Pinhole theory, Part A, coverage power and angle of view


Judging by the many examples of pinhole photographs available on internet or in many publications, quality of pinhole image can vary from grossly out of focus (even unwelcome) to quite sharp with good resolution and contrast. Evidently, there are underlying reasons for this. The image perceived sharpness will be discussed in a separate article. While pinhole itself is a critical component of image quality, perhaps THE component of all design decisions we must make, other factors have compounding effect and should not be ignored.

Here we’ll focus on a couple of key elements of pinhole camera construction:

  • angle of coverage (AoC) or coverage power
  • angle of view (AoV)

Both are important criteria in camera design as they ultimately affect quality of the image, its illumination and overall sharpness.

Angle of Coverage determines physical limitations of the image circle a particular pinhole can theoretically produce. In the simplest of terms, it is a function of pinhole size and thickness of material the hole is made in. There are far more involved elements of physics that will visibly limit simple geometrical coverage (as depicted in diagram below). However, we can simplify discussion complexity by assuming established physicists got it right and ought not to be challenged.

Pinhole theory, part A, coverage powerpdf_dwn

Looking further down the design path, AoC must be taken account when deciding on actual angle of view (AoV) for a particular effect we wish to achieve in the final set up. Unless we intend to allow for a severe vignetting in the image, the covering power must exceed chosen angle of view, the more the better.

As above diagrams clearly show, simple geometrical angle of coverage is quite substantial for most pinhole/material combinations. However, while it is difficult to imagine, a hole in a material must be considered as a cylinder and for a given hole diameter produced in a specific thickness, this cylinder may have adverse effect on behavior of the light rays. This in turn may degrade image quality.

General consensus is that material used for pinhole making should be as thin as possible. There are however practical limits of this, as when material gets too thin its handling becomes a real issue for hole making, mounting, and durability. Minimum thickness is further limited when more typical home methods are considered for pinhole making.

Commercially made pinhole apertures seem to be made in materials of about 0.001″ thickness (which translates to about 0.0254 mm). Thinner are available, but usually by special order.

On the other end of the spectrum, an often suggested material for starters is a wall of a soda can. While these are of widely varied specifications, the thickness can be measured with a micrometer (relatively inexpensive tool) and one can assume it will be in a range of 0.1 – 0.2 mm (or about 0.004″ – 0.008″). While substantially thicker than a typical metal shims mentioned above, it is a workable starting thickness.

Material thickness also has hole making implications. Not only the difficulty of handling a very thin plate, but quality of the hole itself is a combination of tools and technique used vs. materials chosen. As in everything else. some methods will deliver superior results for a given material.

Angle of View is what film of a chosen size actually sees. This is squarely dependent on the film/frame size and its distance from the pinhole. Its dependence on pinhole size is only remote, as the latter governs angle of coverage which, if smaller than AoV, will cause vignetting thus essentially limiting AoV.

Pinhole theory, part A, angle of viewpdf_dwn

Above we see a relationship between position of film plane and the corresponding angle of view (AoV). As we move film away from “normal” (middle) position, our AoV changes correspondingly with most other factors remaining constant. The one important change also taking place, is the f-stop. While optimal pinhole size changes with FHD somewhat, the effective f-stop changes much faster, which could result in a very small value effecting extremely long exposure times. Long exposures can be of advantage, but generally introduce additional challenges quite difficult to control. Ultimately it is going to be a compromise of several factors when deciding on the final design.

  • Optimal Pinhole Diameter (OPD)
  • George Airy's diffraction-limited formula
    OPD = √(2.44*FHD*λ)
  • Rayleigh's formula
    OPD = √(3.66*FHD*λ)

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