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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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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
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“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
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“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 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
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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
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“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
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“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
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“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
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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
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“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 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
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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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“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
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“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
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“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
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“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
plaindirect- Asserted: passes — The authors put it forward as true.
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“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
plaindirect- Asserted: passes — The authors put it forward as true.
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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
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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]
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Optical properties of DAST in the THz range
Cunningham, P. D., & Hayden, L. M. (2010) · Optics Express · doi:10.1364/oe.18.023620 · Cited by 95
Characterization of aqueous alcohol solutions in bottles with THz reflection spectroscopy
Jepsen, P. U., Jensen, J. K., & Møller, U. (2008) · Optics Express · doi:10.1364/oe.16.009318 · Cited by 96
Self-citationTerahertz antenna technology for imaging applications: a technical review
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Unferdorben, M., Szaller, Z., Hajdara, I., Hebling, J., & Pálfalvi, L. (2015) · Journal of Infrared Millimeter and Terahertz Waves · doi:10.1007/s10762-015-0165-5 · Cited by 78
The Christiansen effect in terahertz time-domain spectra of coarse-grained powders
Franz, M., Fischer, B. M., & Walther, M. (2008) · Applied Physics Letters · doi:10.1063/1.2831910 · Cited by 82
Self-citationTHz Absorption in Fabric and Its Impact on Body Scanning for Security Application
Knipper, R., Brahm, A., Heinz, E., et al. (2015) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2015.2474115 · Cited by 78
Qin, J., Xie, L., & Ying, Y. B. (2014) · Analytical Chemistry · doi:10.1021/ac503212q · Cited by 77
Metrology Issues and Solutions in THz Time-Domain Spectroscopy: Noise, Errors, Calibration
Naftaly, M. (2013) · IEEE Sensors Journal · doi:10.1109/jsen.2012.2208624 · Cited by 76
“One of the most important papers dealing with the dynamic range of THz TDS systems and its implications on the bandwidth was published by Jepsen and Fischer [6].”
BackgroundTerahertz spectroscopy of enantiopure and racemic polycrystalline valine
Williams, M. R. C., True, A. B., Izmaylov, A. F., French, T., Schröck, K., & Schmuttenmaer, C. A. (2011) · Physical Chemistry Chemical Physics · doi:10.1039/c1cp20594c · Cited by 75
Data Extraction from Terahertz Time Domain Spectroscopy Measurements
Scheller, M. (2014) · Journal of Infrared Millimeter and Terahertz Waves · doi:10.1007/s10762-014-0053-4 · Cited by 74
Rapid and inexpensive fabrication of terahertz electromagnetic bandgap structures
Wu, Z., Kinast, J. M., Gehm, M. E., et al. (2008) · Optics Express · doi:10.1364/oe.16.016442 · Cited by 72
Chiral Spectroscopy of Nanostructures
Kwon, J., Park, K. H., Choi, W. J., Kotov, N. A., & Yeom, J. (2023) · Accounts of Chemical Research · doi:10.1021/acs.accounts.2c00756 · Cited by 74
Invited Article: Terahertz microfluidic chips sensitivity-enhanced with a few arrays of meta-atoms
Serita, K., Matsuda, E., Okada, K., Murakami, H., Kawayama, I., & Tonouchi, M. (2018) · APL Photonics · doi:10.1063/1.5007681 · Cited by 70
Optical modulation of terahertz pulses in a parallel plate waveguide
Cooke, D. G., & Jepsen, P. U. (2008) · Optics Express · doi:10.1364/oe.16.015123 · Cited by 66
Self-citationLimitation in thin-film sensing with transmission-mode terahertz time-domain spectroscopy
Withayachumnankul, W., O’Hara, J. F., Cao, W., Al-Naib, I. A. I., & Zhang, W. (2014) · Optics Express · doi:10.1364/oe.22.000972 · Cited by 71
Kühne, P., Armakavicius, N., Stanishev, V., et al. (2018) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2018.2814347 · Cited by 65
Optimizing third-harmonic generation at terahertz frequencies in graphene
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THz-Spectroscopy on High Density Polyethylene with Different Crystallinity
Sommer, S., Raidt, T., Fischer, B. M., Katzenberg, F., Tiller, J. C., & Koch, M. (2015) · Journal of Infrared Millimeter and Terahertz Waves · doi:10.1007/s10762-015-0219-8 · Cited by 67
Self-citationThe application of terahertz spectroscopy to liquid petrochemicals detection: A review
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“The reflection THz-TDS system mainly includes vertical incidence (61,62), oblique incidence (63,64), and attenuated total reflection (ATR) (65, 66), and each kind of optical path has advantages and”
BackgroundBrodie, C. H., Spotts, I., Reguigui, H., Leclerc, C. A., Mitchell, M. E., Holzman, J. F., & Collier, C. M. (2022) · Optical Materials Express · doi:10.1364/ome.465820 · Cited by 62
THz TDS study of several sp2 carbon materials: Graphite, needle coke and graphene oxides
Chamorro‐Posada, P., Vázquez-Cabo, J., Rubiños, Ó., Martín‐Gil, J., Hernández-Navarro, S., Martín‐Ramos, P., Sánchez‐Arévalo, F. M., Tamashausky, A. V., Merino, C., & Dante, R. C. (2015) · Carbon · doi:10.1016/j.carbon.2015.11.020 · Cited by 59
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“Furthermore, detection sensitivity often rolls off at higher frequencies; as a result, typical commercially available TDS data extraction is restricted to < 5 THz due to low dynamic range (DR) at higher frequencies [11].”
