Editing Pinhole camera (section)

== Construction ==
[[File:PinholeCameraAndRelatedSupplies.jpg|thumb|left|alt=A pinhole camera made from an oatmeal container, wrapped in opaque plastic to prevent light leaks; a box of photographic paper; tongs and dishes for developing film; bottles of film developing chemicals|A home-made pinhole camera (on the left), wrapped in black plastic to prevent light leaks, and related developing supplies]]
Pinhole cameras can be handmade by the photographer for a particular purpose. In its simplest form, a pinhole camera includes a light-tight box with a pinhole in one end, and a piece of film or other light-sensitive material at the other end. Suitable containers include empty cylindrical cans, with one open end having a removable lid to facilitate loading film, and the other (closed) end equipped with the pinhole. Instructions for building a pinhole camera were published by Kodak, using either a [[126 film]] cartridge or an empty can.<ref name=Kodak-AA5>{{cite web |url=https://archive.org/details/how-to-make-a-pinhole-camera-kodak/ |title=How To Make and Use a Pinhole Camera, publication no. AA-5 |date=April 1980 |publisher=Consumer Markets Division, Eastman Kodak Company}}</ref> The pinhole may be punched or drilled using a sewing needle or small diameter bit through a piece of aluminum foil or thin aluminum or brass sheet. This piece is then taped to the inside of the light-tight box, behind a hole cut or drilled through one end of the box. A flap of cardboard covering the pinhole, hinged with a piece of adhesive tape, can be used as a shutter.<ref name=Kodak-AA5/> The interior of an effective pinhole camera is painted black to suppress internal stray light reflections.<ref name=Kodak-AA5/><ref>{{cite web|url=http://www.kodak.com/ek/US/en/Pinhole_Camera.htm|title=How to Make and Use a Pinhole Camera|archive-url=https://web.archive.org/web/20160305015755/http://www.kodak.com/ek/US/en/Pinhole_Camera.htm|archive-date=2016-03-05}}</ref>

Pinhole cameras can be constructed with a sliding film holder or back to adjust the distance between the film and the pinhole. This effectively changes the [[focal length]], which affects both the [[angle of view]] and also the effective [[f-stop]] ratio. Moving the film closer to the pinhole will result in a wide angle field of view and shorter exposure time. Moving the film farther away from the pinhole will result in a telephoto or narrow-angle view and longer exposure time.

Instead of simple household materials, pinhole cameras also can be constructed by replacing the lens assembly in a conventional camera with a pinhole. In particular, compact 35&nbsp;mm cameras whose lens and focusing assembly have been damaged can be reused as pinhole cameras, maintaining the use of the shutter and film winding mechanisms. As a result of the enormous increase in [[f-number]], to maintain similar exposure times, the photographer must use a fast film in direct sunshine or other bright light conditions. Homemade or commercial pinholes also can be used in place of the lens on a [[single lens reflex camera]] (SLR) or [[mirrorless interchangeable lens camera]]. Use with a [[digital SLR]] allows metering and composition by trial and error, and since development is effectively free, it is a popular way to try pinhole photography.<ref name=PCW>{{cite web|url=http://www.pcw.co.uk/personal-computer-world/features/2213298/hands-digital-pinhole-camera|title=V3 - digital transformation news, analysis and insight|website=v3.co.uk|access-date=18 October 2018|archive-date=19 April 2009|archive-url=https://web.archive.org/web/20090419000206/http://www.pcw.co.uk/personal-computer-world/features/2213298/hands-digital-pinhole-camera|url-status=dead}}</ref>

{{Clear}}

=== 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]].
{{Multiple images
|align=left
|direction=horizontal
|header=
|footer=
|width1=334
|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
|width2=210
|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
}}
{{Clear}}

