Editing Pinhole camera (section)

=== Selection of pinhole size ===
Up to a certain point, the smaller the hole, the sharper the image, but the dimmer the projected image. Optimally, the diameter of the aperture should be less than or equal to {{frac|100}} of the distance between it and the projected image.

Within limits, a small pinhole through a thin surface will result in a sharper [[image resolution]] because the projected [[circle of confusion]] at the image plane is practically the same size as the pinhole. An extremely small hole, however, can produce significant [[diffraction]] effects and a less clear image due to the wave properties of light.<ref name=hecht>{{cite book|first=Eugene|last=Hecht|title=Optics|year=1998|isbn=0-201-30425-2|chapter=5.7.6 The Camera|publisher=Addison-Wesley |edition=3rd}}</ref> Additionally, [[vignetting]] occurs as the diameter of the hole approaches the thickness of the material in which it is punched, because the sides of the hole obstruct the light entering at anything other than 90 degrees.

The best pinhole is perfectly round (since irregularities cause higher-order diffraction effects) and in an extremely thin piece of material. Industrially produced pinholes benefit from [[laser]] etching, but a hobbyist can still produce pinholes of sufficiently high quality for photographic work.

A method of calculating the optimal pinhole diameter was first published by [[Joseph Petzval]] in 1857. The smallest possible diameter of the image point and therefore the highest possible image resolution and the sharpest image are given when:<ref>{{cite book |last1=Petzval |first1=J. |authorlink1=Joseph Petzval |title=Bericht über dioptrische Untersuchungen |trans-title=Report on dioptric examinations |language=de |pages=33–90 |url={{GBurl|96E5AAAAcAAJ|p=33}} |series=Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, mathematisch-naturwissenschaftliche Classe |volume=26 |date=1857 |publisher=Aus der Kais. Kön. Hof- und Staatsdruckerei, in commission bei Karl Gerold's Sohn |oclc=16122711 }}</ref>
:<math>d=\sqrt{2f\lambda}=1.41\sqrt{f\lambda}</math>
where
:{{mvar|d}} is the pinhole diameter
:{{mvar|f}} is the distance from pinhole to image plane or "focal length"
:{{mvar|λ}} is the wavelength of light 

The first to apply  [[Wave theory of light|wave theory]] to the problem was [[John William Strutt, 3rd Baron Rayleigh|Lord Rayleigh]] in 1891. But due to some incorrect and arbitrary deductions he arrived at:<ref>{{cite journal |doi=10.1038/044249e0 |title=Some Applications of Photography |author=Lord Rayleigh |date=1891 |volume=44 |pages=249–254 |journal=Nature |author-link=John William Strutt, 3rd Baron Rayleigh |quote=What, then, is the best size of the aperture? That is the important question in dealing with pin-hole photography. [...] The general conclusion is that the hole may advantageously be enlarged beyond that given by Petzval's rule. A suitable radius is <math>r=\sqrt{f\lambda}</math>.|url=https://zenodo.org/records/2039337/files/article.pdf }}</ref><ref>{{cite journal |last1=Rayleigh |first1=Lord |title=X. On pin-hole photography |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |date=February 1891 |volume=31 |issue=189 |pages=87–99 |doi=10.1080/14786449108620080 |url=https://zenodo.org/record/1786469/files/article.pdf }}</ref>
:<math>d=2\sqrt{f\lambda}</math>     
So his optimal pinhole was approximatively {{#expr:100*(2/(2^0.5)-1) round 0}}% bigger than Petzval's.

Another optimum pinhole size, proposed by Young (1971), uses the [[Fraunhofer diffraction equation|Fraunhofer approximation]] of the diffraction pattern behind a circular aperture,<ref name=Young-71/> resulting in:
:<math>d=\sqrt{2.44}\sqrt{f\lambda}=1.562\sqrt{f\lambda}</math>

This may be simplified to:  <math>d=0.0366\sqrt{f}</math>, assuming that {{mvar|d}} and {{mvar|f}} are measured in millimetres and {{mvar|λ}} is 550 [[Nanometre|nm]], corresponding to the central (yellow-green) wavelength of visible light. For a pinhole-to-film distance of {{convert|1|in|1}}, this works out to a pinhole of {{#expr:(2.44*25.4*(550e-6))^0.5 round 3}}&nbsp;mm in diameter. For {{mvar|f}} = 50 mm the optimal diameter is {{#expr:(2.44*50*(550e-6))^0.5 round 3}}&nbsp;mm. The equivalent f-stop value is {{f/|{{#expr:50/((2.44*50*(550e-6))^0.5) round 0}}}}.

The [[depth of field]] is basically [[Infinity|infinite]], but this does not mean that no optical blurring occurs. The infinite depth of field means that image blur depends not on object distance but on other factors, such as the distance from the aperture to the [[film plane]], the aperture size, the wavelength(s) of the light source, and motion of the subject or canvas. Additionally, pinhole photography can not avoid the effects of [[haze]].
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|image1=LongExposurePinhole.jpg
|alt1=An example of a 20-minute exposure taken with a pinhole camera
|caption1=An example of a 20-minute exposure taken with a pinhole camera
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|image2=PinholeCameraImage.jpg
|alt2=A photograph taken with a pinhole camera using an exposure time of 2s
|caption2=A photograph taken with a pinhole camera using an exposure time of 2s
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