JPS63236930A - Fourier transform type spectrophotometer - Google Patents

Abstract

PURPOSE:To improve a wave number resolution by measuring the wave number spectrum in the state of satisfying the sampling theorem and the wave number spectrum in which folding arises in the state of not satisfying the sampling theorem. CONSTITUTION:An interferogram In of white light in a position P2 is measured and is subjected to discrete Fourier transform by which the wave number spectrum f(v) is obtd. In of the white light of the position P3 is then obtd. and is subjected to the discrete Fourier transform, by which the wave number spectrum h(v) is obtd. and the folding is generated. The spectrum f(v) measured in the position P2 is subjected to frequency transfer, inversion and scale conversion etc. in a signal analysis part 5 and is subtracted from the actually measured spectrum h(v) in the position P2, by which the spectrum having no folding is calculated. The wave number spectrum g(v) eliminated of the influence of the folding from the wave number spectrum h(v) in which the folding arises is obtd. by this computation. The wave number resolution is thus improved.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to a Fourier transform spectrophotometer used, for example, to identify the component composition of chemical substances, and in particular, to a high-wavenumber-resolved Fourier transform spectrophotometer. Regarding spectrophotometers.

[Prior art] A two-beam interferometer is used to create an interferogram spatially, the pattern is sampled with a linear two-odd diode array, etc., and the wavenumber spectrum before interference is obtained by performing ML Fourier transform. Fourier spectroscopy for reconstruction is attracting attention. Since this method creates and samples a spatially static interferogram, there is no mechanical driving member during sampling, so it can be applied from the visible/ultraviolet region to the near-infrared. It's promising. However, although the achievable wavenumber resolution improves in proportion to the truncation width of the spatial interferogram, it is inevitably limited by the truncation width (i.e., the length of the linear 2-odd diode array (beam, chi x number of elements)). Therefore, the use is limited to specific areas.

[Problems to be Solved] This solution can be improved by using a linear photodiode array with a larger number of elements and a longer length, but it is difficult to obtain such a linear photodiode array based on current semiconductor technology. Another method to improve wavenumber decomposition, which is difficult and results in a large shape, is to use Zer when performing fast Fourier transform (FFT).
Although o-Filling is available, it has problems in terms of storage capacity and calculation time. On the other hand, software super-decomposes (5upe)
Although a method of performing r-resolution (r-resolution) has also been reported, doubts remain in terms of calculation time and reliability.

[Object of the Invention] The present invention solves the above-mentioned problems, and its purpose is to use existing sampling means such as linear photodiode arrays as they are, and to obtain wavenumber spectra with substantially improved wavenumber resolution. An object of the present invention is to provide a Fourier transform spectrophotometer that can be obtained.

[Principle] First, the principle adopted by the present invention can be obtained from the following discussion of the sampling theorem and discrete Fourier transform.

As shown in Fig. 1(A), Fig. 2(A), and Fig. 3(A), a spatial white light interferogram pattern is detected by a two-beam interferometer using a linear photodiode array (pitch d, N elements, total length x=dN) is created in the transverse direction. Figure 1 (A), Figure 2 (A
), FIG. 3(A) shows a state in which a part of the optical element (plane mirror, etc.) of the two-beam interferometer is slightly moved (moved or rotated) to change the spacing of the interference fringes from sparse to dense. If the interference fringes of only the light component with the maximum wave number σlaH in the interferogram of this white light are shown as N=6 for convenience, each of the first
This is the state fE in Figure (B), Figure 2 (B), and Figure 3 (B). The black circles indicate sampling positions by the linear photodiode array. The state shown in FIG. 1(B) fully satisfies the sampling theorem and is oversampling. That is, since the spatial wavelength is x/2, it is sufficient to sample with 4 samples with a sampling interval ΔX=x/4, but a large number of samples are sampled with 6 samples. Second
Since the state shown in Figure (B) has a spatial wavelength of x/3, it just satisfies the sampling theorem. The state shown in FIG. 3(B) does not satisfy the sampling theorem and is undersampling. That is, the spatial wavelength is x/4.

