Van Cittert Zernike Theorem and associated Optical phenomenon

[Tachyonomad]

Hello colleagues

So I've been trying to make head and tail of a paper concerning coherence holography.
As I see it, it involves a sound understanding of the Van Cittrt Zernicke theorem
I have linked the paper below, and I was wondering if someone could explain the physics
going on behind and some mathematical pointers to help me understand it.

http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-23-9629

Regards
Tachyonomad

 

[Andy Resnick]

It can seem very abstract- let's start with this: do you understand what the 'mutual coherence function' is?

 

[Tachyonomad]

Hmm, so as I see it, the mutual coherence function is basically the average/correlation between two fields separated by a time (i.e. time of travel for some separation) t.
And it will be smaller for highly incoherent sources, but increase at very far ranges.

(Yeah, mainly wikipedia level, but just started readong about these topics, so still a newbie)

 

[Andy Resnick]

Close- the mutual coherence function (MCF) is the correlation between two fields whose sources are separated in space and time. From the MCF you can extract both spatial and temporal coherence., and the MCF can be thought of as a propagating field.

Considering just the spatial coherence between two independent sources- the sources can be quasi-monochromatic- the field (from both sources) at points far from the sources will exhibit correlations arising during the process of propagation.

There is a good analogy between the van Cittert-Zernike theorem and diffraction from an aperture (Huygens-Fresnel principle).

 

[sardar]

Hello Tachyonomad,

The Van Cittert Zernike theorem is a fundamental principle in the field of optics that describes the relationship between the spatial coherence of light and its intensity distribution. It states that the intensity distribution of an incoherent light source can be calculated by taking the spatial coherence of the source into account. This theorem is often used in the field of holography, where it helps to understand and predict the behavior of coherent light sources.

The paper you have linked discusses coherence holography, which is a technique for creating holograms using spatially incoherent light sources. This technique relies on the Van Cittert Zernike theorem to calculate the intensity distribution of the incoherent light source and use it to reconstruct the object's hologram.

In terms of the physics behind the theorem, it is based on the concept of coherence, which is a measure of the degree of correlation between two waves. In the case of light, coherence describes the relationship between the electric fields of different parts of the wave. The Van Cittert Zernike theorem takes into account the spatial coherence of the light source, which is affected by factors such as the size and shape of the source, as well as the distance between the source and the object being illuminated.

In terms of mathematics, the theorem involves calculating the mutual coherence function, which is a measure of the coherence between two points in space. This function can then be used to calculate the intensity distribution of the light source, which is essential for holography applications.

I hope this helps to provide some insight into the Van Cittert Zernike theorem and its role in coherence holography. It is a complex topic, but with further study and practice, I am confident you will gain a better understanding. Best of luck in your research!

Best regards,