  Conventional tomographic techniques are becoming increasingly infeasible for
reconstructing the operators of quantum devices of growing sophistication. We
describe a novel tomographic procedure using coherent states which begins by
reconstructing the diagonals of the operator, and then each successive
off-diagonal in a recursive manner. Each recursion is considerably more
efficient than reconstructing the operator in its entirety, and each successive
recursion involves fewer parameters. We apply our technique to reconstruct the
positive-operator-valued measure (POVM) corresponding to a recently developed
coherent optical detector with phase sensitivity and number resolution. We
discuss the effect of various parameters on the reconstruction accuracy. The
results show the efficiency of the method and its robustness to experimental
noise.
