Subsampling phase retrieval for rapid thermal measurements of heated microstructures

A subsampling technique for real-time phase retrieval of high-speed thermal signals is demonstrated with heated metal lines such as those found in microelectronic interconnects. The thermal signals were produced by applying a current through aluminum resistors deposited on soda-lime-silica glass, and the resulting refractive index changes were measured using a Mach-Zehnder interferometer with a microscope objective and high-speed camera. The temperatures of the resistors were measured both by the phase-retrieval method and by monitoring the resistance of the aluminum lines. The method used to analyze the phase is at least 60x faster than the state of the art but it maintains a small spatial phase noise of 16 nm, remaining comparable to the state of the art. For slowly varying signals, the system is able to perform absolute phase measurements over time, distinguishing temperature changes as small as 2 K. With angular scanning or structured illumination improvements, the system could also perform fast thermal tomography.