(Fresnel) diffraction in on-axis holography

Question

In on-axis holography one can consider

• the plane wave from source
• the scattered wave from object (spherical if the object is a point)

Then it is possible to model the transmission on the photographic plate with a transmission coefficient $T$ $$T=\alpha I-1$$

And calculate the transmitted wave intensity, which comes out to be made of

• an attenuated plane wave
• two spherical waves, one converging on the object (from a virtual image), one converging on the simmetrical point on the other side of the plate, hence forming a real image.

(This is the derivation suggested by, e.g. Hariharan - Basics of Holography, 1.2)

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My question is: The transmitted wave above described is the wave "just after" the plate. All the (Fresnel) diffraction phenomena have not been taken into account, so is that wave to be considered the diffracted wave already? Or should one do diffraction calculations, based on Fresnel diffraction on that wave? If so, what is the result?

Answer 1

Holography is about the storage of an optical wave (rather than an image of an object) in an interferogram. Since an optical wave involves the diffraction of the wave, Fresnel diffraction is incorporated into the process.

The formulation of the reconstruction process in terms of mathematics may sometimes be misleading in that it only describes the two-dimensional function in a specific plane, perhaps the plane of the hologram or the plane of an image that this optical wave would produce. However, this function would propagate according to Fresnel diffraction away from this plane to produce the full optical wave that was stored into the hologram.