# APEX system

APEX system

APEX stands for Additive system of Photographic EXposure, whichwas proposed in the 1960 ASA standardfor monochrome film speed, ASA PH2.5-1960,as a means of simplifying exposure computation.

Exposure equation

Until the late 1960s, cameras did not have built-in exposure meters, andmany photographers did not have external exposure meters. Consequently,it often was necessary to calculate exposure fromlighting conditions. The relationship of recommended photographic exposureto a scene's average luminance is given by the camera exposure equation

:$frac \left\{A^2\right\} \left\{T\right\} = frac \left\{B S_x\right\} \left\{K\right\}$

where

* $A$ is the relative aperture (f-number)
* $T$ is the exposure time ("shutter speed")
* $B$ is the average scene luminance ("brightness")
* $S_x$ is the ASA arithmetic film speed
* $K$ is the reflected-light meter calibration constant

Use of the symbol $B$ for luminance reflects photographicindustry practice at the time of ASA PH2.5-1960;current SI practice prefers the symbol $L$. Many authors now use$N$ and $t$ for relative aperture and exposuretime.

Recommendations for the value of the calibration constant $K$ inapplicable ANSI and ISO standards have varied slightly over theyears; this topic is discussed in greater detail under
Exposure meter calibrationin the Light meter article.

Exposure value

In the late 1950s, Hasselblad introduced lenses withcoupled shutters and apertures, such that adjusting either the shutter speedor aperture made a corresponding adjustment in the other to maintain aconstant exposure. Combinations of shutter speed and relative
aperture that resulted in the same exposure were said to have the same"exposure value" $E_v$, a base-2 logarithmic scaledefined by

:$E_v = log_2 \left\{frac \left\{A^2\right\} \left\{T\right\} \right\} = log_2 \left\{frac \left\{B S_x\right\} \left\{K\right\} \right\}$

When applied to the left-hand side of the exposure equation,$E_v$ denoted combinations of camera settings; when applied tothe right-hand side, $E_v$ denoted combinations of luminanceand film speed. For a given film speed, the recommended
exposure value was determined solely by the luminance. Once the
exposure value was determined, it could be directly set on a camerawith an $E_v$ scale such as was included on some Hasselbladlenses. Adjustment of exposure was simple, because achange of 1 $E_v$ corresponded to a change of 1
exposure step, i.e., either a halving or doubling ofexposure. Use of the $E_v$ scale on such cameras is discussedbriefly by Adams (1981, 39).

Although some photographers (Adams 1981, 66) [Ansel Adams described the exposure equation in a slightly different form:&ldquo;To use the Exposure Formula, take the film speed number (on the ASAscale) and determine its approximate square root. This number isremembered as the "key stop" for that film. . . ."At the key stop, the correct shutter speed is the reciprocal of the luminance expressed in c/ft2".&rdquo; The relationship to the ASA exposureequation may not be obvious;however, substituting for $A$ and $T$ gives:$frac \left\{A^2\right\} \left\{T\right\} = LS$The calibration constant$K$ might appear to be missing, but with luminance inc/ft2, it was unity(greatly simplifying the calculation). With luminance incd/m2, $K$ = 10.8, slightlyless than current recommendations.] routinely determined camera settings using the exposure equation, itgenerally was assumed that doing so would prove too daunting for the casualphotographer. 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 proposedextending the concept of exposure value to all exposureparameters. Taking base-2 logarithms of both sides of the exposureequation and separating numerators and denominators reduces exposurecalculation to a matter of addition:

:$E_v = A_v + T_v = B_v + S_v$

where

* $A_v$ is the aperture value: $A_v = 2$ $log_2$ $A$

* $T_v$ is the time value: $T_v = log_2$ $\left(1/T\right)$

* $E_v$ is the exposure value: $E_v = A_v + T_v$.

* $S_v$ is the speed value: $S_v = log_2$ $\left(N S_x\right)$

* $B_v$ is the luminance value: $B_v = log_2$ $\left(B / N K\right)$

* $N$ is a constant that establishes the relationship between the ASA arithmetic film speed $S_x$ and the ASA speed value $S_v$. The value of $N$ is approximately 0.30 (precisely, $2^\left\{-7/4\right\}$). [The origin of the value of $2^\left\{-7/4\right\}$ for $N$ is arcane,apparently so much so that ASA PH2.12-1961included an explanation of what ASA PH2.5-1960had intended.]

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

:$frac \left\{A^2\right\} \left\{T\right\} = frac \left\{I S_x\right\} \left\{C\right\}$

where

* $I$ is the scene illuminance

* $C$ is the incident-light meter calibration constant

The use of $I$ for illuminance reflects photographic industrypractice at the time of the 1961 ASA standard for exposure meters,
ASA PH2.12-1961; current SI practiceprefers the symbol $E$.

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

:$E_v = A_v + T_v = I_v + S_v$

where

* $I_v$ is the incident-light value: $I_v = log_2$ $\left(I / N C\right)$

APEX in practice

APEX made exposure computation a relatively simplematter; the foreword of ASA PH2.5-1960recommended that exposure meters,exposure calculators, and exposure tables be modified to incorporate thelogarithmic values that APEX required. In many instances, this was done:the 1973 and 1986 ANSI exposure guides, ANSI PH2.7-1973and ANSI PH2.7-1986, eliminated exposure calculator dials infavor of tabulated APEX values. However, the logarithmic markings for
aperture and shutter speed required to set the computed exposurewere never incorporated in consumer cameras. Accordingly, no reference toAPEX 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 1960seliminated the need to compute exposure, so APEX saw little actual use.

