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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 13 — Jun. 20, 2011
  • pp: 12628–12633
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Multichannel Fourier-transform interferometry for fast signals

S. P. Heussler, H.O. Moser, S. M. Kalaiselvi, C. G. Quan, and C. J. Tay  »View Author Affiliations


Optics Express, Vol. 19, Issue 13, pp. 12628-12633 (2011)
http://dx.doi.org/10.1364/OE.19.012628


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Abstract

Multichannel Fourier transform interferometry to measure the spectrum of arbitrarily short pulses and of fast time-varying signals was achieved using a micro/nanomanufactured multimirror array. We describe the performance of a demonstrator FTIR that works in the mid-infrared (MIR) range of 700-1400 cm−1 and reaches a spectral resolution of 10 cm−1 taking into account apodization. Spectral measurements down to pulse lengths of 319 µs were carried out using a mechanical camera shutter. Arbitrarily short pulses are expected feasible provided the source can deliver enough photons to overcome the noise equivalent number of photons.

© 2011 OSA

1. Introduction

Based on two-beam interference, Fourier transform interferometry is the workhorse of infrared spectroscopy [1

1. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

3

3. E. B. Brown, Modern Optics (Reinhold Publishing Corporation, Chapman&Hall Ltd, 1966), pp. 437–441. [PubMed]

]. Pioneered by devices such as the lamellar grating by Strong and Vanasse in which every second grating ridge is translated [4

4. J. Strong and J. Vanasse, “Applications of Fourier Transformation in Optics: Interferometric Spectroscopy” in Concepts in Classical Optics, J. Strong (W.H. Freeman&Co., 1958), pp. 419–434.

], state-of-the-art interferometers are based on mechanical scanning of an interferometer mirror. This implies that, ideally, the signal to be measured must vary only a little during a typical scan period depending on the level of tolerable error. Such spectrometers are able to achieve scan frequencies of 20-100 Hz with scanning velocities of 0.05 to 10 cm/s as for the Bruker IFS66 that has a linear translation stage [5

5. Bruker Optics, “Step and Rapid Scan,” http://www.brukeroptics.com/stepscan.html.

]. For satisfactory time resolution, Smith et al. [6

6. G. D. Smith and R. A. Palmer, “Fast Time-resolved Mid-infrared Spectroscopy Using an Interferometer,” in Handbook of Vibrational Spectroscopy: Volume 1, (John Wiley and Sons Ltd, 2002).

] state that the duration of the scan should be at least one order of magnitude shorter than the half-life of the dynamic event being examined. Baurecht et al. [7] claimed that such instruments can then reach a time resolution of 33 ms at 8 cm−1 spectral resolution when running in rapid scan double-sided forward-backward mode.

Attempts to further extend time resolution include rotary as well as stationary interferometers, some of them produced by micromanufacturing. Hashimoto and Kawata [8

8. M. Hashimoto and S. Kawata, “Multichannel Fourier-transform infrared spectrometer,” Appl. Opt. 31(28), 6096–6101 (1992). [CrossRef] [PubMed]

] used a Savart plate to obtain multi-channel interferograms in a stationary way. The Savart plate is based on a stack of two birefringent plates that split the incoming beam into two partial beams that have a λ-dependent phase shift and are brought to interference. This device reached a spectral resolution of 27.6 cm−1. The Savart plate implies that the spectral range depends on its spectral transmission window. Moser and Möller [9

9. H. O. Moser and K. D. Möller, “Gitterstruktur und deren Verwendung”, European patent EP 0 765 488 B1, June 18, 1994.

] proposed a micromanufactured multimirror device, thus spawning the present work. Manzardo et al. [10

10. O. Manzardo, R. Michaely, F. Schädelin, W. Noell, T. Overstolz, N. De Rooij, and H. P. Herzig, “Miniature lamellar grating interferometer based on silicon technology,” Opt. Lett. 29(13), 1437–1439 (2004). [CrossRef] [PubMed]

