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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Written from the paper’s full text.
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.
Model-written summary. Check it against the paper before relying on it.
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Claims the paper makes
0 of 2 cited sources checked · 0 supported · 0 flagged
- Findingown data
The measured absorption spectrum of amorphous glucose in the range 0.1-5 THz is dominated by a broad peak centered at 2.2 THz.
“The absorption spectrum recorded on the 0.25-mm-thick sample is dominated by a broad peak centered at 2.2 THz.”
Quote in the paperNot a substantial claim - Findingown data
In the reflection measurement, the full dielectric function of polycrystalline CsI is measured across the fundamental phonon band, including the Reststrahlen band above the resonance.
“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.”
Quote in the paperSubstantial claim - Findingreasoning
Assuming a phase accuracy δφ=1°, an amplitude accuracy δr=0.01, and a frequency of 1 THz, the maximum absorption coefficient that can be measured is αmax=3.7×10^4 cm^-1, well above absorption coefficients normally encountered in dielectric and semiconductor materials.
“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.”
Quote in the paperSubstantial claim - Findingown data
The dynamic range of a THz-TDS spectrometer is strongly frequency dependent.
“In conclusion, we have shown that the dynamic range of a THz-TDS spectrometer is strongly frequency dependent.”
Quote in the paperSubstantial claim - Findingown data
For polylactide, at frequencies up to 1.25 THz the two measurements on samples of thickness 0.58 mm and 2.79 mm are identical except for slightly stronger etalon effects in the thinner sample.
“At frequencies up to 1.25 THz the two measurements are identical except for the slightly stronger etalon effects in the thinner sample.”
Quote in the paperSubstantial claim
- Findingown data
For that transmission experiment, the dynamic range of αd decreases in an almost linear fashion toward higher frequencies until a cutoff frequency of 4.6 THz.
“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.”
Quote in the paperSubstantial claim - Interpretationown data
For the thinner polylactide sample, the absorption in reality continues to grow at least until the dynamic range of the experiment is reached at 1.9 THz.
“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.”
Quote in the paperSubstantial claim - Interpretationown data
In transmission THz-TDS, the frequency dependence of the dynamic range originates from the finite level of electronic white noise in the detection system.
“In transmission experiments its origin is found in the finite level of electronic white noise in the detection system.”
Quote in the paperSubstantial claim - Interpretationown data
The sharp bend of the absorption curve, especially for the thick polylactide sample, shows that the measured absorption coefficient can be trusted until the detection limit set by the dynamic range is met.
“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.”
Quote in the paperSubstantial claim - Interpretationreasoning
In a reflection experiment with measurement |r|=1±σr and φ=0±σφ, the maximum absorption coefficient is approximately αmax ≈ (4πv/c) * (2σφ)/(σr^2 + σφ^2).
“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”
Quote in the paperSubstantial claim - Interpretationreasoning
If the measured absorption is within the dynamic range, it is a faithful representation of the real absorption coefficient.
“if the measured absorption is within the DR, it is indeed a faithful representation of the real absorption coeff icient.”
Quote in the paperSubstantial claim - Interpretationnone given
Operating a THz spectrometer in reflection mode is a method to circumvent the limitations of transmission THz-TDS described above.
“A method to circumvent the limitations of THz-TDS described above is to operate the THz spectrometer in the ref lection mode.”
Quote in the paperSubstantial claim - Premisecitation
The dielectric function of polycrystalline CsI is difficult to measure with transmission techniques in the frequency range of its strong fundamental phonon mode at 1.84 THz.
“CsI has a strong fundamental phonon mode at 1.84 THz.Therefore the dielectric function is diff icult to measure with transmission techniques in this frequency range.12”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [12] Ralph, 1994, J. Opt. Soc. Am. B source
- Rests on an assumption: Polycrystalline CsI has a strong fundamental phonon mode at 1.84 THz.
- Interpretationown data
Above the cutoff frequency of 4.6 THz, the apparent absorption coefficient will always be zero.
“Above this frequency the apparent absorption coeff icient will always be zero.”
Quote in the paperSubstantial claim - Interpretationnone given
The normalized frequency spectrum relative to the noise floor is a good measure of the frequency-dependent dynamic range of a THz-TDS experiment.
“This normalized spectrum is a good measure of the frequency-dependent dynamic range (DR) of the experiment.”
Quote in the paperSubstantial claim - Interpretationown data
In the amorphous glucose example, without a quantitative analysis of the dynamic range it is not obvious that the absorption coefficient above 2.2 THz is not valid.
“In this example the quality of the absorption data is such that without a quantitative analysis of the DR of the spectrometer it is not obvious that the absorption coefficient above 2.2 THz is not valid.”
Quote in the paperSubstantial claim - Interpretationreasoning
Interpretation of data from transmission THz-TDS, especially on the high-frequency wing of the spectrometer bandwidth, requires caution.
“Our considerations show that interpretation of data from transmission THz-TDS, especially on the high-frequency wing of the spectrometer bandwidth, requires caution.”
Quote in the paperNot a substantial claim - Interpretationreasoning
If the absorption coefficient exceeds αmax, the analysis will show an apparent absorption coefficient equal to αmax.
“In other words, if the absorption coeff icient exceeds a max , the analysis will show an apparent absorption coefficient equal to a max .”
Quote in the paperSubstantial claim - Premisecitation
The limitation of transmission THz-TDS due to dynamic range was recognized in a qualitative way by Walther et al.
