WO2002071014A1 - A method and a system for sampling an interferogram to obtain a fourier transform spectrum - Google Patents

A method and a system for sampling an interferogram to obtain a fourier transform spectrum Download PDF

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Publication number
WO2002071014A1
WO2002071014A1 PCT/FI2002/000161 FI0200161W WO02071014A1 WO 2002071014 A1 WO2002071014 A1 WO 2002071014A1 FI 0200161 W FI0200161 W FI 0200161W WO 02071014 A1 WO02071014 A1 WO 02071014A1
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WO
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Prior art keywords
signal
sampling
fourier transform
interferogram
frequency
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PCT/FI2002/000161
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French (fr)
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WO2002071014A8 (en
Inventor
Ismo Kauppinen
Jyrki Kauppinen
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Noveltech Solutions Ltd
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Publication of WO2002071014A1 publication Critical patent/WO2002071014A1/en
Publication of WO2002071014A8 publication Critical patent/WO2002071014A8/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
    • G01J3/28—Investigating the spectrum
    • G01J3/45—Interferometric spectrometry

Definitions

  • the present invention relates to a method and a system for sampling an interferogram to obtain a Fourier transform spectrum, especially in the ultraviolet region, as described in more detail in the preamble of the appended independent claims.
  • the invention also relates to a computer program used in the system.
  • a Fourier transform spectrum is calculated on the basis of the measured data, the interferogram.
  • an accurate information of the position of the moving mirror is needed.
  • the standard method for detecting the motion of the mirror is using a reference laser to define the positions of the mirror. This procedure guarantees that the sampling will occur in equidistant points, which is essential in using the Fast Fourier Transform (FFT) routine.
  • FFT Fast Fourier Transform
  • Connes and Michel [2] used in their solution quarter-wave plates and polarisers in the two arms of the interferometer for producing two laser signals in quadrature. Taking a sample by every zero-crossing of each signal gives four samples per one wavelength of laser. With He-Ne laser this would produce a free spectral range of about 31 600 cm "1 .
  • Phase-locked loop is a technique which tracks the frequency of the input signal, forms a voltage proportional to the frequency and drives a voltage-controlled oscillator producing a desired multiple of frequency as output. Thus, it can be used to subdivide the laser fringe spacing by any power of two. Let us presume that the division factor is 2 3 . This means that a single wavelength of the laser will be split into eight parts, which will produce a clock pulse, each. As a consequence, the free spectral range will be now from 0 to 63200 cm "1 .
  • PLL PLL
  • PLL uses the frequency of the previous cycle for determining the clock frequency of the current cycle. If now the speed of the mirror is different between consecutive cycles, the sampling will happen with wrong frequency, and the clock errors will distort the spectrum.
  • DSP digital signal processing
  • the method for sampling an interferogram to obtain the Fourier transform spectrum, preferably in the ultraviolet region, using a reference laser interference signal comprises a step of squaring the interference signal at least once in order to multiply the frequency of the signal.
  • a constant component added to the signal during squaring is removed.
  • the constant component is preferably removed for example by using a high pass filter.
  • squaring is performed n times and the constant component is removed after every squaring.
  • the system for sampling an interferogram to obtain the Fourier transform spectrum, preferably in the ultraviolet region, using a laser interference signal comprises means for squaring the interference signal at least once in order to multiply the frequency of the signal.
  • the system according to the invention further comprises means for removing a constant component added to the signal during squaring.
  • the signal processing in the method according to the invention can be done in real time so that the sampling signal follows accurately the movement of the mirror.
  • FIG. 1 shows schematically an optical layout of the interferometer
  • FIG. 2 shows schematically a principle of sampling of the interferogram
  • FIG. 3A-D shows schematically an interference signal
  • FIG. 4 shows schematically picture of the processed sampling signal
  • FIG. 5 shows schematically an emission spectrum of a mercury spectral lamp, recorded by the carousel interferometer using sampling method according to the invention.
  • Figure 1 shows an optical layout of the above-mentioned interferometer which typically comprises an UV-source, a laser source, a moving mirror, a fixed mirror and a beam splitter and which is used at prior art methods for detecting the motion of the mirror using a reference laser signal to define the position of the mirror.
  • the optical path difference x of the interferometer is 2d.
  • the sampling of the interferogram is accomplished by taking one sample every zero crossing of the He-Ne laser signal as illustrated in figure 2.
  • the sampling interval ⁇ x is limited by the wavelength of the laser.
  • a preferred embodiment of the invention deals with a low resolution applications of the interferometry, e.g. the carousel interferometer [6].
  • This kind of compact instruments are utilized especially in transportable Fourier analyzers. This fact sets special requirements for all the technology in the spectrometer.
  • the sampling and subdivision of the laser fringes call for special attention, since the velocity of the moving mirror system can vary for several reasons. Practically it means, that the sampling has to follow the mirror motion in real time.
  • the interference signal of the reference laser is a cosine wave with certain amplitude A and wavenumber Vo (see fig. 3a).
  • a system according to the invention can be built as an electronic board.
  • One built in order to test the idea of the invention contained three identical stages, each of which squared their input signals.
  • the system gave the He-Ne signal raised to the power three, thus having a frequency three times higher than the input.
  • the electronics was carried out with commercially available integrated circuits.
  • the analog multiplier circuit was AD633, manufactured by Analog Devices, Inc. Between the multiplier circuits there had to be external components for taking away the constant level (see Eq. (7)) and for amplifying the signal. For removing the DC simple RC filters were used and the amplifiers were made of general purpose operational amplifiers (TL081).
  • the first multiplier stage Before the first multiplier stage there is a filter to remove the DC level from the input signal. After that the signal is brought in both of the input channels of the AD633, which results in a squared signal as an output, as stated in the Eq. (7).
  • an offset trim is used in the negative input terminals of each multiplier. After every AD633 the DC level has to be filtered, and after that the signal is amplified with TL081.

