1. Why is a lens image inverted?

2. image=Fourier(Fourier (object))
Scattered lightwave
imaging lightwave z1 z2
Fourier transform
(with extra phase)
Fourier transform again
(extra phase subtracted by lens)
image=Fourier(Fourier (object))

3. Fourier transform
Inverse Fourier transform
Fourier of Fourier transform

4. Fourier optics Fresnel Lens Fraunhofer Scattered lightwave
imaging lightwave z1 z2
Fresnel
Lens
Fraunhofer

5. Classical Lens-Based (Fourier Optics) Imaging
Large angle scattered light: uncollected: loss of azimuthal information
Spherical wave:
ãä k r/r
Paraxial light collected by lens
Point scatter origin
(x,h)
(u,v)
(x,y)
Fresnel diffraction
paraxial
Fresnel diffraction z1 z2
Fresnel
Lens
Fraunhofer

6. Every time you look at something, remember this…
light already does Fourier transform, twice, for your vision