] studied both, stationary and microfabricated scanning approaches. While microtechnology has the potential to go to frequencies in the kHz range, this was not achieved in the work of Scharf et al. [11

11. T. Scharf, D. Briand, S. Buehler, O. Manzardo, H. P. Herzig, and N. F. de Rooij, “Miniaturized Fourier Trans-form Spectrometer for Gas Detection in the MIR Region,” Sens. Actuators B Chem. 147(1), 116–121 (2010). [CrossRef]

]. Building a MEMS lamellar grating scanning interferometer, they required 5 s time to measure one spectrum of 20 cm−1 spectral resolution as they needed to average a 1000 spectra with a 200 Hz scanner resonant frequency. A stationary device of Manzardo et al. suffered from low spectral resolution of 5 nm at 730 nm with 1024 detector pixels which transforms into about 100 cm−1 [12

12. O. Manzardo, Micro-sized Fourier spectrometers, PhD thesis, University of Neuchatel, (1999).

]. Building an interferometer based on a fast rotating wedge mirror with a nominal rate of 1000 interferograms per second, Griffiths et al. [13

13. P. R. Griffiths, B. L. Hirsche, and C. J. Manning, “Ultra-Rapid-Scanning Fourier Transform Infrared Spectrometry,” Vib. Spectrosc. 19(1), 165–176 (1999). [CrossRef]

] demonstrated spectroscopy with a scan rate of up to 166 Hz at 4 cm−1 spectral resolution.

Furthermore, techniques were developed to speed up data acquisition such as the so-called step scan [1

1. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

,6

6. G. D. Smith and R. A. Palmer, “Fast Time-resolved Mid-infrared Spectroscopy Using an Interferometer,” in Handbook of Vibrational Spectroscopy: Volume 1, (John Wiley and Sons Ltd, 2002).

]. Here, the spectral signal is repeated a certain number of times and, for each shot, the interferometer is set at a different path difference. However, such a technique requires a rather accurate repeatability of the signal which might be the case rather rarely.

In this paper, we analyse the influence of time-dependent signals on Fourier transform spectroscopy and present a multichannel Fourier transform spectrometer (MC-FTIR) to measure such signals exploiting novel micro/nano manufacturing techniques as described in [9

9. H. O. Moser and K. D. Möller, “Gitterstruktur und deren Verwendung”, European patent EP 0 765 488 B1, June 18, 1994.

]. Our MC-FTIR does away with mechanical scanning using instead a truly parallel processing device to generate an interferogram by means of many micro/nanomanufactured interferometer cells. It is able to measure arbitrarily short non-repetitive pulses as well as fast varying continuous signals. The noise-equivalent energy of a pixellated detector would determine the shortest detectable pulse duration from a sufficiently intense source whereas the read-out rate of the detector and signal-processing system would limit the frequency of continuous signals. Owing to the absence of movable parts, the MC-FTIR can be extremely rugged and capable of demanding field applications.

2. Fourier transform interferometry of time-dependent signals

Fourier transform interferometry uses two beams
u1(k,x,t)=g(k)A1(t)ei(kxωt)
(1)
u2(k,x,t)=g(k)A2(t)ei[k(xδ(t))ωt]
(2)
with a controllable optical path difference δ(t)that are recombined to interfere. Here, g(k) is a real function describing the spectral dependence that is assumed independent of time and identical for both waves. Furthermore, real functions A1(t), A2(t) represent the time dependence of the amplitude. Finally, k=/λand ω=2πν are the wavenumber and angular frequency, respectively. The time-dependence of the amplitudes takes all temporal variations into account except that of the carrier wave itself which is expressed by the exponentials. Adding Eqs. (1) and (2), forming the absolute square, setting G(k)g2(k), and integrating over k, we obtain the detector signal

J(δ,t)=(A12(t)+A22(t))0G(k)dk+2A1(t)A2(t)0G(k)cos()dk
(3)

