Blur Radius vs Blur Falloff ~ Nikon Nikkor 85mm f/2 Ai

The following is on the heals of looking at another very well corrected, very sharp lens, the ISCO Westromat 50mm f/1.9.  My sweet little Nikon Nikkor 85mm f/2 is a unit focusing ernostar 5 element, 5 group formula lens and is the subject of today's investigation.

Reading the Minolta Portrayer filter instruction manual led me to understand that longer lenses (85mm to 135mm) could respond better to certain kinds of filtration. 

Here's how to read the following graph. 

 

Comments ~

There are several lens/filter combinations that fall into the old brass soft focus lens blur ranges.  This is rather exciting to see and it makes me wonder if soft focus filter designers knew/know more about their craft than I've in the past given them credit for?

One aspect of using a well-corrected lens for soft focus work is that the edges of the field may behave differently than they did in early optics.  

However, as is carefully noted in many journals and writings of the day, including  Biblioteque de la Revue de Photographie -  L. de Pulligny - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique" - Biblioteque national de France (BnF), longer lenses were often the focal lengths of choice to very specifically avoid field edge aberrations at wide apertures (ie: portraiture).

In fact, the only photographer I know of who has succeeded, to my way of thinking, of leveraging field edge problems to outstanding effect is Alex Timmons.  Which means the Nikkor 85mm may be just perfect when used with soft focus filters in the more traditional way.  The time has come for me to validate this in the "real" world.

Blur Radius vs Blur Falloff ~ ISCO Westromat 50mm f/1.9

The ISCO Westromat 50mm f/1.9 is a unit focusing plasmat 6 element, 4 group formula lens. 

I've been looking at adapting certain kinds of somewhat difficult to find lenses to miniature format for soft focus work in using the first and second element separation control of the focusing ring to manage softness level.  However, I also have quite a stack of unit focusing normal 35mm SLR style lenses, and the brilliant little ISCO Westromat is one of them.  

While I am "on a roll" what better time to check two things about unit focusers with regards to potential soft focus work.  First, look at the bare lens wide open (I expect it to be sharp - it takes a lot to design a "bad" lens).  Second, look at what the effect of the filters might be on a very well corrected, sharp, not-at-all-bad lens.

Here's how to read the following graph. 

 

Comments ~

Only the Westromat/Nikon Nikkor Soft 1 combination falls within one of the two old soft focus lens zones.  All other combinations give varying blur radii outside of the old brass lens softness.

Looking at the Blur Falloff tells me that this will give a "fat" blur rendition (40% to 50% luminance measured half way between the leading and trailing edges of blur), even as the Blur Radii measured small compared with first element focusing lenses.  Wherefore I expect this lens used with Soft Focus Filters to deliver a different from Pictorialist softness "look." 

I'll have to spend some time with the ISCO Westromat to see how it behaves in the "real world." It may be just another excellent, sharp, boring 'ol 50mm plasmat that is indistinguishable from fully modern AF.  If that turns out to be the case, there'd be nothing wrong with that, right?

Blur Radius vs Blur Falloff ~ ISCO Iscotar 50mm f/2.8

The ISCO Iscotar 50mm f/2.8 is a Cooke formula, first element focusing, triplet lens.  I'm adapting these kinds of lenses to miniature format for soft focus work by using the first and second element separation control of the focusing ring to manage softness level.  Mated to a helicoid and setting the softness level on the focusing ring, the helicoid is used to effectuate the focus itself.

To show how first and second element separation effects softness level, I graphed Blur Radius against Blur Falloff.  Further, to control highlight "softness", I added a number of different Soft Focus filters to the investigation see to what degree they do their job. 

Here's how to read the following graphs. 

 

Comments ~

These illustrate how the focus ring on the ISCO 50mm can effect the level of softness in an image.  And we can see how Soft Focus filters add softness over the base optics.

Cooke triplets are bog simple, but very well corrected lenses.  I wondered if the German 35mm SLR triplets were derived from the same detailed design specifications, but they are not.  The ISCO is contrasty where the Steinheil is lower contrast but sharper.  

There are other German Cooke triplets, but they are unit focusers and it might be difficult to adapt them to soft focus work.  At this point I'm unable to find any Japanese Cooke triplets.  The closest I can find in first element focusers are tessar formula lenses (such as the Cosina 55mm f/2.8).  If someone knows of a cheap Japanese triplet first element focuser let me know, please.

