Exposure mapping

[antbiker]

I am certain you understand that pinhole cameras, to varying degrees, will vignette or darken the corners of the frame.

But have you thought any further than this?
Have you thought by how much this occurs & precisely where it occurs on the negative?

I have spent some time producing 'exposure maps' showing how exposure affects the negative with different camera designs.

My following comments refer to flat plane designs only.
When people state the specification of their camera, one detail given will be the f-number of that camera.
This is a convenient number which anyone can use to calculate exposures for that particular camera.
However, it is an incomplete specification. The stated f-number will be based around the 'Focal length' of the camera in question. But, the f-number actually changes for all pinhole cameras once we examine any other part of the negative beyond the centre of the negative (the point where the focal length is arrived at).
This is because light has further to travel at the corners of the negative, or put another way the focal length is longer at the corners.
This effect becomes progressively more pronounced the wider the camera (a product of a progressively shorter focal length).

So for my own 50mm camera, I always state that the camera (with a 0.010" pinhole) is f197.
To be completely accurate I should state that it is f197-f252. That is from centre to corner.

The following maps assume that EV0 is set at the centre of the frame & at the specified focal length of the camera.
Each ring marked is one f-stop apart. Obviously, the exposure is progressively less away from the centre point & the final print will show a gradual darkening.

If you look at the examples I have posted with each map, it is a surprise to note that the vignetting of the frame is not always as pronounced as one would expect. Conversely it is sometimes more pronounced!
Your thoughts are invited on this aspect, is the exposure affecting the corner shading? What about the brand of film? Or scanning of the negative? Does reciprocity failure affect vignetting (as you will have part of the negative correctly exposed & part of it under exposed).

Finally, if you have a short focal length design (let's take the first map below, a 4x5" camera, as an example), no doubt you are using the f-number at the centre of the frame to calculate your exposures. The resultant negative will be correctly exposed in the centre of the frame & progressively underexposed toward the corners.
But why not take the f-number of the camera to be one stop less? So now in theory you would have a ring on the negative which is correctly exposed, the centre of the frame would be one stop under & each ring outward would be as before, progressively one stop under.
The advantage would be that by the time you reach the corner of the frame you will be one stop under, rather than two stops.
Exposure latitude of the film would be allowed to deal with this +/-1 stop shift.
Is it worth the bother?

[antbiker]

The first example is a 4x5" camera fitted with a 0.010" pinhole & having a focal length of 25mm (based on the Zero). This gives a f-number of f98.
You can see that this camera will darken the corners of the frame by a factor of 2 stops.
Attached files

[antbiker]

This map shows a very short focal length (19mm), 6x6cm design of my own. It is similar to the 4x5" do you think?
Examples :-
http://f295.f295.org/uploads/Blah.pl?m-1223671776/
http://f295.f295.org/uploads/Blah.pl?m-1226697569/
http://f295.f295.org/uploads/Blah.pl?m-1228332725/
http://f295.f295.org/uploads/Blah.pl?m-1224876123/ Attached files

[antbiker]

This map is for another 6x6cm camera, this time with a focal length of 33mm.
Examples :-
http://f295.f295.org/uploads/Blah.pl?m-1248978044/
http://f295.f295.org/uploads/Blah.pl?m-1249409177/ Attached files

[antbiker]

This map is for my 50mm design. I specifically designed this one so that I wouldn't get corner shading. It can be seen that the first 'one-stop underexposure' line appears well out of the frame. It is therefore a little surprising to see some shading on a few of these examples......
Examples :-
http://f295.f295.org/uploads/Blah.pl?m-1257968153/
http://f295.f295.org/uploads/Blah.pl?m-1253281494/
http://f295.f295.org/uploads/Blah.pl?m-1229200119/
http://f295.f295.org/uploads/Blah.pl?m-1225571426/ Attached files

[antbiker]

I have a design drawn up ready to be built. It is as extreme a design as I can come up with in focal length terms. Very, very short. It makes no compromise toward producing a pinhole with a wide enough view. Nor does it make any compromise toward the useability of a camera with such a very bright f-number (almost comparable to a lens).
So the question is..... looking at the exposure map for this design would you waste effort making such a radical design???

Attached files

[polka]

Hi Tony,

I have to say, I do not agree with your results : at 45° incidence you do not have 1EV underexposure but 2. I developped a model shown here that takes in account not only the variations of the "focal" but also the squeezing of the apparent aera of the pinholes and the expansion of the image depending on grazing angles, yielding thus a factor "cosine to the fourth power". And I developped the same kind of model also for anamorhic cams.

Paul

[antbiker]

Mmmm, yes Paul. That is something I had not considered. Is the elliptical effect to so pronounced, even with a very thin pinhole material (0.001" or less)?
And by my estimation that would leave the 2EV line on my map more like maybe 4EV underexposed or more. Is that really what we are seeing in the examples and others examples posted by photographers who use a Zero 4x5"? Could you produce an exposure map for 4x5" using your figures Paul?

And it does leave me wondering where we all are now with pinhole calculators found online - I would bet they do not take this effect into account.

[earlj]

Tony:

This is a very interesting exercise in theory vs practice. I agree with Paul's theoretical cosine to the fourth power of light falloff. As soon as you move away from the the center of the film, the projected aperture is no longer circular, but elliptical. This decreases the light irrespective of the distance to the film plane. There should be vignetting even on a spherical light-sensitive image area that is equidistant from the aperture. This type of light falloff happens with lenses, as well as with pinhole apertures.

Another factor that bothers me about your maps is that the light falloff is not zonal, but it is rather a smooth gradient. Since both the distance between aperture and image plane as well as the projected aperture shape are in play, the gradient is not linear. The further away from the axis you get, the faster the image darkens.

These types of theoretical discussions often assume a perfectly round pinhole in a material with zero thickness. In real life, neither condition is perfectly true.

I have long thought that reciprocity failure characteristics of the image-forming material contribute to the apparent vignetting in an image, but I have not done any systematic testing or measurements. It would be interesting to compare images of a range of gray scale values on films with different reciprocity characteristics, and then measure densities to put some real numbers to this discussion. I do not have the time or the money to do this, even though I do have a densitometer.

However, success in pinhole photography does not depend on knowing these things. I think that when all is said and done, we all compare what we get with what we thought we would get, and adjust accordingly. For me it is enough to know that a super wide angle camera gives a whole lot more vignetting than a longer format. A flat film plane gives more vignetting than a curved film plane. I have enough cameras of different sizes and shapes that I pretty much know what I am looking for when I start to build, and that is good enough.

But it is still fun to speculate and calculate and predict and measure . . .

[renon]

I define the f/stop of my cameras not in the center. My point for the calculations is 30% of the half diagonal away from the center -> focal length @ 30% and I take in account that the pinhole under this angle is an ellipse and no longer a circle. This works very well for me. The position 30% away from the center has no scientific background I chosen it arbitrary. To get the maximum differences I calculate the f/stop at the center (overexposed compared to the 30% point) and the f/stop at the corners (underexposure). With this method I cannot change the light fall-off from the center to the corners but I can balance the exposure.