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Dynamic range in terahertz time-domain transmission and reflection spectroscopy
Open accessAbstract
We present a quantitative method for identification of the dynamic range of the detectable absorption coefficient in the analysis of transmission terahertz (THz) time-domain spectroscopy data. In transmission measurements the largest detectable absorption coefficient is determined by the dynamic range of the THz signals, whereas in reflection measurements the largest detectable absorption coefficient is determined by the scan-to-scan reproducibility of the signal.
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TL;DR
The paper quantifies how the frequency-dependent dynamic range of terahertz time-domain spectroscopy limits the absorption coefficient that can be measured reliably in transmission and reflection geometries. It shows that transmission spectra can falsely flatten at high frequencies when true absorption exceeds this limit, whereas reflection measurements can access much larger absorption values.
Key findings
- In transmission, the maximum detectable absorption–thickness product is set by the dynamic range and refractive index; once true absorption exceeds it, the extracted absorption saturates at that maximum. For a representative pulse, αd reached 14 at the spectral peak, corresponding to 280 cm⁻¹ for a 0.5-mm sample, decreased almost linearly toward higher frequencies, and cut off at 4.6 THz where the apparent absorption becomes zero.
- Amorphous glucose (0.25 mm) showed a broad absorption peak centered at 2.2 THz; comparison with the dynamic range indicated valid absorption data only below 2.2 THz, and the invalid high-frequency roll-off was not obvious without a quantitative dynamic-range analysis.
- Polylactide samples of 0.58 mm and 2.79 mm gave identical results up to 1.25 THz; the thicker sample followed the dynamic range above 1.25 THz, while the thinner sample showed absorption continuing until the dynamic-range limit at 1.9 THz.
- Reflection THz-TDS can measure larger absorption coefficients; assuming phase accuracy of 1° and amplitude accuracy of 0.01 at 1 THz, the maximum measurable absorption was about 3.7 × 10⁴ cm⁻¹. A polycrystalline CsI phonon mode at 1.84 THz was resolved, including the Reststrahlen band.
Methods
- Theoretical derivation of the dynamic range and maximum measurable absorption for transmission and reflection THz-TDS, based on reference and sample spectral ratios and the noise floor.
- Transmission examples used amorphous glucose prepared by melt-quenching between cold glass plates and polylactide samples of two thicknesses measured near room temperature below the glass transition.
- Reflection example used polycrystalline CsI with a metal mirror reference at normal incidence, comparing measured absorption with the frequency-dependent dynamic range.
Limitations
- Stated: transmission absorption measurements are limited by the dynamic range, especially on the high-frequency wing, so interpretation requires caution. The reflection treatment considered only normal incidence with a metal mirror reference, and detailed temperature-dependent CsI and signal-to-noise analyses were described as ongoing.
- Stated: in reflection, the limiting factor is noise in the phase and amplitude change upon reflection, mainly from laser fluctuations.
- Evident: the quantitative examples rely on specific samples and instrument conditions, and the paper does not present a broad validation across many materials or a general uncertainty propagation.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The absorption spectrum recorded on the 0.25-mm-thick sample is dominated by a broad peak centered at 2.2 THz.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Strength:plain· not yet calibratedSingle caseTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this ref lection measurement, on the other hand, the full dielectric function is measured across the fundamental phonon band, including the Reststrahlen band above the resonance.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If we assume a phase accuracy df 1 ± , an amplitude accuracy dr 0.01, and a frequency of 1 THz, the maximum absorption coefficient that can be measured is a max 3.7 3 10 4 cm 21 , well above absorption coefficients that are normally encountered in dielectric and semiconductor materials.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
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In the paper
“In conclusion, we have shown that the dynamic range of a THz-TDS spectrometer is strongly frequency dependent.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At frequencies up to 1.25 THz the two measurements are identical except for the slightly stronger etalon effects in the thinner sample.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The DR of ad decreases in an almost linear fashion toward higher frequencies, until the cutoff frequency, which in this case is 4.6 THz.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, measurement of a thinner sample shows that the absorption in reality contin-ues to grow, at least until the DR of the experiment is reached, this time at a frequency of 1.9 THz.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In transmission experiments its origin is found in the finite level of electronic white noise in the detection system.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The very sharp bend of the absorption curve, especially that of the thick sample, shows that the measured absorption coefficient can be trusted until the detection limit set by the DR is met.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In a ref lection experiment the measurement jrj 1 6 s r , and hence f 0 6 s f corresponds to an absorption coeff icient larger than”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The noise f loor is normally independent of frequency and corresponds to the spectrum recorded with a completely blocked THz beam path.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The absorption spectrum recorded on the thick sample follows the DR at frequencies above 1.25 THz, with a relatively low noise level up to 4 THz.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“At the peak of the spectrum we can measure values of ad up to 14, corresponding to an absorption coeff icient of 280 cm 21 in a 0.5-mm-thick sample.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We have shown two examples where the frequency dependence of the DR may lead to artifacts in the absorption spectrum and obscure the interpretation of the experimental data.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Inspection of Eq. ( 2) shows that the largest absorption coeff icient that can be measured reliably with a given DR corresponds to the situation where the sample signal is attenuated to a level equal to the noise f loor:”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe quote only partly states this claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Larger absorption coefficients can be measured reliably with THz-TDS ref lection spectrometers, where the limiting factor in absorption measurements is the noise of the phase and amplitude change upon ref lection, which is determined mainly by laser f luctuations.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The origin of this noise is of an electronic nature, whereas f luctuations of the THz signal itself are caused mainly by laser intensity f luctuations.”