Blur Radius vs Blur Falloff ~ Cosina Cosinon 55mm f/2.8

The Cosina Cosinon 55mm f/2.8 is a tessar formula, first element focusing lens.  I'm trying to adapt is to miniature format soft focus work by using the first and second element separation control of the focusing ring to manage softness level.  Mated to a helicoid and setting the softness level on the focusing ring, the helicoid is used to effectuate the focus itself.

To show how first and second element separation effects softness level, I graphed Blur Radius against Blur Falloff.  Further, to control highlight "softness", I added a number of different Soft Focus filters to the investigation see to what degree they do their job. 

Here's how to read the following graphs. 

Comments ~

It should be easy to see how the focus ring on the Cosina 55mm can effect the level of softness in an image.  And it should be easy to see how Soft Focus filters add softness over the base optics.

While not shown here, but illustrated earlier, the Cosina tessar formula lens is better corrected for closer focused subjects when the lens is shot wide open.  Stopped down, infinity cleans up nicely. 

I believe this proves the concept of using first element focusing lenses on miniature formats in Soft Focus work.

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. 

 

Soft Focus Photography ~ Then vs Now ~ Materials and Process Comparison

Working in miniature formats, specifically 35mm digital Full Frame and APS-C, I've been trying to understand, then look for a way of matching the Expressionist/Pictorialist as a starting point for art that uses photography.  My choice of lenses as a starting point is because it seemed obvious to me.  However, there are other starting points that might be useful as well.  

 

Sony A7, Ricoh 50mm f/2.8, Zeiss Softar 1 

The following is one way to consider and compare image making materials and processes for Expressionist/Pictorialist, and their adaptation to miniature digital work.  Keeping in mind these are very broad generalizations and that there are a great many details that I'm now glossing over.

Original Expressionist/Pictorialist materials ~

Large format cameras - typically 6.5inch x 8.5inch Whole Plate, sometimes larger formats used for landscape work

Lenses - The base glass types were heavy crown and flint.  They had certain properties that were well understood at the time where designers had to work within the limits of the materials.  Two types of lenses were commonly designed.  One type was as well corrected for sharpness across the field as the technologies of the time would allow.  Classic Sharp Photographers as well as Expressionist/Pictorialists used this kind of optic.  The other lens type was designed for a specific soft focus "look" which took advantage of specific optical imperfections.  A lot of attention is paid to just this one area of Expressionist/Pictorialist images (including by me with all the little things that I've written over the years and somehow insist on continuing here).

Light Sensitive Plates - Wet Plate Collodion, then dry plate isochromatic moving into orthochromatic were the only options.  These "saw" UV/blue light only for the earliest emulsions, and started to "see" into green light with orthochromatic emulsions later.

Original Expressionist/Pictorialist processes ~

Image Taking - Lenses of any type projected the whole spectrum of light onto a focusing ground glass, with emphasis on the yellow portion.  There was a problem, however, in that lenses were under-corrected for chromatic and spherical aberrations.  What the eye "saw" on the ground glass was not what the light sensitive emulsion "saw" as the point of focus.  The phenomenon is called "chemical focus" and much was written on this very specific topic to help photographers of any kind correct for the point of focus offset between what the photographer saw and what the lens/emulsion delivered.

Image Making - Classic Photographers let the materials dictate the outcome and they did little to nothing to intervene after composition/lighting/exposure on the way to making a print.  These were the "sharp" image makers.

Expressionist/Pictorialist Photographers started where the Classic Photographer left off.

After processing a negative, paper internegatives could be used to (literally) draw on.  Background scene creation, retouching, dodging/burning, multiple image overlays were the things artists used on their way towards making a final print.

The materials for the final image could minimally be platinum/palladium, carbon tissue, gum bichromate, or bromoil.

How much character of a lens that made it into a final print depended on how much rework had been done and how much texture was added.  Anything was possible, from a nearly "straight" print where a lens' full character might come through, all the way to bromoil where an image is brushed on photo print paper where a lens' character might be completely lost.  In this way, lenses might have been used for making sketches over which an artist might impose their art. 

This is where the idea of "lenses that draw" comes from. 

