored in the frequency list storage unit 190. As a result of determining that a difference value d_kis greater than the threshold value t, it is determined that this portion corresponds to a spectrum frequency of water vapor. Thus, this frequency is stored in the frequency list storage unit 190. Consequently, the data of the intensity values of the plots of the black circles are discarded, and intensity values of remaining triangular plots are used for linear interpolation of the eliminated data to restore plots of white circles.

Next, the operation of the absorption spectrum computation unit 270 will be described. The absorption spectrum computation unit 270 includes an absorbance calculation unit 271 and a smoothing unit 275. The absorbance calculation unit 271 calculates an absorbance A (absorption spectrum) of a specimen to be measured in accordance with [Math. 6] below.

$\begin{matrix} A = - \log_{10} (R_{1} / R_{0}) & [Math . 6] \end{matrix}$

The smoothing unit 275 smooths a spectrum by using, for example, the Savitzky-Golay filter or a simple moving average method. A spectrum converted to an absorbance is denoted as an absorption spectrum of the specimen. By the above-described procedure, an absorption spectrum in which the influence of water vapor absorption is reduced from a spectrum acquired under the humid condition can be acquired from a spectrum output unit 280.

An example of the processing by the water vapor absorption peak frequency determination unit 250 will be described in details with reference to FIG. 2C. In the difference calculation unit 170, a difference d_kbetween a spectrum intensity value r_(k)of the spectrum R₀acquired at the k-th frequency and a spectrum intensity value r_(k+δ)of the R₀acquired at the (k+δ)-th frequency is calculated as shown in [Math. 7].

$\begin{matrix} d_{k} = r_{(k + δ)} - r_{(k)} & [Math . 7] \end{matrix}$

Here, as described above, the difference interval δ is determined by the difference interval calculation unit 165 based on the full width at half maximum δw input by the water vapor absorption peak half-value width input unit 160. The difference interval δ is desirably an approximate integer value such that δ×Δ corresponds to a frequency width of approximately twice δ_w. Specifically, the difference interval δ can be defined as shown in [Math. 8] which is represented by the frequency interval Δ and an INT function (rounded down to the nearest integer).

$\begin{matrix} \begin{matrix} δ = INT (2 δ w / Δ + 0.5) & (where δ \end{matrix} >= 1) & [Math . 8] \end{matrix}$

The threshold value t (t>0) for determining a water vapor absorption peak frequency is input from a threshold value input unit 175. In the threshold processing unit 180, a magnitude relationship between the threshold value t and the difference dk is determined, and a water vapor absorption peak frequency is determined (selected) in accordance with the determination result. Specifically, after the threshold value t is input, the threshold processing unit 180 executes threshold value determination shown in [Math. 9] and [Math. 10]. By determining the threshold value t based on the minimum amount of attenuation that water vapor absorption causes on the spectrum R₀, a frequency at which water vapor absorption is observed can be extracted with high accuracy.

$\begin{matrix} d_{k} > t & [Math . 9] \end{matrix}$

$\begin{matrix} d_{k} < - t & [Math . 10] \end{matrix}$

When d_ksatisfies [Math. 9], the k-th frequency is determined to be a water vapor absorption peak frequency. On the other hand, when d_ksatisfies [Math. 10], the (k+δ)-th frequency is determined to be a water vapor absorption peak frequency. The frequency determined to be the water vapor absorption peak frequency is stored in the frequency list storage unit 190. This determination is repeated from k=1 to k=(n−δ).

In the far-infrared spectroscopic apparatus 100, the measurement frequency f is determined, and the measurement is performed while the measurement frequency f is increased from the measurement start frequency f₁to the measurement end frequency, whereby the reference spectrum I₀, the specimen spectrum I₁, and the noise spectrum N can be acquired. The reference spectrum I₀, the specimen spectrum I₁, and the noise spectrum N can be acquired continuously at a certain fixed measurement frequency f. For this reason, the water vapor absorption peak frequency in the reference spectrum I₀is coincident with the water vapor absorption peak frequency in the specimen spectrum I₁, and this is also true when a plurality of specimens are measured. Thus, the processing by the water vapor absorption peak frequency determination unit 250a needs to be performed only once for the set of measurement of the reference spectrum I₀and measurement of the specimen spectrum I₁, without need for separately performing the processing for them.

An example of the first embodiment is illustrated in FIGS. 3A and 3B. FIGS. 3A and 3B illustrate a case in which the measurement start frequency f₁is set to 0.9 THz, the measurement end frequency f_nis set to 2.5 THz, the frequency interval Δ is set to 10 GHz, and a reference spectrum, a specimen spectrum, and a noise spectrum composed of n=161 pieces of date are acquired. In addition, the difference interval δ is set to 1 (equivalent to 10 GHz) and the threshold value t is set to 50.

