Technical calculators for Photography

Here is a list of documents where calculators for all technical aspects of Photography can be found: movement blur, light intensity, film sensitivity, relative opening, exposure time, optical systems design, or Stenopeic (Pin Hole) Photography.

Imaginatorium
A diversity of useful photographic calculators
http://www.imaginatorium.org/stuff/photo.htm

Martin Dale Center
Camera calculators, and many other resources
http://www.martindalecenter.com/Calculators1_1_CatoClocks.html#CAM

Mr Pinhole
Calculators specifically for Stenopeic Photography
http://www.mrpinhole.com/calcpinh.php

Stenopeic Photography

Pin Hole Photography

The simplest of all photographic cameras is made of just a box, perfectly light-proof, with a tiny hole through which light can enter and hit the photo sensitive emulsion. Only the hole is enough for forming the inverted image, lens or mirror is not necessary. The Greek name for the hole is "stenopos", and hence the technical name for this technique: Stenopeic Photography. It is also known as "Pin Hole Photography", because the hole is often made using a pin or a needle.

For strict stenopeic work, the diameter of the hole must be calculated according to two factors:

-Focal length of the camera

-Average wave length of the light that will mainly be used for photographing

It means that Stenopeic Photography working, for instance, in the infra-red or in the ultra-magenta part of the spectrum, require different diameters of the stenopo than working in the visual part. In a vacuum the stenopo could in theory be as small as the wave length of the light, but if using the camera in a diffracting medium like air or water, then there is a minimum diameter for preventing the phenomenon of diffraction reaching an extent that would seriously damage image formation.

In the case of photographing in the atmosphere at or near sea level, then the minimum practical diameter has to be of about two millimetres. In the case of photographing under water the minimum diameter has to be bigger. And in the case of photographing at high altitudes in the atmosphere, then it can be smaller than at sea level. There is no maximum diameter, the maximum will only be limited by focal length and by wave length, as it has been said.

The oldest known mention of the phenomenon on which Stenopeic Photography is based, was an observation made by the Greek philosopher Aristotle in the IV century before Jesus Christ. Aristotle wrote that a ray of sun light passing through interstices in the leaves of a tree, projected a circular or nearly circular disc of light on the ground, even though the form of the interstices might not be circular. In the XV century the Italian sage Leonardo da Vinci also wrote some remarks about observing inside the dark room of a house the inverted shadows of passing pedestrians, with light that entered through a fence in the blind or the window panes, and projected on the opposite wall.

It is clear that many other people must have observed those phenomena, but they did not write about them. The English scientist Sir Francis Bacon made some experimenting with a darkened room that had a tiny hole in one of the walls, and formed on the opposite wall and inverted image of the strongly sun lit landscape outside. The first camera known to have been built for this purpose was made in the XVII century by the Italian inventor Giovanni della Porta, with the aim of aiding draughtsmen and painters in the making of drafts, before starting their main illustration works.

Stenopeic Photography was theoretically known to the earliest photographers, but it was not a practical proposal for most of the XIX century, because the slow emulsions of that time forced to work with prohibitively long exposures. Even so, Colson made in 1891 the first calculations about the optimal diameter of the stenopo. He considered focal length but he did not consider wave length of light, because panchromatic emulsions had not been invented yet, and orthochromatic emulsions, although already invented, were still rare.

Stenopeic Photography knew an important advance with the introduction of faster emulsions, gradually during the XX century. Good stenopeic photographs were made by the Italian photographer Speri della Chiesa in the 1920's, therefore we may think of those years as the definitive consolidation of this photographic technique. However, wave length began to be seriously considered only when Photography began to work with infra-red emulsions, in the 1930's, but restricted to scientific or military use. Infra-red Photography was not available for most photographers until the 1950's. It is not available even today, in backward countries.

Stenopeic Photography presents the following distinct advantages:

The images are free of any deformation.

The perspective is the most perfect that can be obtained.

The depth of field is at its maximum: all planes are in focus. This may not be desirable in Monoscopy, because the effect of depth given by planes slightly out of focus strongly enhances the main plane, but in Stereoscopy it is an advantage to have a good depth of field.