Abstract

The present invention relates to a method and a system for sampling an interferogram to obtain a Fourier transform spectrum, especially in the ultraviolet region, wherein the interference signal is squared at least once in order to multiply the frequency of the signal.

Description

A method and a system for sampling an interferogram to obtain a Fourier transform spectrum
The present invention relates to a method and a system for sampling an interferogram to obtain a Fourier transform spectrum, especially in the ultraviolet region, as described in more detail in the preamble of the appended independent claims. The invention also relates to a computer program used in the system.
A Fourier transform spectrum is calculated on the basis of the measured data, the interferogram. When recording the interferogram, an accurate information of the position of the moving mirror is needed. At present the standard method for detecting the motion of the mirror is using a reference laser to define the positions of the mirror. This procedure guarantees that the sampling will occur in equidistant points, which is essential in using the Fast Fourier Transform (FFT) routine.
If one sample of the measured interferogram is taken for every zero crossing on the reference laser signal, which for example for a He-Ne laser means two samples for 632.8 nm, we will get a spectrum that covers a wavenumber range from zero to a certain maximum wavenumber, vmax. According to the Nyquist sampling theorem, this maximum depends reciprocally on the sampling interval Δx:
v ma = - (Equation 1)
2Δx
This means that by using He-Ne laser we will get an unaliased spectrum between wavenumbers 0 - 15 800 cm"1, which is sufficient only for the infrared region. However, if we want to measure spectra in the visible or ultraviolet region we have to make vmax greater, and thus the sampling interval Δx smaller. Several methods for this purpose have already been used. Different kinds of sampling methods for FT-UV spectroscopy have been reported by several authors. One of the earliest was introduced by Horlik and Yuen [1]. Their system is based on undersampling, and letting the spectra to be folded.
Connes and Michel [2] used in their solution quarter-wave plates and polarisers in the two arms of the interferometer for producing two laser signals in quadrature. Taking a sample by every zero-crossing of each signal gives four samples per one wavelength of laser. With He-Ne laser this would produce a free spectral range of about 31 600 cm"1.
In 1983 Burton, Mok and Parker published a paper where they introduced a sampling system that based on the use of phase-locked loop [3]. Phase-locked loop (PLL) is a technique which tracks the frequency of the input signal, forms a voltage proportional to the frequency and drives a voltage-controlled oscillator producing a desired multiple of frequency as output. Thus, it can be used to subdivide the laser fringe spacing by any power of two. Let us presume that the division factor is 23. This means that a single wavelength of the laser will be split into eight parts, which will produce a clock pulse, each. As a consequence, the free spectral range will be now from 0 to 63200 cm"1. The use of PLL, however, makes it necessary to use highly constant speed of the moving mirror in order to avoid sampling errors. The reason for this is, that PLL always uses the frequency of the previous cycle for determining the clock frequency of the current cycle. If now the speed of the mirror is different between consecutive cycles, the sampling will happen with wrong frequency, and the clock errors will distort the spectrum.
Braun [4] and Thorne [5] have used Zeeman-split lasers in measuring the position of the moving mirror. The two Zeeman components are set apart with polarisers in both arms of the interferometer. The velocity of the moving mirror is then measured by means of Doppler shift on the frequency of the recombined signals from the two arms of the interferometer. The advantage of this system is that the fringes are divided on the basis of phase of the signal instead of the intensity.
It is an object of the present invention to provide a new, reliable and as to its design simple method and a system for sampling an interferogram to obtain the Fourier transform spectrum preferably in the ultraviolet region.
It is a particular object of this invention to provide a method and a system which can be accomplished by using an analog circuit or digital signal processing (DSP) in real time.
The above stated objects are achieved by means of systems and methods which are characterized by what have been stated in the characterizing part of the appended independent claims.
According to a preferred embodiment of the invention the method for sampling an interferogram to obtain the Fourier transform spectrum, preferably in the ultraviolet region, using a reference laser interference signal, comprises a step of squaring the interference signal at least once in order to multiply the frequency of the signal.
In the method according to a preferred embodiment of the invention a constant component added to the signal during squaring is removed. The constant component is preferably removed for example by using a high pass filter.
Preferably squaring is performed n times and the constant component is removed after every squaring.
According to a preferred embodiment of the invention the system for sampling an interferogram to obtain the Fourier transform spectrum, preferably in the ultraviolet region, using a laser interference signal comprises means for squaring the interference signal at least once in order to multiply the frequency of the signal. Preferably the system according to the invention further comprises means for removing a constant component added to the signal during squaring.
The signal processing in the method according to the invention can be done in real time so that the sampling signal follows accurately the movement of the mirror.
The advantages of the method are strong and accurate sampling signal, simplicity of the structure, and low-cost implementation. This method solves the problem encountered in using PLL (phase locket loop), where the speed changes of the mirror result as distortions in the spectrum.
