Spatial Filter (Optics)

1. Nov 8, 2009

forty

Consider a 2f:2f filtering setup with f = 1000mm. The system is illuminated with a uniform plane wave of uni amplitude and wavelength $$\lambda$$ = 1.0$$\mu$$m. The input transparency (object) has amplitude transmittance g(x,y) and the spatial filter has amplitude transmittance s(x,y).

Write an expression relating the complex amplitude q(x,y) in the image plane to g(x,y) and s(x,y).

Determine s(x,y) such that q(x,y) = $$\nabla$$2g(x,y) for arbitrary g(x,y).

So an incident plane wave will exit the transparency with a field given by Eoeig(x,y) (but unit amplitude so Eo = 1) and the same for the filter eis(x,y)

So wouldn't it just be the multiple of the 2? q(x,y) = ei(g(x,y)+s(x,y))

I'm really not sure about that... I can't seem to figure out the 2nd part using that which leads me to thinking its completely wrong :S

Any help on this greatly appreciated!