FIG. 3A is a graph in which the difference D_k=r_(k+δ)−r_(k)of the reference spectrum I₀is plotted at each measurement frequency. In FIG. 3, lines of threshold values t=50 and −50 are indicated by straight lines. As a result of the threshold value determination, data acquired at 41 frequencies out of n=161 are subject to elimination and interpolation.

FIG. 3B illustrates an example of data (the spectrum R₀in FIG. 2A and a spectrum R′₀after the spectrum elimination and interpolation) before and after the operation of eliminating spectrum of the water vapor absorption peaks in accordance with the water vapor peak frequencies identified as illustrated in FIG. 3A. The reference spectrum R₀′ in which the influence of water vapor is reduced can be acquired by eliminating the spectrum attenuated by the influence of water vapor absorption and linearly interpolating the eliminated portion.

Although not illustrated, similarly, for the specimen spectrum R₁, a spectrum R₁′ in which absorption of water vapor is reduced can be acquired by eliminating the spectrum of water vapor absorption peaks and performing linear interpolation based on data acquired as illustrated in FIG. 3A.

The graph on the left side in FIG. 4 shows an example of the result of acquiring an absorption spectrum of the specimen using the spectra R₀′ and R₁′ in which the influence of absorption peaks of water vapor is reduced. In addition, the graph on the right side in FIG. 4 shows the spectrum of the same specimen output using the spectra R₀and R₁in which the influence of absorption peaks of water vapor remains. The procedure for outputting the spectrum of the graph on the right side in FIG. 4 is as shown in a Comparative Example of FIG. 5. Sharp absorption (represented by inverted triangles) appearing due to the influence of water vapor is reduced in the graph on the left side in FIG. 4, and the absorption derived from the specimen (represented by white inverted triangles) can be clearly observed.

The operation of the control unit 226 will be described in further detail. The control unit 226 controls a wavelength of a wavelength-tunable laser used in the light source 213 and generates a terahertz wave of an arbitrary frequency. In order to adjust the change in the optical axis of the seed light (horizontal direction on the paper surface of the drawing) along with the change in the wavelength, the angle (horizontal direction on the paper surface of the drawing) of the galvanometer mirror used as the optical element 214 is also controlled at the same time. In addition, the direction of the optical axis of the terahertz light generated from the non-linear optical crystal 221a slightly changes (horizontal direction on the paper surface of the drawing) depending on the frequency. The control unit 226 controls the movable stage RM in response to the amount of the change in the direction (horizontal direction on the paper surface of the drawing) of the optical axis of the terahertz light. Accordingly, the specimen table ST can be arranged at an appropriate position for each measurement frequency. Further, when necessary, the control unit 226 can control the opening and closing of the dry air inflow control unit 228 to adjust the humidity in the chamber 229 to an appropriate humidity for the specimen.

Differences between absorption peaks of water vapor and absorption peaks of a specimen will be described. The full width at half maximum of absorption peaks of a solid specimen can be observed over a very wide frequency width as compared to absorption peaks of water vapor (in the embodiment, the full width at half maximum of the absorption peaks of water vapor is about 5 GHz, while the absorption of a solid specimen is about 50 GHZ). This broad absorption peak width is deemed to be derived from collective oscillations of a plurality of molecules in a solid specimen. Thus, by eliminating the absorption peaks of water vapor, a spectrum can be interpolated without significantly impairing the absorption peaks of the specimen.

Another specific application example of the first embodiment (FIG. 2A) will be described below. FIG. 6A illustrates an example of a reference spectrum composed of detection signal values of n=401 acquired under a humid condition with measurement conditions of the measurement start frequency f₁=0.87 THz, the measurement end frequency f_n=2.87 THz, and Δ=5 GHZ. Each of the reference spectrum I₀, the specimen spectrum I₁, and the noise spectrum N is acquired in the above-described method, and the noise spectrum N is subtracted from the reference spectrum I₀and the specimen spectrum I₁, thereby acquiring the spectra R₀and R₁. Here, the observed full width at half maximum of the absorption peaks of water vapor is δw=0.005 THz, and thus δ=2 is determined from [Math. 8] described above. In addition, the threshold value t=50 is set.

FIG. 6A illustrates an example of the reference spectrum R₀obtained under the above-described conditions. FIG. 6B illustrates an example of the spectrum R₀in which the data at the frequencies stored in the frequency list storage unit 190 is excluded as a result of threshold determination. The frequencies affected by the absorption of water vapor can be accurately determined, indicating that the influence of the absorption peaks of water vapor can be effectively eliminated.