===Basis for optimum pinhole size===
[[File:RL of PH Camera vs FL.jpg|thumb|upright=2|A graph of the resolution limit of the pinhole camera as a function of focal length (image distance)]]
In the 1970s, Young measured the resolution limit of the pinhole camera as a function of pinhole diameter<ref name=Young-71>{{cite journal |last1=Young |first1=M. |title=Pinhole Optics |journal=Applied Optics |date=1 December 1971 |volume=10 |issue=12 |pages=2763–2767 |doi=10.1364/ao.10.002763 |pmid=20111427 |bibcode=1971ApOpt..10.2763Y }}</ref><ref>{{cite journal |last=Young |first=M. |title=Pinhole Imagery |date=May 1, 1972 |volume=40 |issue=5 |pages=715–720 |journal=American Journal of Physics |doi=10.1119/1.1986624}}</ref> and later published a tutorial in ''The Physics Teacher''.<ref>{{cite journal |last1=Young |first1=Matt |title=The pinhole camera: Imaging without lenses or mirrors |journal=The Physics Teacher |date=December 1989 |volume=27 |issue=9 |pages=648–655 |doi=10.1119/1.2342908 |bibcode=1989PhTea..27..648Y }}</ref> He defined and plotted two normalized variables: the normalized resolution limit, <math>\frac{RL}{s}</math>, and the normalized focal length, <math>\dfrac{f}{\left ( \frac{s^2}{\lambda} \right )}</math>, where
: {{mvar|RL}} is the resolution limit
: {{mvar|s}} is the pinhole radius ({{mvar|d}}/2)
: {{mvar|f}} is the focal length
: {{mvar|λ}} is the wavelength of the light, typically about 550&nbsp;nm.

On the left-side of the graph (where the normalized focal length is less than 0.65), the pinhole is large, and geometric optics applies; the normalized resolution limit is approximately constant at a value of 1.5, meaning the actual resolution limit is approximately 1.5 times the radius of the pinhole, independent of the normalized focal length. (Spurious resolution is also seen in the geometric-optics limit.)

On the right-side (normalized focal length is greater than 1), the pinhole is small, and [[Fraunhofer diffraction]] applies; the resolution limit is given by the far-field diffraction formula shown in the graph, which increases as the pinhole size decreases, assuming that {{mvar|f}} and {{mvar|λ}} are constant:
:<math>RL = \frac{0.61 \cdot \lambda f}{s}</math>
In this version of formula as published by Young, the radius of the pinhole is used rather than its diameter, so the constant is 0.61 instead of the more usual 1.22.

In the center of the plot (normalized focal length is between 0.65 and 1), which is the region of near-field diffraction (or [[Fresnel diffraction]]), the pinhole focuses the light slightly, and the resolution limit is minimized when the normalized focal length is equal to one. That is, the actual focal length {{mvar|f}} (the distance between the pinhole and the film plane) is equal to <math>\frac{s^2}{\lambda}</math>. At this focal length, the pinhole focuses the light slightly, and the normalized resolution limit is approximately {{frac|2|3}}, i.e., the resolution limit is ~{{frac|2|3}} of the radius of the pinhole. The pinhole, in this case, is equivalent to a Fresnel zone plate with a single zone. The value {{mvar|s}}<sup>2</sup>/{{mvar|λ}} is in a sense the natural focal length of the pinhole.{{fact|date=April 2024}}

The relation {{mvar|f}} = {{mvar|s}}<sup>2</sup>/{{mvar|λ}} yields an optimum pinhole diameter {{mvar|d}} = 2{{radic|{{mvar|fλ}}}}, so the experimental value differs slightly from the estimate of Petzval, above.

=== Calculating the f-number and required exposure ===
The [[f-number]] of the camera may be calculated by dividing the distance from the pinhole to the imaging plane (the [[focal length]]) by the diameter of the pinhole. For example, a camera with a 0.5&nbsp;mm diameter pinhole, and a 50&nbsp;mm focal length would have an f-number of 50/0.5, or 100 (''f''/100 in conventional notation).

Due to the large f-number of a pinhole camera, exposures will often encounter [[reciprocity (photography)|reciprocity]] failure.<ref>{{cite web|url=http://www.nancybreslin.com/pinholetech.html|title=Nancy Breslin's pinhole camera exposure tips|first=nancy a.|last=breslin|website=www.nancybreslin.com|access-date=29 January 2018}}</ref> Once exposure time has exceeded about 1 second for film or 30 seconds for paper, one must compensate for the breakdown in linear response of the film/paper to intensity of illumination by using longer exposures.

Exposures projected on to modern light-sensitive photographic film can typically range from five seconds up to as much as several hours, with smaller pinholes requiring longer exposures to produce the same size image. Because a pinhole camera requires a lengthy exposure, its [[shutter (photography)|shutter]] may be manually operated, as with a flap made of opaque material to cover and uncover the pinhole.