廣義傅里葉變換及其光學(xué)實(shí)現(xiàn)

1、2022-3-2222022-3-2232022-3-224-2222oodxdysinf)yvxu(2 itgf)vyux(iexp) y, x(C)y, x(F2022-3-2252022-3-2262022-3-2272022-3-2282022-3-2292022-3-2210 )( d)(gsinix2tgiexp tg2ixexpsin2)2/( iexp)(g-22F2022-3-2211 )( d)(gsinix2tgiexp tg2ixexpsin2)2/( iexp)(g-22F2022-3-2212 d)ixexp()(g21)(g d)ixexp()(g21)(g 2/

2、2/FF2022-3-2213)x(gd)(g2i2i /)x(expF20 )x(i)i /xexp(lim 202022-3-22142022-3-22152022-3-22162022-3-22172022-3-22182022-3-22192022-3-22202022-3-2221dx)x(g)2/xexp()x(H! n21a2nnn2022-3-22222022-3-22232022-3-2224 )4/sin(/ ff )8/(tg f)4/cos(1 fd f2022-3-22252022-3-2226 )N2/sin(/ff )N4/(tgf)N2/cos(1 fd f20

3、22-3-2227-22221o2212121)fdd(ikdxdy)yvxu(2)yx(fd1ddiexp)y, x()vu(fd1ddiexpfddie)v, u(21(7)2022-3-2228),(fie dxdy)yvxu(f2iexp)y, x(fie)v, u(o2kf2i-o2kf2iF(10)2022-3-2229-22221o2212121)fdd(ikdxdy)yvxu(2)yx(fd1ddiexp)y, x()vu(fd1ddiexpfddie)v, u(21 )( d)(gsinix2tgiexp tg2ixexpsin2)2/( iexp)(g-22F(7)5.2(

4、1)2022-3-2230 )4/sin(/ff )8/(tgf)4/cos(1 fd sinff )2/(tgf)cos1 (fd sinfsinf)cos1 (f )cos1)(cos1 (f)f /1d/2(dd22222022-3-2231-2222o2)fd2(ikdxdysinf)yvxu(2 itgf)vyux(iexp) y, x(fie) v, u( , vv, uu, yy, xx sinf/2f/2 -2222oydxdsin)vyux( itg2)vyux( iexp)y, x(C)v, u( fi /)fd2(ikexpC 22022-3-2232 )( d)(gsi

5、nix2tgiexp tg2ixexpsin2)2/( iexp)(g-22F-2222oydxdsin)vyux( itg2)vyux( iexp)y, x(C)v, u(2022-3-2233 )y,x(FC)v,u( oo2022-3-2234f2022-3-2235-2222oodxdysinf)yvxu(2 itgf)vyux(iexp) y, x(C)y, x(F sinfi)2/(tgfk2iexpsinfi)kd2iexp(C 2022-3-2236-2222opo)p(dxdy) 2/psin(f)yvxu(2 i) 2/p(tgf)vyux(iexp) y, x(C)y,

6、x(F2022-3-2237 )2/(tgf)cos1 (fd f sinff 2022-3-22381-2222o1dxdyd)yvxu(2 ifd)vyux)(df (iexp) y, x() v, u(2022-3-2239同同-2222o1dxdy)cos1 ( f)yvxu(2 i)cos1 ( f)vyux(cosiexp) y, x() v, u( /2) tg(f)/sincos-f(1f sinf)cos1 (fd -2222o2)fd2(ikdxdysinf)yvxu(2 itgf)vyux(iexp) y, x(fie) v, u(2022-3-2240f )cos1 (

7、fd)2/ tg(ff 2022-3-2241 )2/psin(fsinff /4) tg(pf/2) tg(ff 2022-3-2242f2022-3-2243 )2/psin(ff i2022-3-2244022022-3-22452022-3-2246 )sin f (-sin fsinff 2312022-3-22472022-3-22482022-3-2249f fsin fsinf 32112022-3-22502f2f2022-3-2251 27 2/f32cos1fd2/fsinff3/1p6/ 111111111）（）（）（， 28 6/f3cos1fd 3/f3sin/ff

8、3/2p3/2/ 1222122112）（）（，2022-3-22522022-3-22532022-3-22542022-3-22552022-3-22562022-3-22572022-3-22582022-3-2259 ndlndl )L(BA 0)dlnndl( )L(2022-3-2260 rln)ln(drndlr rdlnndlr BAoBAoBABAoBA dldlrdndldnr dldlrdndldrdl)nr( BABABA ndlrdndld 2022-3-2261ndlrdndld )zn/nsin(r)zn/ncos(r)z(r 12,o12o 2022-3-226

9、2 )zn/ncos(r)z(r 12o n/nL2 12 nn2L 12 2022-3-2263 )N2/sin(/ff 2022-3-22642022-3-2265 )0,1,(n )/xexp()/x2(HN)x(E 22nnn 2022-3-2266 )x(En )ziexp()/xexp()/x2(HN)z, x(E n22nnn onn12o1nkN , nn2/1nkn11nN nnk2nn 21o212 2022-3-2267 /2/x2x ， )/xexp()/x2(Ha)x(a)x(g 0n22nn0nnn !n2h xd)x()x(gh1a nnnnn2022-3-226

10、8 )pLiexp()/xexp()/x2(Ha )pLiexp()x(a)pL,x(g0nn22nn0nnnn n2/L)/2(nk )/2(2/)2/1n(Lnk p2/)2/1n(LnkpL 1o1o1on 2022-3-2269 )2/Lnk2( iexpA )x()inexp(a)pL,x(g 1o0nnn 式中式中 )0 ,(gA)0 ,(gA )(gA )(aA)(aA)pL,x(g (p)0nnn0nnn F FF FF FF FF F2022-3-22702022-3-2271 dx) x2iexp()2/ xx(*g)2/ xx(g), x(W 2022-3-2272 d)

11、2/ xx(2iexp)(*G)2/ xx(*g d)2/ xx(2iexp)(G)2/ xx(g dIdx)(2iexp)(*G) (GW )2(2dx x22iexpI d)x2iexp()2/ (*G)2/ (G), x(W 2022-3-2273 )0(*G)2(Gdx)x4iexp(), x(W )0(*g)x2(gd)x4iexp(), x(W )(Gdx), x(W )x(gd), x(W 22 dxd), x(WE o 2022-3-2274 d)xf2iexp()2/ (*G)2/ (G), x(W dx)f/ x2iexp()2/ xx(*g)2/ xx(g), x(W 2

12、022-3-2275), W(-x dxf/ x)(2iexp)2/ xx(*g)2/ xx(g dx)f/x2iexp()2/xx(*g)2/xx(g xx 令令2022-3-2276 xdcba x x x1001 x 2022-3-2277 MM/x xM00M/1 x 2022-3-2278 )Qx, x(W dx)f/ x)Qx(2iexp)2/ xx(*g)2/ xx(g dx f/2)x(x-/2)xQ(xi -exp )f/ x2iexp()2/ xx(*g)2/ xx(g), x(W 22 Qxx x1Q01 x 2022-3-2279)f /zR ( ),R-W(x d) )fzx(f2iexp()2(*G)2(G), x(W 其其中中2022-3-2280 Rx x10R1 x 2022-3-2281 dx)z/xx2iexp()x(g)x(g ooo oo,o*,odxx)1R(2zx2iexp2x)R21(g 2xgW )x,(W dxzxx2iexp2xg 2xgWoo,o*,o x x0110