Friday, December 7, 2018

Was Lord Rayleigh talking about sharpness?

June 2019. When my university retiree account disappeared with a new change in policy, the pictures I uploaded to this blog while logged into that account disappeared. I'm working on fixing that but it's going to be at least a summer long project. 

This all started because of a comment in the Lensless Podcast Facebook group that a longer distance to the pinhole always results in a reduction in sharpness.

What he means is, according to physics worked out by John William Strutt, 3rd Baron Rayleigh in the 19th century, the farther the pinhole is from the image plane, it will take a relatively larger pinhole in order to minimize diffraction. A bigger hole will result in a loss of sharpness. (Perfection of the pinhole is also a significant variable here. Think of it as a lot of tiny holes on the edge of the pinhole that the photons have to squeeze through.)

I've always preferred a smaller than optimum pinhole for my longer cameras.

Everybody checks Mr. Pinhole’s calculator for the optimal results of these equations, and everybody thinks of this in terms of focus.

That started me on a thought experiment.

These equations predict the formation of an Airy disk around a point of light.

.15mm electron microscope aperture, 24mm from the image plane, about 5m from the subject.

Even the best optics in focus form an Airy disk determined by some algebraic gymnastics on the wavelength of light. The Hubble Space Telescope forms an Airy disk. Billions are spent minimizing them. Even with adaptive optics it’s still there, it’s just very, very small for a perfect 30 meter telescope mirror.

This is different from circle of confusion which is associated with depth of field and focus. With a pinhole aperture, circle of confusion always gets greater with a bigger hole. Diffraction varies on both sides of “optimum.”

The Airy disk is still there out of focus, it’s just more diffuse. With a pinhole, it’s just always there, no focusing is going on. It will vary in brightness and radius as a certain size pinhole moves toward or away from the image plane or from a source, will be least bright at some point and the disk itself will vary in some predictable wavy pattern, always rather less bright than the point itself.

How does this really impact the image?

Think about your average American holiday image.  How many point sources of light are there when you have a decorated tree in the picture? An infinite number of course.  Every point in the image is a source. They all have an Airy disk. You just don’t notice them unless it’s a picture of a mini-light, which is also overexposed anyway, so its Airy disk is going to be a whopper. The Airy disk around each theoretical point of the soft glow of your kid’s dreamy face isn’t probably going to rise to the level of the film’s sensitivity, and if it does, it’s a soft glow, it’s not out of focus. Sharpness is determined by the size of the pinhole. At extremes, diffraction reduces the contrast between all the points and all the the disks to unmanageable levels, and it’s not going to be happy with overexposure.

That's assuming you could get the kid to sit still long enough for a pinhole portrait by the light of the Yule decorations with a smaller than optimum pinhole. Motion blur is something else again and like circle of confusion is determined by light acting like a particle which allows us to make pinhole images. Diffraction is evidence of it’s wavelike behavior that gives pinhole some of its unique quality and also affects all optics. Happy Holidays.

The pinhole holiday is April 28 in 2019.


  1. I agree, Nick. The ‘optimal’ pinhole cannot be calculated. Smaller is always better until it is not. Diffraction blur from a hole too small does not make a difference until the hole is ‘way’ too small. Besides, all that Lord Rayleigh stuff is based on monochrome light, and I don’t know of many photographs made in monochrome light. So put a high quality hole in your camera, and use one smaller than the recommendations.

  2. Don't forget that the formula and its derivatives also try to minimize vignetting for a particular frame geometry at the same time as satisfying the diffraction vs. "circle of confusion" tradeoff. Its not a minimum but an optimum.