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# SN~ (~6) lff 2It 3k_~ , 5 ",,x_J {b)

SN~ (~6) lff 2It 3k_~ , 5 ",,x_J {b)

## Let I be the diagonal in

Let I be the diagonal in 9. By ~ we denote the set of oriented lines in (U,o)) that do not intersect the screen. Thus we have Proposition 5.1 In edge diffraction in an arbitrary Euclidean space, the canonical variety A c ~ has two components A= A I uA D where A I --- f~ x f~ c I and A D is a pure diffraction of rays passing through the edge of an aperture. Let L c (U,(o) be a generic incident system of rays. Then the edge-diffracted system of rays 240 I_. = d o A) (L) is a regular intersection of two smooth components: L1 = (I(, A I) (L) and I~ 2 = (I~ ° A D) (L), i.e. I_~ -- L1 uI~2, dimI~l nI~2 = dim I'l - 1 and Tx(I~ 1 nI~ 2) -- Txl_. 1 nTxL 2. Thus we see that the caustic by edge diffraction has three components: 1. The caustic of L1, which is part of the caustic in the incident wavefront L. 2. The caustic arising purely by diffraction at the edge, i.e. the caustic of L'2, 3. The image gV(I~l n I~2) of the rays passing exactly through the edge. Proposition 5.2 1 Generic caustics by diffraction in a half-line aperture on the plane are diffeomorphic to the boundary caustics ,(2, £3, B 2 -- C 2, B 3- Normal forms for the generating families as images A(L) (or pairs (A,L) in general position) are as follows: A2: - l~'3+~'(q2-a)- lql~'2, a > 0 and C = {q 1 --- 0, q2

Proof q 241 aperture aperture aperture Fig.5.2 Generic caustics by diffraction in a half-fine aperture. d) v ql aperture It is easily seen that I~ -- graph (rCM) c_ E is generated locally by K(r,ql,q2) = q2 r + ql 1 ~ -r2 ~'q2 r -~ 1 ql r 2 • The only stable systems of rays I~(L) c_ (T'V, ~0V) are generated in (M,o0 by where aF (r)}, L = {(r,s); s = - -~ 1 2 A 1 :Fl(r) = -~r ; 1 r3 " A 2 : F2(r) --- _ ~- , 1 A 3 : F3(r) = _ ¥ r4,

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