The invention will now be described more in detail in the following with reference to the accompanying drawing, in which
FIG. 1 shows schematically an optical layout of the interferometer,
FIG. 2 shows schematically a principle of sampling of the interferogram,
FIG. 3A-D shows schematically an interference signal,
FIG. 4 shows schematically picture of the processed sampling signal, and FIG. 5 shows schematically an emission spectrum of a mercury spectral lamp, recorded by the carousel interferometer using sampling method according to the invention.
Figure 1 shows an optical layout of the above-mentioned interferometer which typically comprises an UV-source, a laser source, a moving mirror, a fixed mirror and a beam splitter and which is used at prior art methods for detecting the motion of the mirror using a reference laser signal to define the position of the mirror. The optical path difference x of the interferometer is 2d. The sampling of the interferogram is accomplished by taking one sample every zero crossing of the He-Ne laser signal as illustrated in figure 2. The sampling interval Δx is limited by the wavelength of the laser.
A preferred embodiment of the invention deals with a low resolution applications of the interferometry, e.g. the carousel interferometer [6]. This kind of compact instruments are utilized especially in transportable Fourier analyzers. This fact sets special requirements for all the technology in the spectrometer. In the UV region the sampling and subdivision of the laser fringes call for special attention, since the velocity of the moving mirror system can vary for several reasons. Practically it means, that the sampling has to follow the mirror motion in real time.
The interference signal of the reference laser is a cosine wave with certain amplitude A and wavenumber Vo (see fig. 3a). Letting x be the optical path difference we can express the signal with the equation
10 (x) = A cos 2π v0 x (Equation 2)
where the wavenumber is an inverse of the wavelength, v0 = — . The detected λ 0 frequency f0 of the signal depends on the wavenumber and the velocity on the moving mirror υm fo = v0 υ m (Equation 3)
Using Eq. (3) we can now write Eq. (2) in a form that tells us the frequency of the signal .
/„ (x) - A cos 2π f0 — (Equation 4)
*> »
If we now multiply the signal of Eq. (2) by itself or, in other words, square it, we will get a new signal
Iγ (x) = A2 cos22π v0x (Equation 5) which can be expressed in the form Iy(x) = A2 ■ -[cos 2(2πv0x)+ 1]
1 1
= — A2 cos 2π (2v0 )x + — A2 (Equation 6)
2 2
Substituting again v0 from Eq. (3) we get Eq. (6) in the form
I, (x) = -A2 cos 2π (2/0 )— + - A2. (Equation 7)
Now we can see that frequency in Eq. (7) has doubled with respect to the frequency in the Eq. (4). We can as well see that the squaring of the signal has produced a
1 1 constant term — A2 (see Fig 3b). By eliminating the constant term — A2 from Iχ(x)
we get a signal with double frequency with respect to I0(x) (see Fig. 3c). By performing the squaring and constant removal again we get a sampling signal with four times the frequency with respect to the original He-Ne laser signal I0(x) (see figs. 3d and 4). This gives an unaliased spectral range up to 63 200 cm"1.
The essential point in the formulas stated above is, that with squaring a cosine signal we will obtain another cosine signal with a frequency twice as high as in the first one. Thus, if we use electronics in making the multiplications, it is possible to built an amplifier that converts the interference signal of the reference laser into a signal with a frequency multiplied by 2", where n is the number of multiplier circuits.
An example of an UV spectrum recorded by using the sampling method according to the invention is presented in figure 5.
A system according to the invention can be built as an electronic board. One built in order to test the idea of the invention contained three identical stages, each of which squared their input signals. A signal of photodiode, that measured the interference of a He-Ne laser, was brought to the multiplier board. As an output the system gave the He-Ne signal raised to the power three, thus having a frequency three times higher than the input.
The electronics was carried out with commercially available integrated circuits. The analog multiplier circuit was AD633, manufactured by Analog Devices, Inc. Between the multiplier circuits there had to be external components for taking away the constant level (see Eq. (7)) and for amplifying the signal. For removing the DC simple RC filters were used and the amplifiers were made of general purpose operational amplifiers (TL081).
Before the first multiplier stage there is a filter to remove the DC level from the input signal. After that the signal is brought in both of the input channels of the AD633, which results in a squared signal as an output, as stated in the Eq. (7). For eliminating the input offset of AD633 an offset trim is used in the negative input terminals of each multiplier. After every AD633 the DC level has to be filtered, and after that the signal is amplified with TL081.
The invention is not limited to the embodiments described and illustrated above, but can be varied in many ways within the scope and spirit of the invention, which is defined in the appended claims.
References:
[1] G. Horlick and W. K. Yuen, "Atomic spectrochemical measurements with a Fourier transform spectrometer," Anal. Chem. 47, 775A-781A (1975).
[2] P. Connes and G. Michel, "Astronomical Fourier spectrometer," Appl.
Opt. 14, 2067-2084 (1975).
[3] N. J. Burton, C. L. Mok, and T. J. Parker, "Laser-controlled sampling in a Fourier spectrometer for the visible and ultraviolet using a phase- locked loop," Opt. Cornmun. 45, 367-371 (1983).
[4] J. W. Brault, "Solar Fourier transform spectroscopy," Ossni. Mem. Oss. Astrofis. Arcetri 106, 33-50 (1979).
[5] A. P. Thorne, C.J. Harris, I. Wynne- Jones, R.C. M. Learner, and
G.Cox, "A Fourier transform spectrometer for the vacuum ultraviolet: desing and performance," J. Phys. E: Sci. Instrum. 20, 54-60 (1987).
[6] J. K. Kauppinen, I. K. Salomaa, and J. O. Partanen, "Carousel interferometer," Appl. Opt. 34, 6081-6085 (1995).

