Progress Towards Obtaining Lineshape Parameters Using Chirped Pulse THz Spectroscopy

Eyal Gerecht, Kevin O. Douglass, David F. Plusquellic

National Institute of Standards and Technology Optical Technology Division, Gaithersburg, MD

Multi-Component Gas MonitorGHGs, VOCs, or breath analysis

Formaldehyde

CO

MethanolAcetone

Ethanol

CO2 (18O)

N2O

NO

0.805 0.875THzL.S. Rothman et al, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 96, 139-204 (2005). H. M. Pickett, R. L. Poynter, E. A. Cohen, M. L. Delitsky, J. C. Pearson, and H. S. P. Muller, "Submillimeter, Millimeter, and Microwave Spectral Line Catalog," J. Quant. Spectrosc. Radiat. Transf. 60, 883-890 (1998).

Spectral Line Shapes

+ =

Re Im Mag√𝑅𝑒2+𝐼𝑚2

Resulting from FFT of a damped oscillator

Dispersion Absorption

FFT

Spectral Line ShapesResulting from FFT of a damped oscillator

AbsorptionFactor of

● Higher resolution Improved spectral discrimination

● measurement of lineshape parameters

Spectral Line Shapes: Issues

Recorded spectra typically appear as a linear combination Re and Im components

Re(F(ω)) = cos ϕ A(ω) + sin ϕ D(ω)

Im(F(ω)) = -sin ϕ A(ω) + cos ϕ D(ω)

The pure Absorption and Dispersion spectra can be determined with the correct phase angle

A(ω) = cos ϕ Re(F(ω)) - sin ϕ Im(F(ω)) = Im(F(ω) exp(-i ϕ)) D(ω) = -sin ϕ Re(F(ω)) + cos ϕ Im(F(ω)) = Re (F(ω) exp(-i ϕ))

ϕ() =arctan

Determining the phase angle over the Full Spectrum

Time delay in acquisition leads to a frequency dependent phase shift (Shift Theorem)

ϕ(ω) = ω tdelay

In NMR zero order term sets initial phase and the linear term accounts for acquisition delay

ϕ(ω) = ϕ0 + tdelay(ω – ωa)

Need to account for quadratic phase accumulation due to chirped pulse excitation

ϕ(ω) = ϕ0 + tdelayω + ω2

Broad bandwidth Phase Correction Approaches in the Past: FT-ICR

Complex Division1

A() = Fourier deconvolution simultaneously corrects amplitude variations and phase

error

Start from well determined experimental parameters and vary2 ϕ0

Iterative quadratic least squares fit to picked peaks3

ϕ(ω) = ϕ0 + ϕ1ω+ ϕ2ω2 + 2n

Variety of automated algorithms developed for NMR4

ϕ(ω) = ϕ0 +

1. Xian, F. et al Anal. Chem. 2010, 82, 8807 – 88122. Beu ,S. C., Anal. Chem. 2004, 76, 5756 – 57613. Qi , Y, J. Am. Soc. Mass Spectrom. 2011, 158 1644. Brouwer, H. de, JMR 201 (2009) 230–238

Broad bandwidth Phase CorrectionCurrent Approach

Challenges rapidly accumulate phase

ϕ(ω) = ϕ0 + tdelay(ω – ωa) + ϕchirp

Obtained by fitting transmitted chirped pulse phase angleEstimate and vary tdelay and ϕ0

until phase is alignedsimplify to NMR approach

x48

White Cell

9 GHz Source

Mix AMCx48

YIG

YIG

AWG 12GS/s

Chirped-Pulse THz Spectrometer

E. Gerecht, K.O. Douglass, D.F. Plusquellic, Optics Express, April 22, 2011, Vol. 19, Issue 9, pp. 8973-8984 (2011),

Time (ns)0 100

Freq

uenc

y (G

Hz)

012

25 ns - 10 GHz Chirped THz pulse 550 – 560 GHz

Direct Absorption of a 5 Component Gas Mix

L.S. Rothman et al, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 96, 139-204 (2005). H. M. Pickett, R. L. Poynter, E. A. Cohen, M. L. Delitsky, J. C. Pearson, and H. S. P. Muller, "Submillimeter, Millimeter, and Microwave Spectral Line Catalog," J. Quant. Spectrosc. Radiat. Transf. 60, 883-890 (1998).

Absorption Data Results

Many improvements in the pipeline

Magnitude Spectrum of FID

0.54600 0.55666THz

FID

Sig

nal

(a.

u.)

0.55133 0.553990.54866

N2O

OCS

EtOHMeOH

Acetone

H2O

x500

100,000:1

x500

L.S. Rothman et al, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 96, 139-204 (2005). H. M. Pickett, R. L. Poynter, E. A. Cohen, M. L. Delitsky, J. C. Pearson, and H. S. P. Muller, "Submillimeter, Millimeter, and Microwave Spectral Line Catalog," J. Quant. Spectrosc. Radiat. Transf. 60, 883-890 (1998).

10.6 GHz in 500 nsec – 80K averages in 60 sec

5 Component Gas Mix

Phase Correcting a Single Peak

ϕ0 = 147⁰A(ω)=Im(F(ω) exp(-i ϕ0 ))

Fit Results (MHz)wG 1.05626 +/- 0.00149wL 0.06852 +/- 0.00208

HITRAN (MHz)wG 0.87wL 0.8

10 mTorr 1% OCS in Ne

L.S. Rothman et al, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 96, 139-204 (2005).

Fit to Quadratic Phase Change

ϕ() =arctan

sin(t + αt2)

Magnitude vs. Im Componentϕ(ω) = ϕ0 + tdelay(ω – ωa) + ϕchirp

Magnitude vs. Im Component

779.760 869.760ν / GHz

Extending to Higher Bandwidths

Justin Neil RC06

90 GHz FID near 850 GHzMeOH -1.2 mTorr Pure2 ms acquisition time

L.S. Rothman et al, “The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 96, 139-204 (2005).

Conclusions

Obtain lineshapes that are in good agreement with HITRAN from direct absorption measurements

Lineshapes measurements from FID are possible and demonstrated for a single transition of OCS at 546.859 GHz

Need to implement automated algorithms developed for NMR to phase the broadband spectrum

Acknowledgements

Virginia L. Perkey – SURF student Eric M. Vess - SURF student Tektronix – equipment loan

Upper Atmospheric Research Program of the National Aeronautics and Space Administration (NNH09AK47I)

NIST National Research Council ProgramPost Doctoral Research Opportunities

http://www.nist.gov/pml/div685/grp08/biophysics-group-research-opportunities.cfm

Spectral Line Shapes: Issues

Recorded spectra typically appear as a linear combination Re and Im components

Re(F(ω)) = cos ϕ A(ω) + sin ϕ D(ω)

Im(F(ω)) = -sin ϕ A(ω) + cos ϕ D(ω)

The pure Absorption and Dispersion spectra can be determined with the correct phase angle

A(ω) = cos ϕ Re(F(ω)) - sin ϕ Im(F(ω))D(ω)= -sin ϕ Re(F(ω)) + cos ϕ Im(F(ω))

ϕ() =arctan