The sampling theorem is satisfied if the number of samples is 8 with the sampling interval ΔX=x/8, but in reality, the number of samples is 6, which is too small.

By the way, Figure 1 (B), Figure 2 (B), Figure 3 (B)
The interference fringes are both at the maximum wavenumber σrna in the wavenumber spectrum.
Since this is the result of the optical component of x, if the scale of the wave number domain is relatively viewed through all Fourier transform by the subsequent data analysis means, it will be recognized as a spectrum of the maximum wave number cIlaX. Therefore, we set the standard for the scale factor in the spatial domain as shown in Figure 2 (B) (the spatial wavelength of the interference fringes matches).
Takeso Ko ln1 and Figure 3 (B) are equivalent to Figure 3 (C).

By the way, the maximum wave number σWaX of the spectrum restored in Fourier spectroscopy is proportional to the reciprocal of the sample interval ΔX,
Wavenumber resolution (resolution) is the length at which sampling is performed and the truncation width (i.e., the total length of the linear photodiode array).
Since the sampling interval ΔX is narrower and the number of samples is larger, the wavenumber range is expanded and the wavenumber resolution that allows discrimination between adjacent spectra is improved.

Now, for the interference fringes in Figures 1(C), 2(B), and 3(C), the number of samples is N, and the discrete Fourier transform (DFT) is applied.
), Figures 4 and 5 respectively.

A wave number spectrum for the impulse-like maximum wave number σWaX shown in FIG. 6 is obtained. In FIG. 4, since there is an oversampling state, impulses appear at long wavelengths below the center wave number (,X3/2d).

Incidentally, the impulse appearing to the right of N/2 is a part of the negative li5 number given by the result of the discrete Fourier transform, which is 1 degree more sharp in terms of the FfA plate. In Fig. 5, the sampling theorem is exactly satisfied, so the maximum wave number σlea! The impulse appears coincident with the center wave number (D/, l/d). In Fig. 6, since there is an undersampling state, the impulse with the maximum wave number cIlaH is aliased to the center wave number (3/4 d).On the other hand, the wave number resolution Δσ is as shown in Fig. 4. In this case, 3/dN, in Fig. 5, 2/dN,
In Fig. 6, they are proportional to 3/4 dN, and in Fig. 6, despite the aliasing, the scale factor in the wave number domain decreases compared to the states in Figs. 4 and 5. However, the wavenumber resolution is apparently improved. Therefore, if the folded portion of the spectral pattern in FIG. 6 can be folded back based on the spectral pattern that satisfies the sampling theorem in FIG. 4 or 5, then
A spectral pattern that is apparently improved by wave number decomposition can be obtained.

[Means for solving the problems] Based on the above considerations, in order to solve the above problems, in the configuration of the Fourier transform spectrophotometer according to the present invention,
In the measurement of the same incident light flux, the wavenumber spectrum f(υ) in a state where the sampling theorem is satisfied by moving or rotating the optical element by a predetermined amount, and the wavenumber spectrum h(υ) with folding in a state where the sampling theorem is not satisfied υ), and folding back the folded wave number spectrum portion of the wave number spectrum h(υ) based on the wave number spectrum f(υ) to obtain a non-folding wave number spectrum g(υ);
is a characteristic component.

[Operation] According to this configuration, the interferogram at the first position of the optical element is measured, and the wave number spectrum f(υ
) is obtained, and then the reduced interferogram at the second position of the optical element is measured for the same incident beam, and the emission line or continuous wavenumber spectrum h(υ) force 7 which does not satisfy the sampling theorem and has folds is obtained. However, by calibrating the wavenumber spectrum h(υ) using the wavenumber spectrum f(υ), the folded part of the wavenumber spectrum h(υ) is reversely folded back, and the wavenumber decomposition is substantially improved. An emission line or continuous wavenumber spectrum g(υ) without folding can be obtained.

