My non-mathematical understanding is that 'optimum' is that, because, if the hole is larger, then excess unfocused or incoherent light rays are allowed and begin to blur the image; and if the hole is smaller, diffraction begins to blur the image.
So the optimum hole size is the least blurry point between those 2 causes of blurriness.
Does that sound accurate to others?
I understand that there's a median point in between those two to get a good result. My question still stands and to why it has to change for different focal lengths. I have a pinhole that works wonderful on a home made pinhole camera that takes a 4x5 negative. Why couldn't I transfer this pinhole to another camera with a longer focal length. Sorry if someone already answered this in their response. Maybe it's just all going over my head and I should let it be what it is. There's a reason I'm an art major - hahah.
Originally Posted by glogan
You can. So long as you don't mind slight increase in image fuzziness and a significant increase in exposure times.
Originally Posted by aaronmichael
Two things make the image on a pinhole camera fuzzy: the size of the pinhole, and the effects of diffraction, the bending of light around an edge. But only the light that 'touches' the circumference of the pinhole will be diffracted. In both cases (i.e. short camera, long camera), the same amount of light is being diffracted (i.e. bent slightly outward radially). That bent light will spread out as it heads toward the film, increasing the overall fuzziness of the image. On a longer camera, it has a longer path in which it can spread out before it hits the film. So you may find that your images will be less sharp on the longer focal length camera, even with the same pinhole. And, you'll still have to pay the price of longer exposure times.
So, you could make yourself a bigger pinhole and shorten your exposure times. True, you'll increase the fuzziness due to the size of the pinhole. But you'll decrease the fuzziness due to diffraction. However the net fuzziness will probably be higher.
And if you really want to get technical, even in the bigger pinhole, the total amount of light being diffracted (i.e. bent or scattered) will increase, but the proportion will be less. And so it's relative contribution to image fuzziness will be less.
Ok, so a hole with radius R has diffraction along circumference 2(pi)R and aperture (pi)R^2.
So doubling the radius doubles the circumference but has a two stop speed increase.
What function describes the image's circle of confusion from the diffraction and the CoC from just the hole?
This probably won't fit in a post, so references are good.
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Originally Posted by michaelbsc
d = the pinhole diameter
λ = the wave length (about 0.000555mm)
f = the focal length
Taken from "Way Beyond Monochrome. 2nd ed." p. 155
Is this the Formula for an optimum size?
Originally Posted by Nick Kanellos
Thank you so much for the reply. I think that's the first reply I've gotten that has directly answered my question and explained it clearly - no offense to the other users, maybe I just wasn't clear enough in my original post.
Originally Posted by Nick Kanellos
Beyond focal length and the physical size of the pinhole, I can think of several more aspects that when considered in the pinhole's design will most likely increase the sharpness (reduce defraction) in the projected image.
1. The shape of the pinhole.
2. The thickness of the pinhole plate material (at the pinhole)
3. The color of the pinhole plate material (at the pinhole)
Would someone care to elaborate further?
Let me take a stab:
Originally Posted by Cesaraugusta
1) The shape of the pinhole. I suppose you could say that the amount of light diffracted is proportional to the perimeter of the pinhole. The smallest perimeter for any given area (e.g. the area of the pinhole itself) is a perfect circle. Anything else adds more 'edge' around which more light can be diffracted. Which results in reducing sharpness. How'd I do?
2) Thickness of the plate material. Let's see. Hmmm.... Imagine light coming into the pinhole at any angle from the axis. Some of that light will "touch" the front edge of the pinhole. Resulting in some diffraction. Some of the light will then "touch" the rear edge of the pinhole. More diffraction. Any thickness greater than zero effectively results in "two" pinholes: one at the front surface of the plate and one at the rear surface. Effectively doubling the diffraction causing edge. Also a thicker plate effectively reduces the pinhole aperture for any light not coming straight from the front.
To remedy this, once you've drilled your pinhole, take a counter sinking drill bit and create a conical shaped hole over your pinhole. If you get it just right, it will result in a near knife edge perimeter for your pinhole. It might make it a bit delicate but no more so than a glass lens.
3) Colour. Not a clue.