# Photoacoustic spectroscopy
Photoacoustic spectroscopy (PAS) determines the absorption spectrum of a gas, liquid, or solid by detecting the sound emitted when modulated light is absorbed in the sample. Radiation that relaxes non-radiatively produces periodic heating, and the resulting pressure wave, read out by a microphone, piezoelectric resonator, or cantilever, is proportional to the absorbed energy to a first approximation; neither scattered nor reflected light contributes to the signal.[1](https://www.spectroscopyeurope.com/system/files/pdf/PAS14_5.pdf) Because the readout depends only on absorbed energy, PAS can analyze completely non-transparent and strongly scattering samples that defeat conventional transmission spectroscopy.[2](https://pmc.ncbi.nlm.nih.gov/articles/PMC11243826/) Modern applications span trace-gas sensing at parts-per-billion to parts-per-trillion levels, infrared analysis of opaque solids, and semiconductor characterization.[3](https://www.intechopen.com/chapters/69765) • [4](https://www.mdpi.com/1424-8220/24/20/6577)
| Key fact | Detail |
|---|---|
| Measured quantity | Acoustic wave at the light-modulation frequency, proportional to absorbed power and hence to absorption coefficient times concentration[1](https://www.spectroscopyeurope.com/system/files/pdf/PAS14_5.pdf) |
| Signal magnitudes | Temperature rises of micro- to millidegrees and pressure changes of nano- to microbar[3](https://www.intechopen.com/chapters/69765) |
| Detection limits | From parts-per-quadrillion (650 ppq HF, cantilever-enhanced)[5](https://doi.org/10.1038/s41598-018-20087-9) to low ppb (QEPAS, FT-PAS)[4](https://www.mdpi.com/1424-8220/24/20/6577) |
| Central theory | Rosencwaig–Gersho model: thermal diffusion length \( \mu_{s} = (D/\pi f)^{1/2} \) sets the probed depth[6](https://doi.org/10.1063/1.322296) • [7](https://www.sciencedirect.com/science/article/abs/pii/S0022285204002875) |
| Linear dynamic range | Typically 4–6 orders of magnitude in absorption coefficient or concentration, allowing two-point calibration[8](https://pub.dega-akustik.de/DAGA_1999-2008/data/articles/003159.pdf) |
| Main variants | QEPAS, cantilever-enhanced PAS, FTIR-PAS, differential and open-cell configurations[9](https://www.nature.com/articles/s41377-025-02075-7) |
## How it works
Absorbed light becomes sound through heat. Modulated radiation absorbed by the sample excites molecules or lattice modes; the non-radiative part of the excitation generates heat in the localized region of the light beam and produces a pressure wave that propagates away from the source and is detected with a suitable sensor.[10](https://gasera.fi/wp-content/uploads/2015/12/PAS_GasAnalysisWithCantileverMicrophone_ApplSpectrosRew_2007.pdf) For a gas the amplitude of the heat production rate is \( H_{0} = \eta \cdot \alpha \cdot I \) (W/m\(^{3}\)), where \( \alpha \) is the absorption coefficient, \( \eta \) is the fraction of absorbed energy released non-radiatively as heat, and \( I = I_{0} \exp(-\alpha l) \) follows the [Beer–Lambert law](https://www.edgepedia.org/beer-lambert-law).[4](https://www.mdpi.com/1424-8220/24/20/6577) Because the source term is proportional to the time derivative of the divergence of the light intensity vector, sound is generated only by nonstationary and inhomogeneous illumination; steady, uniform heating is silent.[8](https://pub.dega-akustik.de/DAGA_1999-2008/data/articles/003159.pdf)
For solids, the Rosencwaig–Gersho theory solves the thermal diffusion equations for a periodically heated sample and shows that only a thin boundary layer of gas adjacent to the surface responds thermally to the periodic heat flow; this layer acts as an acoustic piston creating the signal detected in the cell.[11](https://doi.org/10.1121/1.2002181) An explicit formula gives the magnitude and phase of the acoustic pressure in terms of the optical, thermal, and geometric parameters, with three regimes set by the sample thickness \( l \), the optical absorption length \( l_{\beta} = 1/\beta \), and the thermal diffusion length \( \mu_{s} \). In the thermally thick, optically opaque regime, where the sample thickness \( l \) greatly exceeds both the thermal diffusion length \( \mu_{s} \) and the optical absorption length \( l_{\beta} \), the signal is proportional to the absorption coefficient and \( \mu_{s} \), so absorption data can be obtained even from samples completely opaque to conventional techniques.[6](https://doi.org/10.1063/1.322296) • [12](https://www.shimadzu.ch/service-support/technical-support/ftir/essential_knowledge/photoacoustic.html) The thermal diffusion length \( \mu_{s} = (D/\pi f)^{1/2} \), set by the sample thermal diffusivity \( D \) and modulation frequency \( f \), is the distance over which the thermal wave decays to 1/e of its original intensity; raising the modulation frequency therefore reduces both the probed depth and the signal.[7](https://www.sciencedirect.com/science/article/abs/pii/S0022285204002875) • [12](https://www.shimadzu.ch/service-support/technical-support/ftir/essential_knowledge/photoacoustic.html)