The second integral is called the interferogram [14

14. K. D. Möller and C. Belorgeot, Cours d’optique, (Springer Verlag France, Paris, 2007), pp. 190.

]

S(δ)=0G(k)cos(kδ)dk
(4)

Its Fourier transform yields the desired spectrum

G(k)=0S(k)cos(kδ)dδ
(5)

To evaluate Eq. (5), we use Eq. (3) to obtain

S(δ)=J(δ,t)(A12(t)+A22(t))S(0)2A1(t)A2(t)
(6)

Obviously, S(δ) can be evaluated from the measurement of J(δ,t) only if the time-dependent amplitudes A1(t), A2(t) are known from additional measurements by individual detectors. In conventional FTIR, the amplitudes are assumed to be constant and identical [14

14. K. D. Möller and C. Belorgeot, Cours d’optique, (Springer Verlag France, Paris, 2007), pp. 190.

] and can be eliminated by a scaling factor and a suitable choice of a baseline. With the present instrument, we can measure arbitrarily short pulses provided enough photons are available, and, thus, time-dependent signals for which the rate of signal change is small compared to either pulse length or rate of data acquisition and processing of the detector and the subsequent data processing chain. The limitations no longer come from the interferometric device, but from the detector and data processing chain.

3. Multichannel FTIR

The MC-FTIR is based on a micro/nanomanufactured multimirror array that has grooves with stepwise varying depths (Fig. 1(a)
Fig. 1 (a) Multimirror array (MMA) with a chess-board-like area of stepped planes that represent the bottom mirrors and a multitude of lamellae the top ridges of which embody the top mirrors (left). Denomination of angles (right): k wave vector of incident plane wave, γ the angle between k and its projection onto the x-z plane, φ the angle between the projection of k onto the x-z plane and the x axis. (b) Extract of simulated and measured interferograms for a spectrum produced by a narrow bandpass filter centered at 961 cm−1 for a Gaussian transmission peak of spectral beam-width (FHWM) of 20 cm−1. (c) Optical layout of MC-FTIR. Mirrors M2 and M3 can be optionally removed. (d) Experimental set up of the MC-FTIR. Image width 50 cm.
). The ridges of the grooves form the reference plane, whereas the bottom surfaces of the grooves are parallel to the reference plane and have different distances from the reference plane. In this way, a chess-board-like multimirror array (MMA) is achieved in which one cell represents a certain optical path difference between rays reflected from the reference plane and the bottom surface, respectively [9

9. H. O. Moser and K. D. Möller, “Gitterstruktur und deren Verwendung”, European patent EP 0 765 488 B1, June 18, 1994.

]. Despite some similarity with the well-known reflection echelon [3

3. E. B. Brown, Modern Optics (Reinhold Publishing Corporation, Chapman&Hall Ltd, 1966), pp. 437–441. [PubMed]

], the MMA is distinct in that it has a 2D chess-board-like arrangement of stepped surfaces and lamellae which form a common reference plane. Each cell of the MMA generates a point on an interferogram. Depending on its spectrum, an incoming parallel beam would generate a specific interference from each cell. An imaging system relates the cells of the whole mirror area to specific groups of pixels that represent individual points of the interferogram. As the reference plane is, in fact, a grating, an order-sorting aperture is used to select the desired 0th order of diffraction.

Assuming monochromatic radiation, a simplified mathematical description of the beam intensity J in Fraunhofer approximation downstream an MMA cell is given by Eq. (7) [4

4. J. Strong and J. Vanasse, “Applications of Fourier Transformation in Optics: Interferometric Spectroscopy” in Concepts in Classical Optics, J. Strong (W.H. Freeman&Co., 1958), pp. 419–434.

,15

15. S. P. Heussler, Design, Micro-Manufacturing, and Characterization of a New Fast Parallel-Processing Fourier Transform Interferometer (FTIR) with Single Non-Periodic Pulse Capability, PhD thesis, National University of Singapore, unpublished (2010).

