Van Cittert Zernike Theorem and associated Optical phenomenon

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Discussion Overview

The discussion revolves around the Van Cittert-Zernike theorem and its implications in coherence holography. Participants explore the underlying physics and mathematics of the theorem, particularly focusing on the mutual coherence function and its role in understanding coherence phenomena.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks clarification on the Van Cittert-Zernike theorem in relation to coherence holography and requests mathematical pointers.
  • Another participant introduces the concept of the mutual coherence function (MCF) and questions the understanding of it among the group.
  • A participant describes the MCF as the correlation between two fields separated by time and space, noting its behavior with incoherent sources.
  • Further clarification is provided that the MCF can be viewed as a propagating field and is essential for extracting both spatial and temporal coherence.
  • There is an analogy drawn between the Van Cittert-Zernike theorem and diffraction from an aperture, referencing the Huygens-Fresnel principle.

Areas of Agreement / Disagreement

The discussion reflects a mix of understanding and uncertainty regarding the mutual coherence function and its implications, with no clear consensus on the interpretations or applications of the Van Cittert-Zernike theorem.

Contextual Notes

Participants express varying levels of familiarity with the concepts, indicating a range of assumptions about prior knowledge and the complexity of the mathematical underpinnings involved.

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