JP2744928B2 - Fourier spectrometer - Google Patents

Description

The present invention relates to an infrared or visible Fourier spectrometer,
In particular, the present invention relates to a Fourier spectrometer that quickly and accurately extracts spectral data in a limited range from a spectrum covering a wide wave number range.

[Prior Art] In Fourier spectroscopy, FFT (Fast Fourier Transform) is performed on interferogram data to restore original spectral data. Here, the N-point interferogram data is converted into N-point spectral data.

[Problems to be Solved by the Invention] However, when trying to improve the wavenumber resolution or expanding the observation wavenumber range, the value of N increases. Particularly in the visible region, the number of data points becomes very large.

This increase in the number of data points causes two problems.
One is an increase in FFT calculation time due to an increase in the number of data points, and the other is an increase in the dynamic range of the A / D converter when acquiring interferogram data.

In the case of a continuous spectrum, the interferogram causes a large center burst, and the number of bits of the A / D converter must be increased in accordance with the accuracy in order to improve the measurement accuracy of the restored spectrum. Eventually, the price of the A / D converter, the conversion speed, and the word length per data point increase, which also affects the overall data processing speed.

As a form of use of the Fourier interferometer, qualitative analysis is often performed using the entire reconstructed spectrum waveform, but information of only a specific region in a wide range of spectral data is often sufficient. This is especially true for quantitative analysis represented by analysis of impurities in semiconductors. This also applies to measurements such as FT Raman. Even in such a case, the spectrum must be restored by performing the FFT on all data points in the past, and the above-mentioned problems of the increase in the calculation time of the FFT and the expansion of the dynamic range of the A / D converter occur. I was

As a data point reduction method, there is a pre-filtering method.

The pre-filtering method, when desired to obtain a spectrum of only the band σ ₁ ~σ ₂ of sample light for all the wavenumber range 0～Shiguma _M, sampling the interferogram data at 1 / (2σ _M) following intervals After performing the convolution operation with the sinc function on the interferogram surface corresponding to the filters of the bands σ _{1 to} σ ₂ , it is necessary to further sample (thin out) the data of the operation result at intervals h ′. . Therefore, the calculation time cannot be reduced much.

Moreover, the spacing h 'must be spaced to the band 0～Shiguma ₂ Eiryajingu (aliasing) does not occur, it is necessary following conditions.

h ≦ 1 / (σ ₂ + σ _M ) h ′ = 1/2 (σ ₂ −σ ₁ ) σ ₁ = (σ ₂ −σ ₁ ) m h ′ = hn (m, n: integer) Understand from these conditions As possible, it is not possible to obtain a spectrum in an arbitrary band (σ _{1 to} σ ₂ ) without any restriction on sampling.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and provides a Fourier spectroscope that can reduce the calculation time and increase the dynamic range of an A / D converter.

It is another object of the present invention to provide a Fourier spectrometer capable of obtaining a spectrum in an arbitrary band.

[Means for Solving the Problems] In order to achieve this object, the present invention provides a Fourier spectrometer including an interferometer (10) for acquiring an interferogram of sample light, wherein the optical path of the interferometer is an optical band pass filter (12) that transmits light of a wave number region of interest of the sample light up wavenumber _{σ M (σ 1 ~σ 2)} , interferogram data of N points obtained by the interferometer A trigonometric function multiplying means (36) for multiplying a cosine wave or a sine wave of a lower edge wave number of the optical bandpass filter or a wave number slightly lower than the wave number.
A low-pass filtering means (38) for extracting a difference wave number component of the multiplication result and setting the number of data points to M points (N> M ≧ N (σ ₂ −σ ₁ ) / σ _M ); And Fourier transform means (40) for obtaining spectrum data by performing Fourier transform on the data of the points.

Embodiment (1) One Embodiment One embodiment of the present invention will be described with reference to the drawings.

FIG. 1 shows a main configuration of a Fourier spectrometer according to one embodiment of the present invention. 2 (a) to 2 (h) show two-sided spectra, and FIGS. 2 (A) to 2 (H) show (a) to 2 (h) respectively.
2 shows a two-sided interferogram corresponding to (h).

