Soft Focus Photography ~ Visualizing Blur Radius vs Blur Dropoff Measurements

I realize that a lot of what I've written about Soft Focus lenses and filters is diagnostic and perhaps difficult to grasp.  So I went back and measured the rate of falloff and plotted it against blur radius to see if I can't illustrate better what I'm finding.

How to read the graph ~

X axis = Blur Radius - as a percentage of the width of an image

Y axis = Blur Falloff = Luminance Value Measured 1/2 way between leading and trailing edges of blur with potential values of 0 to 255

The smaller the Blur Radius (X axis) the sharper an image will be.  The higher the Blur Radius, the softer an image will be.

The higher the Blur Falloff value (Y axis) the "thicker" blur will look.  The lower the Blur Falloff value the sharper the underlying image will be with a more subtle overlaying veil of softness.

I've included two regions in yellow.  These illustrate the approximate ranges of "softness" achieved by early 1800's/1900's Soft Focus lenses for large format plate and film.

How I came up with these ranges is important.  First, I calculated the blur radius of chromatic aberration of several lenses using the formula found in Biblioteque de la Revue de Photographie -  L. de Pulligny - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique".  

Then I inspected and measure the blur radius of early Pictorialist images.  I found that the Dallmeyer Bergheim Models 1 and 3 are, indeed, quite soft.  Other lenses, such as Pinkham Smith, Darlot, Wollensak, etc appear to return half the blur radius of the earlier Dallmeyer-Bergheim, so I broke my ranges of softness of lenses into two.

Old Soft Focus lenses would vary their levels of softness using focal length, aperture, and/or marginal light controls (such as those found on Heinrich Kuhn's Tiffenbuilder/Imagon and Mamiya RB 150mm SF).  So exact Blur Radius is variable.  Additionally, without being able to inspect old lenses directly, I'm unable to measure Blur Falloff.  Hence the use of these rather vague approximations.  

However, I surmise that the amount of blur seen in early prints was pleasing to practitioners and therefore useful to measure and understand as a target for adapting miniature format lenses and filters in the present time.

I keep in mind, in addition to all the above, that this look at image softness fails to include flare, astigmatism, coma, emulsion and print technologies and techniques.  In this way, adapting miniature format lenses and filters to the Pictorialist Task may, at best, be an approximation of the original style and, really, can only be a First Step.  It's my hope that considering Blur Radius and Blur Falloff may yet prove to have been a useful starting point. 

Here's what a graph looks like.  In future blog posts I will present what I've measured for specific lens, first element separation (where applicable), and Soft Focus filters.