A maximum-likelihood analysis framework for terahertz time-domain spectroscopy
Abstract
We present a maximum-likelihood framework for analyzing terahertz time-domain spectroscopy measurements. This approach has several advantages other commonly-used methods, especially for evaluating goodness of fit. We also demonstrate a simple time-domain noise model that accurately describes the noise amplitude in a set of repeated measurements. These techniques are broadly applicable to material parameter estimation.
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Such an algorithm struggles to distinguish between accurate and inaccurate models.
“As a result, such algorithm struggles to distinguish between accurate and inaccurate models, as explained in [30], [31].”
From A New Metric for the Comparison of Permittivity Models in Terahertz Time-Domain Spectroscopy (2024) · cites this paper as [31]
One of the specificities of THz-TDS is that the data are in the time domain; when one performs a FFT to get the spectrum, the FFT will transform the noise as well to the frequency domain, and by construction the noise at a given frequency will be correlated to the one at another, making the weighting quite difficult in the frequency domain.
“However, as well explained in [23, 24], one of the specificities of THz-TDS is that the data are in the time domain. It means that when one performs a FFT to get the spectrum, the FFT will transform the noise as well to the frequency domain. By construction, the noise at a given frequency will be correlated to the one at another, making the weighting quite difficult in the frequency domain.”
From Terahertz time domain spectroscopy data processing: analysing uncertainties to push boundaries (2022) · cites this paper as [24]
One needs to use the noise correlation matrix (precision matrix) as weighting in the fit.
“Thus, the weighting function does not apply any more, but one needs to use the noise correlation matrix (precision matrix) as weighting in the fit as explained in [23, 24].”
From Terahertz time domain spectroscopy data processing: analysing uncertainties to push boundaries (2022) · cites this paper as [24]
When the signal includes any noise correlated to the signal, the algorithm mistakenly incorporates it into the analysis, potentially confusing it with genuine signal attributes.
“Thus, when the signal includes any noise correlated to the signal, the algorithm mistakenly incorporates it into the analysis, potentially confusing it with genuine signal attributes.”
From A New Metric for the Comparison of Permittivity Models in Terahertz Time-Domain Spectroscopy (2024) · cites this paper as [31]
Cites
Material parameter estimation with terahertz time-domain spectroscopy
Dorney, T. D., Baraniuk, R. G., & Mittleman, D. M. (2001) · Journal of the Optical Society of America A · doi:10.1364/josaa.18.001562 · Cited by 807 · see citing works
Duvillaret, L., Garet, F., & Coutaz, J.-L. (1999) · Applied Optics · doi:10.1364/ao.38.000409 · Cited by 505 · see citing works
Metrology State-of-the-Art and Challenges in Broadband Phase-Sensitive Terahertz Measurements
Naftaly, M., Clarke, R. G., Humphreys, D. A., & Ridler, N. M. (2017) · Proceedings of the IEEE · doi:10.1109/jproc.2016.2644108 · Cited by 49 · see citing works
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Beyond the "Dynamic range" approach In noise evaluation for Terahertz Time domain spectrometers
Muller, C., Lavancier, M., Bichon, J., Hannotte, T., Lampin, J.-F., Eliet, S., & Peretti, R. (2021) · 2021 46th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz) · doi:10.1109/irmmw-thz50926.2021.9566941 · Cited by 7 · see citing works
A New Metric for the Comparison of Permittivity Models in Terahertz Time-Domain Spectroscopy
Lavancier, M., Vindas-Yassine, N., Vlieghe, J., Hannotte, T., Lampin, J.-F., Orieux, F., & Peretti, R. (2024) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2024.3431202 · Cited by 5 · see citing works
“As a result, such an algorithm struggles to distinguish between accurate and inaccurate models, as explained in [30] and [31].”
BackgroundTerahertz time domain spectroscopy data processing: analysing uncertainties to push boundaries
Lavancier, M., Eliet Barois, S., Denakpo, E., Vlieghe, J., Vindas, N., Hindle, F., Cuisset, A., & Peretti, R. (2022) · Terahertz Photonics II · doi:10.1117/12.2620069 · Cited by 2 · see citing works
Peretti, R. (2023) · Optical Methods for Inspection, Characterization, and Imaging of Biomaterials · doi:10.1117/12.2675742 · Cited by 2 · see citing works
From Noise analysis to Error Bars on Refractive Index in THz-TDS
Osseiran, N., Bichon, J., Raj, A., Hannotte, T., Eliet, S., & Peretti, R. (2023) · International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) · doi:10.1109/irmmw-thz57677.2023.10299169 · Cited by 2 · see citing works
- Authors
- Dodge, J. S., Mohtashemi, L., Westlund, P., Mousavi, P., & Sahota, D. G.
- Affiliations
- Canadian Institute for Advanced Research (CA)
- Simon Fraser University (CA)
- Venue
- 2020 45th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz)
- Publisher
- IEEE
- Published
- 2020-11-08
- Pages
- 1-1
- OpenAlex
- W3136696939
- Cited by
- 5
- References
- 3
- Citations by year
- 2024: 1 · 2023: 2 · 2022: 1 · 2021: 1
- FWCI
- 1.41
- Type
- conference paper
- Language
- en
- Open access
- closed
- Licence
- Locations
- International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (publishedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Microwave and Dielectric Measurement Techniques
- Physical Sciences › Chemistry › Spectroscopy › Spectroscopy and Laser Applications
- Keywords
- terahertz time-domain spectroscopy, maximum likelihood estimation, goodness of fit, repeated measures, material parameter identification, data analysis framework
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