[Example] Next, one embodiment of the present invention will be described based on the drawings.

FIG. 7 is an apparatus configuration diagram showing an embodiment of a Fourier transform spectrophotometer according to the present invention.

In the figure, l is a beam splitter of a triangular optical path interferometer as a two-beam interferometer, which splits the white incident light beam, which is the light beam to be measured, into two. Ml is a fixed plane mirror arranged at an angle of 45'' with respect to the optical axis.

M2 is a movable plane mirror that is arranged at an angle of 77.5° with respect to the optical axis and can be translated slightly in the optical axis direction. L is a Fourier transform lens that transfers the interferogram generated at infinity to the third linear photodiode array.

In addition to the triangular optical path interferometer, a Michelson interferometer is used, and one of the plane mirrors is slightly rotated (tilted).
A linear photodiode array (image sensor) 3 serving as a sampling means is configured by arranging a large number of photodiodes in a straight line at each pitch d. These are scanned at fixed scanning time intervals, and the received light intensity signals of each photodiode are sequentially sent out. Reference numeral 4 denotes a signal processing section including a filter, an analog/digital converter, etc., which mainly converts the analog received light intensity signal from the linear photodiode array 3 into a digital signal. Reference numeral 5 denotes a signal analysis and control section, and 1 is composed of, for example, a microcomputer. Signal analysis and control section 5
It stores a data string of a received light intensity signal, that is, an interferogram, and has a built-in fast Fourier transform (FFT) function that performs a discrete Fourier transform on the data string, and stores the Fourier transform string, that is, a wave number spectrum. For example, it is output to a display unit 6 such as a CRT for display. Further, the signal analysis and control unit 5 outputs the plane mirror displacement signal to the drive circuit 7, and moves the movable plane mirror M2 by a predetermined amount by any drive element 8, such as an electrostrictive element.
As described later, it has a function of outputting a wavenumber spectrum pattern calibrated by a predetermined calculation based on the first wavenumber spectrum pattern and the second wavenumber spectrum pattern obtained by the calculation of the discrete Fourier transform.

Next, the above-mentioned embodiment will be explained by first taking the measurement of a continuous spectrum as an example.

For example, a He-Ne laser beam (wavelength 0.8
33 h-) is made incident on the interferometer. Note that, at this time, the movable plane mirror M2 is set at a position Pi slightly to the right of a position PO that is conjugate with the fixed plane mirror Ml. Since there is no aliasing in the interferogram (sinusoidal interference fringes) obtained by this, the wave number spectrum obtained by applying discrete Fourier transform to this is the zero-order, movable, state shown in Figure 4. The plane mirror M2 is moved in the direction of the arrow to a certain extent fiP
If the interferogram in 2 is subjected to a discrete Fourier transform, the bright line spectrum as shown in FIG. 5 will match the central wave number. That is, the movable plane mirror M2 is moved to a position P2 where the bright line spectrum matches the center wave number, and the position P2 of the movable plane mirror M is stored. Furthermore, the movable plane mirror M2 is moved in the direction of the arrow to the position P3 to the first position ii! At P3, folding as shown in FIG. 6 occurs in the wave number spectrum obtained by the a-dispersive Fourier transform. Here, the folding length b (unit: wave number) and position P3 in the wave number spectrum are stored.

With the above preparations, the wave number resolution of the continuous spectrum is improved as follows. First, a white light interferogram at position P2 is measured and subjected to a discrete Fourier transform. In such measurement conditions, the wavelength is 0.83
For spectra with wavelengths longer than 3 g m, the T-degree sampling theorem is satisfied and no aliasing occurs, so
A wave number spectrum f(υ) as shown in FIG. 8(A) is obtained.

