The paper investigates the semiclassical limit of the defocusing Davey-Stewartson II (DS-II) equation, focusing on the direct spectral transform for smooth initial data. The authors introduce a WKB-type method to solve the singularly perturbed elliptic Dirac system in two dimensions, proving its formal validity for large spectral parameters \( k \). Numerical evidence supports the accuracy of this method for sufficiently large \( k \). The study also explores the eikonal problem, which is independent of \( \epsilon \), and provides a rigorous analysis for real radial potentials at \( k = 0 \). The reflection coefficient is analyzed, showing that it converges pointwise to a limiting function supported in the domain where the eikonal problem does not have a global solution. The paper includes numerical examples and comparisons with the WKB method, providing insights into the behavior of the solution in the semiclassical limit.The paper investigates the semiclassical limit of the defocusing Davey-Stewartson II (DS-II) equation, focusing on the direct spectral transform for smooth initial data. The authors introduce a WKB-type method to solve the singularly perturbed elliptic Dirac system in two dimensions, proving its formal validity for large spectral parameters \( k \). Numerical evidence supports the accuracy of this method for sufficiently large \( k \). The study also explores the eikonal problem, which is independent of \( \epsilon \), and provides a rigorous analysis for real radial potentials at \( k = 0 \). The reflection coefficient is analyzed, showing that it converges pointwise to a limiting function supported in the domain where the eikonal problem does not have a global solution. The paper includes numerical examples and comparisons with the WKB method, providing insights into the behavior of the solution in the semiclassical limit.