# Methods of Calculating Relative Background Blur

Started Nov 28, 2012 | Discussions thread
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 An Easy Method of Mental Estimation of Relative Background Blur Ratios In reply to Detail Man, Sep 1, 2013

In the general case (non-constant-framing) the ratio of the relative background blurs is equal to:

B2 / B1 = ( HFD2 / HFD1 ) * ( DF1 / DF2 )

where:

B is Relative Background Blur (relative to linear image dimensions, such as the diagonal);

HFD is the Hyperfocal Distances (reported by most DOF calculator applications and sites);

DF is the Camera (front nodal-plane) to Background Distances.

Note: Interestingly, the individual Camera to Subject Distances (D) "drop out of the equation". If the Background Distances are the same, it just simplifies to the ratio of Hyperfocal Distances.

.

In the constant-framing case, things are even simpler (no HFD values required to proceeed):

B2 / B1 = ( L2 / L1 ) * ( D2 / D1 ) * ( F1 / F2 ) * ( DF1 / DF2 )

where:

B is Relative Background Blur (relative to linear image dimensions, such as the diagonal);

L is the Focal Lengths;

F is the F-Numbers;

D is the Camera (front nodal-planes) to Subject (plane-of-focus) Distances;

DF is the Camera (front nodal-plane) to Background Distances.

.

In summary, the ratio of the relative background blurs (for the constant-framing case) is:

(1) Directly proportional to ratio of change in Focal Length (L) and Camera to Subject Distance (D);

(2) Inversely proportional to ratio of change in F-Number (F) and Background Distance (DF)

... and is easy enough to do mentally (or to easily calulate using any simple calculator application).

The effects of individual camera system Image Magnifications and Pupillary Magnification factors very elegantly "drop out of the equations" along the way in the derivation of both identities above.

DM ...

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