Digital Expressionist/Pictorialist materials ~

Cameras and Sensors - To take advantage of certain lenses it is best to have a camera with interchangeable lenses. Sensors typically cut off UV and IR.  It's the UV that could be useful if the goal is to precisely match isochromatic or orthochromatic emulsions from the 1800s.  For this a user can use a "full spectrum" sensor coupled with specific filters that allow UV and blue wet plate spectrum, or UV, blue and green as in the case of orthochromatic emulsion light sensitivities.

Lenses - Modern lenses are very well corrected for just about any optical defect, due, in part, to the need to "hold onto sharpness" when an image is enlarged.  

To implement this narrow area of Expressionist/Pictorialist image expression it can be helpful to seek out specific lenses and, possibly, certain soft focus filter types.

• Find lenses used perhaps with filters that give between 0.35% and 0.60% blur radii as calculated on the narrow target image dimension.  Solutions include, but are no means limited to - 
• First element focusing lenses 
• Ricoh 50mm f/2.8 m42 tessar design
• Cosina Cosinon/Reveunon/etc 50mm f/2.8 tessar design 
• ISCO Iscotar/Iscovitar 50mm f/2.8 m42 Cooke triplet design
• Steinheil Auto-Cassaron 50mm f/2.8 m42 Cooke triplet design 
• Ricoh 55mm f/2.2 Pentax K four element four group design 
• Soft Focus filters - potentially used with the above listed lenses
• Duto concentric circle
• Heliopan Duto concentric circle 
• Zeiss Softar 1
• Hoya/Kenko/Hama Softener "A" 
• NOTE:  I use blur percentage here as it frees up considerations for image print/viewing size and camera format.  The calculation is simple.  
  Percent Blur Radius = ( Measured Blur Radius / Width of Image ) x 100 - where units for radius and image are equal (ie: millimeters or pixels or inches)
  NOTE 2: First element focusers show the most blur when shot wide open.  Sometimes good blur can be had one stop down, but it depends on the lens, so it's worth checking and measuring before proceeding.
  NOTE 3: Duto and micro-lens filters can show their diffusion patterns when a lens is stopped too far down.  So these are best used with the lens shot wide open, which fits nicely with NOTE 2.
  NOTE 4: Frosted soft focus filter types tend to blur beyond the 0.35% to 0.60% target radii.  So I'm learning to avoid them.  Similarly number 2 Softar and Softener B filters.
  NOTE 5: SLR lenses that give user control over element separation may be worth examining.  The Minolta Varisoft 85mm is well known, but the Sigma YS and XQ series with macro rings might be worth a visit to measure blur radii. 
•  Expressionst/Pictorialist landscape photography typically deployed focal lengths where the edges of the field were well corrected with as minimal optical distortion (coma, astimatism, spherical aberration) as possible, while still achieving a certain level of softness (in French terms, chromatic aberration, though in modern optical implementations can be controllable spherical aberration with a touch of chromatic aberration - depending upon the lens deployed).  Potential optical solutions include, but are certainly not limited to -
• First element focusing lenses 
• Ricoh 50mm f/2.8 m42 tessar design
• Cosina Cosinon/Reveunon/etc 50mm f/2.8 tessar design  
• Ricoh 55mm f/2.2 Pentax K four element four group design 
• Soft Focus filters - potentially used with the above listed lenses
• Zeiss Softar 1
• Hoya/Kenko/Hama Softener "A" 
• Expressionst/Pictorialist portrait and still life photography typically deployed lenses of sufficient speed to keep exposures to a minimum, and accepted optical defects towards the edges of the field as a compromise, and what they found back in the day to be pleasing.  For current day practitioners it can be a real task to find lenses that exhibit these kinds of imperfections near the edges of the field.  Here are potential, but by no means the only, solutions -
• First element focusing lenses 
• ISCO Iscotar/Iscovitar 50mm f/2.8 m42 Cooke triplet design
• Steinheil Auto-Cassaron 50mm f/2.8 m42 Cooke triplet design 
• Soft Focus filters - potentially used with the above listed lenses
• Hoya/Kenko/Hama Duto concentric circle
• Heliopan Duto concentric circle 

Adapting First Element Focusing Lenses - When adapted to a helicoid focusing device, first element focusing lenses can vary blur radii based on focusing ring position.  Set the lens' focusing ring to the desired position that defines a blur radius of interest, then use a helicoid adapter between the lens and digital mirrorless camera to effectuate the actual focus.  This is why I've found it useful/important to measure blur radii for each lens.  Radii vary be implementation.  Some lenses are better corrected at infinity than close up.  Some are better corrected close up.

