  The physical interpretation of weak measurements has been the subject of much
debate. It is known that anomalous phenomena and results that appear in weak
measurements are essentially related to the phase of the quantum system being
measured. Consideration of the phase is important to clarify its physical
interpretation. In classical wave optics, there has long been studies on
methods of measuring or retrieving the phase of a wave function. We here
present that one of those methods, the analytic phase retrieval based on the
properties of entire functions, has a close connection with weak measurements
in quantum physics. We explain such a connection for two emblematic optical
weak-measurements that have the same mathematical formalism as quantum systems:
one is a system for weak measurements of polarized light displacement in a
birefringent crystal, and the other is a system for the direct measurement of a
wave function by weakly coupling it to a pointer. In those two systems, we show
that the pre- and post-selection of polarized light provides a filtering effect
similar to that utilized in the analytic phase retrieval.
