Pinhole camera

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A pinhole camera is a simple camera . Light that falls through a small opening (the hole) into an otherwise light-tight and relatively small box-shaped hollow body results in an upside-down and reversed image on its back. Because the hole is usually poked with a pin , the English term is called pinhole camera . The real image on the opposite inside can be captured on light-sensitive material ( photo paper or film) or via an electronic image converter ( image sensor ). If the picture side is made of transparent material, the picture can be viewed from the outside. Technical applications arise in the area of X-ray radiation , gamma radiation and particle radiation , since pinhole diaphragms represent one (sometimes the only) possibility of generating images. Lens-free holes are found in nature, among other things, on pearl boats ( water-dwelling cephalopods ).

The term is much more specific and younger than the term camera obscura , which is sometimes used synonymously , with which both the basic technical concept, large-scale and more complex versions expanded with lenses, as well as metaphorical uses.

functionality

How a pinhole camera works

The imaging principle of a pinhole camera consists in that almost all light rays are masked out by a pinhole , except for the smallest possible bundle in a straight connection between the object and the image point. Since, in contrast to a focusing camera with a lens, no further bundling of the light is carried out, the diameter of the pinhole alone determines the sharpness and the brightness of the image. In ray optics: the smaller the aperture, the sharper the image, but the lower the light intensity .

The light intensity of real pinhole cameras is 10 to 500 times smaller than that of focusing cameras (they only capture 1 / 100th to 1 / 250,000th part of the light), but the depth of field is therefore 10 to 500 times greater. However, this depth of field can only be used in rare cases, as it begins immediately behind the pinhole (which is seldom needed) and the image is nowhere really sharp.

Mathematically, the image is the result of a convolution from an ideal representation of the object in the surface of the pinhole.

Geometric imaging properties of a pinhole camera

Circles of confusion

Imaging geometry of a pinhole camera
Comparison: Photo of a row of houses with pinhole camera (black and white image on film material) and lens camera (color image on semiconductor sensor)

The smaller the hole diameter D and the greater the distance g of the object to be imaged from the hole, the smaller the diameter of the circles of confusion S are . From the theorem of rays we get with the image distance b :

${\ displaystyle {\ frac {D} {g}} = {\ frac {S} {g + b}}}$

For the circle of confusion diameter S it follows from this:

${\ displaystyle S = D \ cdot {\ frac {g + b} {g}}}$

For greater distances  g ≫ b  the back term tends to one, and the expression then simplifies to:

${\ displaystyle S \ approx D}$

In order to obtain a sufficiently sharp image, the diameter of the circle of confusion must not exceed a certain size (see depth of field ). The exact value of this maximum permissible diameter of the circle of confusion depends on the subsequent enlargement of the image and the viewing distance. In photographic practice, one often assumes a circle of confusion diameter d F  / 1500 ( d F corresponds to the diagonal dimension of the recording format ). However, this value can only be approximately achieved for meter-sized pinhole cameras; smaller pinhole cameras only have a low maximum possible sharpness .

The diffraction of light results in a lower sensible limit for the hole diameter D , below which the disk of confusion becomes larger again. This is slightly larger for red light than for blue light.

Image size

Designated  G  , the article height (actual size of the viewed object),  g  the object distance (distance of the object from the perforated disk ),  b  is the image distance (distance from the perforated disc to the ground glass) and  B  , the image height (the height of the generated image on the screen), so applies:

${\ displaystyle {\ frac {B} {b}} = {\ frac {G} {g}}}$

This equation is known from geometry as the theorem of rays . The image size only depends on the distances, but not on the aperture size or hole size.

Note: The terms object distance and image distance must not always be equated with the corresponding terms in geometric optics . There, the distances relate to the position of the main levels and not to the position of the panel . The term image distance also refers to the area in which the circles of confusion become minimal, and this area does not exist with a pinhole camera or coincides with the object point to be imaged itself.

Effective light intensity

Although a hole (unlike a lens) has no focal length, a pinhole camera has an image distance that is comparable to the focal length , which also determines the image size. The effective light intensity  L eff  = D / b can be calculated from this image distance .

Pinhole cameras in nature

Gaps in the wickerwork create sun images on the wall

In everyday life, one sometimes observes random images at openings that geometrically correspond to the pinhole camera. The Sonnenkringel (sun talers), which can be observed under trees or on the forest floor when the sun is shining , are known. The spaces in between in the dense foliage function as many pinhole diaphragms and depict the solar disk as blurred circular disks. If you do not know the reason for this, you will be very surprised that they appear as "half-moon" during a partial solar eclipse .

