APEX system
Encyclopedia
APEX stands for Additive system of Photographic EXposure, which
was proposed in the 1960 ASA standard
for monochrome film speed, ASA PH2.5-1960,
as a means of simplifying exposure
Exposure (photography)
In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...

 computation.

Exposure equation

Until the late 1960s, cameras did not have built-in exposure meters, and
many photographers did not have external exposure meters. Consequently,
it often was necessary to calculate exposure
Exposure (photography)
In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...

 from
lighting conditions. The relationship of recommended photographic exposure
to a scene's average luminance is given by the camera exposure equation


where
  • is the relative aperture
    Aperture
    In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...

     (f-number
    F-number
    In optics, the f-number of an optical system expresses the diameter of the entrance pupil in terms of the focal length of the lens; in simpler terms, the f-number is the focal length divided by the "effective" aperture diameter...

    )
  • is the exposure time ("shutter speed
    Shutter speed
    In photography, shutter speed is a common term used to discuss exposure time, the effective length of time a camera's shutter is open....

    ") in seconds
  • is the average scene luminance
    Luminance
    Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

     ("brightness
    Brightness
    Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target...

    ")
  • is the ASA arithmetic film speed
    Film speed
    Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....

  • is the reflected-light meter calibration constant


Use of the symbol for luminance reflects photographic
industry practice at the time of ASA PH2.5-1960; current SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

 practice prefers the symbol . German sources typically used for the relative aperture. Many authors now use
and for relative aperture and exposure
time.

Recommendations for the value of the calibration constant in
applicable ANSI
Ansi
Ansi is a village in Kaarma Parish, Saare County, on the island of Saaremaa, Estonia....

 and ISO standards have varied slightly over the
years; this topic is discussed in greater detail under
Exposure meter calibration
in the Light meter
Light meter
A light meter is a device used to measure the amount of light. In photography, a light meter is often used to determine the proper exposure for a photograph...

 article.

Exposure value

In an attempt to simplify choosing among combinations of equivalent camera settings, the concept of exposure values (German: Lichtwert) was originally developed and proposed to other manufacturers by the German shutter manufacturer in the early 1950s. Combinations of shutter speed
Shutter speed
In photography, shutter speed is a common term used to discuss exposure time, the effective length of time a camera's shutter is open....

 and relative aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...

 that resulted in the same exposure were said to have the same exposure value
Exposure value
In photography, exposure value denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer in the 1950s...

, a base-2 logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

ic scale defined by


When applied to the left-hand side of the exposure equation,
denoted combinations of camera settings; when applied to the right-hand side, denoted combinations of luminance
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

 and film speed
Film speed
Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....

. For a given film speed
Film speed
Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....

, the recommended exposure value
Exposure value
In photography, exposure value denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer in the 1950s...

 was determined solely by the luminance
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

. Once the exposure value
Exposure value
In photography, exposure value denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer in the 1950s...

 was determined, it could be directly set on cameras with an scale. Adjustment of exposure
Exposure (photography)
In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...

 was simple, because a change of 1 corresponded to a change of 1 exposure step, i.e., either a halving or doubling of exposure.

Starting 1954, the so called Exposure Value Scale (EVS), originally known as Light Value Scale (LVS), was adopted by Rollei
Rollei
Rollei is a German manufacturer of optical goods founded in 1920 by Paul Franke and Reinhold Heidecke in Braunschweig, Lower Saxony, and maker of the Rolleiflex and Rolleicord series of cameras...

, Hasselblad
Hasselblad
Victor Hasselblad AB is a Swedish manufacturer of medium-format cameras and photographic equipment based in Gothenburg, Sweden.The company is best known for the medium-format cameras it has produced since World War II....

, Voigtländer
Voigtländer
Voigtländer is an optical company founded by Johann Christoph Voigtländer in Vienna in 1756 and is thus the oldest name in cameras. It produced the Petzval photographic lens in 1840, and the world's first all-metal daguerrotype camera in 1841, also bringing out plate cameras shortly afterwards...

, Braun
Carl Braun camera-werk
Carl Braun Camera-Werk of Nuremberg, Germany, or Braun, as it was more commonly called, was originally founded as an optical production house. It is best known for its 35mm film cameras, the Paxettes, and for slide projectors.-History:...

, Kodak, Seikosha
Seikosha
was a branch of the Japanese company Seiko that produces clocks, watches, shutters, computer printers and other devices. It was the root of the manufacturing companies of the Seiko Group.*1881 — Kintarō Hattori opens the watch and jewelry shop "K...

, Aires
AIRES
Aerovías de Integración Regional S.A. is a low-cost airline headquartered in the AIRES Hangar in Bogotá, Colombia. It operates scheduled regional domestic and international services, as well as a domestic cargo service...

, Konica
Konica
was a Japanese manufacturer of, among other products, film, film cameras, camera accessories, photographic and photo-processing equipment, photocopiers, fax machines and laser printers.- History :...

, Olympus
Olympus Corporation
is a Japan-based manufacturer of optics and reprography products. Olympus was established on 12 October 1919, initially specializing in microscope and thermometer businesses. Its global headquarters are in Shinjuku, Tokyo, Japan, while its USA operations are based in Center Valley, Pennsylvania,...

