Measurement of thermally induced deformations by means of phase retrieval

We show that phase retrieval from a set of intensity measurements can be used to determine the thermally induced deformation of a diffusely reflecting surface. The presented approach is based on an experimental setup with a spatial light modulator (SLM) located in the Fourier domain of a 4f-configuration. The SLM is used to modulate the incident light with the transfer function of propagation. Since no mechanical adjustment is required throughout the measurement process, the setup is capable of capturing the intensity distributions associated with a large number of propagated representations of the same wave field in a short instance of time. Consequently, it enables the investigation of quasi static scenes, e.g. object surfaces under thermal load which are common in the field of non destructive testing for example. The result of the measurement process can be subjected to well established, iterative phase retrieval algorithms in order to recover the deformation from the lateral phase distribution directly in front of the object. As a proof of principle we show experimental investigations which address the deformation of a resistors surface under thermal load. Eventually, the results obtained from phase retrieval are compared to those of standard interferometry.