FIG. 6C illustrates a modification example of the first embodiment. The water vapor absorption peak frequency determination unit 250 in FIG. 2A detects water vapor absorption peak frequencies by obtaining one difference d_kand performing threshold determination. On the other hand, in the modification example illustrated in FIG. 6C, two differences are obtained and water vapor absorption peaks are detected in accordance with a result of threshold determination. Specifically, a difference c_kshown in [Math. 11] below is acquired simultaneously with the difference d_k, and a water vapor absorption peak frequency determination unit 250b illustrated in FIG. 6C performs determination processing. Here, d_kand c_kare differences called and defined as a forward difference and a backward difference, respectively. In other words, in this modification example, the forward difference dx is computed as a difference between a signal intensity of the reference spectrum R₀at one frequency and a signal intensity of the reference spectrum R₀at a frequency greater by the interval Δ than the one frequency. In addition, the backward difference c_kis computed as a difference between a signal intensity of the reference spectrum R₀at one frequency and a signal intensity of the reference spectrum R₀at a frequency smaller by the interval Δ than the one frequency. When the two differences c_kand d_ksatisfy either one of two conditions of [Math. 12], a frequency f_kat which a signal intensity r_kis acquired is stored in the frequency list storage unit 190.

$\begin{matrix} c k = r_{(k)} - r_{(k - δ)} & [Math . 11] \end{matrix}$

$\begin{matrix} c_{k} < - t or d_{k} > t & [Math . 12] \end{matrix}$

Since c_kand d_(k−δ)are the same calculation expression, when used at the same difference interval δ, the same frequencies as in the example of FIG. 2A are stored in the frequency list storage unit 190. Thereafter, elimination and interpolation of the data acquired at this frequency in the same manner as described above can be performed in the same manner as described above.

As described above, according to the far-infrared spectroscopic apparatus of the first embodiment, it is possible to accurately measure an absorption spectrum derived from a specimen by effectively reducing absorption peaks due to water vapor even in moist air atmosphere with a small computing amount.

Second Embodiment

Next, a far-infrared spectroscopic apparatus according to a second embodiment will be described with reference to FIG. 7. The overall configuration of the apparatus is the same as the first embodiment, and thus duplicated descriptions will be omitted. The far-infrared spectroscopic apparatus of the second embodiment differs from the first embodiment in terms of the configuration of a water vapor absorption peak frequency determination unit 250c. According to the second embodiment, it is possible to effectively reduce the influence of absorption peaks of water vapor even in a frequency region where a detection light intensity of a reference spectrum is low. The intensity of light obtained by parametric generation shows a frequency dependence specific to a non-linear optical crystal used. Thus, it is assumed that there are a frequency band with a low detection light intensity and a frequency band with a high detection light intensity within a certain measurement frequency range.

The water vapor absorption peak frequency determination unit 250c of the second embodiment includes a difference calculation unit 171 and a threshold value input unit 179, in addition to the components of the water vapor absorption peak frequency determination unit 250 of the first embodiment. The difference calculation unit 171 computes, in addition to the difference d_kand the threshold value t used in the first embodiment, a relative value difference d_k′ obtained by relativizing a difference itself using reference spectrum data as shown in [Math. 13]. The threshold value input unit 179 inputs a threshold value t′ which is different from the threshold value t. In addition to detecting water absorption peak frequencies by comparing the difference d_kwith the threshold value t, the threshold processing unit 180 detects water absorption peak frequencies by comparing the relative value difference d_k′ with the threshold value t′. Accordingly, absorption peaks of water vapor can be detected even when a signal intensity fluctuates within a measurement frequency range. For example, the threshold value t′=0.25 can be set.

$\begin{matrix} d_{k}^{'} = d_{k} / r_{k} & [Math . 13] \end{matrix}$

Water vapor absorption peak frequencies determined only from the difference d_kand the threshold value t correspond to the frequencies of the data eliminated in FIG. 6B. FIG. 8 illustrates frequency data newly stored in the frequency list storage unit 190 as a result of separately performing threshold determination using the relative value difference d_k′ and the threshold value t′. This indicates that a frequency of 1.005 THz at which the intensity of the reference spectrum is low and is attenuation due to absorption of water vapor is small determined using d_k′ and t′. It should be noted that, in the second embodiment, an example in which both the difference d_kand the relative value difference d_k′ are used has been described, but a configuration in which water vapor absorption peak frequencies are detected using only the relative value difference d_k′ can be employed. It is possible to reduce the influence of water vapor absorption peaks in a frequency region where a detection light intensity of a reference spectrum is low even by using only the relative value difference d_k′, and in this case, such effect can be obtained by simpler processing.

A modification example of the second embodiment will be described below. In this modification example, as shown in [Math. 14] instead of [Math. 11], a ratio of spectrum signal intensities (signal intensity ratio) at different sampling points (for example, sampling points adjacent to each other) is calculated, and water vapor absorption peak frequencies are detected based on this signal intensity ratio d_k″.

