How does blur circle size change with defocus in macro photography?
Asked 7/8/2018
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In macro photography, is there a known relationship between a point’s distance from the focus plane and the size of its blur circle on the sensor? I’m looking for the blur radius/diameter for a point source versus physical distance from the focused subject distance, ideally in image pixels, assuming a circular aperture. I know the usual circle-of-confusion formula from thin-lens optics, but I’m specifically asking whether it still applies at macro distances or whether a different model is needed for real lenses.
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
8y ago
2 Answers
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I've just been researching this topic myself so here's a late answer to your question.
The equation you provide doesn't only apply to thin lens, it also applies to ideal thick lens with no abberations. It even applies to macro photography, assuming you have symmetric lens (pupil magnification = 1). Unfortunately, you probably don't.
This false assumption is completely negligible for non-macro photography, but the error becomes significant as magnification grows.
In case you have information on your lens' principal (or nodal) points and pupil magnification (or positions), you can use this formula for more accurate results:
- f is focal distance
- p is pupil magnification
- u is the position of the focused point (measured from the front principal (or nodal) point of the thick lens)
- u_d is the position of the defocused point
- m is magnification at focused point: f / (u - f)
- N is f-number at infinity focus
- k is the diameter of the blur spot in the image plane
This is from page 23 of Depth of Field in Depth by Jeff Conrad, referenced by the related Wikipedia page.
As you can see, the relationship is not exactly linear, but my mathematical analysis skills are not that great so I can't really tell you more about its behaviour.
Originally by user76583. Source · Licensed CC BY-SA 4.0
user76583
8y ago
0
Generated from our catalog & community — verify before relying on it.
Yes. In macro work, blur circle size is still determined by geometric defocus, so the usual thin-lens-style circle-of-confusion relationship remains a good starting point. It is not uniquely a thin-lens result; it also applies to an ideal thick lens without aberrations.
What changes at macro distances is that real lenses may no longer behave like the simplified model, especially if the lens is not symmetric. As magnification increases, pupil magnification and the locations of the principal/nodal points can matter, so the simple formula becomes less accurate.
So the practical answer is:
- For an ideal or symmetric macro lens, use the standard defocus/blur-circle formula.
- For higher accuracy with a real macro lens, use a thick-lens model that includes principal points and pupil magnification.
The blur circle is zero at the plane of focus and increases as you move away from it. Over small defocus ranges it behaves smoothly and approximately linearly with defocus at the image plane, but the exact mapping from subject-space distance to sensor blur depends on magnification and lens geometry.
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