An experimental and simulation study of the full strain tensor and of strain-induced magnetocrystalline anisotropies in arrays of lithographically patterned (Ga,Mn)As on GaAs(001) is performed using a coherent diffraction lensless microscopy technique. We demonstrate the ability of our technique to get an insight into the strain field propagating in the crystal part belonging to the substrate. The experimentally reconstructed strain fields are in good agreement with those obtained from simulations based on elasticity theory.