]
J[sin(12kwsinα)12kwsinα]2[sin(12klsinβ)12klsinβ]2[sin(12kwNsinα)kwsinα]2cos[12k(wsin(α)+2hcosγsinφ)]2
(7)
where α and β denote the diffraction angles perpendicular and parallel to the trenches of the MMA, w, l, and N, the width, the length and the number of mirror facets per cell, respectively. Angles γ and φ are the incidence angles shown in Fig. 1(a). Optical path difference δ corresponds to 2khcosγ/sinφ for a detector plane perpendicularly oriented to the reflected k.

Here, the cos2 term describes the modulation of the intensity as a function of the optical path difference δ. A spectral simulation of an interferogram and the experimental result generated by an MMA for a narrow band-pass filter centered at 961 cm−1 are depicted in Fig. 1(b).

The theoretical spectral resolution RILS defined by the instrumental line shape function [1

1. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

] as well as the free spectral range versus the geometric parameters of the multimirror for perpendicularly incident light are presented in Table 1

Table 1. Geometric Parameters of MMA

table-icon
View This Table
[15

15. S. P. Heussler, Design, Micro-Manufacturing, and Characterization of a New Fast Parallel-Processing Fourier Transform Interferometer (FTIR) with Single Non-Periodic Pulse Capability, PhD thesis, National University of Singapore, unpublished (2010).

], where hmax denotes the maximum depth of the MMA, Δh the depth difference from one MMA cell to the next, Δσ the spectral bandwidth, given by σmax - σmin the difference between the highest and the lowest wavenumber component in the spectral working band, and P is the lamellar grating period.

Since the MC-FTIR uses the whole beam at any given moment, there is no loss of incident beam power. As a rough comparison to state-of-the-art FTIR, the conventional FTIR is using one half (due to the beam splitter) of the incident power delivered to one detector with the points of the interferogram spread in time while the MC-FTIR is delivering the whole incident power at the same time to many groups of pixels of a pixellated detector. Spread in time is replaced by spread in space.

The MMA is part of an optical system that includes a source-matching optics delivering a parallel beam of suitable cross-section to the MMA, an imaging optics to relate beamlets from MMA cells to groups of pixels such that the interferogram can be reconstructed, an order-sorting aperture, and a pixellated detector (focal plane array). The detector signal is read out by a frame-grabber and fed to a computer that transforms the interferogram into the spectrum. An optical layout and experimental set-up of the MC-FTIR are shown in Fig. 1 (c) and (d). All components are available commercially except the MMA which is manufactured by means of deep X-ray lithography with synchrotron radiation [16

16. E. W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, and D. Muenchmeyer, “Fabrication of Microstructures With High Aspect Ratios and Great Structural Heights by Synchrotron Radiation Lithography, Galvanoforming, and Plastic Moulding (LIGA Process),” Microelectron. Eng. 4(1), 35–56 (1986). [CrossRef]

] using a novel multiple moving mask technique [17

17. S.P. Heussler, H.O. Moser, 3D micro/nanomanufacturing of arbitrary multilevel plane surfaces, US Provisional Application No.: 61/407,502, Filing Date: 28 October 2010.

]. Different exposure times in conjunction with two X-ray masks, one fixed and one movable, are used to generate the grooves of varying depth while maintaining the top ridge level of the reference plane. Figure 2 (a)
Fig. 2 (a) SEM of a fractional area of the MMA. Grooves deepen towards the right. Scale bar 500 μm. (b) Average surface roughness (Ra) of groove bottoms versus etch depth.
shows an SEM image of the

MMA surface made in PMMA resist (poly methyl methacrylate) covered by a thin gold layer for good reflectivity. The roughness of the bottom surface of grooves versus etch depth is depicted in Fig. 2(b). It defines optical quality and is sufficient to achieve an unapodized spectral resolution of 5 cm−1.