Stenopeic Photography, however, also has the following serious disadvantages:

For preserving the total absence of deformation and the perfect perspective that only a stenopeic camera can offer, all points in the emulsion should in theory be at the same distance from the stenopo. This means that the film or plate should ideally have the form of the inner face of a sphere, with the stenopo centred in front of it at the distance corresponding to the focal length. However, in practice it is enough to use film that could be curved in front of the stenopo, forming the inside of a cylinder rather than forming the inside of a sphere. For this reason the camera bodies used for Stenopeic Photography are often those of panoramic cameras, because they are already built with a half circular back, inside of which the film is put for exposure.

The very small relative opening of a stenopeic camera forces to tremendously long exposure times, in which the reciprocity failure (Schwartzschild Effect) must be taken into account. Of course, the camera must be immobilised on a tripod or some other secure support.

The phenomenon of diffraction forces to work with a mininum diameter of the stenopo, and because that diameter must be in proportion to the focal length for a given average wave length, then it forces to enormously long cameras. Tubes of one or two metres, or even of several metres in length, are not at all uncommon for serious Stenopeic Photography. For amateurs, however, much shorter cameras may offer acceptable results, with stenopo diameters of as little as 200 micrometres, but in normal circumstances these small diameters will provoke diffraction of light.

The resolution in any optical system (the discrimination as distinct of lines that appear very close together) is the inverse of the depth of field. This means that Stenopeic Photography, having as it has a maximum of depth of field, by needs has also a minimum of optical resolution. Therefore the grain of the emulsion can be relatively disconsidered, and thus faster (more sensitive) emulsions are usually preferable. This is good, because even with fast emulsions the exposure time is always long. The Pin Hole photographer must be armed with a good dose of patience.

Fresnel Zone Plates

A derivation of Stenopeic Photography is the Photography made by the use of Fresnel Zone Plates. Those plates consist of alternating transparent and opaque rings, with thickness decreasing in integral proportion from the central ring to the peripherical one. The plates themselves are often made by photographic processes, and afterwards they are used in place of what in a true stenopeic camera would be the stenopo or 'pin hole'. In certain aspects, Fresnel Zone Plates are a half way between stenopo cameras that use pin holes, and refracto cameras that use lenses or reflexo cameras that use mirrors. The first document listed below is specific on Fresnel Zone Plates. The other documents deal with Stenopeic Photography in general. See also the hyper link to calculators for Stenopeic Photography, listed in the section on calculators, above.

Hyper links on Stenopeic Photography

Whizkid
Fresnel Zone Plates
http://www.whizkidtech.redprince.net/zoneplate

Unblinking Eye
Stenopeic Photography
http://unblinkingeye.com/

Some useful formulas

Of the plenty of formulas that can be used for many aspects of photographic work, a few are presented here for calculating exposure. This is extremely important for photographers such as P. A. Stonemann, CSS Dixieland, who never use a light meter (a photo meter). Instead, Mister Stonemann mentally performs all the necessary calculations, and he manually adjusts the camera controls accordingly. Of course, experience is necessary for determining intensity of light by the naked eye, but otherwise the mental-manual method is faultless.

ASA is a measure of the general photo-sensitivity of emulsions (as opposed to the chromatic photo-sensitivity). ASA was initially specified by the American Standards Association (hence the name), and many years later it was approved by the International Standards Organisation (since then, ASA is also called ISO). Other measures for general photo-sensitivity exist or have existed in the History of Photography, such as DIN (Deutsche Industrie Norm), but ASA-ISO is today the most common in most countries. A typical emulsion of the early XXI century has from 100 ASA-ISO, or 21 DIN, to 400 ASA-ISO, or 27 DIN. Emulsions tended to be less sensitive in the past. Increasing sensitivity also tends to increase grain size, resulting in images with poor definition.

Lux is a measure of intensity of light, derived from the units candle, lumen, square metre and second, of the Systeme International d'Unites, or Decimal Metric System. Photographers who cannot estimate light intensity by the naked eye, may use a luximeter for exact values, or may use a posographic table (a list of typical light conditions and their approximate values).

Second is the unit of time of the Systeme International d'Unites, or Decimal Metric System. Using some kind of chronometer is advisable for long exposures.

"Opening" or "f/opening" is the result of dividing the focal length of the camera among the diameter of the opening hole (the diaphragm, or another device for controlling the amount of light that enters the camera).