Specifically, the difference calculation unit 171 of FIG. 7 calculates a signal intensity ratio d_k″ of the reference spectrum in accordance with [Math. 14]. The expressions of threshold determination are defined as shown in [Math. 15] and [Math. 16]. The (k+8)-th frequency when [Math. 15] is satisfied and the k-th frequency when [Math. 16] is satisfied are stored in the frequency list storage unit 190. The subsequent procedure is the same as the second embodiment. According to the modification example, it is possible to effectively reduce the influence of absorption peaks of water vapor even in a frequency region where a detection light intensity of a reference spectrum is low. From the relationship between the relative value difference dk′ and the signal intensity ratio d_k″ shown in [Math. 17], the modification example in which the signal intensity ratio d_k″ is used to determine water vapor absorption peak frequencies is equivalent to the case where the relative value difference dk′ is used.

$\begin{matrix} d_{k}^{″} = r_{k + δ} / r_{k} & [Math . 14] \end{matrix}$

$\begin{matrix} d_{k}^{″} < 1 - t^{'} & [Math . 15] \end{matrix}$

$\begin{matrix} d_{k}^{″} > 1 + t^{'} & [Math . 16] \end{matrix}$

$\begin{matrix} D_{k}^{'} = d_{k} / r_{k} = (r_{k + δ} - r_{k}) / r_{k} = r_{k + δ} / r_{k} - 1 = d_{k}^{″} - 1 & [Math . 17] \end{matrix}$

It should be noted that, instead of the signal intensity ratio d_k″, a difference d_lnkof the natural logarithm of r_kcan be used as shown in [Math. 18] below.

$\begin{matrix} d_{l n k} = \ln (r_{k + δ}) - \ln (r_{k}) = \ln (r_{k + δ} / r_{k}) & [Math . 18] \end{matrix}$

[Math. 18] is an expression in which a natural logarithm is used as the ratio in [Math. 14], and since the natural logarithm is a function whose slope can be approximated to 1 in the vicinity of 1, the threshold determination may be determination using [Math. 15] and [Math. 16]. That is, an effect substantially equivalent to the case where the threshold processing is performed on a relative value difference can be obtained.

Third Embodiment

Next, a far-infrared spectroscopic apparatus according to a third embodiment will be described with reference to FIG. 9. The overall configuration of the apparatus is similar to the first embodiment, and thus duplicated descriptions will be omitted. The far-infrared spectroscopic apparatus of the third embodiment differs from the first embodiment in terms of the configuration of the noise processing unit 240 and a spectrum elimination and interpolation unit 260b.

While the water vapor absorption peak frequency determination unit 250 of the first embodiment acquires the reference spectrum I₀and determines water vapor absorption peak frequencies for every measurement, this procedure is omitted in the third embodiment. In the spectrum elimination and interpolation unit 260b, the spectrum elimination unit 261a and the interpolation unit 265a for the reference spectrum R₀are omitted, and the operation of data elimination and interpolation is performed only for the specimen spectrum R₁in the spectrum elimination unit 261b and the interpolation unit 265b. That is, in the third embodiment, spectrum data affected by water vapor is eliminated from the specimen spectrum R₁including absorption peaks of water vapor, and interpolation operation is performed. The specific procedure thereof will be described below with reference to FIG. 9.

In the third embodiment, the reference spectrum I₀and the noise spectrum N₀are acquired in dry air (dry condition) separately from the specimen spectrum I₁which is a measurement result of a specimen to be measured, and input to the noise processing unit 240. In the measurement of the specimen to be measured, the specimen is placed on the specimen table ST in moist air, and the specimen spectrum I₁and the noise spectrum N₁are acquired in the same procedure as in the above-described embodiments.

It is desirable that the reference spectrum I₀and the noise spectrum N₀are n-th-order row vectors of the same order acquired at the same measurement start frequency, the same measurement end frequency, and the same frequency interval as those for the specimen spectrum I₁and the noise spectrum N₁. However, the data satisfying the following conditions may be used.

When the reference spectrum I₀and the noise spectrum N₀are acquired at a measurement start frequency f₁′, a measurement end frequency f_n′, and a frequency interval Δ′, the order n′ as vector data of the specimen spectrum I₀and the noise spectrum N₀is determined as shown in [Math. 19] below. All the measurement frequencies of the reference spectrum I₀and the noise spectrum N₀are represented by F′=(f₁′, f₂′, . . . , f_n′). When the order of the specimen spectrum I₁and the noise spectrum N₁as vector data is defined as m and all the measurement frequency are defined as a frequency sequence F=(f₁, f₂, . . . , f_m), the reference spectrum I₀and the noise spectrum N₀may be n′-order vector data acquired at a measurement frequency F′ satisfying [Math. 20].

n
′

=

1
+

(

f
n
′