4. Experimental results and discussion

The spectral range of the present MC-FTIR extends from 700 to 1400 cm−1 equivalent to about 7-14 μm. It is given by the spectral response of the detector. Here we used an amorphous Silicon microbolometer focal plane array detector with a NETD of 50 mK (ULIS UL 03081). The test source was a blackbody calibration source (EOI CS1250-100) at a temperature of 1250 °C and an aperture diameter of 2.54 cm. Figure 3(a)
Fig. 3 (a) Comparison of normalized spectra of a narrow bandpass filter taken with the IFS 66 interferometer over 60 s (solid line) and MC-FTIR taken at 20 ms (dashed line). (b) Shape of measured spectrum versus exposure duration ranging from 31.48 ms to 320 µs. Spectra are shifted vertically for better viewing. For all measurements, the pulse duration was reproducible within a tolerance of 20 µs.
shows a spectrum of a commercial narrow band-pass filter at 961 cm−1 taken by means of the MC-FTIR (dashed line) in 20 ms in comparison with a spectrum measured by means of a Bruker IFS 66 v/S (solid line) over a period of 60 s. The agreement is excellent. The exposure time with the MC-FTIR is 3000 times shorter than with the conventional Bruker IFS 66 v/S. Figure 3(b) shows single pulses taken from a reference source at a resolution of 100 cm−1 for various pulse durations defined by a camera shutter from 31.48 ms down to 319 μs. The grey-hatched spectrum represents the continuous exposure case. It can be seen that normalized spectra maintain their shape perfectly down to about 4 ms after which a distortion appears that grows such that at 319 μs the spectral shape is substantially different. The distortion is attributed to an increasing influence of noise as the number of photons per pixel decreases from 1.5×1013 at 31.48 ms to about 1.5×1011 at 319 μs. Accordingly, the shot-by-shot changes of the spectral shape become important. The shortest useful pulse length is thus defined by the number of photons reaching the pixel as given by the source intensity and pulse length. Without moving parts, the MC-FTIR should be able to measure femtosecond pulses or shorter provided there is a sufficient number of photons for a given detector system.

5. Concluding remarks

The capability of measuring, by Fourier transform interferometry, the spectra of single arbitrarily short pulses and continuous signals that vary in time opens up potential applications in chemistry, fast processes such as explosions, lightnings, gas discharges for X-ray sources, diagnostics of pulsed plasmas in inertial fusion or pinch discharges. The measurement rate is only limited by the detector acquisition and data processing rates. The obvious requirement that the number of photons per spectrum must exceed the noise level makes the system specifically appropriate for laser-based methods such as laser induced breakdown spectroscopy [18

18. C. S.-C. Yang, E. E. Brown, U. H. Hommerich, S. B. Trivedi, A. C. Samuels, and A. P. Snyder, “Mid-infrared emission from laser-induced breakdown spectroscopy,” Appl. Spectrosc. 61(3), 321–326 (2007). [CrossRef] [PubMed]

]. Combined with the ruggedness of the device, field applications in coarse environments become feasible.

Acknowledgment

Work partly performed at SSLS under NUS Core Support C-380-003-003-001 and NRF POC Project NRF2009NRF-POC001-124. The authors like to thank Mark B.H. Breese for his continuous support.

References and links

1.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

2.

L. Genzel, “Fourier-Transform-Spektroskopie im Infraroten”, Fresenius’ J. Anal. Chem. 273, 391–400 (1975). [CrossRef]

3.

E. B. Brown, Modern Optics (Reinhold Publishing Corporation, Chapman&Hall Ltd, 1966), pp. 437–441. [PubMed]

4.

J. Strong and J. Vanasse, “Applications of Fourier Transformation in Optics: Interferometric Spectroscopy” in Concepts in Classical Optics, J. Strong (W.H. Freeman&Co., 1958), pp. 419–434.

