Fundamental Limits in Chirped Laser Dispersion Spectroscopy A Theoretical Comparison to Direct Laser Absorption Spectroscopy

Transcription

1 Princeton University Laser Sensing Laboratory Princeton University Princeton New Jersey MIRTHE Summer Symposium June 15, 2015 Fundamental Limits in Chirped Laser Dispersion Spectroscopy A Theoretical Comparison to Direct Laser Absorption Spectroscopy Genevieve Plant, Andreas Hangauer, Gerard Wysocki* Electrical Engineering Department, Princeton University, Princeton, NJ, 08544, USA * gwysocki@princeton.edu pulse.princeton.edu

2 Absorption vs. Dispersion Sensing Laser absorption spectroscopy has fundamental limitations CLaDS Chirped Laser Dispersion Spectroscopy Transmission (%) Wavenumber (cm -1 ) Signal is encoded in the intensity Signal is measured with baseline Absorption is non-linear above 10% Kramers-Kronig Change in Refractive Index 6.0x x x x x x Wavenumber (cm -1 ) Signal is encoded phase Immunity to power fluctuations Baseline free Dispersion is proportional to absorbance Large dynamic range 2

3 How it Works Two Color Beam Sample PD FM Demod. CLaDS Signal I(f) f = Ω I(f) f = Ω f CCCCC = Ω Add freq. I(f) f f n(f) chirp Advantages of Chirped Laser Dispersion Spectroscopy (CLaDS): Linear response (no Beer-Lambert non-linearity) Ability to measure optically thick samples Immunity to intensity variations Measurement of phase not intensity I(f) f f f CCCCC = Ω + ΔΩ 3

4 N 2 O Sensing with CLaDS - Baltimore, MD (2011) MIRTHE SLIP Campaign N 2 O concentration (ppb) N 2 O concentration (ppb) / Oct 28 noon 10/27 10/28 10/ CM-CLaDS 30sec avg WMS for both 340 midnight Oct 29 noon Time 10/ midnight Rain rate (mm/min) 2 x 35 m 4

5 Multi-Path CH 4 Sensing with CLaDS NH (2013) SECO grant with PSI Average Daily Conc. (ppm) Day # 5

6 Fundamental Limit Two Color Beam Sample PD FM Demod. CLaDS Signal I(f) f = Ω f Shot noise: N i [ A2 HH ] Advantages of Chirped Laser Dispersion Spectroscopy (CLaDS): Linear response (no Beer-Lambert non-linearity) Ability to measure optically thick samples Immunity to intensity variations Measurement of phase not intensity How does CLaDS compare to Direct Laser Absorption Spectroscopy (DLAS) at the fundamental limit (i.e. shot noise)? Identical spectroscopic conditions (trace measurement) Shot noise limited at the output of the photodetector 6

7 Comparison of DLAS & CLaDS (Noise & Signal models) Assume same total optical power (P T ), noise (N i ) Bandwidth is directly proportional to chirp rate, S (rad/s 2 ) DLAS [absorbance] CLaDS [Hz] Noise I I = N i B R P T 2 N i B 3 3 η hee R P T 2 Signal α c L 1 2π S L c dd ω c dd dd dd ω Ω ω 7

8 Comparison of DLAS & CLaDS (Noise & Signal models) Assume same total optical power (P T ), noise (N i ) Bandwidth is directly proportional to chirp rate, S (rad/s 2 ) DLAS [absorbance] CLaDS [Hz] Noise S 1/2 S 3/2 Signal -- S 8

9 Single Point SNR: DLAS vs. CLaDS Averaging Considerations DLAS CLaDS Noise S 1/2 S 3/2 Signal - S # Averages S S SNR (single shot) SNR (optimum averaging) S 1/2 S 1/2 - - SNR SNR Ratio SNR Comparison Direct Absorption CLADS Comparison point Normalized Bandwidth, BT o Single Point analysis (peak to noise in the wing) Using 100% duty cycle (i.e. optimum averaging), the output SNR for given spectroscopic and noise conditions is independent of S For a trace measurement, DLAS outperforms CLaDS by a factor of 6 9

10 Fitting Considerations Power spectral density (Hz 2 /Hz) 3.0x x x x x x10-6 chirp rate = 1e13 Hz/s sample Rate = 125 ks/s α c *L = n = 4e-12 A/Hz 1/2 Signal Noise Power spectral density (A 2 /Hz) 3.0x10-10 Signal Noise 2.0x x Frequency (khz) Frequency (khz) CLaDS frequency demodulation process f 2 noise (violet, derivative of white noise) Signal and noise spectrums do not fully overlap Must use a proper fitting model to address this non-white noise 10

11 Fitting Considerations Fit parameters: Absorbance: α c L Halfwidth: f L Line center: ν c CLaDS only: Offset DLAS only: 2 nd order baseline coefficients (to mimic practical systems) Ampltiude (absorbance) Frequency (Hz) x nd order baseline ν c wavenumber (ν, [cm -1 ]) offset Spectral scan range (12 HWHMs) chosen to minimize noise in the DLAS analysis. Eliminate coupling between spectrum and baseline fitting 11

12 Observation Factor Fitting Considerations σα ( c L) σ(( α L) ) c ideal uncertainity of the fit single point noise O.F. of 1 = fit of only concentration (effectively single point) Measure of how well the desired information is extracted from the measured signal. Observation Factor Direct Absorption CLaDS (violet noise, generalized least sq.) CLaDS (white noise, least sq.) 5 Comparison point Normalized Bandwidth, BT o Results: When the proper noise model is considered for CLaDS fitting, the same amount of information is extracted from both DLAS and CLaDS. 12

13 Conclusions Assuming shot-noise limited performance: Single-point analysis: DLAS outperforms CLaDS by a factor of 6 Extraction from fitting analysis When the proper noise model is used for CLaDS analysis, both techniques show comparable performance i.e. the same amount of information is extracted from both fits Future work: Analysis for : Optically think samples (additional bandwidth considerations) Chirp-modulated (CM) CLaDS 13

14 Acknowledgements NSF CMMI CAREER grant NSF SECO grant with Physical Sciences Inc. NSF ERC MIRTHE MIRTHE SLIP Campaign Corning for a 4.5um DFB QCL PSI for 1650nm DFB laser diode 14