Claims

1. A method for sampling an interferogram to obtain a Fourier transform spectrum, preferably in an ultraviolet region, using a laser interference signal, characterized in that the interference signal is squared at least once in order to multiply the frequency of the signal.
2. A method according to claim 1, characterized in that a constant component added to the signal during squaring is removed.
3. A method according to claim 2, characterized in that the constant component is removed by using a high pass filter.
4. A method according to any of the previous claims, characterized in that the squaring is performed n times and the constant component is removed after every squaring.
5. A system for sampling the Fourier transform spectrum, preferably in the ultraviolet region, using a laser interference signal, characterized in that the system comprises means for squaring the interference signal at least once in order to multiply the frequency of the signal.
6. A system according to claim 5, characterized in that the system comprises means for removing a constant component added to the signal during squaring.
PCT/FI2002/000161 2001-03-05 2002-03-04 A method and a system for sampling an interferogram to obtain a fourier transform spectrum WO2002071014A1 (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2078939A1 (en) * 2008-01-11 2009-07-15 FOSS Analytical A/S Interferometer
JP2019015616A (en) * 2017-07-07 2019-01-31 株式会社島津製作所 Fourier transform infrared spectrophotometer

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4511986A (en) * 1982-08-30 1985-04-16 International Business Machines Method and apparatus for simultaneously recording multiple FT-IR signals
US5838438A (en) * 1997-01-17 1998-11-17 University Of Central Florida Method of time-resolving fourier-transform spectroscopy to allow interferogram sampling at unevenly spaced path-length differences.
US5914780A (en) * 1996-10-09 1999-06-22 Perkin-Elmer Ltd. Digitisation of interferograms in Fourier transform spectroscopy

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4511986A (en) * 1982-08-30 1985-04-16 International Business Machines Method and apparatus for simultaneously recording multiple FT-IR signals
US5914780A (en) * 1996-10-09 1999-06-22 Perkin-Elmer Ltd. Digitisation of interferograms in Fourier transform spectroscopy
US5838438A (en) * 1997-01-17 1998-11-17 University Of Central Florida Method of time-resolving fourier-transform spectroscopy to allow interferogram sampling at unevenly spaced path-length differences.

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2078939A1 (en) * 2008-01-11 2009-07-15 FOSS Analytical A/S Interferometer
JP2019015616A (en) * 2017-07-07 2019-01-31 株式会社島津製作所 Fourier transform infrared spectrophotometer

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FI20010435A0 (en) 2001-03-05
FI20010435A (en) 2002-09-06
WO2002071014A8 (en) 2003-12-04
FI110893B (en) 2003-04-15

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