Our investigation of the balance between lens performance and sensor spatial resolution wouldn’t be complete without considering how we, the ultimate sensors, will judge the result. If there are physical differences between two imaging systems, are we able to perceive and evaluate them with our essential vision in customary and reasonable situations?
A Circle of Confusion is a spatial entity that represents a coarsely calculated, subjective threshold relative to normalized human vision. The particular threshold established for the CoC is one where sharpness (e.g. focus, when measuring Depth of Field) becomes objectionable, or better, where a sharp point is perceived a blur and not a sharp point. This obviously may distill to matters of opinion ranging from political expediency to whether or not vanilla is actually a flavor. We’ve already explored how variable human vision is-in fact, William Dawes, who produced the Dawes Limit (a subjectively derived measurement) was rumored to have particularly keen vision, but whether or not it was physiologically excellent or simply well trained is a lingering question that keeps me up late some nights.
Therefore, the effective CoC actually increases or decreases in size with the application. In the case of photographic prints the effective CoC varies with the rate of enlargement. The most common use of the CoC principle is in determining Depth of Field.
For example, if a 35mm Full Frame Sensor image acquired with a 50mm lens is enlarged to 10 inches wide, it’s correct viewing distance will be 7 (inches, the linear enlargement of the 36mm/1.5 inch wide sensor) times 2 (the focal length of the 50mm lens, in inches), or 14 inches.
At 14 inches with normalized human vision (let’s use an unqualified ~2.5 minutes of arc), we encounter an Angular Size of .087 inches…that’s .29mm, or roughly 1/100 of an inch. Our CoC for normalized human vision on such a print will be 1/100 of an inch.
On a 36″ print, the proper viewing distance is approximately 48 inches, producing a CoC of about 1/35 of an inch. Note that the expansion of the effective CoC does not enjoy a linear relationship with viewing distance.
Please remember that our CoC is established using a normalized (think “ideal but realistic”) human vision standard, which is scarce at best. We have also presumed a perfectly calculated viewing distance, and there is no guarantee of compliance. Even the 2.5 minutes of arc measure is subject to dissent-Kodak has recommended a 2 minutes of arc standard, while a Snellen Chart uses 5 (with each letter line, such as the lower line in the letter “L” subtending 1 minute of arc) as the ideal measurement context. Perhaps the most important element of the CoC criteria is the use of the “objectionable” epithet, which is an extremely fluid criteria subject to horse racing results and wind direction. We’re not talking about being able to resolve a black dot on a white background, we’re talking about being able to sense and quantify whether or not that black dot is blurry.
Since you’re already familiar with the Nyquist Frequency, you can probably imagine the challenges for the raster-like sensing grid in your eyes as they’re trying to judge the blur of a dot near the limits of their ability to absolutely resolve said dot in the first place. It’s almost the same as your camera sensor encountering the Diffraction Rings on an Airy Disk…
This all ties together beautifully, doesn’t it? The issue of CoC gives you a reasonably reliable tool for quantifying how much spatial resolution you need from your camera (but you’ll have to do your own math…). It also allows us to calculate at which point a 12 MegaPixel camera will begin to show its limits when competing with an 18 MegaPixel camera, provided the sensor and not the lensing is being tested.
Finally, it should give you some idea of how incredibly convoluted the science behind our craft is. I will leave you with a challenging, very disturbing though: The technical underpinnings of the digital camera and lensing disciplines do not deeply scratch the surface of the body of knowledge concentrated on human vision.
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