The picture on the right shows a wicker chair that is lit from the side by the sun and casts a shadow on the wall on the left. The narrow gaps in the wickerwork create light patterns on the wall in the form of round discs of uniform size. These are images of the circular sun, not the outlines of the mesh.

Loopholes create projections of the surroundings.

The picture on the left shows projections of the surroundings on an opposite wall caused by loopholes : You can see the red roofs of the houses and the trees in front of them. The projections are about 1.50 meters high.

Furthermore, eyes of simple living beings also represent pinhole cameras (pinhole camera eye).

Pinhole cameras in technology

In the area of X-rays , gamma rays and particle radiation , pinhole diaphragms are one (sometimes the only) possibility to generate images, since no classic lenses can be produced for these types of radiation. For X-rays there is also the option of using mirror optics or diffraction gratings , for charged (monochromatic) particles electron optics can be used. Another possibility is through lighting with a point-shaped radiation source (pinhole on the lighting side!) Or, in the case of high-energy particles, through the detection and evaluation of trajectories .

The disadvantage of pinhole cameras is the low light intensity. For medical x-rays they would be e.g. B. completely unsuitable.

So-called coding diaphragms are often used in astronomy . The light intensity is increased compared to a single hole, the resolving power after unfolding is higher than that of a single hole. Radio telescope arrays also use this principle.

Resolution limit of pinhole cameras due to light diffraction

Image of the sharp-edged sun with a pinhole camera with a circular pinhole. Short wavelengths of light (blue) are more strongly diffracted than long wavelengths of light (red).

Diffraction phenomena at the pinhole set limits to the classic approach. The diameter S of the blur spot increases by the diameter ΔS of the diffraction disk. For this, the following applies in simplified form:

${\ displaystyle \ Delta S = c \ cdot {\ frac {b} {D}}}$. Here, c is a light wave-dependent constant that can be set to the approximate value of 1 micrometer.

According to the ray-optical observation, the size of the blur spot decreases linearly with the aperture size (see above). The diffraction of light shows the opposite behavior: the blurring is inversely proportional to the hole diameter. The optimal diameter D opt is the value for which the two together are the smallest. The extreme value search yields:

${\ displaystyle D _ {\ mathrm {opt}} = {\ sqrt {c \ cdot {\ frac {bg} {b + g}}}}}$
For g 'b , the approximation applies: .${\ displaystyle D _ {\ mathrm {opt}} \ approx {\ sqrt {c \ cdot b}}}$
With c = 1 µm, the formula provides the value for D opt in millimeters if b is used in meters .${\ displaystyle D _ {\ mathrm {opt}} \ approx {\ sqrt {b}}}$

The optimal diameter is thus a little smaller than the inner zone of a Fresnel zone plate .

 Image width b Length of the pinhole camera Image sharpness at image size ( ) Exposure time minimum (sec) 1 cm 10 centimeters 1 m 10 m ${\ displaystyle d_ {F}: S}$ Optimal aperture D opt for distant objects Size of the blur spot S for ∞ distant objects B eff = b / D APS-C KB 4 "× 5" 8 "× 10" A0 ISO 100 ISO 800 ISO 6400 0.1 mm 0.2 mm 100 1: 133 1: 216 1: 810 1: 1620 1: 7300 0.4 1/20 1/160 4.4 cm 0.21 mm 0.42 mm 210 1:63 1: 103 1: 390 1: 780 1: 3500 1.6 (2) 1/5 1/40 7.4 cm 0.27 mm 0.54 mm 270 1:49 1:80 1: 300 1: 600 1: 2700 3 (4) 0.4 1/20 0.32 mm 0.63 mm 320 1:42 1:68 1: 260 1: 520 1: 2300 4 (6) 0.5 1/15 21 cm 0.46 mm 0.92 mm 460 1:29 1:47 1: 180 1: 360 1: 1600 15 (30) 2 (2.5) 1/4 1 mm 2 mm 1000 1:13 1:22 1:81 1: 162 1: 730 40 (100) 5 (8) 0.6 3.2 mm 6.3 mm 3200 1: 4.2 1: 6.8 1:26 1:52 1: 230 400 (1800) 50 (120) 6 (10)

The "optimization" refers exclusively to the image sharpness . The effective light intensity of these cameras (read from the effective f-number B eff ) is very low. When exposing film material, the Schwarzschild effect must be taken into account , even in bright sunshine .

The exposure times refer to full sunshine or bright subjects. The values ​​with the Schwarzschild effect are in brackets.

