  We show that a general linear transformation from one single photon qudit to
another, the dimension of which can be either equal or unequal to that of the
first one, can be implemented by linear optics. As an application of the scheme
we elaborate a method to deterministically realize any finite-element Positive
Operator Value Measure (POVM) on single photon signals, which is also
generalizable to any quantum system in principle.