Japanese SLR Soft Focus Lenses - Special purpose Soft Focus lenses for 35mm and 120 tend to deliver blur radii well beyond the 0.35% to 0.60% blur radii of early soft focus lenses. However, aperture can help tame blur, so it's worth testing and measuring.

I once owned a Pentax 85mm f/2.2 SF that I could never come to grips with and nearly gave it away out of frustration.  This is not to mean they are unworkable.  Certainly photographers more talented than I have made them work the treat.  It's just that they're not workable for me, and certainly in the narrow environment I'm exploring here. 

However, the Last Great Pictorialist has hinted that a Minolta Varisoft 85mm can be pressed into proper service.  The secret I'm told is to set the softness ring between "0" and "1".  Anything more than that becomes too "soft."

Digital Expressionist/Pictorialist processes ~

Digital image processing software, particularly those adapted to graphics use (the Gimp, Photoshop, etc) provide a nearly limitless landscape of possibilities.  There's not much more to be said.  The only thing I can think is just how much early practitioners might have appreciated what we have today to work with.

Comments ~

There is no magic in choosing blur radii of 0.35% to 0.60%.  It is simply the balance point between sharp and soft that practitioners of the era seemed to appreciate the most.

Not all Expressionist/Pictorialist work is soft focus.  There is beauty to be found in sharp images and I'm of the increasing opinion that this is related to the tonal relationships, which are easy to mimic in digital work. 

----------- Essential Reading --------------

Dr. Russell Young's thesis paper on soft focus photography

Biblioteque de la Revue de Photographie -  L. de Pulligny - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique" - Biblioteque national de France (BnF) (in French)

Robert Demachy. Impressions de Normandie (photographies du Calvados, 1880-1920) [2016] - Julien Faure-Conorton (this paper and M. Faure-Conorton's other works are very insightful and worth the time to read through - particularly his thesis paper)

----------- Notable Practitioners of Art through Photography ------------

Robert Demachy

Celine Leguarde

Hugo Henneberg 

Hans Watzek

----------- On Soft Filters -------------- 

Soft Filters in Cinematography 

M. David Mullen, ASC

M. David Mullen, ASC on cinema and photography 

Soft filtration options 

A question of diffusion  

----------- Additional Resources ------------

An illustrated guide to early soft focus lenses

Are you a softie?

Frederick H. Evans was actually a soft focus photographer 

History of Dallmeyer optics (on the Dallmeyer 3b in use)

Neo-Pictorialism by Guy Tal 

Objectifs de flou artistique (in French) 

Portraiture - Franz Xaver Setzer

Portraiture - Leonard Misonne 

When did Photography of Soft? 

Wollensak Velostigmat Series II as a first element focuser Expressionist/Pictorialist optic 

Tessar design - with scatter plots that show chromatic aberration distributions 

 

Soft Focus Photography ~ Comments

Can we, in the present day, appreciate just how much opticians, photographers (some, probably not all), as well as former artillery and naval officers knew when they designed lenses, classic and soft, in the early days of photography (1800's)?

  

Sony A7
Cosina Cosinon 55mm f/2.8
Nikon Nikkor Soft 1 

The soft effect is too strong compared
with early Expressionist/Pictorialist work 

 

The field of lens development for photography was not based on feelings nor emotions nor misunderstandings.  No.  Not at all.  Instead, early designers were able to apply knowledge of material science and math in a way that produced informed, repeatable, accurate solutions.  They did this including as it was applied to soft focus photography.

Remember that Herren Petzval und Voigtlander hired naval officers to calculate lens element shapes from the very beginning.  Herr Steinheil's optical designs were all based on calculations he'd made.  Monsieurs Pulligny et Puyo calculated the chromatic aberration diffusion disk at the point of focus which ultimately led to the les objectifs d'Ariste et le Hermagis Eidoscope.  And these guys were not at all unique.  

Anyone who ground lenses knew the math and the limitations and opportunities afforded by the materials at hand.  Knowledge diffused through the community such that people like Herr Kuhn and Mr. Taylor of Cooke Triplet fame all knew what each-other were doing and why.  Letters sent between opticians and interested parties as well as photography club proceedings, lectures, and articles show this was very much the case.

It came as little surprise to me when I recently stumbled across a calculation for optical "softness." The formula came after a long exploration of Expressionist/Pictorialist photography  possibilities through the use of lens imperfections.  "Softness" designed with purpose.

