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Jbryant611-Visitor
1-Visitor
May 6, 2010
Question

Convolution Problem

  • May 6, 2010
  • 2 replies
  • 7883 views
Hi, can anyone point out any obvious mistakes with my convolution - it apppears to create a convolved object smaller than the original object itself which can't be right.

2 replies

I
IRstuff1-Visitor
1-Visitor
May 6, 2010
On 5/6/2010 8:25:28 AM, Jbryant61 wrote:
>Hi, can anyone point out any
>obvious mistakes with my
>convolution - it apppears to
>create a convolved object
>smaller than the original
>object itself which can't be
>right.

I think you're not considering "width" correctly. The usual definitions, FWHM, 1/e, 1/e2, etc, would show that your resultant is larger than the original.

However, that specifically does not mean that input curve will be smaller at EVERY point. Just consider the RECT function you applied to the pixel; it's definitely not smaller at the top, compared to the resultant.

TTFN,
Eden
J
Jbryant611-VisitorAuthor
1-Visitor
May 7, 2010
Where I perform the convolution, for the bead and pixel function, should I normalise these to unity (I haven't done yet, only have done it for the graphic at the top). I think ther eis no need to normalise the psf, as this can have an influence of less than unity.

Thanks
Jason
P
PhilipOakley1-Visitor
1-Visitor
May 7, 2010
rescaling doesn't really affect the result.

Rather it is the perception of the result that causes the issue. This is partly a optical illusion effects (for the greyscale image of the spot) and partly a misunderstanding of what the effect should be (which affects how we see the graph.

To take an analogy, the effect of the psf is not to pile dirt against the side of the kerb(solid step), rather, it needs to erode the top of the curb so as to create the dirt that it can then pile up at the bottom.

The problem comes when we have the classic explanation of the point source. for the point source there is no edge to erode back, merely a narrow tall spire with the top eroded away. we never really see the height of the original spire.

For example, think of starting with a butte that is 1000m high that is then eroded to dust; see Black Butte or Signal Butte in http://en.wikipedia.org/wiki/Butte rather than thinking Merrick's Butte. In these case we "think" that the psf has widened the original spike. However if we apply that to an edge....

Philip Oakley
P
PhilipOakley1-Visitor
1-Visitor
May 6, 2010
Isn't it a visualisation artefact due to the normalisation when being displayed.

That is, the graph shows that the psf has spread the bead shape (the slopes are shallower), which is to be expected.

When they are viewed as grey scale then the auto adjust of brightness makes the eye percieve just the central part of the top.

It hasn't narrowed the top, rather it has shaved away the corners leaving less top.

Try with a larger bead to see if this is the effect?

Philip Oakley
J
Jbryant611-VisitorAuthor
1-Visitor
May 6, 2010
I see it even on the centroid line scan towards the end.


Thanks
Jason
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