Science of photography

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This page provides information on the science used in all aspects of photography: the camera, its lenses, physical operation of the camera, electronic camera internals, and the process of developing film.

Contents 1 The optical system 1.1 Law of Reciprocity 1.2 Lenses 1.2.1 Focal length 1.2.2 Aperture 1.2.3 Depth of field and Bokeh 1.2.4 Motion blur 2 Physics 2.1 Autofocus 2.2 Workings of a typical manual camera system 2.3 Effects limiting resolution (detail) 2.4 Focus 2.5 Aberration 2.6 Film grain resolution 2.7 Diffraction limit 2.8 Contribution to noise (grain) 2.8.1 Quantum efficiency 2.8.2 Film 2.8.3 CCDs and other photodiodes 2.8.4 Photomultiplier tubes 2.8.5 Aliasing 3 See also

[edit] The optical system

[edit] Law of Reciprocity

Main article: Reciprocity (photography)

Exposure ∝ ApertureArea × ExposureTime × SceneLuminance

The law of reciprocity describes how light intensity and duration trade off to make an exposure—it defines the relationship between shutter speed and aperture, for a given total exposure. Changes to any of these elements are often measured in units known as "stops"; a stop is equal to a factor of two.

Halving the amount light exposing the film can be achieved either by either:

1. Closing the aperture by one stop
2. Descreasing the shutter time (increasing the shutter speed) by one stop

Likewise, doubling the amount of light exposing the film can be achieved by the opposite of one of these operations.

The luminance of the scene, as measured on a reflected light meter, also affects the exposure proportionately. And the amount of light required to make a proper or suitable exposure depends on the film speed, which can also be varied in stops or fractions of stops. If either of these changes, the aperture or shutter speed can be adjusted by an equal number of stops to get to a suitable exposure.

Light is most easily controlled through the use of the camera's aperture (measure in f-stops), but it can also be regulated by adjusting shutter speed. Using faster or slower film is not usually something that can be done quickly, at least using roll film. Large format cameras use individual sheets of film and each sheet could be a different speed. And digital cameras can easily adjust the film speed they are simulating.

For example, starting with an exposure of 1/60^th at f/16, the depth-of-field could be made shallower by opening up the aperture to f/4, an increase in exposure of 4 stops. To compensate, the shutter time would need to be increased as well by 4 stops, that is, adjust exposure time down to 1/1000^th.

Closing down the aperture also limits the resolution due to the diffraction limit.

The reciprocity law specifies the total exposure, but the response of a a photographic material to a constant total exposure may not remain constant for very long exposures in very faint light, or very short exposures in very bright light. This is known as reciprocity failure of the material (film, paper, or sensor).

[edit] Lenses

Main article: Photographic lens

A photographic lens is composed of several lenses, to reduce the effects of chromatic aberration, coma, spherical aberration, and other aberrations and to allow focusing, and possibly zooming capabilities. A simple example is the Cooke triplet, which was used in early cameras, but has since been replaced by more complex systems. Another, the Angenieux retrofocus allows the distance between the last lens and the film to be larger than it would be otherwise. This design is necessary for wide angle lenses on manual cameras, since otherwise the last lens would need to be so close to the film so as to interfere with the mirror. Aberrations generally can be reduced by using a small aperture to prevent light from striking the outer parts of the internal lens elements, since aberrations generally get worse further from the central axis of the lens. Aberrations can be reduced dramatically by using an aspheric lens, but these are more complex to grind than spherical or cylindrical lenses. However, with modern manufacturing techniques the extra cost of manufacturing aspherical lenses is decreasing, and small aspherical lenses can now be made by molding, allowing their use in inexpensive consumer cameras. Fresnel lenses are not used in cameras even though they are extremely light and cheap, because they produce poor image quality.

See also the diagram Movement of lenses in an afocal zoom system under Zoom lens. It is harder to correct for chromatic aberration with zoom lenses, as they must be calibrated to focus over a range of focal lengths. Zoom lenses will also generally have a smaller range of f-stops than fixed focal length lenses.

[edit] Focal length

The focal length of any lens is defined as the distance from the rear principal plane of the lens to the point at which rays of parallel light incident on that lens will be focussed. Since modern photographic lenses are almost always constructed from several simple lenses, the effective focal length of the lens is a complicated function of the optical powers of the surfaces of these simple lenses and the relative distances between them. The greater the focal length of a lens, the greater the magnification of the image on the focal plane. This increase in magnification is gained at the cost of reduced viewing angle and decreased image brightness, since the same light is spread over a larger area in the image plane.

[edit] Aperture

The amount of light admitted to a camera is controlled by an iris or diaphragm inside the lens. This diaphragm is the aperture stop of the camera. Its opening is typically manually or automatically variable, with the size of the opening represented by the f-number. F-numbers typically vary in discrete steps, called f-stops. The f-number is equal to the ratio of the focal length to the diameter of the entrance pupil of the lens. For a given lens configuration, the pupil diameter is proportional to the physical diameter of the opening in the diaphragm.

[edit] Depth of field and Bokeh

When a camera lens is focused to image an object some distance away onto the film or detector, objects some distance closer to and farther away from the camera are also approximately in focus. The range of distances that are nearly in focus is called the depth of field. Depth of field generally increases with decreasing aperture diameter (increasing f-number). The unfocused blur outside the depth of field is sometimes used for artistic effect in photography. The subjective appearance of this blur is known as bokeh.

If the camera lens is focused at or beyond its hyperfocal distance, then the depth of field becomes large, covering everything from half the hyperfocal distance to infinity. This effect is used to make "focus free" or fixed-focus cameras.