BackgroundSelf-citationDevelopments in the integration and application of terahertz spectroscopy with microfluidics
Alfihed, S., Holzman, J. F., & Foulds, I. G. (2020) · Biosensors and Bioelectronics · doi:10.1016/j.bios.2020.112393 · Cited by 49
Gelatin embedding: a novel way to preserve biological samples for terahertz imaging and spectroscopy
Fan, S., Ung, B. S. ‐., Parrott, E. P. J., & Pickwell‐MacPherson, E. (2015) · Physics in Medicine and Biology · doi:10.1088/0031-9155/60/7/2703 · Cited by 51
“The dynamic range is the dominant factor affecting the accuracy of the parameters calculated from the transmission geometry, while in the reflection geometry, pulse fluctuation (Jepsen and Fischer 2005) and sample misplacement (Nishizawa et al 2005) are the main error sources.”
BackgroundHuang, L., Cao, H., Chen, L., et al. (2023) · Talanta · doi:10.1016/j.talanta.2023.125481 · Cited by 50
“The real and imaginary part of chemical substance permittivity can be expressed as [22 – 24]: Fig.”
Terahertz metasurfaces with a high refractive index enhanced by the strong nearest neighbor coupling
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Metrology State-of-the-Art and Challenges in Broadband Phase-Sensitive Terahertz Measurements
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“[45] P. U. Jepsen and B. M. Fischer, Dynamic range in terahertz time domain transmission and reflection spectroscopy, Opt.”
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“This determines the detectable upper frequency limit of optical constants [29,30].”
BackgroundEffects of surface roughness on reflection spectra obtained by terahertz time-domain spectroscopy.
Dikmelik, Y., Spicer, J., Fitch, M., & Osiander, R. (2006) · Optics Letters · doi:10.1364/ol.31.003653 · Cited by 49
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Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements
Withayachumnankul, W., Fischer, B. M., & Abbott, D. (2008) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2007.0294 · Cited by 49
Self-citationUltra-broadband terahertz pulses generated in the organic crystal DSTMS
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Pulsed THz imaging for thickness characterization of plastic sheets
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“accounts for transmission coefficients t at the front air/plastic and back plastic/air interfaces (nair = 1) [23].”
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Terahertz spectroscopy on adhesive bonds
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Bernier, M., Garet, F., & Coutaz, J. (2013) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2013.2247793 · Cited by 42
On the Influence of Delay Line Uncertainty in THz Time-Domain Spectroscopy
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“, the complex refractive index n(ω) [8].”
Terahertz Geoscience: THz Time-Domain Spectroscopy for Mineral Materials
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Origin of Birefringence in Wood at Terahertz Frequencies
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Linearity calibration of amplitude and power measurements in terahertz systems and detectors
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Windowing of THz time-domain spectroscopy signals: A study based on lactose
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Terahertz Spectroscopy: System and Sensitivity Considerations
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“The former means that the -ratio, calculated from the intensity divided by its standard deviation, is much smaller than the dynamic range defined by the ratio of the maximum in the intensity spectrum to the noise floor which is about equal to the noise level without THz irradiation [40], [41].”
BackgroundSoltani, A., Jahn, D., Duschek, L., Castro-Camus, E., Koch, M., & Withayachumnankul, W. (2016) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2015.2505909 · Cited by 37
“A standard transmission THz TDS setup is not ideal since the maximum measurable absorption is limited by the system dynamic range [14].”
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“5 THz where our SNR is maximum – note that both the DR and SNR of THz-TDS measurements are very frequency dependent [46].”
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Linearity of Air-Biased Coherent Detection for Terahertz Time-Domain Spectroscopy
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“DR and SNR are important and fundamental factors to quantify the performance of any THz spectrometer [44].”
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Sensing Water Absorption in Hygrothermally Aged Epoxies with Terahertz Time-Domain Spectroscopy
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Efficient terahertz en-face imaging
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Real-time terahertz material characterization by numerical three-dimensional optimization
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Optical and Dielectric Properties of Chalcogenide Glasses at Terahertz Frequencies
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Terahertz optical activity of sucrose single-crystals
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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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