On Spherical Aberration ~

The primary optical "softening" agent that I've been familiar with is spherical aberration.  It came as a surprise to read where the French did not like to use this optical fault. 

Biblioteque de la Revue de Photographie by L. de Pulligny - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique", page 20

[Aberration spherique] résulte un épaississement cotonneux du trait qui n’est pas agréable, et on ne peut admettre cette aberration que pour une très petite part à 1 oeuvre de simplification que nous poursuivons. En diaphragmant suffisamment, on peut atténuer a volonté l'aberration sphérique et en laisser juste assez pour qu’elle soit utile dans certains cas où cette réduction du diaphragme est admissible : par exemple, dans
la photographie du paysage...

In English... 

[Spherical aberration] results in an unpleasant, cottony thickening of the lines; in the simplification process we are pursuing, we can tolerate this aberration only to a very limited extent. By stopping down sufficiently, one can attenuate spherical aberration at will, retaining just enough to be useful in certain cases where such a reduction in aperture is acceptable—for example, in landscape photography. 

So, scratch spherical aberration off the list as being largely uncontrollable as far as the French were concerned.  There is a "however" to this that I'll talk about later, perhaps in a separate post since the topic is rather interesting, but will require more than a few words to work through.  

On other optical aberrations ~

Of the other optical imperfections, field curvature (sharpness variation across a flat field), coma (insect shaped highlights off-axis), and field distortion (pincushion, barrel) are mostly of little use in soft focus photography.  Only field curvature can be of some interest and then only in portraiture where we might accept increased image diffusion toward the edges of a scene.

On Chromatic Aberration as the preferred optical "softening" agent ~

From Biblioteque de la Revue de Photographie by L. de Pulligny - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique", page 29

Simplification des surfaces sans altération du trait, ce que nous cherchions, l’aberration chromatique tend à nous le donner. C’est donc un agent utile ; c’est, de plus, un agent docile, puisque nous possédons deux moyens simples et surs de régler l’énergie de son action.

In English...

Chromatic aberration tends to provide exactly what we were seeking: a simplification of surfaces without altering the outlines. It is therefore a useful agent; moreover, it is a controllable one, since we possess two simple, reliable ways to regulate the intensity of its effect. 

The authors then state that the use of Chromatic Aberration as an optical "softening" agent can help render a photograph in the sfumato style of many Jean-Jacques Henner paintings.  This is the painting technique first used by Leonard da Vinci and the effect can be stunningly gorgeous.  Just recently I was explaining to someone how I felt how Expressionist/Pictorialist soft focus images in photography can be as sfumato is to painting.  Of course I am very pleased to read that the French beat me to this observation by 120+ years!

Miniature Format Lens Selection -

I am interested in applying this as best I can to current materials and processes since I no longer have access to a darkroom, film, nor large format camera/lens gear.  I wanted to see if I can somehow duplicate the old Expressionist/Pictorialist soft focus "look" to digital 35mm/Full Frame/APS-C formats. 

The first step was to look at lenses.  I'd noticed that Wollensak's Velostigmat Series II is an old Tessar formula lens that came with a special feature.  It allows for the unscrewing/extending of the first element to introduce and control the level of "softness" in a photograph.  This was an important clue as to how I could proceed.  If moving the first element of an old lens design did as claimed, then something similar for miniature formats might duplicate the "look."

There are several Cooke Triplet and Zeiss Tessar design lenses that use this focusing technique.  To bend first element focusers to the Expressionist/Pictorialist task, the idea is to repurpose the traditional focusing ring to manage "softness." Then, use a separate focusing helicoid to do the actual focusing.  

The idea works on 35mm/Full Frame/APS-C digital formats just as anticipated (see: this chart from a prior post on this site). 

On Soft Focus Filters - 

Relatedly, I spent this summer trying to come to grips with the only soft focus filters I had at the time, which were one each Nikon Nikkor Soft 1 and 2.  I used these on both fully corrected lenses as well as a couple first element focuser "softies."  

It was a fruitful exercise in learning to view images small. But for viewing at Whole Plate size (on a 10inch tablet, for instance) the images nearly always "fell apart" and appeared to be too soft compared with Expressionist/Pictorlialist works.

What I wanted was a way to gently soften the highlights (to make them "glow") while expanding the blur radius in a way that adhered to the old brass lens Chromatic Aberration French formula. 

