LENS BLUR FOLLOWUP
Jan 27, 2019
∙This is a followup to my Lens Blur article.
∙In case you're not familiar with the term "equisolid," it means uniform magnifcation across the field.
∙The following is excerpted from an email exchange I had with an app developer who's contemplating writing a blur circle calculator:
One more topic, and this is something that you can deduce from the lens blur article but that I don’t spend any time on there because it’s going down a big rabbit hole to explain an issue that has only a very small practical impact:
Firstly no, lens is either perfectly rectilinear or perfectly equisolid, so there is always slight variations in the 2D distortion, which means that the exact AoV [Angle of View] may be slightly off even with two different lens models of the same nominal focal length on the same format size — since a different amount of the image could be squeezed into the frame at the edges by the variation in distortion.
Now, this issue of differences between real-world models is even slightly more nuanced and confusing than just what’s mentioned in the above paragraph, becuase most real-world lenses are not even trying to be equisolid, they’re trying to be rectilinear (except for some models of fish-eyes and anamorphics which aren’t really trying to be either, but might be closer to equisolid than to rectilinear). Rectilinear lenses [whether perfectly rectilinear or only approximately so] don’t have uniform magnification across the field: they graduate from less magnification in the center to more magnification on the edges.
This means that it’s not even clear what to name a lens when giving it a millimeter name (like a “a 50mm lens”), because any given focal length has a single fixed magnification associated with it, but real-world lenses have varying magnification across the field. So, even if two manufacturers somehow managed to make lenses with the exact same imperfections in their 2D distortions, they might name them differently (like maybe one manufacturer calls it a 27mm lens and the other calls it a 29mm lens), since there is no one unambiguous way to assign a variable-magnification optical system with a fixed-magnification name.
Anyway, this footnote does not add up to very much more than a triviality in the real world, where lenses that have been marked with the same focal length tend to be pretty damn similar in most cases, but it’s an issue that's worth noting in case you’re going to have users who complain about AoV equivalents not being dead perfect down to the micron.
Oh, and one last note about matching AoV — if you’re indeed going to have an AoV calculator along with your blur circle calculator. You probably already know this, but just wanted to throw it out there to be sure:
It’s when one of the formats is anamorphic and the other isn’t (or if the two formats are both anamorphic with different squeeze ratios).
Any given focal length number is, of course, mathematically linked to an associated fixed amount of magnfication. But anamorphic lenses have two different magnifications: the vertical has a higher power of magnification than the horizontal. But manufacturers name anamorphic lenses with only one focal length (like, they’ll name a lens “a 50mm lens” not “a 50mm x 100mm lens"). By sheer convention, the focal length name is mathematically correct for the vertical, not for the horizontal. This means that when matching an anamorphic lens to a non-anamorphic (or to an anamorphic with a different squeeze ratio), you need to multiply the film-back width by the squeeze factor (or, alternately, you could use the vertical film-back size instead of the horizontal).
Hope that helps.
-Steve