Soft Focus Photography ~ Calculating Blur Radius

Using the blur radius calculations and test setup from 1906 in Biblioteque de la Revue de Photographie by L. de Pullignyt - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique" I would like to begin to apply a bit of objectivity and rigor to Soft Focus lens evaluations.  Recognizing, of course, that this is _not_ the only evaluation important in understanding how old lenses worked.  If done correctly, an objectif/measurable outcome would be excellent for better understanding what would, hopefully, be adaptable using more modern miniature format optics.

Goal ~

To see if it is possible to mimic old brass lens blur/softness using optics designed for miniature formats. 

Methods ~

Selecting Whole Plate 6.5inch by 8.5inch print size as the target viewing framework...  

• Calculate the blur radius of two meniscus "portrait" heavy crown lenses
• Using a sharp white to black line, measure the blur radius of more recently designed lenses in various configurations using...
• Unit focusing lenses
• First element focusing lenses at various first element separation distances
• Several varieties of soft focus filters 

Calculation -

Pulligny/Puyo calculate the radius of blur as -

    ( Focal Length / Aperture ) / 100

The formula is very simple, but is based on several other formulas that aren't quite so simple.  Reading "Objectifs d'Artiste Practique et Theorie..." is helpful to understand what's going on.

Selecting 300mm f/5 and 450mm f/6 as the old brass lens soft focus lens reference focal lengths, we see that...

• 300mm f/5 blur radius = 0.6mm
• 450mm f/6 blur radius = 0.75mm

To measure the sample lenses in the digital domain, it is helpful to convert the mm measurement of these old lenses to pixels.  In this case I've chosen a 24mpixel sensor and its 4,000pixel narrow dimension.

Number of pixels per mm is calculated as -
    ( Pixel Width of Digital Sensor ) / ( Whole Plate Width inches x 25.4 mm/inch )

Therefore, the reference lens blur radius is calculated as -

    (( Pixel Width of Digital Sensor ) / ( Whole Plate Width x 25.4 mm/inch )) x (( Focal Length / Aperture ) / 100 )

Reference lenses -

• 300mm f/5 blur radius in pixels = 14pixels = 4000 / ((6.5inches x 25.4mm/inch) x (300mm / f5 ) / 100 ))
• 450mm f/6 blur radius in pixels = 18pixels = 4000 / ((6.5inches x 25.4mm/inch) x (450mm / f6 ) / 100 ))

Recap of the calculations - 

- Blur radii in millimeters
    - 450mm f/6 = 0.75mm
    - 300mm f/5 = 0.6mm

- Blur radii converted to 24mpixel sensor pixels in whole frame size
    - 450mm f/6 = 18 pixels
    - 300mm f/5 = 14 pixels

Measuring blur radius of more recent optics ~ Test Setup

Using a simple, empirical approach...

• Place a white sheet of paper on a black background 
• Photograph it an import it into, in this case, the Gimp
• Enlarge to 200percent
• Viewing the center of the image
• Using the measurement tool
• Note the radius of blur from pure white to black

Repeat for as many lens setups/configurations/etc as there are on hand. 

 

Results ~

Comment ~ 

This sets an interesting foundation for understanding how lenses behave.  However, this is not all.  If I carefully study prints/images made with old lenses it's easy to note that the transition from light to dark in blur is not always/often equal between lenses.  

To develop a more complete understanding of what's going on with soft focus lenses I will address blur transition in the next post.  Further, recognizing that I'm moving very quickly on this topic and not explaining things in my haste to get to the bottom of all this, I will address the "why" of my choice of lenses and filters in an analysis that will come after looking at blur falloff.