Optical transfer function characterization using a weak diffuser

We present a simple technique which uses a random phase object for single-shot characterization of an optical system's phase transfer function. Existing methods for aberration measurement typically involve holography, requiring complicated wavefront sensing optics or through-focus measurements with known test objects (e.g. pinholes, fluorescent beads) for pupil recovery from the measured wavefront. Here, it is demonstrated that a weak diffuser can be used to recover the pupil of an imaging system in a single measurement, without exact knowledge of the diffuser's surface. Due to its stochastic nature, the diffuser scatters light to a wide range of spatial frequencies, thus probing the entire pupil plane. A linear theory based on the weak object approximations predicts the spectrum of the measured speckle intensity to depend directly on the pupil function. Numerical simulations of diffusers with varying strength confirm the validity of the theory and indicate sufficient conditions under which diffusers act as weak phase objects. Using index matching oils to modulate diffuser strength, experiments are shown to successfully recover aberrations from an optical system using coherent illumination. Additionally, this technique is applied to the recovery of defocus in images of a weak phase object obtained through a commercial microscope under partially coherent illumination.