Berkhamsted

Conundrum

I have recently been reading an interesting paper (Unconventional methods of imaging: computational microscopy and compact implementations) where the author's present a propagator that describes how an electromagnetic wave will propagate from an object to a sensor: $$E(x,y,z) = \mathcal{P}_z \left\{ E(x,y,0) \right\} $$ The paper is great because among other things it presented the way to extend Holographic reconstruction through a medium with refractive index \(n\) not explained in other review papers (Practical algorithms for simulation and reconstruction of digital in-line holograms). However every paper I read always seems to highlight a new question that is not answered! The paper by Euan McLoid et. al. is no exception.. Given that \(\mathcal{P}_z\) propagates an electromagnetic wave it seems strange that they then use the same propagator in the reverse direction, but with no explanation, they use an intensity (See Goodman Section 4.1.1) where the irradiance of a scalar monochromatic wave at point \( P\) as the squared magnitude of the complex phasor representation \(U(P)\) of the disturbance: $$I(P) = \lvert U(P) \lvert^2 $$ So Euan McLoid et. al. derive the \(\mathcal{P}_z \left\{ E \right\}\) with a complex wave (\(E\)) and then use the square of a complex wave without explanation in the reverse direction: $$\mathcal{P}_{-z} \left\{ I(x,y,z_i)\right\} = E_r(x,y,z_s) $$ In addition other work (Manfred H. Jericho and Hans Juergen Kreuzer in 2010) indicate that the twin image artifacts are removed if the intensity of the contrast hologram is used rather than from the intensity of the hologram \(H(x_s, y_s, z_s)\). So a paper written in 2016 makes assertions about twin image artifacts that have been dismissed by and earlier work!

My job is to make sense of conflicting information like this and create a product. Welcome to my world!