Wavefront Sensing and Analysis Using GPC

The need to perceive invisible phase perturbations can arise in a wide range of imaging systems, from phase microscopes that non-invasively image transparent biological samples in vivo to adaptive optical systems that measure and compensate for phase aberrations to improve quality in more general imaging situations. The common-path interferometer (CPI) is an appealing tool for extracting and quantifying phase perturbations. A CPI applies the same principle of phase-to-intensity transformation as amplitude-dividing interferometers (e.g. Michelson or Mach-Zender) but with the advantage of heightened robustness to mechanical vibrations and ambient air fluctuations owing to the internally synthesized reference wave. Having laid out the framework for the generalized phase contrast, a natural extension is to exploit GPC to accurately measure unknown phase, which we will explore in this chapter. We will apply GPC analysis to determine how filter parameters can be adapted in order to tailor a CPI for accurate wavefront sensing. This involves optimizing the fringe visibility and peak irradiance, as well as extending the linear phase-to-intensity mapping regime. GPC can prescribe the appropriate filter size to prevent scattered light at the input from propagating through the central filtering region and thereby prevent an erroneous interpretation of the output interference patterns. GPC can also be used to tailor the other filter parameters to extend the linear regime of the phase-to-intensity mapping. Moreover, one may take note of the actual filter parameters and apply the GPC model to extract accurate information. The generalized phase contrast framework allows us to properly describe the synthetic reference wave (SRW), which enables proper interpretation of the CPI output intensity over an arbitrarily wide phase range. Thus, one does not always have to minimize the SRW curvature since the GPC description of the SRW can be exploited to accurately determine the unknown phase input. Whether using GPC to expand the linear regime of the phase-to-intensity mapping, or to account for the SRW-based inhomogeneity, the method paves the way for shifting from qualitative to quantitative phase imaging that can be utilized both for microscopy and other generalized wavefront-sensing applications.