Fraunhofer Diffraction. Wed. Nov. 20, 2002. Kirchoff integral theorem. This gives the value of disturbance at P in terms of values on surface enclosing P. It represents the basic equation of scalar diffraction theory. Geometry of single slit. Have infinite screen with aperture A.
Wed. Nov. 20, 2002
This gives the value of disturbance at P in terms of values on surface enclosing P.
It represents the basic equation of scalar diffraction theory
Have infinite screen with aperture A
Let the hemisphere (radius R) and screen with aperture comprise the surface () enclosing P.
Radiation from source, S, arrives at aperture with amplitude
E=0 on .
Also, E = 0 on side of screen facing V.
Fresnel Kirchoff diffraction formula
If either S or P are close enough that wavefront curvature is not negligible, then we have Fresnel diffractionFraunhofer vs. Fresnel diffraction
Now calculate variation in (r+r’) in going from one side of aperture to the other. Call it
sin ≈ h/d
sin’ + sin = ( h’/d + h/d )
Second term = measure of curvature of wavefront
Fraunhofer or far field limit
Assume S on axis, so
Assume small ( < 30o), so
r’ >> so is constant over the aperture
r will not vary much in denominator for calculation of amplitude at any point P
consider r = constant in denominator
y = b
r = ro - ysin
dA = L dy
where L ( very long slit)
Fraunhofer single slit diffraction pattern