In this embodiment, for the sake of simplicity, it is assumed that the spectrum (a) of the sample light has two bright lines in the linear baseline. Also, it is assumed that the user is interested only in these two bright lines and wants to obtain only the spectrum in the wave number range σ _{1 to} σ ₂ including these lines.

As shown in FIG. 1, this embodiment shows a case where a continuous wavelength variable interference filter 12 is installed in a normal Michelson interferometer 10.

The Michelson interferometer 10 is for temporally acquiring the interferogram of the sample light by scanning the moving mirror, and includes an aperture 14 and a collimating lens 16 for collimating the sample light from the aperture 14. , A beam splitter 18 for splitting the light beam from the collimating lens 16 into two
And a fixed mirror that reflects and reverses one of the split light beams
20, a moving mirror 22 that reflects the other of the divided light beams and travels backward, an imaging lens 24 that forms an image of the interference light multiplexed by the beam splitter 18, and a light intensity disposed at the image forming position. And a photodetector 26 for detecting.

The continuous wavelength variable interference filter 12 is arranged on an optical path between the imaging lens 24 and the photodetector 26. The continuous wavelength variable interference filter 12 has a disk shape, and the transmission wavelength changes continuously or stepwise along the circumferential direction.
The transmission band in the portion on the optical path of the continuous wavelength variable interference filter 12 changes continuously as the disk is rotated by the drive signal from the control unit 28.

The output signal of the photodetector 26 is amplified by the amplifier 30,
The digital conversion is performed by the D converter 32.

Control unit 28 is a continuous wavelength variable interference filter
A desired wavelength transmission range is designated for 12, the movable mirror 22 is moved by one step, and a digital conversion command is issued to the A / D converter 32 for each step. Data sequentially obtained from the A / D converter 32 is written to an interferogram memory 34, and a two-sided interferogram is created in the interferogram memory 34.

FIG. 2A shows the spectrum of the sample light in the front wavenumber range of 0 to σ _M when the continuous wavelength variable interference filter 12 is omitted,
(B) shows a modeled transmission characteristic at a certain rotation angle position of the continuous wavelength variable interference filter 12, and (c) shows a spectrum after the sample light has passed through the continuous wavelength variable interference filter 12. That is, (a) × (b) = (c).

In general, the product on the spectral plane and the convolution operation correspond to the convolution and the product on the interferogram plane, respectively. Means convolution operation. (B) is a sinc function.

Accordingly, the interferogram (C) obtained by Fourier-transforming (c) is stored in the interferogram memory 34.
Is written.

The trigonometric function multiplier 36 converts the interferogram (C) into a trigonometric function shown in (d), for example, a cosine wave co.
Multiply by s (2πfx) to obtain (E). The wave number f is equal to the wave number set by the setting device 37 and slightly lower than the lower-side edge wave number σ ₁ or σ ₁ of the wave number range σ _{1 to} σ ₂ of the spectrum to be obtained (f in FIG. 2). = Σ ₁ ), specified by the control unit 28. X is the horizontal axis of the interferogram (the optical path difference between the beam splitter 18 and the beam splitter 18).
A discretized version of this is the interferogram memory 34
Corresponding to the address. (C) and (e) have a relationship in which the wave number is shifted. In (e), the spectrum of (c) is shifted by a wave number f to the lower frequency side (difference wave number component based on the multiplication) and the higher frequency is shifted. There is a wave number f shifted to the side (sum wave number component based on multiplication).

Next, in order to remove the sum wave number component, a digital signal that transmits from the wave number 0 to the 1 / (σ ₁ −σ ₂ ) component on the spectrum surface so as to satisfy the sampling theorem with respect to the multiplication result. Pass through a low pass filter 38. (F) shows a modeled filtering characteristic of this low-pass filter on the spectrum plane. This allows Is obtained.

