In the mathematics literature, this example is a basic one for SYZ mirror symmetry, going back at least to Gross' seminal paper
http://arxiv.org/pdf/math/0012002v2.pdf
See Chan,Leung,Lau JDG 2012 for a treatment fully within the realm of symplectic geometry. There were also contributions in Seidel and Thomas from the point of view of homological mirror symmetry in http://arxiv.org/abs/math/0001043.