## How it is done
Most gas-phase instruments combine four components: a modulated light source, a photoacoustic cell, an acoustic sensor, and a signal-processing unit.[4](https://www.mdpi.com/1424-8220/24/20/6577) The modulation frequency is bounded by molecular physics: it must be faster than the inverse molecular diffusion time, so that a pressure wave forms, and slower than the inverse relaxation time.[13](https://www.mdpi.com/1424-8220/20/9/2745) Gas measurements run from single hertz to several thousand hertz, detected by microphones, piezoelectric devices, or optical methods.[13](https://www.mdpi.com/1424-8220/20/9/2745) • [14](https://web.archive.org/web/20101216163043/http:/spectroscopyonline.findanalytichem.com/spectroscopy/article/articleDetail.jsp?id=373774)
Cells are either non-resonant, operated at a few tens of hertz, or resonant, where the signal scales with the resonator quality factor; gas-viscosity losses keep cell Q values clearly below 100, whereas a quartz tuning fork reaches Q of 20,000 in vacuum and 8,000 at atmospheric pressure.[4](https://www.mdpi.com/1424-8220/24/20/6577) • [10](https://gasera.fi/wp-content/uploads/2015/12/PAS_GasAnalysisWithCantileverMicrophone_ApplSpectrosRew_2007.pdf) Wavelength-modulated lasers are typically read out at the 2f harmonic with a lock-in amplifier, because the 1f signal contains direct intensity-modulation contributions.[4](https://www.mdpi.com/1424-8220/24/20/6577) In FTIR-PAS the modulated infrared beam from a [Michelson interferometer](https://www.edgepedia.org/michelson-interferometer), with modulation frequency \( f = 2 \cdot V \cdot v \) for mirror velocity \( V \) and wavenumber \( v \), heats the sample in a sealed small-volume cell mounted on a vibration-isolation stand, and Fourier transformation of the microphone signal yields an absorption-like spectrum.[12](https://www.shimadzu.ch/service-support/technical-support/ftir/essential_knowledge/photoacoustic.html)
## Origin
[Alexander Graham Bell](https://www.edgepedia.org/alexander-graham-bell) reported the effect in 1880 in "On the production and reproduction of sound by light," published in the American Journal of Science, finding that a thin disk exposed to mechanically chopped sunlight emitted sound, with a similar effect under infrared or ultraviolet light.[15](https://doi.org/10.2475/ajs.s3-20.118.305) • [14](https://web.archive.org/web/20101216163043/http:/spectroscopyonline.findanalytichem.com/spectroscopy/article/articleDetail.jsp?id=373774) During Bell's 1880 visit to England, John Tyndall repeated the experiment in gases and attributed the effect mainly to radiant heat.[3](https://www.intechopen.com/chapters/69765) A "spectrophone" was proposed for the examination of absorption spectra in portions of the spectrum that are invisible.[1](https://www.spectroscopyeurope.com/system/files/pdf/PAS14_5.pdf) The field then lay largely dormant until the twentieth century.[16](https://ris.utwente.nl/ws/files/6943761/photoacoustics.pdf)
The laser era revived research: laser-illuminated spectrophones for gas analysis appeared in 1968, using a pulsed ruby laser and a chopped continuous-wave CO\(_{2}\) laser with capacitance-microphone detection.[16](https://ris.utwente.nl/ws/files/6943761/photoacoustics.pdf) In 1971 L. B. Kreuzer reported ultralow (ppb) gas detection with chopped He–Ne laser excitation and an electret microphone in the [Journal of Applied Physics](https://www.edgepedia.org/journal-of-applied-physics), arguably the first use of the term "optoacoustic" in this context.[17](https://doi.org/10.1063/1.1660651) In 1973 J. G. Parker discovered strong acoustic signals from non-IR-active gases caused by light absorption in essentially transparent windows and derived the theory for low-absorbing samples in Applied Optics.[18](https://doi.org/10.1364/ao.12.002974) Two 1973 papers revived the effect in solids, one by A. Rosencwaig in Optics Communications[19](https://doi.org/10.1016/0030-4018%2873%2990039-4) and one by William R. Harshbarger and Melvin B. Robin in Accounts of Chemical Research,[20](https://doi.org/10.1021/ar50070a001) both using a high-pressure Xe lamp, monochromator with chopper, and electret foil microphones; Rosencwaig introduced the term "photoacoustic" for solids to avoid confusion with the acousto-optic effect.[16](https://ris.utwente.nl/ws/files/6943761/photoacoustics.pdf) Rosencwaig and Gersho published the comprehensive theory of the photoacoustic effect with solids in the Journal of Applied Physics in 1976.[6](https://doi.org/10.1063/1.322296)