Here, since the highest wave number component of the spectrum data of (a) was σ _M , sampling had to be performed at an interval of 1/2 σ _M or a denser interval, but the highest wave number component of (g) was (Σ ₂ −σ ₁ ), the interval 1 / ｛2
Sampling may be performed at (σ ₂ −σ ₁ )} or at a denser interval.

Then, the interferogram data of (g) is sampled at regular intervals, the number N of data points is set to M (H), and supplied to the fast Fourier transformer 40. Here, M is N> M ≧ N (σ ₂ −σ ₁ ) / σ _M.

The fast Fourier transformer 40 Fourier-transforms (H) to obtain a spectrum (h) in the wavenumber range 0 to (σ ₂ −σ ₁ ), and supplies this to the spectrum output device 42. This spectrum data is visualized and extracted from the spectrum output device 42.

Thus, the fast Fourier transformer with a long operation time
Substantially the number of data points of the interferogram supplied to _{40 (σ 2 -σ 1) /} σ can reduce the _M times, it is possible to shorten considerably the FFT computation time.

As can be seen by comparing (a) and (c), the peak of the interferogram is dispersed to both sides by passing through the continuous wavelength variable interference filter 12, so that the A / D converter 3
The required dynamic range of ₂ is given by K (σ ₂ −σ ₁ ) /
It can be reduced to sigma _M times. Here, K is K ≧ 1, and K = 1 when the sample light spectrum is perfect white light.
It is.

Furthermore, the arbitrary band (σ ₁ to
σ ₂ ) can be obtained.

(2) Extension The present invention includes various other modified examples.

For example, in the above embodiment, the continuous wavelength tunable interference filter 12 is used as an optical bandpass filter.However, for example, an interference filter having a plurality of different transmitted wave number ranges is prepared, and these are set according to the target wave number range. It may be configured to switch.

The digital low-pass filter 38 as low-frequency filtering means samples the interferogram (E) multiplied by the trigonometric function at intervals of 1 / {2 (σ ₂ −σ ₁ )} or less, and (E) (H) may be obtained directly from

Further, it goes without saying that various types of interferometers for producing an interferogram, for example, those which form an interferogram spatially and obtain it can be used.

[Effects of the Invention] As described above, according to the Fourier spectrometer according to the present invention, there is no need to perform a complicated convolution operation between the interferogram and the sinc function, so that the calculation time can be shortened, and the interferogram can be reduced. Since the gram peaks are dispersed on both sides, the dynamic range required by the A / D converter can be narrowed, and further, an effect is obtained in which a spectrum in an arbitrary wavenumber range can be obtained.

[Brief description of the drawings]

1 and 2 relate to one embodiment of the present invention, FIG. 1 is a block diagram of a main part of a Fourier spectrometer, and FIG. 2 is a diagram for explaining the operation, and (a) to (h). Is the spectrum diagram,
(A) to (H) are interferograms corresponding to (a) to (h), respectively. In the figure, 10: Michelson interferometer 12: Continuously tunable interference filter 16: Collimating lens 18: Beam splitter 20: Fixed mirror 22: Moving mirror 24: Imaging lens 26: Photodetector 38: Digital low-pass filter 40: Spectrum Output device

Claims (1)

(57) [Claims] In a Fourier spectrometer provided with an interferometer (10) for acquiring an interferogram of a sample light, a target wave number range (σ) of the sample light having the maximum wave number σ _M is provided in an optical path of the interferometer. _{1 to} σ ₂ ), and an N-point interferogram data obtained by the interferometer with respect to the interferogram data at the N points. Alternatively, a trigonometric function multiplying means (36) for multiplying a cosine wave or a sine wave of a wave number slightly lower than the wave number, and a difference wave number component of the multiplication result is extracted and the number of data points is set to M points (N
> M ≧ N (σ ₂ −σ ₁ ) / σ _M ) low-pass filtering means (38), and a Fourier transform means (40) for obtaining spectrum data by performing a Fourier transform on the data at the extracted M points. And a Fourier spectrometer, comprising: