Spectrum Reconstruction of a Spatially Modulated Fourier Transform Spectrometer Based on Stepped Mirrors

Abstract

Based on the basic configuration and interference principle of a static step-mirror-based Fourier transform spectrometer, an image segmentation method is proposed to obtain a one-dimensional interferogram. The direct current component of the interferogram is fit using the least squares (LS) method and is subsequently removed. An empirical-mode decomposition-method-based high-pass filter is constructed to denoise the spectrum and enhance the spectral resolution simultaneously. Several experiments were performed and the spectrum is reconstructed based on these methods. The spectrum resolution is 81 cm^–1 at 2254 cm^–1.

Keywords

Step mirror Fourier transform (FT) spectrometer image segmentation spectrum reconstruction empirical-mode decomposition denoising

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References

Horton

R.B.

Duranty

McConico

Vogt

“Fourier Transform Infrared (FT-IR) Spectroscopy and Improved Principal Component Regression (PCR) for Quantification of Solid Analytes in Microalgae and Bacteria”. Appl. Spectrosc 2011; 65(4): 442–453.

Parodi

Dickerson

Cloud

“Pollen Identification by Fourier Transform Infrared Photoacoustic Spectroscopy”. Appl. Spectrosc 2013; 67(3): 342–348.

Picollo

Bartolozzi

Cucci

Galeotti

Marchiafava

Pizzo

“Comparative study of Fourier transform Infrared Spectroscopy in Transmission, Attenuated Total Reflection, and Total Reflection Modes for the Analysis of Plastics in the Cultural Heritage Field”. Appl. Spectrosc 2014; 68(4): 389–397.

Sarioglu

O.F.

Tamer

Y.T.

Ozkan

A.D.

Atabay

H.I.

Molva

Tekinay

“Fourier Transform Infrared Spectroscopy as a Novel Approach for Analyzing the Biochemical Effects of Anionic Surfactants on a Surfactant-Degrading Arcobacter Butzleri Strain”. Appl. Spectrosc 2013; 67(4): 470–475.

Zhang

Wan

Yuan

Duan

Zhang

“Chemical Structure and Interlayer Distance Correlation of Graphite Oxide in the Heating Process as Revealed by in situ Fourier Transform Infrared Spectroscopy and Wide-Angle X-ray Diffraction Techniques”. Appl. Spectrosc 2014; 68(5): 570–576.

Saptari

“Spectroscopy Instrumentation”. In: Weeks

A.R.

(ed). Fourier-Transform Spectroscopy Instrumentation Engineering, 1st ed. Bellingham, WA: SPIE, 2003. Chap. 1, Pp. 3–6.

Lee

Krishnamoorthy

Park

Solgaard

“Micromachined Fourier Transform Spectrometer on Silicon Optical Bench Platform”. Sens. Actuators, A 2006; 130: 523–530.

Reyes

Schildkraut

E.R.

Kim

Conners

R.F.

Kotidis

Cavicchio

D.J.

“A Novel Method of Creating a Surface Micromachined 3D Optical Assembly for MEMS-Based Miniaturized FTIR Spectrometers”. Proc. SPIE 6888, MEMS Adaptive Optics II 2008; 68880D.

Moeller

K.D.

“Miniaturized Wavefront-Dividing Interferometers without Moving Parts for Field and Space Applications”. Proc. SPIE, Miniature and Micro-Optics and Micromechanics 1993; 130. http://dx.doi.org/10.1117/12.165681 .

10.

Lacan

Bréon

F.M.

Rosak

Brachet

Roucayrol

Etcheto

Casteras

Salaun

“A Static Fourier Transform Spectrometer for Atmospheric Sounding: Concept and Experimental Implementation”. Opt. Express 2010; 18(8): 8311–8331.

11.

F. Brachet, P.J. Hébert, E. Cansot, et al. “Static Fourier Transform Spectroscopy Breadboards for Atmospheric Chemistry and Climate”. Proc. SPIE 7100, Optical Design and Engineering III. 710019 (27 September 2008). doi: 10.1117/12.797686.

12.

Ivanov

E.V.

“Static Fourier Transform Spectroscopy with Enhanced Resolving Power”. J. Opt. A: Pure Appl. Opt 2000; 2(6): 519.

13.

Zheng

Liang

J.Q.

Liang

Z.Z.

“Design and Fabrication of Step Mirrors used in Space-Modulated Fourier Transform Infrared Spectrometer”. Opt. Express 2013; 21(1): 884–892.

14.

J.G.

Liang

J.Q.

Liang

Z.Z.

Qin

Y.X.

Tian

Wang

W.B.

“Design and Manufacture of Micro Interference System in Spatial Modulation Fourier Transform Spectrometer”. Key Engineering Materials 2013; 562: 973–978.

15.

Chen

Liang

J.Q.

Liang

Z.Z.

Qin

Tian

Wang

“Fabrication and Analysis of Tall-Stepped Mirror for use in Static Fourier Transform Infrared Spectrometer”. Opt. Laser. Technol 2015; 75: 6–12.

16.

Feng

Wang

Liang

Z.Z.

Liang

“Miniaturization of Step Mirrors in a Static Fourier Transform Spectrometer: Theory and Simulation”. J. Opt. Soc. Am. B 2011; 28(1): 128–133.

17.

Liang

J.Q.

Liang

Z.Z.

J.G.

Zheng

Feng

Wang

W.B.

Zhu

W.B.

Yao

J.S.

Zhang

“Simulation and Experiment of the Static FTIR based on Micro Multi-Step Mirrors”. Proc. SPIE 8191, International Symposium on Photoelectronic Detection and Imaging 2011. International Society for Optics and Photonics 2011, pp. 819104–819104-8.

18.

Feng

Liang

J.Q.

Liang

Z.Z.

“Spectrum Constructing with Nonuniform Samples Using Least-Squares Approximation by Cosine Polynomials”. Appl. Opt 2011; 50(34): 6377–6383.

19.

R.C. Gonzalez, R.E. Woods, S.L. Eddins. “Image Segmentation”, In: R. Qiuqi (ed.) Digital Image Processing Using MATLAB, 2nd ed. Publication house of electronics industry, 2013, Chap. 7, Pp. 209–211.

20.

Griffiths

P.R.

de Haseth

J.A.

“Theoretical Background”. In: Griffiths

P.R.

de Haseth

J.A.

(eds). Fourier Transform Infrared Spectrometry, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2007. , Chap. 2, Pp. 26–30.

21.

T. Hirschfeld. “Quantitative FT-IR: A detailed look at the problems involved”. In: J.R. Ferraro and L.J. Basile (eds) Fourier Transform Infrared Spectroscopy: Application to Chemical Systems. Vol. 2, New York, NY: Academic Press, 1979, Pp. 193–242.

22.

Xiangli

Huang

“Advance in Interferogram Data Processing Technique”. Guang Pu Xue Yu Guang Pu Fen Xi [Spectrosc. Spect. Anal.] 2011; 31(4): 865–870.

23.

Furstenberg

White

J.O.

“Phase Correction of Interferograms Using Digital All-Pass Filters”. Appl. Spectrosc 2005; 59(3): 316–321.

24.

Zhang

M.J.

Zhang

J.L.

Wang

Z.B.

Jing

Hao

“Phase Correction Technology Research and Improvement Based on Single-Sided Interferograms in FTIR”. Guang Pu Xue Yu Guang Pu Fen Xi [Spectrosc. Spect. Anal.] 2012; 32(5): 1203–1208.

25.

Griffiths

P.R.

De Haseth

J.A.

“Fourier Transforms”. In: Griffiths

P.R.

de Haseth

J.A.

(eds). Fourier Transform Infrared Spectrometry, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2007. Chap. 7, Pp. 85–88.

26.

Huang

N.E.

Shen

Long

S.R.

M.C.

Shih

H.H.

Zheng

Yen

N.-C.

Tung

C.C.

Liu

H.H.

“The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis”. Proc. R. Soc. London, Ser. A 1998; 454(1971): 903–995.

27.

Deléchelle

Lemoine

Niang

“Empirical Mode Decomposition: An Analytical Approach for Sifting Process”. IEEE Signal. Proc. Let 2005; 12(11): 764–767.

28.

Hsu

C.H.

Lee

C.Y.

Liang

W.K.

“An Improved Method for Measuring Mismatch Negativity Using Ensemble Empirical Mode Decomposition”. J. Neurosci. Meth 2016; 264: 78–85.

29.

Yang

“Empirical Mode Decomposition as a Time-Varying Multirate Signal Processing System”. Mech. Syst. Signal. Pr 2016; 76: 759–770.

30.

Zhou

Yang

Zhou

Yang

“Optimal Averages for Nonlinear Signal Decompositions: Another Alternative for Empirical Mode Decomposition”. Signal Process 2016; 121(C): 17–29.

31.

C. Chen. Optical Design and Core Components Study for Static Fourier Transform Infrared Spectrometer. University of Chinese Academy of Sciences, [Ph.D. dissertation]. 2016. Chap. 7, Pp. 117–125.