What's Optimal About Optimal?

[aaronmichael]

Without getting much into the math aspect of this in the replies, I want to ask a simple and hopefully not that obvious question. I'm aware that there's an optimal pinhole diameter based on the focal length. My question is, what about this optimal pinhole diameter is optimal? I realize that the further away the image plane becomes from the focal plane, the dimmer the project image becomes (if the pinhole diameter was fixed). Therefore a larger pinhole should be used as the focal length increases so exposure time aren't ridiculous. I also know that sharpness (resolution?) decreases as the pinhole increases in diameter. I'm asking this because I just built a pinhole camera with a focal length of 190mm and based on a couple websites I should have a pinhole of about .58-.62mm. I feel like that's large compared to my previous cameras. With my previous pinhole cameras (at shorter focal lengths) I've been using home made pinholes of around .30mm and have gotten pretty sharp images with it.

Anyway, my question boils down to what is optimal about optimal and what would be the problem with using a smaller pinhole (to preserve sharpness) in a longer focal length camera? Any replies greatly appreciated -thank you.

[polyglot]

Diffraction increases as the pinhole gets smaller, which means that if you go smaller than the optimum size, you will get a softer image as well as longer exposure.

The optimum is the optimum because it is the point with greatest sharpness - too small and you're diffraction-limited, too large and you're limited by the tube of light coming through the hole.

[aaronmichael]

Diffraction increases as the pinhole gets smaller, which means that if you go smaller than the optimum size, you will get a softer image as well as longer exposure.

The optimum is the optimum because it is the point with greatest sharpness - too small and you're diffraction-limited, too large and you're limited by the tube of light coming through the hole.

Suppose I'll have to do a little more research on diffraction. Thanks for the reply.

[Jim Jones]

To further complicate the discussion, in a flat film camera, a pinhole of optimum size for the center of the image is too small for the corners of the image. Also, the corners exhibit astigmatism. For the curved film "Oatmeal box" camera, the pinhole can be made slightly elliptical to improve edge performance. Even something as simple as a pinhole camera can become awfully complicated.

[aaronmichael]

To further complicate the discussion, in a flat film camera, a pinhole of optimum size for the center of the image is too small for the corners of the image. Also, the corners exhibit astigmatism. For the curved film "Oatmeal box" camera, the pinhole can be made slightly elliptical to improve edge performance. Even something as simple as a pinhole camera can become awfully complicated.

This is because the focal length is measured in a straight line from the pinhole to the center of the image plane, and in online calculators that is what the pinhole diameter is optimized for, correct? And the corners of the image plane are further away from the pinhole than the center is.

[Q.G.]

Seen from under an angle, not from straight behind, a circle appears as an ellips, is smaller.
Make the hole ellips shape, and from the side the long axis points to, the effect is negated. But only from that side, and only at a certain angle/distance from the image's centre.

I don't know how that would creat astigmatisme, except that the shape is echoed in the pencil of light's shape. But that's not astigmatism.

[aaronmichael]

Seen from under an angle, not from straight behind, a circle appears as an ellips, is smaller.
Make the hole ellips shape, and from the side the long axis points to, the effect is negated. But only from that side, and only at a certain angle/distance from the image's centre.

I don't know how that would creat astigmatisme, except that the shape is echoed in the pencil of light's shape. But that's not astigmatism.

Hmm - interesting. I'm still confused on the answer to my original question though. I know that the hole isn't supposed to be too small because you'll run into problems. I just don't understand why a pinhole optimized for a focal length of 100mm couldn't be used with a 200mm camera - since the smaller the hole, the better (up to a certain point).

[Q.G.]

The smaller the hole, the more diffraction will ruin the already not so great image quality.

But you need a small hole to limit the 'angle of view', creating a sharper image. The smaller the hole, the smaller the area outside that is visible through it, the smaller the blur on each point on the film behind it. But get it too small, and the blur caused by diffraction will hit in big time, and it gets more blurry again. Just as when you make the hole too big.

[2F/2F]

It should also be noted that at least one of the commonly-used formulas for calculating optimum diameter requires the input of a wavelength. Thus the optimum size will vary with the color temperature in which you are shooting. Most people just use a wavelength somewhere near the middle of the visible spectrum (550 nM, yellow-green, I believe).

[Jim Jones]

Seen from under an angle, not from straight behind, a circle appears as an ellips, is smaller.
Make the hole ellips shape, and from the side the long axis points to, the effect is negated. But only from that side, and only at a certain angle/distance from the image's centre.

I don't know how that would creat astigmatisme, except that the shape is echoed in the pencil of light's shape. But that's not astigmatism.

Here is the results of off-axis resolution tests done decades ago. Notice the difference in off-axis resolution between tangential and radial target lines. Perhaps this isn't astigmatism, but the results are the same. According to Pinhole Designer with a user constant of 1.5, the pinhole for optimum on-axis resolution in this test would have been .013 inches.