Megawatt-scale laser optical systems face fundamental performance limitations imposed by the material properties of their optics. Even the most stringently designed optical coatings inherently absorb a small fraction of the intense incident radiation, typically around 0.5 parts per million. Although fractionally miniscule, at extreme power this absorption can result in more than a watt of steady-state heating of each optic. This generates large temperature gradients within the optics and drives thermo-elastic surface deformations and thermo-refractive substrate lensing, which introduce performance-limiting optical aberrations in reflection and in transmission, respectively.

In the field of gravitational-wave detection, the Laser Interferometer Gravitational-Wave Observatory (LIGO) aims to achieve 1.5 MW of laser power in its 4-kilometer arm cavities in the coming years. Megawatt-scale power, together with high levels of quantum enhancement through squeezing, are critical to further reduce quantum noise in the LIGO interferometers. Achieving this will vastly expand the volume of the universe accessible to gravitational-wave observation. But thermally induced aberrations cause power losses and the degradation of the injected squeezed field, which limit the interferometer’s sensitivity to gravitational waves.

Thermal compensation actuators

To mitigate these thermal distortions, gravitational-wave interferometers must use thermal compensation actuators for active wavefront correction. For instance, the LIGO interferometers already use ring heaters to correct low-order aberrations on their main 40-kilogram mirrors. In the future, a newly developed actuator known as the FROnt Surface Type Irradiator (FROSTI) will be incorporated to project tailored annular heating patterns onto each mirror’s periphery to correct higher-order aberrations.^{1, 2}

A critical limitation in deploying these sophisticated actuators is the absence of a full-aperture error signal to inform their optimal power settings. Standard wavefront sensing techniques, such as Hartmann wavefront sensors or phase cameras, rely on the presence of a reference beam or probe beam. Their field of view is limited to the transverse extent of this beam, which is subject to practical size limitations. In systems using large optics, such as LIGO, these sensors can only monitor the central region of the optics, which renders them blind to the necessary wavefront corrections near the edges where actuators like FROSTI operate.

Our recent paper published in Classical and Quantum Gravity presents a breakthrough solution to this sensing limitation by demonstrating that the complete internal thermal state and full-aperture wavefront errors of a large optic can be accurately reconstructed using front-surface thermal imaging.³ The thermal imaging camera captures the two-dimensional (2D) temperature profile of the optic across its entire surface. This technique uses the optic’s central region—where the fields of view of LIGO’s Hartmann wavefront sensors and the thermal imaging cameras overlap—to calibrate the raw thermal fluxes into a precise temperature map.

The core advancement lies in coupling these calibrated surface temperature maps with finite element analysis (FEA) modeling. In a thermal steady state, we find that the optic’s surface temperature profile can be decomposed into a linear combination of the individual temperature responses generated by each distinct heating source present. In LIGO, for instance, these heating sources include the main laser beam, the ring heater, and the future FROSTI actuator.

By computing the 2D spatial overlap integrals between the measured temperature map and FEA-generated “unit-heating maps” for each individual source, the technique yields the amount of power absorbed from each heating source. Iterating this procedure over different beam positions can jointly identify the precise location of the laser beam’s centroid on the optic. With complete thermal state information, the FEA model can then be used to reconstruct the actual wavefront errors in reflection and transmission over the full aperture of the optic.

Hardware requirements to achieve this high-fidelity wavefront reconstruction are surprisingly accessible. We found that commercial thermal imaging cameras, equipped with a 600 × 600 pixel sensor array and a thermal sensitivity of 20 mK, are adequate for this purpose. Using this off-the-shelf hardware, the absorbed power levels from the laser beam, ring heater, and FROSTI actuator can all be determined with a relative error of <0.1%. The true position of the laser beam can be inferred to an accuracy of 0.5 mm. To guarantee a thermal steady-state condition during operation, as required to accurately apply this technique, optical systems can use an offline heating system to maintain the optics’ thermal state when the primary laser beam is not present, as LIGO plans to incorporate in a future upgrade.

Broad translational potential for laser science

This methodology has broad translational potential across the laser science industry, particularly for fields dependent on large optics under extreme thermal loads due to high-power continuous-wave radiation. By using external thermal imaging cameras, the thermo-refractive and thermo-elastic aberrations of large optics can be accurately reconstructed without the need for wavefront sensor probe beam coverage of the entire aperture. This sensing technique provides the precision error signals needed to effectively deploy advanced adaptive optics, particularly those that actuate at large radii, by enabling continuous optimization of their heating profiles.

ACKNOWLEDGEMENT

This material is based upon work supported by the U.S. National Science Foundation under Award No. 2409496. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

REFERENCES

1.  L. Tao et al., Phys. Rev. Lett., 134, 5, 1401 (2025); https://doi.org/10.1103/physrevlett.134.051401.

2.  T. Rosauer et al., Optica, 12, 10, 1569 (2025); https://doi.org/10.1364/optica.567608.

3.  ​​L. Tao, P. Goodarzi, and J. Richardson, Class. Quantum Grav., 43, 14, 5008 (2026); https://doi.org/10.1088/1361-6382/ae86aa.