§ Dynamic range in terahertz time-domain transmission and reflection spectroscopy > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper relies on this without support.
The effect of dynamic range on quantitative limits of absorption in THz-TDS had not been described quantitatively before this work.
“To the best of our knowledge this important effect has to date not been described in a quantitative way.”
The paper relies on this without support.
Polycrystalline CsI has a strong fundamental phonon mode at 1.84 THz.
“CsI has a strong fundamental phonon mode at 1.84 THz.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Frequently, the THz TDS system performance is characterized by its maximal achievable Signal-to-Noise Ratio (SNR) in frequency domain which is defined as the maximal signal power 𝑆𝑆 divided by the average noise power 𝑁𝑁 [8]”
From On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy (2016) · cites this paper as [8]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In THz-TDS, various noise effects compromise the signal quality [23 -25]. Noise contributions include optical and electronic effects [26, 27], laser intensity variations [28], and jitter noise [29, 30].”
From Terahertz-time domain spectrometer with 90 dB peak dynamic range (2014) · cites this paper as [23]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“For example, Eq. 21 for n r (ω) aligns with Eq. 1 in Jepsen and Fischer [47] and Eq. 22 in Jepsen et al. [42], and Eq. 22 for α r (ω) aligns with Eq. 2 in Jepsen and Fischer [47] and Eq. 24 in Jepsen et al. [42].”
From Tutorial: Accurate Determination of Refractive Index and Absorption Coefficient in Terahertz Time-Domain Spectroscopy (2025) · cites this paper as [47]
Citations
Cites
Integrated THz technology for label-free genetic diagnostics
Nagel, M., Haring Bolivar, P., Brucherseifer, M., Kurz, H., Bosserhoff, A., & Büttner, R. (2002) · Applied Physics Letters · doi:10.1063/1.1428619 · Cited by 543
THz reflection spectroscopy of liquid water
Thrane, L., Jacobsen, R. H., Uhd Jepsen, P., & Keiding, S. R. (1995) · Chemical Physics Letters · doi:10.1016/0009-2614(95)00543-d · Cited by 339
Self-citationTHz time domain spectroscopy of biomolecular conformational modes
Markelz, A., Whitmire, S., Hillebrecht, J., & Birge, R. (2002) · Physics in Medicine and Biology · doi:10.1088/0031-9155/47/21/318 · Cited by 309
Nature of Conduction in Doped Silicon
Jeon, T.-I., & Grischkowsky, D. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.1106 · Cited by 231
Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy
Jeon, T.-I., & Grischkowsky, D. (1998) · Applied Physics Letters · doi:10.1063/1.121531 · Cited by 162
Terahertz pulsed imaging and spectroscopy for biomedical and pharmaceutical applications
Wallace, V. P., Taday, P. F., Fitzgerald, A. J., Woodward, R. M., Cluff, J., Pye, R. J., & Arnone, D. D. (2004) · Faraday Discussions · doi:10.1039/b309357n · Cited by 160
THz time-domain spectroscopy of nonpolar liquids
Pedersen, J. E., & Keiding, S. R. (1992) · IEEE Journal of Quantum Electronics · doi:10.1109/3.159558 · Cited by 153
Component spatial pattern analysis of chemicals using terahertz spectroscopic imaging
Watanabe, Y., Kawase, K., Ikari, T., Ito, H., Ishikawa, Y., & Minamide, H. (2003) · Applied Physics Letters · doi:10.1063/1.1595132 · Cited by 140
Wang, S., Ferguson, B., Abbott, D., & Zhang, X.-C. (2003) · Journal of Biological Physics · doi:10.1023/a:1024457212578 · Cited by 119