However, light with a wavelength of 0.8334 ts or less is cut off in advance by a suitable optical filter. Note that the interferogram of the white light at the position P3 is acquired at the zeroth order, where the center wave number a is given by the reciprocal of the wavelength 0.8331Lm. Discrete Fourier transform is applied to this, but in such a measurement state aliasing occurs, as shown in Figure 8 (
A wavenumber spectrum h(υ) as shown in B) is obtained.

A portion E of this wave number spectrum h(υ) folded back with respect to the center wave number a is in the range a-a-b as shown by diagonal lines. Wavelength 0. This is because the spectrum of E133 ILm overlaps a-b at position P3. In the wavenumber spectrum h(υ), no aliasing occurs on scales 0 to ab, and the wavenumber decomposition is compared to that at position P2.

(a+b)/a times, whereas in scale b-a, the true wavenumber spectrum is not obtained due to the effect of aliasing.In scale m-b to g(υ),
The part ■ in the range of scale me a + b is folded back symmetrically to the reference line aa', and the part ■ in the range of scale me b - a
It corresponds to the one superimposed on the . Therefore, if we find the portion E of the wavenumber spectrum h(υ) that is folded back with reference to the center wavenumber a, and then fold it back with the center wavenumber a as a reference, we can obtain wavenumber decomposition even in the range a - b - a + b. A wavenumber spectrum g(υ) with improved can be obtained.

Now, with reference to the above illustrated method, the function of the signal analysis and control unit 5 that outputs g(υ) based on the measured wave number spectra f(v) and h(υ) will be explained.

The following equation holds true for the wavenumber spectrum h(υ).

h (υ) = g (υ)
・・・・・・・・・・・・IHowever, O≦υ≦(a-b) h (υ) = g (υ)+g(2a −υ)...
・・・・・・・・・IIHowever, (a 7 b )≦υ≦
a On the other hand, the following relationship holds between f(υ) and g(υ).

g(υ)=f(aυ/(a+b)) ・・・・・・・・・
...from mI, II, m formula.

h (V) = f (aυ/ (a+ b) )
−・・・−・・・・−rV However, O≦υ≦(a−b) h (v)=f (av/(a+b))+f (a
(2a-v)/(a+b)) ”...VHowever, (
a-b)≦υ≦a The first term on the right side of equation V indicates the spectrum without folding, and the second term on the right side indicates the spectrum with folding. Therefore, in the signal analysis and control unit 5, frequency transition 2 inversion, scale conversion, etc. are performed on the spectrum f(υ) measured at position P2, and f (a (2a-V)/(a+b)) is calculated,
This is subtracted from the actually measured spectrum h(υ) at (a−b)≦υ≦a at position P2, and a spectrum f(aυ/(a+b)) without folding is calculated and obtained. Also, h
f (aυ/ (a + b)) is subtracted from (υ), and the result is shown in Figure 8 (C
) is calculated. Through such calculation, a wave number spectrum g(υ) from which the influence of aliasing has been removed is obtained from a wave number spectrum h(υ) in which aliasing has occurred.

The above operation is calibrating (correcting) h(υ) with f(υ), so from f(υ) to f (a (2a-
When calculating v)/(a+b)) and correcting the -CV equation, an error occurs due to the difference in wave number decomposition. However, when the original spectrum is a set of emission line spectra,
Its impact is significantly reduced. Therefore, this method is particularly effective when measuring bright line spectra.

FIG. 9 shows the case of ms spectrum measurement. FIG. 9(A) shows the measured spectrum f(υ) without folding at one position P2. FIG. 9(B) shows the position! ! FIG. 9(B), which shows the actually measured spectrum h(υ) with aliasing at P3, refers to the above-mentioned actually measured spectrum and obtains a wavenumber spectrum g(υ) from which the influence of aliasing has been removed by the above algorithm.

Note that when the Zero-Filling method described at the beginning is used in combination, the above effect becomes even more remarkable.

