Why is a lens image inverted?

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))

Fourier transform Inverse Fourier transform Fourier of Fourier transform

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

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

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