With the passage of time, formatting of APEX quantities has variedconsiderably; although the $v$ originally was subscript, itsometimes was given simply as lower case, and sometimes as uppercase.Treating these quantities as acronyms rather than quantity symbolsprobably is reasonable because several of the quantity symbols($E$, $B$, and $I$ for exposure,
luminance, and illuminance) used at the time APEX was proposed arein conflict with current preferred SI practice.

A few artifacts of APEX remain. Canon cameras use 'Av' and 'Tv' toindicate relative aperture and shutter speed. Some meters, such as
Pentax spot meters, directly indicate the exposure value forISO 100 film speed. For a given film speed, exposure value isdirectly related to luminance, although the relationship depends on thereflected-light meter calibration constant $K$. Mostphotographic equipment manufacturers specify metering sensitivities in EVat ISO 100 speed (the uppercase 'V' is almost universal).

It is common to express exposure steps as "EV steps," aswhen adjusting exposure relative to what the light meter indicates. Acompensation of +1 EV (or +1 step), for example, means to expose for alonger time or with a smaller $f$-number. This usage can beconfusing, because an exposure compensation of +1 EV actuallycalls for a smaller EV&mdash;a greater EV results in less exposure.

Use of APEX values in Exif

APEX has seen a partial resurrection in the Exif standard, which callsfor storing exposure data using APEX values. There are some minordifferences from the original APEX in both terminology and values. Theimplied value (1/3.125) for the speed scaling constant $N$ givenin the Exif 2.2 specification (&ldquo;Exif 2.2&rdquo;; JEITA 2002)differs slightly from the APEX value of $2^\left\{-7/4\right\}$ (0.2973);with the Exif value, an ISO linear film speed of 100 corresponds exactly to aspeed value [Exif 2.2 refers to $S_mathrm \left\{v\right\}$ as &ldquo;film sensitivity.&rdquo;] $S_mathrm \left\{v\right\}$ of 5.

The relationship between $B_\left\{mathrm \left\{v$ and luminance depends on both thespeed scaling constant $N$ and the reflected-light metercalibration constant $K$:

:$B_mathrm \left\{v\right\} = log_2 frac \left\{B\right\} \left\{NK\right\}$

Because Exif 2.2 records ISO linear speed ratherthan film sensitivity, the value of $N$ affects the recordedvalue of $B_\left\{mathrm \left\{v$ but not the recorded film speed.

Exif 2.2 does not recommend a range of values for $K$, presumably leaving the choice to the equipment manufacturer.The example data in Annex C of Exif 2.2give 1 footlambert for $B_\left\{mathrm \left\{v$ = 0. This is in agreement with the APEX valuefor $B$, but would imply $K = 1/N$, or 3.125 with$B$ in footlamberts. With $B$ incd/m2, this becomes 10.7, which isslightly less than the value of 12.5 recommended by and currently used by manymanufacturers. The difference possibly arises from rounding $B$in the example table; it also is possible that the example data simply were copiedfrom an old ASA or ANSI standard.

Notes

References

* Adams, Ansel. 1981. "The Negative." Boston: New York Graphic Society. ISBN 0-8212-1131-5

* ANSI PH2.7-1973. "American National Standard Photographic Exposure Guide". New York: American National Standards Institute. Superseded by ANSI PH2.7-1986.

* ANSI PH2.7-1986. "American National Standard for Photography &mdash; Photographic Exposure Guide". New York: American National Standards Institute.

* ANSI PH3.49-1971. "American National Standard for general-purpose photographic exposure meters (photoelectric type)". New York: American National Standards Institute. After several revisions, this standard was withdrawn in favor of ISO 2720:1974.

* ASA PH2.5-1960. "American Standard Method for Determining Speed of photographic Negative Materials (Monochrome, Continuous Tone)". New York: United States of America Standards Institute.

* ASA PH2.12-1961. "American Standard, General-Purpose Photographic Exposure Meters (photoelectric type)". New York: American Standards Association. Superseded by ANSI PH3.49-1971.

* ASA Z38.2.2-1942. "American Emergency Standard Photographic Exposure Computer". New York: American Standards Association.

* [http://www.iso.org/iso/en/CatalogueDetailPage.CatalogueDetail?CSNUMBER=7690 ISO 2720:1974] . "General Purpose Photographic Exposure Meters (Photoelectric Type)&mdash;Guide to Product Specification". International Organization for Standardization.

* Japan Electronics and Information Technology Industries Association. 2002. [http://www.exif.org/Exif2-2.PDF JEITA CP-3451, Exchangeable image file format for digital still cameras: Exif Version 2.2] (PDF). Japan Electronics and Information Technology Industries Association.

* JEITA. "See" Japan Electronics and Information Technology Industries Association.

ee also

* Exposure meter calibration

* [http://doug.kerr.home.att.net/pumpkin/#APEX Doug Kerr's in-depth description of APEX]

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