## Chapter 14. What Is the “Circle of Confusion”?

### ...and Why Is It Such a Slippery Value?

Imagine a perfect white point in an empty black room. The point has no height, and no width. If you focus an optically perfect lens on that point, it forms a perfect point on the imaging area as well. If, however, you focus slightly in front of or behind the point, the point will appear on the imaging area as a small blurry circle. If that circle is small enough, it will still look like a point when enlarged for printing. The “circle of confusion” is typically calculated as the largest on-imaging area circle that you see as a point when you make an 8 × 12 print and view it from a “normal” viewing distance, typically 2 to 3 feet. Anything larger is seen as a small circle, and is therefore perceived as out of focus.

ƒ/Calc calculates the CoC using the Zeiss formula: d/1730, where d is the diagonal measure of the imaging area, in millimeters. This formula yields acceptable values for most purposes.

You might be wondering, if the CoC is such a slippery value, why is it reasonable for ƒ/Calc to calculate it?

Many lenses have depth of field markings engraved on the barrel: the CoC affects DoF, so obviously these manufacturers are comfortable giving you a very fixed definition for CoC. This is because the main factor affecting CoC is the imaging area: lenses are designed for a particular kind of camera, and thus a particular imaging area.

The imaging area is important because the larger the imaging area, the less you have to enlarge the image to get a particular sized print. So, because a 6 × 4.5 camera has an imaging area roughly twice the size of a 35 mm frame, will have a CoC that’s roughly twice the size of that for a 35 mm frame. In other words, if a fuzzy disc 0.025 mm wide looks like a point when printed from 35 mm imaging area, you can have an 0.043 mm disc on 6 × 4.5 cm imaging area and still have the same apparent degree of sharpness if you enlarge it to the same size print as you made from the 35 mm frame.

You’ll recall above that we defined the CoC above in fuzzy, arbitrary terms of “normal” viewing distances and particular print sizes. But due to human factors, CoC isn’t actually all that dependent on image size in practice. If you have to show a picture to many people in a large room (which we will call a “movie theater”), you don’t make them look at an 8 × 10 image, you project it so it covers the entire wall. And if you’re like me, you prefer to avoid sitting in the first several rows in the theater. So, while the image size is huge compared to a typical photographic print, the viewing distance is proportionally larger, too, so the differences usually cancel out.

So now that I’ve gone and defended ƒ/Calc’s CoC calculation, why does it let you override it?

Mainly, this is to account for exceptional conditions, like prints hung in an art gallery: a gallery setting often demands large photos which will be viewed relatively close up.

The CoC value also takes into account imperfections in the camera and enlarging lenses used, and the resolution of the imaging area and paper used to make the image. Since most people take pictures with typical cameras and have the photos printed by generic photo labs on standard photo paper with typical photo printing machines operated by technicians of average talent, it is usually not important to take these various quality issues into account: they’re effectively built into the Zeiss formula. Your situation may be atypical, however. If you’re priting digital photos from an old 3 megapixel camera on a low-end inkjet printer, for example, you might need a smaller CoC to account for the low resolutions in each device. Cheap lenses will also require smaller CoC values than sharp ones to achieve the same degree of apparent sharpness. (Smaller CoCs can only go so far in improving sharpness, however.)