Caustic and focal expansions

Geometrical optics and its refinement, ray expansions, are inapplicable near caustics. The error of the GO approximation and ray expansions increases when the point of observation approaches a caustic and at the caustic these approximations become infinite. Therefore, these ray expansions are termed nonuniform asymptotic expansions. In this chapter we explore another type of field asymptotics, called the caustic expansion, applicable to points of observation in the vicinity of caustics. The error of these asymptotic approximations remains bounded (and tends to zero as £- oo) however close the caustic is approached. Therefore, the caustic expansions are called uniform expansions of ray fields.