Thick-plate vignetting

Lifted from Break/Fix — unexpectedly soft images and wrong reciprocity corrections, case 2.

What you see

Not softness at all, on inspection. The edges and corners are dark, and the boundary is comparatively hard rather than the gentle gradient of cos-fourth falloff.

It is read as softness because a corner with no light in it has no detail in it, and the eye reports missing detail as unsharpness.

Likely causes

1. A plate substantially thicker than the hole is wide. The geometry rule the course teaches is to keep the thickness at or below one fifth of the diameter.
2. A hole made with a drill rather than pierced and abraded, so that the bore is a parallel-sided cylinder rather than an hourglass.
3. Steel shim at 0.5 mm chosen because it was to hand.

What is happening: the chemistry and physics

A hole in a plate of thickness t is a short cylinder, and looking into a cylinder from the side you see less of the far opening the further off axis you go. The overlap closes completely at

θ_cut = arctan(d / t)

Tunnel cut-off angle

Past that angle the film receives nothing whatever. That is vignetting in the strict sense — an obstruction in the path rather than a falling-off of the light — so it does not stand in for the geometric cos-fourth term; it multiplies it.

The numbers are startling and they are why this entry exists. A 0.30 mm hole in 0.5 mm steel — a perfectly ordinary shim thickness — cuts off at arctan(0.30/0.5) = 31.0°. On 4 × 5 inch paper the corner sits at 34.1° at f = 120 mm and 58.4° at f = 50 mm. The corners are gone at every setting such a camera has, and at the wide setting most of the frame goes with them. Keeping t ≤ d/5 puts the cut-off beyond 78.7°, which is past the corner of anything you are likely to build.

Diagnostic questions

• Photograph nothing but a large, evenly lit blank wall, filling the frame. The negative is then a map of the camera’s illumination with no subject structure in it. This is the confirming test.
• Is the boundary hard or gradual? Cos-fourth falloff is a smooth gradient all the way to the corner. A tunnel cut-off has a visible boundary at a computable radius, f tan θ_cut. At f = 120 mm and θ_cut = 31° that radius is 72 mm, inside the 81 mm half-diagonal — so the corners are dark and the edge centres are not.
• Measure the plate thickness with a micrometer or a feeler gauge. This is the number people never record and then need.
• Compute arctan(d/t) and compare it with the corner angle of the format at the focal distance you used.

Corrective action

A thinner plate. Drinks-can aluminium is about 0.1 mm and brass shim is available at 0.05 mm; either is a better home for a 0.3 mm hole than 0.5 mm steel.

If the thick plate must be used, counter-sink or chamfer the hole from both sides so that the cylinder becomes a short hourglass — which is what a laser-drilled pinhole in a thicker carrier is — and then re-measure the diameter, because chamfering changes it.

Prevention

Put the plate thickness in the pinhole register beside the diameter, and compute θ_cut for every plate when it is entered. It is one line of arithmetic and it retires a plate before it wastes a session.

Choose the material for the thickness rather than for what is in the drawer.