The rapid growth in the development of new optical materials such as 2D materials, layered heterostructures, active phase changing materials, optical metasurfaces, and metamaterials, requires new methods which enable accurate, broadband, and real-time microscopic characterization of their optical and physical properties. Here, this necessity is addressed and a novel method is presented to dynamically and accurately obtain the spectral phase of a microscopic sample, either in reflection or transmission. The method is based on a designed optical relay that couples the output port of a typical microscope setup to an imaging spectrometer. By post-processing the acquired images, a stable, accurate, and easy-to-align broadband spectral microscopic interferometer is obtained. This approach is experimentally demonstrated by measuring the spectral phase response of two different types of metasurfaces in reflection and in transmission and also by accurately measuring the dispersion of a thick glass slab in transmission. Moreover, the method's applicability to broadband dynamic measurements is demonstrated by real-time tracking the phase response of optically driven nematic to isotropic and isotropic to nematic phase transitions of a liquid crystal. Altogether this method enables accurate, dynamic, and easy microscopic phase characterization and can become widely used for materials characterization.
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