In order to determine the presence or absence of folding, a He-Ne laser beam (wavelength: 0.633 m) was used in the above example, but a laser beam with a shorter wavelength than this was used to determine the presence or absence of folding. It goes without saying that it is also possible to measure the wavenumber spectrum of

In addition, in the above embodiment, He-Ne laser light (wavelength 0.
833 gtm) is used to cut the shorter wavelength component with an optical filter, etc., but without cutting it, the length of the shorter wavelength component light reflected from the center wave number is used as a landmark H.
It may also be calculated and determined using e-Ne laser light.

Furthermore, a plurality of bright line spectra that serve as marks for determining the scale may be used, or they may be made to simultaneously enter the interferometer when acquiring the measured wave number spectrum.

[Effects of the Invention] As explained above, the Fourier transform spectrophotometer according to the present invention can actually measure a wavenumber spectrum without folding, and can also reduce the interferogram by displacing the optical elements of the interferometer. Since this method actively obtains a wavenumber spectrum including folded portions and outputs a wavenumber spectrum without folding based on both actually measured wavenumber spectra, the following effects are achieved.

■The obtained wavenumber spectrum has apparently improved wavenumber resolution in the entire range up to the maximum wavenumber. Conventionally, in order to increase the wavenumber range, it was necessary to actually measure the wavenumber spectrum without aliasing, and on the other hand, wavenumber resolution was limited to a low level.However, in the present invention, as a conventional sampling means, Even if a linear photodiode array is used, a wavenumber spectrum with an expanded truncation width can be obtained, so wavenumber resolution is substantially improved. Therefore, it has become possible to perform precise discrimination of interesting spectra over a wide range.

■It requires acquisition of data strings at least twice and their discrete Fourier transformation, but unlike Fourier spectroscopy using a normal scanning Michelson interferometer, sampling methods such as linear photodiode arrays can be used in a short time. Since a data string can be obtained by simply scanning electrically twice, high-speed processing is possible, and as a means of improving wave number decomposition, there is not much of a problem in terms of processing time.

[Brief explanation of the drawing]

FIG. 1, FIG. 2, and FIG. 3 are explanatory diagrams of sampling methods using various aspects of interferograms in order to derive the principle of the present invention. FIG. 4, FIG. 5, and FIG. 6 are spectral pattern diagrams showing wave number spectra of discrete Fourier transform corresponding to each of the above-mentioned sampling methods. FIG. 7 is an apparatus configuration diagram showing an embodiment of a Fourier transform spectrophotometer according to the present invention. FIG. 8 is a spectral pattern diagram showing an actually measured wave number spectrum and a calibrated wave number spectrum when a continuous spectrum was measured in the same example. FIG. 9 is a spectral pattern diagram showing an actually measured wave number spectrum and a calibrated wave number spectrum when the bright line spectrum was measured in the same example. 1...Beam splitter, M1φφ/fixed plane mirror, M
2...Movable plane mirror, L@Φ/Fourier transform lens, 3
...Linear photodiode array as sampling means, 4. Signal processing section, 5. Signal analysis and control section, 6. Display section, 7. Shakenφ drive circuit, 8. Drive Element, f(υ)...wavenumber spectrum without folding at φ position P2, h(υ)...-wavenumber spectrum with folding at position P3, g(υ)...-actual purchase position P
Calibrated wavenumber spectrum without folding at 3. (C) Figure 4 Figure 5 Figure 6 Figure 8 Item 1' C

Claims (1)

[Claims] An interferometer that spatially creates an interferogram that can be expanded or contracted by moving or rotating an optical element, a means for sampling the spatial interferogram, and a discrete Fourier method for a data string obtained by the sampling means. A Fourier transform spectrophotometer comprising signal analysis means that performs transformation to obtain a wavenumber spectrum, and satisfies the sampling theorem by moving or rotating the optical element by a predetermined amount in measuring the same incident light flux. The wavenumber spectrum f(υ) at wave number spectrum f
A Fourier transform spectrophotometer characterized in that a wave number spectrum g(υ) without folding is obtained by folding back based on (υ).