Maximum achievable sharpness:

Maximum permissible
vignetting
[aperture values]
Image width [mm] for image size Optimal aperture [µm]
D opt for image size
Image sharpness with image size
APS-C KB 4 "x5" 8 "x10" A0 APS-C KB 4 "x5" 8 "x10" A0 APS-C KB 4 "x5" 8 "x10" A0
4th 7.7 12.5 47 94 420 88 112 217 306 650 1: 150 1: 195 1: 375 1: 530 1: 1100
3 10 16 60 120 540 100 125 245 350 730 1: 135 1: 170 1: 330 1: 470 1: 1000
2 13.5 21.5 80 160 730 115 150 285 400 850 1: 115 1: 147 1: 285 1: 400 1: 850
1.5 16 26th 98 197 880 127 160 315 445 940 1: 105 1: 135 1: 260 1: 360 1: 780
1 20.7 33.5 126 253 1130 144 183 355 500 1060 1:93 1: 118 1: 230 1: 324 1: 680

Large image sizes are necessary for acceptable image sharpness (typically over three square meters). Strong vignetting has to be accepted when working in the super wide-angle range . The aperture must be in a film that is as thin as possible to avoid additional vignetting and ghosting .

Compared to the focusing camera

Digital pinhole camera: system camera with internal plastic cone and bayonet connection . The perforated diaphragm is located in the center of the cone and consists of a silver-colored metal foil with an etched hole diameter of 0.1 mm and an image width of 11 mm.
Reproduction of a pinhole camera picture: Taken with a cardboard camera on Kodak slide film, 9 cm × 6 cm, exposure time approx. 180 sec

Compared to those of a focusing camera, the images are a pinhole camera

• free of distortions, the projection is usually a gnomonic projection , with curved film mounts cylindrical projections are also possible
• free from chromatic aberration,
• free from astigmatism, coma, spherical aberration and field curvature,
• shows strong vignetting (cos 4 ) compared to retrofocal wide-angle lenses
• Due to the large depth of field on the image side, the image plane can theoretically be curved as desired, so other projections (cylindrical, elliptical, parabolic, hyperbolic) are possible if the sensor allows it.

The images are much more blurred than those of a focusing camera. A pinhole camera is only on par or superior in extreme border areas if the reproduction scale of the subject differs extremely strongly within an image (e.g. from 1: 0 (∞) to 1: 1 (macro)). The following values ​​can be achieved with a conventional camera:

• APS-C sensor, f = w = 10 mm , focusing camera with aperture 22
• Depth of field with ∞ setting and pinhole camera sharpness: 2 cm to ∞
• Depth of field with hyperfocal setting and pinhole camera sharpness: 1 cm to ∞
• 8 "× 10" photo material, f = b = 120 mm , focusing camera with aperture 64
• Depth of field with ∞ setting and pinhole camera sharpness: 38 cm to ∞
• Depth of field with hyperfocal setting and pinhole camera sharpness: 19 cm to ∞

Only when significantly more depth of field is required is a (large) pinhole camera, among many other options, a possible option.

Experiments

The functional principle of a pinhole camera and the propagation of light can be illustrated with simple experiments, which are also suitable for children. Pinhole cameras can be built from matchboxes, beverage or biscuit tins - but even water bins or construction containers are possible.

Photo taken with a concrete pinhole camera
Original portrait photo: On the left, the original created in 1951 using a pinhole camera, which was assembled from a photo kit for schoolchildren according to instructions. On the right is the later restoration of the picture.
Canon AV 1, converted to a pinhole camera

For example, a box or can can be blackened matt inside and provided with a 0.1 to 0.5 mm hole on one side. If the pinhole camera is intended for viewing pictures, the back is a matt screen (transparent paper) that is protected from stray light by a tube or cloth. But you can really take photos with such a container. For this purpose, a film or other light-sensitive material is fixed on the inner wall opposite the hole in absolute darkness and the hole is then sealed. Then the subject is selected for brightness, the shutter is opened and closed again at the end of the exposure time . The duration of the exposure (as with conventional photography) depends on many factors: the existing light intensity, the size of the hole, the movement of the subject; it can be between one second and several months. When developing the film, a negative is created that can be converted into a positive by a contact copy , if necessary . Exact rounding of the hole is important for a good result. Frayed hole edges increase the diffraction of light described above and lead to blurred images. Since the edges of the negative receive significantly less light at larger angles of view , they remain brighter (with the same brightness of the object); the positive becomes darker at the edge. If this drop-off in edge light is undesirable, you have to ensure uniform exposure by manual dodging when copying .

