Can conjugate images be used in place of dark field filters?

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Discussion Overview

The discussion revolves around the potential substitution of dark field filters with a different configuration involving conjugate images. Participants explore the implications of using a completely black filter with a light-passing hole versus traditional dark field filters, focusing on the theoretical aspects of Fourier transforms and imaging techniques.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes the idea of using a black filter with a light-passing hole as an alternative to a dark field filter, questioning if this would yield similar effects.
  • Another participant argues that a small hole cannot replace an annulus in dark field imaging, as they serve different functions regarding spatial frequencies and DC components.
  • A later reply seeks clarification on whether the two filters are Fourier transforms of each other and questions the deeper significance of the term "conjugate images."
  • One participant suggests a connection to phase contrast imaging, indicating that this might clarify the original question regarding filter configurations.
  • There is mention of a pattern recognition technique involving matched filters, although specific details are not provided.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of substituting dark field filters with alternative configurations, indicating that the discussion remains unresolved regarding the equivalence of the proposed filters and their theoretical implications.

Contextual Notes

The discussion includes assumptions about the roles of spatial frequencies and DC components in imaging, as well as the definitions of conjugate images and their relationship to Fourier transforms, which are not fully explored or resolved.

Ruddiger28
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I was working on some dark field filters and I was wondering if you could substitute the black spot in the centre of a dark field filter for a completely black filter with a light passing hole in the middle. Sort of an inverted dark field filter.
I seem to remember reading something like this involving conjugate images when I was doing Fourier theory a while ago.
Would the filters have the same effect? Or are conjugate images Fourier transforms of each other?
 
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In a darkfield imaging setup, you cannot substitute a small hole for an annulus; the annulus passes high spatial frequencies while the hole passes the DC component. Offsetting the hole to the radius of the annulus can be acceptable, however (google: synthetic aperture radar).
 
Thank you for replying, I was afraid that was the case. So on the conjugate images point, are the two filters in this case Fourier transforms of each other? Why are they called conjugate images? Is the link between the two simply that they appear as inverted forms of each other or is there something deeper?
 

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