“This limitation was recognized in a qualitative way by Walther et al. 9”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Walther et al. 9
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationown data
For the amorphous glucose measurement, comparison of the absorption spectrum with αmax shows that the absorption measurement is valid for frequencies below 2.2 THz.
“Comparison between the two curves makes it clear that the absorption measurement is valid for frequencies below 2.2 THz.”
Quote in the paperSubstantial claim - Interpretationreasoning
In transmission THz-TDS, the measurement of the refractive index is not subject to the same principal limitations as the measurement of the absorption coefficient.
“In transmission THz-TDS the measurement of the refractive index is not subject to the same principal limitations as the measurement of the absorption coefficient.”
Quote in the paperSubstantial claim - Interpretationreasoning
In a reflection experiment, the largest absorption coefficient is measured in the vicinity of |r|=1 and φ=0.
“The largest absorption coeff icient is measured in the vicinity of r 1 and f 0.”
Quote in the paperSubstantial claim
- Classified as probably not a substantial claim. 1
- May combine two claims. 6
- The quote only partly states this claim. 1
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Findingnone givenThe noise floor is normally independent of frequency and corresponds to the spectrum recorded with a completely blocked THz beam path.
“The noise f loor is normally independent of frequency and corresponds to the spectrum recorded with a completely blocked THz beam path.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataFor the thick polylactide sample, the absorption spectrum follows the dynamic range at frequencies above 1.25 THz, with a relatively low noise level up to 4 THz.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningFor a transmission experiment based on the THz pulse in Fig. 1(a) and assuming sample index n=3, at the peak of the spectrum values of αd up to 14 can be measured, corresponding to an absorption coefficient of 280 cm^-1 in a 0.5-mm-thick sample.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown dataThe frequency dependence of the dynamic range may lead to artifacts in the absorption spectrum and obscure the interpretation of experimental data.
“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.”
Quote in the paperSubstantial claimThe quote only partly states this claim.
InterpretationreasoningThe largest absorption coefficient that can be measured reliably with a given dynamic range corresponds to the situation where the sample signal is attenuated to a level equal to the noise floor, αmax d = 2 ln[DR 4n/(n+1)^2].
“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:”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningLarger absorption coefficients can be measured reliably with THz-TDS reflection spectrometers, where the limiting factor in absorption measurements is the noise of the phase and amplitude change upon reflection, determined mainly by laser fluctuations.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe origin of the noise floor is electronic, whereas fluctuations of the THz signal itself are caused mainly by laser intensity fluctuations.
“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.”
Quote in the paperSubstantial claim
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 THz TDS system performance is characterized by its maximal achievable SNR in frequency domain.
“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]
The passage labeled Abstract (page unavailable) says the frequency spectrum normalized to the noise floor measures a THz-TDS experiment’s frequency-dependent dynamic range, and that the analysis uses signal-to-noise ratio. It does not characterize system performance specifically by a maximal achievable frequency-domain SNR or define that SNR as maximal signal power divided by average noise power. (LLM, conf=0.82)
Experimental — accuracy not yet measuredIn THz-TDS, various noise effects compromise signal quality; noise contributions include optical and electronic effects, laser intensity variations, and jitter noise.
“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]
The passage labeled Abstract (page not provided) identifies electronic noise as the source of the noise floor and laser-intensity fluctuations as a cause of THz-signal fluctuations. Its conclusion says these limits can produce artifacts in absorption spectra. Our copy does not identify jitter noise or a distinct optical-noise contribution, so it supports only part of the attributed list. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe expressions for refractive index and absorption coefficient of a weakly terahertz-absorbing material in this tutorial align with those in Jepsen and Fischer [47] and Jepsen et al. [42].
“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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Self-citationWafer‐Scale Synthesis of Graphene on Sapphire: Toward Fab‐Compatible Graphene
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Optical properties of DAST in the THz range
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Characterization of aqueous alcohol solutions in bottles with THz reflection spectroscopy
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Self-citationTerahertz antenna technology for imaging applications: a technical review
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The Christiansen effect in terahertz time-domain spectra of coarse-grained powders
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Self-citationTHz Absorption in Fabric and Its Impact on Body Scanning for Security Application
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“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 · see citing works
Data Extraction from Terahertz Time Domain Spectroscopy Measurements
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Rapid and inexpensive fabrication of terahertz electromagnetic bandgap structures
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Chiral Spectroscopy of Nanostructures
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Invited Article: Terahertz microfluidic chips sensitivity-enhanced with a few arrays of meta-atoms
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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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
THz TDS study of several sp2 carbon materials: Graphite, needle coke and graphene oxides
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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
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Gelatin embedding: a novel way to preserve biological samples for terahertz imaging and spectroscopy
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“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.”
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“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.
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Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements
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“, the complex refractive index n(ω) [8].”
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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].”
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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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Efficient terahertz en-face imaging
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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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- 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
- 388
- References
- 12
- Citations by year
- 2026: 20 · 2025: 19 · 2024: 15 · 2023: 24 · 2022: 20 · 2021: 15 · 2020: 16 · 2019: 17 · 2018: 20 · 2017: 22 · 2016: 15 · 2015: 16 · 2014: 29 · 2013: 23 · 2012: 18
- FWCI
- 14.43
- 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)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Chemistry › Spectroscopy › Spectroscopy and Laser Applications
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Photonic and Optical Devices
- Keywords
- dynamic range, terahertz time-domain spectroscopy, transmission spectroscopy, reflectance spectroscopy, absorption coefficient
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