## Variants
**Quartz-enhanced PAS (QEPAS)** replaces the microphone with a piezoelectric quartz tuning fork, a resonator whose atmospheric-pressure [Q factor](https://www.edgepedia.org/q-factor) (quality factor: how sharply a resonator is tuned, amplifying signal) is fork-dependent (typically of order 10,000) and which has no power consumption; the standard 32,768 Hz fork converts acoustic resonance into a measurable current, and the acoustic amplitude is directly proportional to gas concentration.[9](https://www.nature.com/articles/s41377-025-02075-7) Acoustic-resonator configurations include on-beam, off-beam,[21](https://doi.org/10.1364/ol.34.001594) and T-shaped cavities, and forks can be driven at overtone modes.[22](https://doi.org/10.1063/1.4937002)
**Cantilever-enhanced PAS (CEPAS)** detects cell pressure variations by measuring the movement of a silicon cantilever with a laser interferometer to picometer resolution; the cantilever operates best non-resonantly at 10–100 Hz, and its spring constant can be 2–3 decades smaller than a membrane's, giving a large dynamic range.[5](https://doi.org/10.1038/s41598-018-20087-9) • [10](https://gasera.fi/wp-content/uploads/2015/12/PAS_GasAnalysisWithCantileverMicrophone_ApplSpectrosRew_2007.pdf) A related fork-based method, light-induced thermoelastic spectroscopy (LITES), detects absorbed light through the fork's own thermoelastic response and needs no acoustic contact, with response from the ultraviolet to the terahertz.[9](https://www.nature.com/articles/s41377-025-02075-7)
## Applications
Trace-gas sensing is a major use: QEPAS sensors detect methane, acetylene, and carbon monoxide at ppb to ppt levels, and instruments tested outside the laboratory include environmental monitoring of CH\(_{4}\), CO, and N\(_{2}\)O, leak detection in mechatronic systems, and hydrocarbon detection in the petrochemical industry.[9](https://www.nature.com/articles/s41377-025-02075-7) • [23](https://onlinelibrary.wiley.com/doi/10.1002/9780470027318.a9760) In FTIR-PAS, spectra recorded at several modulation frequencies in a single step-scan probe different thermal diffusion lengths, and independent component analysis can separate layer spectra of a multilayer sample, such as a 7 ± 1 µm HDPE film on 27 ± 2 µm tape, without user intervention.[7](https://www.sciencedirect.com/science/article/abs/pii/S0022285204002875) For semiconductors, photoacoustic measurements yield carrier diffusion length, surface recombination velocity, and bulk lifetime along with the absorption coefficient.[24](https://onlinelibrary.wiley.com/doi/10.1002/pssb.2221200203)
## Limitations and alternatives
The dominant systematic background is laser absorption at the cell windows or walls; because it matches the frequency of the gas-phase signal, it is extremely hard to remove by data analysis.[4](https://www.mdpi.com/1424-8220/24/20/6577) PAS sensors are susceptible to ambient noise and mechanical vibration in industrial, vehicular, and agricultural settings, and high-power lasers add cost, size, and thermal-management concerns.[4](https://www.mdpi.com/1424-8220/24/20/6577) [Humidity](https://www.edgepedia.org/humidity) matters physically: the efficiency of non-radiative relaxation, a quantity between 0 and 1, depends on humidity, and ambient methane data must be corrected for it.[25](https://amt.copernicus.org/articles/16/4263/2023/amt-16-4263-2023.html) High-Q transducers trade sensitivity for speed, since the higher the Q factor, the longer the time between two independent measurements.[13](https://www.mdpi.com/1424-8220/20/9/2745)
Against direct absorption spectroscopy (DAS), PAS showed a lower limit of detection in all three tested wavelength regimes (NIR, MWIR, LWIR), with a lowest noise-equivalent concentration of 7 ppb in the LWIR. DAS suffers from etalon-fringe "optical noise" that drifts, whereas the PAS background is a constant offset with white noise reducible by longer lock-in integration; the two can be combined, using calibration-free DAS at high concentrations to calibrate the linear PAS response at trace levels.[26](https://jsss.copernicus.org/articles/10/25/2021/)