, Ricoh
Ricoh
or Ricoh, is a Japanese company that was established in 1936 on February 6th, as , a company in the RIKEN zaibatsu. Its headquarters is located in Ricoh Building in Chūō, Tokyo....

 and others, introducing lenses with coupled shutters
Shutter (photography)
In photography, a shutter is a device that allows light to pass for a determined period of time, for the purpose of exposing photographic film or a light-sensitive electronic sensor to light to capture a permanent image of a scene...

 and aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...

s, such that, after pre-setting the exposure value, adjusting either the shutter speed
Shutter speed
In photography, shutter speed is a common term used to discuss exposure time, the effective length of time a camera's shutter is open....

 or aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...

 made a corresponding adjustment in the other to maintain a constant exposure. On some models, the coupling of shutter speed and aperture setting was optional, so that photographers could chose their preferred method of working depending on the situation. Use of the scale on such cameras is discussed briefly by Adams (1981, 39).

Modern cameras no longer display exposure values as such, but continue to offer exposure modes, which support users in employing the concept of counter-adjusting shutter speed and aperture at a fixed point of exposure. This can be found in features such as Manual Shift on some Minolta
Minolta AF
The Minolta Alpha camera system was a collection of photographic equipment from Minolta. The system used a lens mount called A-mount, with a flange focal distance 44.50 mm. The new mount was larger than the older SR-mount making old manual lenses incompatible with the new system...

, Konica Minolta
Konica Minolta
is a Japanese manufacturer of office equipment, medical imaging, graphic imaging, optical devices, and measuring instruments. It is headquartered in the Marunouchi Center Building in Marunouchi, Chiyoda, Tokyo, with a Kansai office in Nishi-ku, Osaka, Osaka Prefecture...

 and Sony Alpha or Hyper Manual on some Pentax (D)SLRs since 1991, where the photographer can change one of the parameters, and the camera will adjust the other accordingly for as long as the Auto-Exposure Lock (AEL) function is activated. In a wider sense, functions like , Pa / Ps Creative Program Control (by Minolta, Konica Minolta and Sony) or Hyper Program (by Pentax) belong to this group of features as well.

The additive (logarithmic) system

Although some photographers (Adams 1981, 66)
routinely determined camera settings using the exposure equation, it
generally was assumed that doing so would prove too daunting for the casual
photographer. The 1942 ASA exposure guide,
ASA Z38.2.2-1942, featured a dial calculator,
and revisions in 1949 and 1955 used a similar approach.

An alternative simplification also was possible:
ASA PH2.5-1960 proposed
extending the concept of exposure value
Exposure value
In photography, exposure value denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer in the 1950s...

 to all exposure
Exposure (photography)
In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...


parameters. Taking base-2 logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

s of both sides of the exposure
equation and separating numerators and denominators reduces exposure
calculation to a matter of addition:


where
  • is the aperture value:
  • is the time value:
  • is the exposure value
    Exposure value
    In photography, exposure value denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer in the 1950s...

    : .
  • is the speed value (aka sensitivity value):
  • is the luminance value (aka brightness value):
  • is a constant that establishes the relationship between the ASA arithmetic film speed
    Film speed
    Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....

      and the ASA speed value . The value of is approximately 0.30 (precisely, ).

  • is the reflected-light meter calibration constant


ASA standards covered incident-light meters as well as reflected-light
meters; the incident-light exposure equation is


where
  • is the scene illuminance
    Illuminance
    In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of the intensity of the incident light, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per...

  • is the incident-light meter calibration constant


The use of for illuminance reflects photographic industry practice at the time of the 1961 ASA standard for exposure meters, ASA PH2.12-1961; current SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

 practice prefers the symbol .

ASA PH2.12-1961 included incident-light metering in the APEX concept:


where
  • is the incident-light value:


(German sources typically use (for Lichtwert or Belichtungswert — but not to be confused with the English term light value
Light value
In photography, light value has been used to refer to a“light level” for either incident or reflected light, often on a base-2 logarithmic scale.The term does not derive from a published standard, and has had severaldifferent meanings:...

) instead of the exposure value's symbol . Consequently, the aperture value is referred to as Blendenleitwert , and the time value as Zeitleitwert . The film speed value is named Empfindlichkeitsleitwert, and the brightness value is known as Objekthelligkeit.)

APEX in practice

APEX made exposure
Exposure (photography)
In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...

 computation a relatively simple
matter; the foreword of ASA PH2.5-1960
recommended that exposure meters,
exposure calculators, and exposure tables be modified to incorporate the
logarithmic values that APEX required. In many instances, this was done:
the 1973 and 1986 ANSI exposure guides, ANSI PH2.7-1973
and ANSI PH2.7-1986, eliminated exposure calculator dials in
favor of tabulated APEX values. However, the logarithmic markings for
aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...

 and shutter speed
Shutter speed
In photography, shutter speed is a common term used to discuss exposure time, the effective length of time a camera's shutter is open....

 required to set the computed exposure
were never incorporated in consumer cameras. Accordingly, no reference to
APEX was made in ANSI PH3.49-1971
(though it was included in the Appendix).
The incorporation of exposure meters in many cameras in the late 1960s
eliminated the need to compute exposure, so APEX saw little actual use.

