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Biomedical Imaging by Sebastian Aeffner, Timo Aspelmeier, Tim Salditt

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(which holds if intensity variations are small compared to phase variations) leads to

I(r_,z)I(r_,0)(1zk2φ(r_,0)),(6.134)

holding for small propagation distances z = Δ behind a plane taken to be at the origin z = 0. TIE based phase retrieval – in its simplest form – is the inversion of this equation, and hence computing φ from I(r, z). To this end, the numerical inversion of the Laplacian is required, which can be achieved based on the Fourier representation of the ∇ operator

2=F11kx2+ky2F,(6.135)
=F1k_F.(6.136)

When boundary conditions are not important, the phase φ can be solved by implementation of FFT filtering. Alternatively, for special requirements regarding ...

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