In a stroke of excellent timing, the Last Great Pictorialist Master pointed friends to the writings and comments of Dave Mullen ASC.  A buying spree ensued and the following are my thoughts on filtered introduction of blur and their radii.

• Nikon Nikkor Soft 1 - Frosted glass diffusion.  Blur at all apertures with no additional artifacts when stopped down.  However, very strong diffusion with blur radii well beyond (2x - 4x) the old heavy crown meniscus Whole Plate optics.
• Zeiss Softar 1 - Micro-lens of variable shape/dimension diffusion pattern.  Usable only at wider apertures without showing the "softener" pattern.  Strong diffusion with blur radii beyond (1.5x depending on the lens) the old heavy crown meniscus Whole Plate optics.
• Minolta Portrayer 1, 2, 3 -  Flat micro-shapes of variable color/dimension diffusion pattern.  Interesting filters, these.  Need to verify, but I'm thinking the Hoya/Kenko/Hama Softener "A" series may be of similar design. The Minolta filters don't add much blur around the edges, but they do soften broad areas of similar luminosities.  If there is a filter that most closely matches sfumato in painting on top of any optical imperfections introduced by a base lens, it would be these.
• Heliopan Duto - Usable only at wider apertures or on longer lenses (85mm - 135mm according to the marketing lit) without showing the "softener" concentric ring pattern.  Beautiful blur is possible in the center of the field, with gently increasing "softness" toward the edges.
• Hoya/Kenko Duto - Usable only at wider apertures or on longer lenses (85mm - 135mm according to the marketing lit) without showing the "softener" concentric ring pattern.  Beautiful blur is possible in the center of the field, with gently increasing "softness" toward the edges.  The "softening" effect is not as strong as the Heliopan.

Expressionist/Pictorialist Blur ~ 

Remembering the "why" of soft focus lenses...

"... Faire de la Photographie avec art est une chose; faire de l'Art par le moyen de la
Photographie en est, sans doute, une autre... aux définitions diverses de l’oeuvre d’art :
Expression d’un tempérament, — Interprétation de la nature, — Déformation systématique et voulue du réel..."

Translated -

"...  Making a photograph with artistry is one thing. Making art through the medium of photography is, undoubtedly, another... given the various definitions of a work of art: the expression of a temperament—the interpretation of nature—the systematic and deliberate distortion of reality..." [emphasis mine]

From   Biblioteque de la Revue de Photographie by L. de Pullignyt - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique"

 Using art and drawing as a guide, I think of it this way.  When a line is drawn by pencil to paper, the edges of the line are soft and rounded, and are not commonly abrupt and sharp.

One way of making art with photography is to use lenses of varying line softness qualities. This, in the same way an artist uses pencils of differing line weights (#2... #9), line opacity (hard... bold), and edge transition (the width of the line softness). 

To verify the level of blur "scales" correctly between old chemical processes and the digital domain I had a close look at old Expressionist/Pictorialist prints and chose images where blur could be more or less accurately measured.  The blur radius is 0.60mm to 0.90mm when the image dimensions are 6.5inches x 8.5inches Whole Plate.  Thus proving L. de Pulligny et C. Puyo correct.

Now have a look at the sample chart I generated using miniature format lenses and softening filters. 

With this I feel the concept of equivalency between old and new is proven and a digital Expressionsit/Pictorialist path forward based on optics and optical effects is possible.

 

----------- Essential Reading --------------

Dr. Russell Young's thesis paper on soft focus photography

Biblioteque de la Revue de Photographie -  L. de Pulligny - C. Puyo "Objectifs d'Artiste Practique et Theorie des Objectifs et Teleobjectifs Anachromatique" - Biblioteque national de France (BnF) (in French)

----------- On Soft Filters -------------- 

Soft Filters in Cinematography 

M. David Mullen, ASC

M. David Mullen, ASC on cinema and photography 

Soft filtration options 

A question of diffusion  

----------- Additional Resources ------------

An illustrated guide to early soft focus lenses

Are you a softie?

Frederick H. Evans was actually a soft focus photographer 

History of Dallmeyer optics (on the Dallmeyer 3b in use)

Neo-Pictorialism by Guy Tal 

Objectifs de flou artistique (in French) 

When did Photography of Soft? 

Wollensak Velostigmat Series II as a first element focuser Expressionist/Pictorialist optic 

Tessar design - with scatter plots that show chromatic aberration distributions