Finite volume simulation of photothermal microscopy for detecting closely spaced subsurface defects in optical materials

A frequency domain finite volume model is developed to describe photothermal microscopy of subsurface absorbing defects in optical substrates and to predict how the measurable signals depend on experimental and material parameters. The harmonic heat conduction equation is solved on an adaptive non uniform three-dimensional grid; pump laser heating is represented by a Gaussian intensity profile with Beer–Lambert absorption, and the absorption of gold particles is estimated from Mie theory. The complex temperature field is integrated along the optical axis and weighted by the probe beam intensity profile to yield amplitude and phase observables. The simulated amplitude and phase trends versus defect depth and modulation frequency reproduce the expected diffusion-limited behavior, supporting the physical consistency of the approach for modeling photothermal microscopy. Parameter maps identify the combinations of pump and probe focus positions and beam waists that maximize detectability, and two particle simulations reveal thermal-overlap effects that make closely spaced defects difficult to resolve. The model provides quantitative relationships between modulation frequency, focus depth, and beam size for selecting experimental conditions, supports calibration samples with embedded gold particles, and enables interpretation of measured signals from clustered or arbitrarily shaped defects. An analytical harmonic point-source result agrees with the finite-volume peak temperature amplitudes within 2.6%.