See also: Circle of confusion

[edit] Motion blur

Generally a tripod is used when the magnification is high or the picture is taken in low light.

[edit] Physics

[edit] Autofocus

The autofocus system in modern SLRs uses a sensor in the mirrorbox to measure contrast. The sensor's signal is analyzed by an Application-specific integrated circuit (ASIC), and the ASIC tries to maximize the contrast pattern by moving lens elements.

The ASICs in modern cameras also have special algorithms for predicting motion, and other advanced features.

[edit] Workings of a typical manual camera system

[edit] Effects limiting resolution (detail)

[edit] Focus

Focus is the tendency for light rays to reach the same place on the CCD or film, independent of where they pass through the lens. For clear pictures, the focus is adjusted for distance, because at a short object distance the rays reach different parts of the lens with different angles. In modern photography, focussing is often accomplished automatically.

[edit] Aberration

Main article: Aberration in optical systems

Aberrations are the (ray optical rather than diffraction) blurring and distorting properties of an optical system, beyond first order focus. The better the lens, the smaller its aberrations.

Spherical aberration is the dependence of the focal length of a spherical lens on the distance from its center. It is compensated by designing a multi-lens system or by using aspheric lenses.

Chromatic aberration is the dependence of the optical properties on color (wavelength), due to dependence of the refractive index of a lens on color. Blue light is generally bent more than is red. Simple chromatic aberration is the difference in focal length for different colors. There are also higher order chromatic aberrations, such as the dependence of magnification on color. Chromatic aberration is compensated by using lens elements made out of different materials, carefully designed so that their chromatic aberrations cancel.

Curved focal surface is the dependence of the first order focus on the position on the film or CCD. This can be compensated with a multiple lens optical design, but curving the film has also been used.

[edit] Film grain resolution

Black-and-white film has a "shiny" side and a "dull" side. The dull side is the emulsion, a gelatin that suspends an array of Silver Halide crystals. These crystals contain silver grains. The size of the silver grains determine both (a) how sensitive the film is to light exposure, and (b) how fine or grainy the negative (and any subsequent prints made from that negative) will look. Larger grains mean faster exposure but a grainier appearance; smaller grains are finer looking but take more exposure to activate. (The graininess of film is represented by its ISO factor -- generally a multiple of 10 or 100. Lower numbers = finer grain but slower film, and vice versa.)

[edit] Diffraction limit

Since light propagates as waves, the patterns it produces on the film are subject to the wave phenomena known as diffraction, which limit the image resolution to features on the order of several times the wavelength of light. Diffraction is the main effect limiting the sharpness of optical images from lens that are stopped down to small apertures (high f-numbers), while aberrations are the limiting effect at large apertures (low f-numbers). Since diffraction cannot be eliminated, the best possible lens for a given operating condition (aperture setting) is one that produces an image whose quality is limited only by diffraction. Such a lens is said to be "diffraction limited". Normally this means that optical aberrations have been reduced to the point where they can be ignored compared to the blur due to diffraction. A better lens will be diffraction limited over a wider range of operating conditions.

The diffraction-limited optical spot size on the CCD or film is proportional to the f-number (about equal to the f-number times the wavelength of light, which is near 0.0005 mm), so the overall detail in a photograph is proportional to the size of the film or CCD divided by the f-number. For a 35 mm camera with f/11, this limit corresponds to about 6000 resolution elements across the width of the film (36 mm / (11 * 0.0005 mm) = 6500.

Another way to put it is that a camera cannot resolve two distant points unless their path lengths to the two sides of the open lens aperture differ by at least a half wave length. Otherwise they will be both in phase at the same point on the film or CCD.

[edit] Contribution to noise (grain)

[edit] Quantum efficiency

Light comes in particles. The energy of a particle (photon) is the frequency of the light times Plank's constant. A fundamental property of any photographic method is how it collects the light on its photographic plate or electronic detector (for example, a Charged coupled device or CCD).

[edit] Film

This is a way of understanding the "grain" in film pictures. The chemistry limits the fraction of light particles that cause chemical change. To make the film sensitive, the silver compounds are in particles so that one captured photon turns a whole grain dark.

[edit] CCDs and other photodiodes

Photodiodes are back-biased semiconductor diodes, in which an intrinsic layer with very few charge carriers prevents current from flowing. Depending on the material, a light particle (photon) has enough energy to raise one electron from the upper full band to the lowest empty band. The electron and the "hole", or empty space were it was, are then free to move in the electric field and carry current, which can be measured. The fraction of incident photons that produce carrier pairs depends largely on the semiconductor material.

[edit] Photomultiplier tubes

Photomultiplier tubes are vacuum phototubes which amplify light by accelerating the photoelectrons to knock more electrons free from a series of electrodes. They are among the most sensitive light detectors but are not well suited to photography.

[edit] Aliasing

Aliasing can occur in optical and chemical processing, but it is more common and more easily understood in digital processing. It occurs whenever an optical or digital image is sampled or re-sampled at a rate which is too low for its resolution. Some digital cameras and scanners have anti-aliasing filters to reduce aliasing by intentionally blurring the image to match the sampling rate. It is common for film developing equipment used to make prints of different sizes to increase the graininess of the smaller size prints by aliasing.

It is usually desirable to suppress both noise such as grain and detail of the real object that are too small to be represented at the sampling rate.

[edit] See also

• Astrophotography
• Infrared photography
• Ultraviolet photography
• Underwater photography