pinhole image area at film plane

hello, i'm designing a pinhole camera for 4x5" sheets. There are a few programs on internet to calculate optimum

hole, and times of exposure, but the critical data i need is the image circle on the film plane for a given focal lenght.

i want to avoid vigneting.

hi gasper,

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but vignetting is the virtue of pinhole images. in an absolute sense, i think you won't be able to avoid it, but it won't be so strong unless you use very short focal lengths if your material is extremely thin. i guess the exact data you need depends on how thick your pinhole material is. i use .015mm steel shim with a bit of a bevel around the hole.

i'm afraid i can't offer a calculator for the data you need, but here's some examples. here's a picture with 24mm on 6x6, and one with 23mm on 4x5, both at the same place.

<img src="http://rjjackson.com/images/img/fi_00976.jpg" /><br><br>

<img src="http://rjjackson.com/images/img/fi_45_00111.jpg" />

How much vignetting do you want to avoid? Pinholes don't really have "image circles", they just fade out at larger angles.

There seem to be many different calculations for coverage area vs. focal length. They're mostly based on "rules of thumb", some say the coverage circle is twice the focal length, some say it's 3 times. Apparently, most of this is based on experimentation with one particular pinhole, and the results vary from measurement to measurement, depending on the thickness of the plate the pinhole is drilled in.

First, do keep in mind the old rule about the thinner the plate the larger the coverage circle. I use thin foil, and sandwich the foil between thinker plates with 1/4 inch holes to accommodate the pinhole. This seems to get me past three focal lengths with no more than cos4 vignetting.

Now, since it's only 4x5, I'd not bother about a curved film plane. 6x9 yeah. 6x17, definitely...

Taking all that into consideration, your vignetting is limited by the cos4 law, amplitude is proportional to cos^4 of angle.

So, if you consider a half stop of vignetting to be acceptable, the angle is arccos(0.707^1/4)= 23 degrees. Half the diagonal for 4x5 is 81mm. The focal length for 23 degrees is 81/tan(23) = 191mm.

Let's do this for a few vignetting levels...

0.5 stop 23 deg 191mm

1 stop 33 deg 125mm

2 stop 45 deg 81mm

3 stop 54 deg 60mm

Have fun

Hi Robert. Wonderful images... I don't think an ultrawide like that one would have occurred to me..

Anyway, in appreciation for your cool shots.

"i'm afraid i can't offer a calculator for the data you need, but here's some examples. here's a picture with 24mm on 6x6, and one with 23mm on 4x5,"

6x6 = 56mm square. Half the diagonal is 39.6mm. For a 24mm focal length pinhole (I take it you had the mirror locked up) that's arctan (39.6/24) = 58.77 deg. Cos^4 58.77 deg = 0.072 = -3.8 stops. Actually, your picture looks pretty good for that level of vignetting.

4x5 has a half diagonal of 81mm. For a 23mm focal length pinhole (are you sure of that) you're at arctan (81/23) = 74.15 deg. Cos^4 74.15 = 0.0056 = -7.4 stops, hence the pretty much black corners.

Although those numbers sound high, so I went and rummaged through Warren Smith's "Modern Optical engineering" and there's something on page 153 that leads me to believe the correct formula for film is cos^3, not cos^4, which would mean your images are at -2.8 stops for the 6x6, -5.6 stops for the 4x5.

Cos^4 is based on illumination at a surface, and I believe that for most films the grains may be considered to be randomly oriented, and the fourth cosine term may therefore be ignored.

hi joseph,

thanks for the kind words. for both these shots i made a cardboard camera body that was mounted on top of the film backs (so no mirrors to bother with). for the 4x5, i used the black cardboard 4x5 film box from kodak placed directly over the film holder (19mm deep plus a few for the film seat and foam light seal). works well, very light and packs up nicely among my heavier gear. i'm making the same thing from maple now with changeable pinhole boards for different kinds of shift.

i have noticed that the quality of the hole has a huge effect on the vignetting. also, to some extent, the film and development. i can tame it a little by pulling the development.

the amount of vignetting described as stops, i presume, is on the zone system?

A few years ago I sat down at the drawing board and decided to see if I could calculate the vignette of a pinhole and design a camera without vignetting, at least in one direction. The first question is what causes the vignette? The vignette is caused by the fact that rays of light entering into the pinhole from an angle are effectively entering through a smaller, oval shaped opening than when they enter into it from straight on. The hole is "squished" by the angle and the "squishing" means that the pinhole is actually a different f-stop when light enters into it an an angle! Squished hole means bigger f-number means less light reaches the film. It also effect the sharpness of the image... remember that pinhole cameras are optimized so that the focal length is the "best" distance for the aperture of the hole. On a pinhole camera with flat film, as you move away from the center, the focal length is increasing, but the effective aperture is also increasing. Because this effect is basically a compounded effect, there really is no optimum "crop" for a flat film pinhole camera that will not produce this effect, as even at the smallest crop, some light fall-off will be occuring.

To reduce vignetting (it's actually light fall-off) as well as focus fall-off, the interior of the camera needs to have a curved surface. The best pinhole cameras in terms of both even brightness and even focus are the type which are a cylinder with a hole on one side. The ratios of distances and angles from the pinhole works out perfectly with a cylinder... at least in one direction. In the other direction, the light and focus fall-off will be the same as any flat film pinhole camera. In addition, these cameras introduce dramatic distortions, especially in horizontal and diagonal lines. A classic example for 4x5 is the "quaker oats" can pinhole camera.

Ideally, a spherical camera with a pinhole in the side of the sphere would produce the sharpest and brightest pinhole images, They don't make spherical film yet, but liquid light could be applied to the inside of a spherical shape to make one-off "perfect" pinhole images.

this calculator will give you the size of the image circle.

http://mrpinhole.com/calcpinh.php

Jason