Far-infrared properties of DAST
Walther, M., Jensby, K., Keiding, S. R., Takahashi, H., & Ito, H. (2000) · Optics Letters · doi:10.1364/ol.25.000911 · Cited by 113
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The dotTHz Project: A Standard Data Format for Terahertz Time-Domain Data
Lee, J., Leung, C. K., Ma, M., Ward-Berry, J., Santitewagun, S., & Zeitler, J. A. (2023) · Journal of Infrared, Millimeter, and Terahertz Waves · doi:10.1007/s10762-023-00947-w · Cited by 28
Tripathi, S. R., Aoki, M., Mochizuki, K., Hosako, I., Asahi, T., & Hiromoto, N. (2010) · Optics Communications · doi:10.1016/j.optcom.2010.02.008 · Cited by 24
Leung, C. K., Ward-Berry, J. N., Wanvig i Dot, E., Lee, J., & Zeitler, J. A. (2025) · Journal of Infrared, Millimeter and Terahertz Waves · doi:10.1007/s10762-025-01070-8 · Cited by 17
“…processed data are only reliable over the frequency range where the measured terahertz signal, especially the sample signal, remains significantly above the system’s noise floor, i.e., within the valid dynamic range of the measurement, the limits of which are discussed by Jepsen and Fischer [47].”
InfluentialMurphy, K. N., Naftaly, M., Nordon, A., & Markl, D. (2023) · Optical Materials Express · doi:10.1364/ome.494825 · Cited by 12
Skorobogatiy, M., Sadasivan, J., & Guerboukha, H. (2018) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2018.2814820 · Cited by 11
Murphy, K. N., Markl, D., Nordon, A., & Naftaly, M. (2023) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2023.3290118 · Cited by 11
Effect of time-delay errors on THz spectroscopy dynamic range
Humphreys, D. A., Naftaly, M., & Molloy, J. F. (2014) · 2014 39th International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) · doi:10.1109/irmmw-thz.2014.6956138 · Cited by 9
Unveiling the Origin of Spurious Features in THz-TDS of Powder Compacts
Gorecki, J., Murphy, K. N., Markl, D., Burnett, A. D., & Naftaly, M. (2025) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2025.3549944 · Cited by 4
“The maximum measurable loss ( α max ) is calculated following the procedure laid out by Jepsen et al. [23] shown in (3), utilizing an experimental measurement of the dynamic range spectrum (DR) of the spectrometer.”
Metadata
- Authors
- Jepsen, P. U., & Fischer, B. M.
- Affiliations
- University of Freiburg (DE)
- Venue
- Optics Letters
- Publisher
- Optica Publishing Group
- Published
- 2005-01-01
- Volume
- 30
- Issue
- 1
- Pages
- 29
- ISSN
- 0146-9592 (ISSN-L)
- 1539-4794
- OpenAlex
- W1975034226
- Cited by
- 382
- References
- 12
- Citations by year
- 2026: 24 · 2025: 16 · 2024: 15 · 2023: 22 · 2022: 20 · 2021: 14 · 2020: 15 · 2019: 17 · 2018: 21 · 2017: 21 · 2016: 15 · 2015: 16 · 2014: 29 · 2013: 23 · 2012: 19
- FWCI
- 14.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Optics Letters (publishedVersion)
- PubMed (publishedVersion)
- Adelaide Research & Scholarship (AR&S) (University of Adelaide) (submittedVersion)
- FreiDok plus (Universitätsbibliothek Freiburg) (submittedVersion)
- Funders
- European Commission
- Bundesministerium für Bildung und Forschung
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Chemistry › Spectroscopy › Spectroscopy and Laser Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Laser-Matter Interactions and Applications
- Keywords
- dynamic range, terahertz time-domain spectroscopy, transmission spectroscopy, reflectance spectroscopy, absorption coefficient
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