What's Optimal About Optimal?

aaronmichael · Jan 11, 2011

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 · Jan 11, 2011

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 · Jan 11, 2011

polyglot said:
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 · Jan 12, 2011

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 · Jan 12, 2011

Jim Jones said:
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. · Jan 12, 2011

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 · Jan 12, 2011

Q.G. said:
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. · Jan 12, 2011

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 · Jan 12, 2011

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 · Jan 13, 2011

Q.G. said:
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.

glogan · Jan 15, 2011

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?

Q.G. · Jan 15, 2011

It does.

aaronmichael · Jan 15, 2011

glogan said:
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.

Nick Kanellos · Jan 15, 2011

aaronmichael said:
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.

You can. So long as you don't mind slight increase in image fuzziness and a significant increase in exposure times.

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.

Easy, eh?

michaelbsc · Jan 15, 2011

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.

MB

Nick Kanellos · Jan 15, 2011

michaelbsc said:
What function describes the image's circle of confusion from the diffraction and the CoC from just the hole?

MB

d=1.56√λf

where
d = the pinhole diameter
λ = the wave length (about 0.000555mm)
f = the focal length

Taken from "Way Beyond Monochrome. 2nd ed." p. 155

michaelbsc · Jan 15, 2011

Nick Kanellos said:
michaelbsc said:

What function describes the image's circle of confusion from the diffraction and the CoC from just the hole?

MB

Click to expand...

d=1.56√λf

where
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?

aaronmichael · Jan 15, 2011

Nick Kanellos said:
You can. So long as you don't mind slight increase in image fuzziness and a significant increase in exposure times.

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.

Easy, eh?

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.

anon12345 · Jan 15, 2011

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?

Nick Kanellos · Jan 16, 2011

Cesaraugusta said:
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:

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.

Nick Kanellos · Jan 16, 2011

michaelbsc said:
Is this the Formula for an optimum size?

Yep

anon12345 · Jan 16, 2011

Nick Kanellos said:
Let me take a stab:

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.

I'll go with that. In my own pinhole creations I strive for a clean, round, and very thin pinhole. This has improved my images. I've attempted this with aluminum foil, but ultimately I end up using thin sheet brass. I found that examination under a microscope is necessary to insure there are no entry or exit burrs, and that the pinhole is as clean and round as possible. Black seems to be the color of choice. I have read that blackening the hole with soot from a candle can help absorb light energy that would otherwise be reflected off the inside surfaces of the hole. For my own purposes I've blackened the hole's inside surfaces with black ink. I have included a basic diagram of a pinhole of my own design that has worked quite well so far. If anyone can use this or improve upon it, please feel free to do so.

aaronmichael · Jan 16, 2011

Cesaraugusta said:
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?

I'm just a newbie into pinhole photography but as for the shape of my pinhole, I've tried to get it as round as possible using a needle. For the material, I use the metal from soda cans and sand it down with an electrical orbital sander using 60 grit sand paper. This gets it pretty thin pretty fast. As for the color of the material, I usually paint both sides black. Below is probably the best shot I've done using the methods described.

http://www.flickr.com/photos/aaronmichael/5256810534/in/set-72157625595921944/

The focal length for the camera it was taken with is 125mm and my new 8x10 camera that I built has a focal length of 190mm - which is what sparked the thread. Wanted to know if there was a reason why making a larger pinhole for the longer focal length would be beneficial. I think the pinhole diameter for the above shot was .46mm.

moki · Jan 16, 2011

I use regular thin aluminium foil for the hole, because it's thin enough to start with and you don't need to do the trick with denting it in and using very finse sandpaper to prepare it. It's not as robust, but good enough if you're careful. The trick is not to push the needle through, but put the foil onto a piece of cardboard, just lightly set the needle onto it and twist is while applying very little pressure and then shave away the edge with a very sharp razor. I can consistently get holes down to 0,2mm with almost perfectly round shape like that. I usually just do 10 holes at a time and see afterwards, which one fits best for my camera by scanning them digitally and getting the exact size that way.
I don't care too much for the optimal size, because the difference is almost invisible anyway. I just try to find a hole that gives me decent exposure times like 1-2sec in bright sunlight with 100ASA film.

Using a piece of high resolution, high contrast film, photographing a tiny black dot on a white wall and using that as pinhole might be even better, though. I know it is used for zone plates or pinhole sieves, but I don't see, why it shouldn't work for single pinholes. It's probably the easiest to way to get exactly the right size, because it can be calculated beforehand.

The thickness of the pinhole material only becomes important, when you want shorter than normal focal length, because thick materials show much more vignetting from blocking the light with the edge. Some unprocessed metal from a soda can might get you an image circle of about 50° without too much light loss, aluminium foil gets you 100° while filed downs brass sheet gives 120° (these are no real or tested numbers, just an example). So if you're not using some ridicilous wide-angle like 30mm on 4x5, it's not that important.
Feel free to criticize me for that - I'm a practical pinhole photographer, not a scientist or someone who examines every picture with a loupe.

Jim Jones · Jan 16, 2011

Nick Kanellos said:
d=1.56√λf

where
d = the pinhole diameter
λ = the wave length (about 0.000555mm)
f = the focal length

Taken from "Way Beyond Monochrome. 2nd ed." p. 155

To simplify the formula for panchromatic film, multiply the square root of the focal length by .007 (all in inches) or use PinholeDesigner with a user constant of about 1.5. Reduce the diameter a bit for macro photography, increase a bit for ultra wide angle. Way Beyond Monochrome, 2nd ed. is a magnificant book, although the section on pinhole photography doesn't thoroughly address the often overlooked problems with wide angle pinholes. I prefer .002" brass shim stock over aluminum for making pinholes. Dimpling it before making the hole reduces thickness around the hole even more. It seems to work cleaner than aluminum. Brass can be chemically darkened. One small sheet of shimstock might last a lifetime.

Pinhole photography sounds simple, but like many simple arts, it demands more of the practicioner than something as complex as digital photography. Entire books have been written on the subject without covering all aspects of it: Eric Renner's fine 260 page Pinhole Photography, for example. The art and technique of pinhole photography are discussed at length on http://www.f295.org/Pinholeforum/

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