  We give a new construction of strict deformation quantization of symplectic
manifolds equipped with a proper Lagrangian fiber bundle structure, whose
representation spaces are the quantum Hilbert spaces obtained by geometric
quantization. The construction can be regarded as a "lattice approximation of
the correspondence between differential operators and principal symbols". We
analyze the corresponding formal deformation quantization. We also investigate
into relations between our construction and Berezin-Toeplitz deformation
quantization.