For instance, in a camera with 50 millimetres of focal length and an opening hole of also 50 millimetres, then the f/opening is:
50 / 50 = 1
Usually expressed as f 1. It means that the emulsion receives as much amount of light as there is light outside the camera. That is an example for making the concept clear, because only a few scientific cameras using mirrors can reach an f/opening of f 1 (or even surpass it, as much as f 0.7), most cameras of high quality begin at f 1.2 or so.

With focal length of 50 millimetres and opening hole of 12.5 millimetres, then the f/opening is:
50 / 12.5 = 4
Usually expressed as f 4. The emulsion receives a fourth part of the light that exists outside the camera. It stands to reason that exposure time must be four-folded, for having on the photo-sensitive emulsion the effect that had had the first example above, other factors being equal (in fact, other factors are not equal, due to reciprocity failure and other technicalities).

The main exposure formulae are four, closely inter-related:

ASA = ((opening^2) x 200) / (lux x second)
Lux = ((opening^2) x 200) / (asa x second)
Second = ((opening^2) x 200) / (lux x asa)
Opening = ((asa x lux x second) / 200) v2

The expression "^2" means "raised to the power of two", and the expression "v2" means "extracted to the root of two". For example, four raised to the power of two equals sixteen: 4^2 = 16, and its inverse operation is sixteen extracted to the root of two, which equals four: 16 v2 = 4
The expression "x" means "multiply" and the expression "/" means "divide".

Example: we are using a film of 100 ASA, photographing under full Sun light, and we wish to adjust the opening to f 4 (for obtaining a certain depth of field). How much time of exposure should we give to the film ?
By posograph or naked eye we estimate full Sun light as about 60 000 Lux.
((opening^2) x 200) / (lux x asa) = Second
Opening f 4^2 = 16
16 x 200 = 3 200
60 000 Lux x 100 ASA = 6 000 000
3200 / 6 000 000 = 0.000 533 333... Second
A tiny fraction of a second. We discover it by 1 / 0.000 533 333 = 1875
The result is 1/1875 of a second. By approximation we adjust the shutter of the camera to 1/2000 of a second (half of a thousandth of a second).

Difficult ? For those who are not used to mathematical calculations it is probably difficult. Then try another approach, less exact but much simpler. It is the "Thumb-rule of opening f 18", which declares that:

Under full Sun Light, using an opening of f 18, the exposure in fraction of a second is approximately equal to the ASA of the film.

Applying the formula only for demonstration, if we use an opening of f 18:
((opening^2) x 200) / (lux x asa) = Second
Opening f 18^2 = 324
324 x 200 = 64 800
60 000 Lux x 100 ASA = 6 000 000
64 800 / 6 000 000 = 0.010 8 Second
A fraction of a second. We know how much by 1 / 0.010 8 = 92.592...
Result almost 1/93 of a second. By approximation we adjust the shutter of the camera to 1/100 of a second (a hundredth of a second). So under full Sun light, for an opening f 18, our shutter to 100 because our film is of 100 ASA.

But we are using an opening f 4, not an opening f 18. Then we perform a very simple mental calculation, counting the number of steps from f 18 to f 4:
Opening f 18, shutter 100
Opening f 16 is a litle bigger, so the shutter should work a little faster:
Opening f 16, shutter 125
Opening f 11 allows double light than f 16, so shutter to double speed:
Opening f 11, shutter 250
We continue the process until we reach f 4:
Opening f 8, shutter 500
Opening f 5.7 (shown as 5.6 in some cameras), shutter 1000
Opening f 4, shutter 2000

Thus we have arrived by a simpler, though also less exact method, to the same result that we had obtained by the more complex formulas above. The good thing is that we do not depend on light meters, either inserted in the camera or hand-held. Light meters that generate their own current (such as selenium light meters) usually do not give trouble, but the more sensitive modern light meters based on conductivity, which need a source of electric current, are more prone to misfunctions. At least for calm work, with plenty of time ahead, photographers should be able to work without need of any light meters.

Hyper links on Photography

History of Photography

Azus Web Works
History of Photography and its diverse techniques
http://www.azuswebworks.com/photography/

Legal or other advice to Photographers

Benedict
Full legal information on copy-right
http://www.benedict.com/

Photo Stuff
Technical information for silver iodide, chloride, bromide or fluoride
http://www.photostuff.co.uk/

Emulsions made of other chemical compounds

Alternative Photography
Technical information for methods that do not use silver hallides
http://www.alternativephotography.com/

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