5.

Bruker Optics, “Step and Rapid Scan,” http://www.brukeroptics.com/stepscan.html.

6.

G. D. Smith and R. A. Palmer, “Fast Time-resolved Mid-infrared Spectroscopy Using an Interferometer,” in Handbook of Vibrational Spectroscopy: Volume 1, (John Wiley and Sons Ltd, 2002).

7.

D. Baurecht, “Schwingungs-Spektroskopie,” p. 32 (2009) http://www.bpc.univie.ac.at/fileadmin/ user_upload/inst_bio_phys_chem/pub/db_IR_und_Raman-Theorie.pdf.

8.

M. Hashimoto and S. Kawata, “Multichannel Fourier-transform infrared spectrometer,” Appl. Opt. 31(28), 6096–6101 (1992). [CrossRef] [PubMed]

9.

H. O. Moser and K. D. Möller, “Gitterstruktur und deren Verwendung”, European patent EP 0 765 488 B1, June 18, 1994.

10.

O. Manzardo, R. Michaely, F. Schädelin, W. Noell, T. Overstolz, N. De Rooij, and H. P. Herzig, “Miniature lamellar grating interferometer based on silicon technology,” Opt. Lett. 29(13), 1437–1439 (2004). [CrossRef] [PubMed]

11.

T. Scharf, D. Briand, S. Buehler, O. Manzardo, H. P. Herzig, and N. F. de Rooij, “Miniaturized Fourier Trans-form Spectrometer for Gas Detection in the MIR Region,” Sens. Actuators B Chem. 147(1), 116–121 (2010). [CrossRef]

12.

O. Manzardo, Micro-sized Fourier spectrometers, PhD thesis, University of Neuchatel, (1999).

13.

P. R. Griffiths, B. L. Hirsche, and C. J. Manning, “Ultra-Rapid-Scanning Fourier Transform Infrared Spectrometry,” Vib. Spectrosc. 19(1), 165–176 (1999). [CrossRef]

14.

K. D. Möller and C. Belorgeot, Cours d’optique, (Springer Verlag France, Paris, 2007), pp. 190.

15.

S. P. Heussler, Design, Micro-Manufacturing, and Characterization of a New Fast Parallel-Processing Fourier Transform Interferometer (FTIR) with Single Non-Periodic Pulse Capability, PhD thesis, National University of Singapore, unpublished (2010).

16.

E. W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, and D. Muenchmeyer, “Fabrication of Microstructures With High Aspect Ratios and Great Structural Heights by Synchrotron Radiation Lithography, Galvanoforming, and Plastic Moulding (LIGA Process),” Microelectron. Eng. 4(1), 35–56 (1986). [CrossRef]

17.

S.P. Heussler, H.O. Moser, 3D micro/nanomanufacturing of arbitrary multilevel plane surfaces, US Provisional Application No.: 61/407,502, Filing Date: 28 October 2010.

18.

C. S.-C. Yang, E. E. Brown, U. H. Hommerich, S. B. Trivedi, A. C. Samuels, and A. P. Snyder, “Mid-infrared emission from laser-induced breakdown spectroscopy,” Appl. Spectrosc. 61(3), 321–326 (2007). [CrossRef] [PubMed]

OCIS Codes
(230.6120) Optical devices : Spatial light modulators
(300.6190) Spectroscopy : Spectrometers
(320.7080) Ultrafast optics : Ultrafast devices
(320.7150) Ultrafast optics : Ultrafast spectroscopy

ToC Category:
Ultrafast Optics

History
Original Manuscript: May 12, 2011
Revised Manuscript: June 8, 2011
Manuscript Accepted: June 8, 2011
Published: June 14, 2011

Citation
S. P. Heussler, H.O. Moser, S. M. Kalaiselvi, C. G. Quan, and C. J. Tay, "Multichannel Fourier-transform interferometry for fast signals," Opt. Express 19, 12628-12633 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-12628