Real pinhole diaphragms also show vignetting , which limits the image circle , because the holes are never completely flat, but actually tubes whose length corresponds to the thickness of the diaphragm. Vignetting can be minimized by increasing the thickness of the aperture in the area of ​​the hole - e.g. B. by grinding - makes it as small as possible in relation to the hole diameter.

Another way to create a pinhole camera yourself is to simply convert a camera . This only needs to have interchangeable optics so that the lens can be completely removed, as well as a release option in which the shutter can be kept open for as long as desired. The optics are removed and replaced by a blind cap that is provided with a corresponding hole. A small attachment holder for various perforated panels is ideal. This construction offers the advantage that you have more than just one “shot” and that the inserted film (black / white or color) can be handed over for development afterwards, so no darkroom or other accessories are required.

Digital pinhole photography

Digital cameras with interchangeable lenses can also be used as pinhole cameras. It is advantageous that digital cameras do not know the Schwarzschild effect , so that there are no exposure uncertainties due to the very long exposure times. In addition, the correct exposure can be checked on the camera monitor after the picture has been taken, so that calibration is very easy and quick. Due to the very long exposure times, increased image noise can be expected from sensor heating , and hot pixels can also appear more clearly.

The exposure times for a wide variety of lighting situations can be determined empirically or with a handheld light meter, as in photography on film, and recorded in tables. With sufficiently sensitive digital cameras, the camera-internal exposure meter can also be used or a histogram with the brightness distribution in the image can be displayed in live view mode .

When using SLR cameras , the distance between the pinhole and the recording sensor is limited: The oscillating mirror requires space, so that the minimum image distance is approx. 42 to 44 mm. The resulting hole diameter (with conventional 35mm sensors) is approx. 0.2 mm. In the case of mirrorless camera systems , the aperture can even be located within the camera housing, so that a relatively large image angle can be achieved with a considerably smaller image distance. With system cameras with live view and corresponding adjustment of the playback brightness, the image can be viewed directly in the electronic viewfinder or on the screen , despite the low light intensity of the pinhole . Furthermore, pinhole video recordings can also be made with it.

In principle, flash photography is also possible. However, because of the small aperture ratio of the receiving hole, very high outputs are required, which can often only be provided by studio flash units.

In addition to the self-made, some commercial pinhole lenses are now available.

Technical aspects

A pinhole camera exhibits interesting technical aspects in the following areas:

• Great depth of field
• Super wide-angle shots
• Long exposure
• Assemble the camera yourself with simple means

However, a very large depth of field can also be achieved

• with super wide-angle lenses on DSLRs (APS-C, f = 10 mm , aperture 22)
• d F  / 1500 : 12 cm to ∞
• d F  / 150 : 1.5 cm to ∞
• with compact cameras (1 / 2.3 ", f = 4 mm , aperture 8)
• d F  / 1500 : 20 cm to ∞
• d F  / 150 : 2.2 cm to ∞

and for most purposes (also for the inclusion of the disused railway bridge) sufficient.

Long exposure is possible through

• Neutral density filter
• Multiple exposure and summation or offsetting

Artistic aspects

Certain features of pinhole photography have particularly fascinated artists. This includes the graphical, two-dimensional effect of such photographs: the depth of field, which is evenly distributed over the image, recedes the spatial perception of the object - everything looks equally blurred from front to back. Another aspect is that objects moving quickly through the image can no longer be found in the photo with long exposure times: This makes it possible, for example, to photograph St. Mark's Square in Venice or the Stachus in Munich without people or vehicles. For this, however, these picture elements are covered with a veil. On the other hand, a landscape photograph must be taken in complete calm if possible, if blurring in the branches of the trees is to be avoided. The effect of multiple exposure can be desired especially for portraits; it gives these recordings a special liveliness.

literature

German

• Thomas Bachler: Working with the camera obscura . Lindemanns, Stuttgart 2001, ISBN 3-89506-222-7
• Reinhard Merz and Dieter Findeisen: Taking photos with the self-made pinhole camera . Augustus, Augsburg 1997, ISBN 3-8043-5112-3
• Peter Olpe: The pinhole camera. Function and DIY . Lindemanns, Stuttgart 1995, ISBN 3-928126-62-8
• Ulrich Clamor Schmidt-Ploch. The pinhole camera - image optimization, physical backgrounds . Books on Demand, Norderstedt 2001, ISBN 3-8311-1261-4

English

• John Warren Oakes: Minimal Aperture Photography Using Pinhole Cameras . Univ. Pr. Of America, Lanham 1986, ISBN 0-8191-5370-2
• Eric Renner: "Pinhole Photography - Rediscovering a Historic Technique", Third Edition, Focal Press (Elsevier Inc.) 2004, ISBN 0-240-80573-9