With the passage of time, formatting of APEX quantities has varied
considerably; although the originally was subscript, it
sometimes was given simply as lower case, and sometimes as uppercase.
Treating these quantities as acronyms rather than quantity symbols
probably is reasonable because several of the quantity symbols
(, , and for exposure
Exposure (photography)
In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...

,
luminance
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

, and illuminance
Illuminance
In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of the intensity of the incident light, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per...

) used at the time APEX was proposed are
in conflict with current preferred SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

 practice.

A few artifacts of APEX remain. Canon, Pentax
Pentax
Pentax is a brand name used by Hoya Corporation for its medical-related products & services and Pentax Ricoh Imaging Company for cameras, sport optics , etc. Hoya purchased and merged with the Japanese optics company on March 31, 2008. Hoya's Pentax imaging business was sold to Ricoh Company, Ltd...

 and Leica
Leica
Leica Camera AG, a German optics company, produces Leica cameras. The predecessor of the company, formerly known as Ernst Leitz GmbH, is now three companies: Leica Camera AG, Leica Geosystems AG, and Leica Microsystems AG, producing cameras, geosurvey equipment, and microscopes, respectively...

 cameras use 'Av' and 'Tv' to
indicate relative aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...

 and shutter speed
Shutter speed
In photography, shutter speed is a common term used to discuss exposure time, the effective length of time a camera's shutter is open....

 as well as to symbolize aperture priority
Aperture priority
Aperture priority, often abbreviated A or Av on a camera mode dial, is a setting on some cameras that allows the user to choose a specific aperture value while the camera selects a shutter speed to match. The camera will ensure proper exposure...

 and shutter priority
Shutter priority
Shutter priority refers to a setting on some cameras that allows the user to choose a specific shutter speed while the camera adjusts the aperture to ensure correct exposure...

 modes. Some Pentax DSLRs even provide a 'TAv' exposure mode to automatically set the ISO speed depending on the desired aperture and shutter settings, and 'Sv' (for sensitivity priority
Sensitivity priority
Sensitivity priority, often abbreviated Sv on a camera dial, and colloquially called "ISO priority", is a setting on Pentax cameras that allows the user to choose a specific Sensitivity value while the camera selects a shutter speed and aperture to match. The camera will ensure proper exposure...

) to pre-set the ISO speed and let the camera choose the other parameters. Some meters, such as Pentax spot meters, directly indicate the exposure value
Exposure value
In photography, exposure value denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer in the 1950s...

 for ISO 100 film speed
Film speed
Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....

. For a given film speed
Film speed
Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....

, exposure value
Exposure value
In photography, exposure value denotes all combinations of a camera's shutter speed and relative aperture that give the same exposure. In an attempt to simplify choosing among combinations of equivalent camera settings, the concept was developed by the German shutter manufacturer in the 1950s...

 is directly related to luminance, although the relationship depends on the reflected-light meter calibration constant . Most photographic equipment manufacturers specify metering sensitivities in EV at ISO 100 speed (the uppercase 'V' is almost universal).

It is common to express exposure increments in EV, as
when adjusting exposure relative to what a light meter indicates
(Ray 2000, 316). For example, an exposure compensation
Exposure compensation
Exposure compensation is a technique for adjusting the exposure indicated by a photographic exposure meter, in consideration of factors that may cause the indicated exposure to result in a less-than-optimal image. Factors considered may include unusual lighting distribution, variations within a...

 of +1 EV
(or +1 step) means to increase exposure, by using either a longer exposure time or a smaller -number.
The sense of exposure compensation is opposite that of the EV scale itself.
An increase in exposure corresponds to a decrease in EV, so an exposure compensation of
+1 EV results in a smaller EV;
conversely, an exposure compensation of −1 EV results in a greater EV.

Use of APEX values in Exif

APEX has seen a partial resurrection in the Exif standard, which calls
for storing exposure data using APEX values. There are some minor
differences from the original APEX in both terminology and values. The
implied value (1/3.125) for the speed scaling constant given
in the Exif 2.2 specification (“Exif 2.2”; JEITA 2002)
differs slightly from the APEX value of (0.2973);
with the Exif value, an ISO linear film speed
Film speed
Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....

 of 100 corresponds exactly to a
speed value
of 5.

The relationship between and luminance
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...

depends on both the
speed scaling constant and the reflected-light meter
calibration constant :


Because Exif 2.2 records ISO linear speed rather
than film sensitivity, the value of affects the recorded
value of but not the recorded film speed.

Exif 2.2 does not recommend a range of values for , presumably leaving the choice to the equipment manufacturer.
The example data in Annex C of Exif 2.2
give 1 footlambert for = 0. This is in agreement with the APEX value
for , but would imply , or 3.125 with
in footlamberts. With in
cd/m2, this becomes 10.7, which is
slightly less than the value of 12.5 recommended by
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