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References

  1. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).
  2. L. Genzel, “Fourier-Transform-Spektroskopie im Infraroten”, Fresenius’ J. Anal. Chem. 273, 391–400 (1975). [CrossRef]
  3. E. B. Brown, Modern Optics (Reinhold Publishing Corporation, Chapman&Hall Ltd, 1966), pp. 437–441. [PubMed]
  4. J. Strong and J. Vanasse, “Applications of Fourier Transformation in Optics: Interferometric Spectroscopy” in Concepts in Classical Optics, J. Strong (W.H. Freeman&Co., 1958), pp. 419–434.
  5. Bruker Optics, “Step and Rapid Scan,” http://www.brukeroptics.com/stepscan.html .
  6. G. D. Smith and R. A. Palmer, “Fast Time-resolved Mid-infrared Spectroscopy Using an Interferometer,” in Handbook of Vibrational Spectroscopy: Volume 1, (John Wiley and Sons Ltd, 2002).
  7. D. Baurecht, “Schwingungs-Spektroskopie,” p. 32 (2009) http://www.bpc.univie.ac.at/fileadmin/ user_upload/inst_bio_phys_chem/pub/db_IR_und_Raman-Theorie.pdf .
  8. M. Hashimoto and S. Kawata, “Multichannel Fourier-transform infrared spectrometer,” Appl. Opt. 31(28), 6096–6101 (1992). [CrossRef] [PubMed]
  9. H. O. Moser and K. D. Möller, “Gitterstruktur und deren Verwendung”, European patent EP 0 765 488 B1, June 18, 1994.
  10. O. Manzardo, R. Michaely, F. Schädelin, W. Noell, T. Overstolz, N. De Rooij, and H. P. Herzig, “Miniature lamellar grating interferometer based on silicon technology,” Opt. Lett. 29(13), 1437–1439 (2004). [CrossRef] [PubMed]
  11. T. Scharf, D. Briand, S. Buehler, O. Manzardo, H. P. Herzig, and N. F. de Rooij, “Miniaturized Fourier Trans-form Spectrometer for Gas Detection in the MIR Region,” Sens. Actuators B Chem. 147(1), 116–121 (2010). [CrossRef]
  12. O. Manzardo, Micro-sized Fourier spectrometers, PhD thesis, University of Neuchatel, (1999).
  13. P. R. Griffiths, B. L. Hirsche, and C. J. Manning, “Ultra-Rapid-Scanning Fourier Transform Infrared Spectrometry,” Vib. Spectrosc. 19(1), 165–176 (1999). [CrossRef]
  14. K. D. Möller and C. Belorgeot, Cours d’optique, (Springer Verlag France, Paris, 2007), pp. 190.
  15. S. P. Heussler, Design, Micro-Manufacturing, and Characterization of a New Fast Parallel-Processing Fourier Transform Interferometer (FTIR) with Single Non-Periodic Pulse Capability, PhD thesis, National University of Singapore, unpublished (2010).
  16. E. W. Becker, W. Ehrfeld, P. Hagmann, A. Maner, and D. Muenchmeyer, “Fabrication of Microstructures With High Aspect Ratios and Great Structural Heights by Synchrotron Radiation Lithography, Galvanoforming, and Plastic Moulding (LIGA Process),” Microelectron. Eng. 4(1), 35–56 (1986). [CrossRef]
  17. S.P. Heussler, H.O. Moser, 3D micro/nanomanufacturing of arbitrary multilevel plane surfaces, US Provisional Application No.: 61/407,502, Filing Date: 28 October 2010.
  18. C. S.-C. Yang, E. E. Brown, U. H. Hommerich, S. B. Trivedi, A. C. Samuels, and A. P. Snyder, “Mid-infrared emission from laser-induced breakdown spectroscopy,” Appl. Spectrosc. 61(3), 321–326 (2007). [CrossRef] [PubMed]

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