  Phase-sensitive properties of light play a crucial role in a variety of
quantum optical phenomena, which have been mostly discussed in the framework of
photoelectric detection theory. However, modern detection schemes, such as
arrays of on-off detectors, are not based on photoelectric counting. We
demonstrate that the theory of homodyning with such click counting detectors
can be established by using a proper detection model. For practical
applications, a variety of typically occurring imperfections are rigorously
analyzed and directly observable nonclassicality criteria are studied.
Fundamental examples demonstrate the general functionality of our technique.
Thus, our approach of homodyne detection with on-off detector systems is able
to bridge the gap between imperfect detection and the phase resolution demands
for modern applications of quantum light.
