  Interferometers provide a highly sensitive means to investigate and exploit
the coherence properties of light in metrology applications. However,
interferometers come in various forms and exploit different properties of the
optical states within. In this paper, we introduce a classification scheme that
characterizes any interferometer based on the number of involved nonlinear
elements by studying their influence on single-photon and photon-pair states.
Several examples of specific interferometers from these more general classes
are discussed, and the theory describing the expected first-order and
second-order coherence measurements for single-photon and single-photon-pair
input states is summarized and compared. These theoretical predictions are then
tested in an innovative experimental setup that is easily able to switch
between implementing an interferometer consisting of only one or two nonlinear
elements. The resulting singles and coincidence rates are measured in both
configurations and the results are seen to fit well with the presented theory.
The measured results of coherence are tied back to the presented classification
scheme, revealing that our experimental design can be useful in gaining insight
into the properties of the various interferometeric setups containing different
degrees of nonlinearity.
