Lock-in thermography on moving samples: amazing mismatch between amplitude and phase

We have obtained an analytical expression for the surface temperature of a sample that is moving at constant velocity when it is illuminated by a modulated and focused laser beam, which remains at rest. From this expression it is found that while the temperature amplitude thermogram shows the expected elongated shape in the direction of the sample movement, the phase thermogram surprisingly shows a cylindrical symmetry about the position of the laser spot. To the best of our knowledge this is the first time that such a mismatch between amplitude and phase is found in photothermal experiments. This behaviour is confirmed from lock-in thermography experiments on moving samples. Moreover, the temperature (amplitude and phase) profiles in both directions, parallel and perpendicular to the sample movement, show a linear behaviour from whose slopes the in-plane thermal diffusivity of the moving sample can be obtained.