Geodesic
The Field of Nonregular Short Wave scattered by a~Smooth Convex Object in Penumbra
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 13-26

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The paper presents asymptotic formula for the field nearly the edge of caustic partially overshuded by a smooth convex object. Tht formula bears resemblance to famous Kravtsov–Ludwig expansions at a caustic, incomplete Airy functions are involved. 
@article{ZNSL_1981_117_a1,
     author = {I. Y. Bylyi},
     title = {The {Field} of {Nonregular} {Short} {Wave} scattered by {a~Smooth} {Convex} {Object} in {Penumbra}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--26},
     publisher = {mathdoc},
     volume = {117},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a1/}
}
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I. Y. Bylyi. The Field of Nonregular Short Wave scattered by a~Smooth Convex Object in Penumbra. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 13-26. http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a1/