# Jumping ships - DoF

Started Sep 29, 2012 | Discussions thread
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 Re: Disk of Confusion diameter is related to ratio of Focal Length divided by F-Number In reply to CarstenKostrzewa, Oct 5, 2012

CarstenKostrzewa wrote:

Detail Man wrote:

Detail Man wrote:

Sf = ( L / F ) x ( ( Df / D ) - 1 )

The form of the identity for Sf in object-space (directly above) is equivalent to your identity above:

b = ((f * ms) / N ) * xd / (s + xd)

... except - the identity for Sf (in "object-space") is not scaled by a magnification-factor ("ms", above), as is your identity for b which appers to be referenced to "image-space".

The Background Distance divided by the Plane of Focus Distance ( Df / D ) remains constant, therefore ( ( Df / D ) - 1 ) remains constant. The diameter of the Disk of Confusion (in "object-space", and as referred back to "image-space") would change by the ratio of the Focal Length divided by the F-Number ( L / F ) - just as is the case in your (stated to be approximate) identity:

b = ((f * ms) / N )

If my thinking is correct, then I agree with your assessment, and it seems precise (not approximate) ...

... except, I think that it's necessary to scale the ratio of Focal length divided by F-Number as stated:

Sf = ( L / F ) x ( ( Df / D ) - 1 )

... and to then multiply the derived ("object-space") Disk of Confusion diameter by the Image Magnification (the ratio of Sensor Size divided by Object Size) in order to refer it back to the image-sensor (in "image-space") if you want to relate blur-diameter to the image-sensor frame dimension(s).

... which is you ask me is exactly formula I used, as b is in in image space and ms which is the Image Magnification.

Anyway ... thanks a lot for your thoughts.

Likewise ! It is a very rare occurance that anybody engages in the language of basic algebra on this forum whatsoever. It seems to be a tabooed (and/or lost, and/or never acquired) art.

I spent a good while last night pondering the exact meaning of "subject magnification" as used in the Wikipedia DOF web-page. The phrase "subject magnification" is often used to refer to a magnification which is affected by Focal Length (and the corresponding Angle of View).

The identities that we seem to agree upon the veracity of show this particular "magnification" as a separate multiplier of Focal Length - so it makes sense to me that Image Magnification (in that case) might have been a more accurate phrase to have used - as it seems that the phrase "subject magnification" imbues some degree of vagary as to what exactly is being described ...

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