開口による回折波の新しい取り扱い

抄録

Maggi ane Rubinowicz's formula of the diffraction by the Kirchhoff's screen is developed into more general cases. It is shown that, as far as the incident wave U⁽ⁱ⁾ satisfies the wave equation, the integrand V of the Kirchhoff's integral
U_k(P)=∫∫_A1/4π[U⁽ⁱ⁾grad expiks/s-expiks/s gradU⁽ⁱ⁾]·ndS
can be always expressed by the vector potential W in the following way,
V=rot W
Then by the Stokes' theorem, the diffracted wave U_k(P) is represented by
U_k(P)=_??_U_j^(s)(P)+_??_W·ldl,
where U_j(s)(P) are contributions from the singular points of the vector potential which correspond to the points of the stationary phase in the Kirchhoff's integral, l being the unit vector along the line edge of the boundary Γ₀ of the aperture A.
For the incident wave which is slightly deformed from the ideal spherical wave, the approxi-mate vector potential is given by
W(Q, P)=U⁽ⁱ⁾(Q)(expiks/s)(4π)^-1(s×p)/(1+s·p),
where s is the distance between the point Q on the aperture and the observing point P, _??_ being the unit vector of _??_/s and p being the unit vector of the geometrical optical ray, This gives us the same asymptotic formula of the contribution from the critical points of the first, second and third kind to the Kirchhof's integral. The accurate but not simple formula of the vector potential is also given for the general incident waves.