A systematic theoretical study of approximations to the Kirchhoff diffraction integral is presented, stressing the improved behavior at large angles. This work was motivated by consideration of diffraction in dual tilted dispersive interdigital transducers for surface acoustic wave generation, but the salient features are applicable to diffraction problems in general. Previous treatments of surface acoustic wave (SAW) propagation were limited to nearly forward directions perpendicular to transducer fingers, where the simple Fresnel diffraction theory was adopted. Improvement of the theory for nonforward angles is obtained in which both the Fraunhofer and Fresnel diffractions are correctly included. The conventional diffraction treatment used in optics (as in the textbook by Born and Wolf) is found inaccurate and a new form is presented.