# Jumping ships - DoF

Started Sep 29, 2012 | Discussions thread
 Like? 1
 Re: Background Blur is related to ratio of Distance / Hyperfocal Distance In reply to Detail Man, Oct 3, 2012

I am afraid I was not able to completely follow. Let me maybe briefly explain what I did.

Maybe to start with a first general comment. The article I was referring to, is actually my own article, which I published in the user generated article section. It was not written by dpreview. Therefore I can comment, on the validity of the formulas, as long as the underlying formulas from Wikipedia are correct and I did not do a mistake. The article I used as a reference is http://en.wikipedia.org/wiki/Depth_of_field

Please have a look at one of the drawings from that wikipedia article:

My intention was to understand the strength of background blur for typical portrait siutations, i.e. the quantitative strength within the resulting picture. I made the following assumption (using the variable names from the drawing):

• subject distance s > > focal lenght f

• background distance from subject xd > > subject distance from lens s

• subject distance s

So in practical terms (not strictly),

• f usually below hundreds of millimeters (e.g. 200mm)

• s one meter to a couple of meters

• H several 10th of meters

You can calculate the blur circle b by starting from the Far Distance formular,

and replace the circle of confusion c by the blur size b for the background at distance B in the drawing above (so don't use the far distance formula to determine the distance at which subject start to appear blurred, but rather extend it to the background). Solving for b and using all the assumptions above, you can simplify the formula a lot and see that the blur spot size is indepent of xd

b = f ^2 / ( N * s )

If you now replace the s by s = f * w1 / w2 (coming from the lens equation also using the assumptions that w2

b / w2 = f / ( N * w1 )

which describes the how big the blur disc is compared to the sensor size, which to me is a good definition of the strength of background blur that you will see in the resulting picture.

The Wikipedia article shows the same formula further down below

in ms is the magnification which is the ration of w2 / w1 .

That's all there is to the article I wrote. I tried to get rid of DoF descriptions that refer to distances as they are unituitive and do not really say how this will look like in the picture. I rather tried to explain the blur, in terms of what you see in the picture, i.e. blur disc size of the background in relation tothe overall picture size.

I hope that clarifies the assumptions

Detail Man wrote:

Interesting. Assigning the same variable-names that I have used in my previous posts on this thread, DPRreview's formula (for comparing the ratio of the resulting blur-diameters between two camera-systems for the same subject at the same camera-subject distance) reduces to:

B2 / B1 = ( L2 / L1 ) x ( F1 / F2 ) x ( H2 / H1 )

where:

B2/B1 is the ratio of the resulting blur-diameters;
L are the (actual) Focal Lengths;
F are the F-Numbers (referred to as the "apertures");
H are the Sensor-Heights (or widths, or diagonals).

When they state:

... note , ... above equation is only valid if the background is sufficiently distant from the subject ...

The requisite assumption is that "background" exists behind Far Focus Distance of DOF of focus. Of course, that implies that it would be necessary to calculate Far Focus Distance to determine validity
.

However, it would be numerically simpler to calculate the Hyperfocal Distances involved, which are:

HFD = ( CF ) x ( ( L )^(2) ) / ( ( F ) x ( 30 ) )

where:
CF is the Crop Factor

I am not sure how the Crop Factor comes into the picture. I thought when using the actual focal length CF should be in, or?

L is the actual focal-length in units of milliMeters;
F is the F-Number.

Full-frame Circle of Confusion of 0.030mm used in the above formula (8"x10" viewing size at 25cm). For larger viewing-sizes, scale COC downwards, and/or for farther viewing distances, scale upwards .

Wouldn't the CoC have to be different for different formats ... ah ok, you probably kept it the same because of CF ... I think I got it.

... and evaluate the validity of applying the formula given by DPReview by determining whether the Camera-Subject Distance of the background subject matter being considered is less than or equal to some designated fraction of the individual Hyperfocal Distances of the camera-systems.

Once such a determination of validity of application has been made, it is only necessary to compare the ratio of the Hyperfocal Distances of the camera-systems to be compared (DOFs unecessary).
.

The ratio of the Hyperfocal Distances of the camera-systems for the general case is:

DHF2 / DHF1 = ( ( L2 / L1 )^(2) ) x ( F1 / F2 ) x ( H1 / H2 )

Under conditions amounting to equal-framing (where L2 / L1 = H2 / H1 ), formula simplifies to:

DHF2 / DHF1 = ( L2 / L1 ) x ( F1 / F2 )

From the formula directly above one can see that in the case of an (equal-framing) "equivalent" configuration of the camera-systems (where L2 / F2 = L1 / F1 ), the ratio = 1.0 (no difference).
.

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