## References
1. [Light and sound, photoacoustic spectroscopy (Spectroscopy Europe)](https://www.spectroscopyeurope.com/system/files/pdf/PAS14_5.pdf)
2. [Quartz Enhanced Photoacoustic Spectroscopy on Solid Samples (2024)](https://pmc.ncbi.nlm.nih.gov/articles/PMC11243826/)
3. [Photoacoustic Spectroscopy of Gaseous and Condensed Matter (IntechOpen)](https://www.intechopen.com/chapters/69765)
4. [A Review on Photoacoustic Spectroscopy Techniques for Gas Sensing (Sensors, 2024)](https://www.mdpi.com/1424-8220/24/20/6577)
5. [Teemu Tomberg and colleagues (2018). Sub-parts-per-trillion level sensitivity in trace gas detection by cantilever-enhanced photo-acoustic spectroscopy. Scientific Reports.](https://doi.org/10.1038/s41598-018-20087-9)
6. [Allan Rosencwaig, Allen Gersho (1976). Theory of the photoacoustic effect with solids. Journal of Applied Physics.](https://doi.org/10.1063/1.322296)
7. [Independent component analysis of photoacoustic depth profiles (Journal of Molecular Structure)](https://www.sciencedirect.com/science/article/abs/pii/S0022285204002875)
8. [Photoacoustics: an acoustic method for trace gas measurements (Miklós, Angelmahr, Angster, DAGA 2007)](https://pub.dega-akustik.de/DAGA_1999-2008/data/articles/003159.pdf)
9. [Quartz-enhanced laser spectroscopy sensing (Light: Science & Applications, 2025)](https://www.nature.com/articles/s41377-025-02075-7)
10. [Photoacoustic gas analysis with cantilever microphone (Applied Spectroscopy Reviews, 2007)](https://gasera.fi/wp-content/uploads/2015/12/PAS_GasAnalysisWithCantileverMicrophone_ApplSpectrosRew_2007.pdf)
11. [Theory of the photoacoustic effect with solids (Rosencwaig & Gersho, J. Acoust. Soc. Am. 58, S52, 1975)](https://doi.org/10.1121/1.2002181)
12. [Photoacoustic Spectroscopy (Shimadzu technical notes)](https://www.shimadzu.ch/service-support/technical-support/ftir/essential_knowledge/photoacoustic.html)
13. [Photoacoustic-Based Gas Sensing: A Review (Sensors, 2020)](https://www.mdpi.com/1424-8220/20/9/2745)
14. [Photoacoustic Spectroscopy (Spectroscopy magazine, David W. Ball)](https://web.archive.org/web/20101216163043/http:/spectroscopyonline.findanalytichem.com/spectroscopy/article/articleDetail.jsp?id=373774)
15. [A. G. Bell (1880). On the production and reproduction of sound by light. American Journal of Science.](https://doi.org/10.2475/ajs.s3-20.118.305)
16. [Photoacoustics: a historical review (Advances in Optics and Photonics 8(4), 2016)](https://ris.utwente.nl/ws/files/6943761/photoacoustics.pdf)
17. [L. B. Kreuzer (1971). Ultralow Gas Concentration Infrared Absorption Spectroscopy. Journal of Applied Physics.](https://doi.org/10.1063/1.1660651)
18. [J. G. Parker (1973). Optical Absorption in Glass: Investigation Using an Acoustic Technique. Applied Optics.](https://doi.org/10.1364/ao.12.002974)
19. [Photoacoustic spectroscopy of solids (Optics Communications, 1973)](https://doi.org/10.1016/0030-4018%2873%2990039-4)
20. [William R. Harshbarger, Melvin B. Robin (1973). Opto-acoustic effect. Revival of an old technique for molecular spectroscopy. Accounts of Chemical Research.](https://doi.org/10.1021/ar50070a001)
21. [Kun Liu and colleagues (2009). Off-beam quartz-enhanced photoacoustic spectroscopy. Optics Letters.](https://doi.org/10.1364/ol.34.001594)
22. [A. Sampaolo and colleagues (2015). Quartz-enhanced photoacoustic spectroscopy exploiting tuning fork overtone modes. Applied Physics Letters.](https://doi.org/10.1063/1.4937002)
23. [Quartz-Enhanced Photoacoustic Spectroscopy for Trace Gas Sensing (Encyclopedia of Analytical Chemistry)](https://onlinelibrary.wiley.com/doi/10.1002/9780470027318.a9760)
24. [The Photoacoustic Effect in Semiconductors (Sablikov & Sandomirskii, physica status solidi (b) 120, 471–480, 1983)](https://onlinelibrary.wiley.com/doi/10.1002/pssb.2221200203)
25. [Comparison of photoacoustic spectroscopy and cavity ring-down spectroscopy for ambient methane monitoring at Hohenpeißenberg (AMT, 2023)](https://amt.copernicus.org/articles/16/4263/2023/amt-16-4263-2023.html)
26. [Comparison of laser-based photoacoustic and optical detection of methane (J. Sens. Sens. Syst., 2021)](https://jsss.copernicus.org/articles/10/25/2021/)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Matter and radiation physics › Atomic and molecular physics*
*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*
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