A combination of in situ birefringence and depolarized light-scattering experiments was used to study the formation of an ordered cylindrical microstructure in a polystyrene-block-polyisoprene copolymer melt under a shear flow field. We demonstrate that our sample forms an imperfect "single crystal" with a fraction of the cylinders aligned in the flow direction. The aligned regions of the sample coexist with randomly oriented grains. The birefringence experiments enable the characterization of the aligned regions while the depolarized light-scattering experiments enable the characterization of the randomly oriented grains. A model for depolarized light scattering from such samples was developed. It was shown that the usual scattering formulas for grains embedded in anisotropic matrix are applicable provided one recognizes that the scattering vector, q, has transverse (q(T)) and longitudinal (q(L)) components even in the small angle scattering limit (q(L) is the component of q in the propagation direction). This result applies when the analyzer (or polarizer) axis is aligned along the direction of the optic axis of the aligned regions. A simplifying feature of block copolymers is that the product w\q(L)\ much less than 1, where w is the characteristic grain size, allowing the approximation q approximate to q(T). We used our model to study the structure of the block copolymer melt after it had been quenched from the disordered to the ordered state under reciprocating shear flow (strain amplitude = 133%). Under slow shear flow (shear rate, (gamma) over dot = 0.067 s(-1)), about 60% of the sample consisted of randomly oriented grains and 40% consisted of aligned cylinders. The average grain size and time required to complete the ordering process obtained under slow shear flow were comparable to those obtained under quiescent conditions. Under fast shear flow ((gamma) over dot = 0.67 s(-1)), however, most of the sample (97%) consisted of aligned cylinders, indicating the formation of a well-aligned crystal.