APEX system 4986342 208940126 2008-04-29T06:05:38Z 63.195.51.225 /* The additive (logarithmic) system */ '''APEX''' stands for '''Additive system of Photographic EXposure''', which was proposed in the 1960 [[American Standards Association|ASA]] standard for [[monochrome film]] speed, [[#CITEREFR ASAPH2.5-1960|ASA PH2.5-1960]], as a means of simplifying [[exposure (photography)|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 (photography)|exposure]] from lighting conditions. The relationship of recommended photographic exposure to a scene's average luminance is given by the camera exposure equation :<math> \frac {A^2} {T} = \frac {B S_x} {K} </math> where * <math>A</math> is the relative [[aperture]] ([[f-number]]) * <math>T</math> is the exposure time ("[[shutter speed]]") * <math>B</math> is the average scene [[luminance]] ("[[brightness]]") * <math>S_x</math> is the ASA arithmetic [[film speed]] * <math>K</math> is the reflected-light meter calibration constant Use of the symbol <math>B</math> for luminance reflects photographic industry practice at the time of [[#CITEREFR ASAPH2.5-1960|ASA PH2.5-1960]]; current [[SI]] practice prefers the symbol <math>L</math>. Many authors now use <math>N</math> and <math>t</math> for relative aperture and exposure time. Recommendations for the value of the calibration constant <math>K</math> in applicable [[ANSI]] and [[ISO]] standards have varied slightly over the years; this topic is discussed in greater detail under [[Light meter#Exposure meter calibration|Exposure meter calibration]] in the [[Light meter]] article. ==Exposure value== In the late 1950s, [[Hasselblad]] introduced lenses with coupled [[shutters]] and [[aperture]]s, such that adjusting either the [[shutter speed]] or [[aperture]] made a corresponding adjustment in the other to maintain a constant exposure. Combinations of [[shutter speed]] and relative [[aperture]] that resulted in the same exposure were said to have the same ''[[exposure value]]'' <math>E_v</math>, a base-2 [[logarithm]]ic scale defined by :<math>E_v = \log_2 {\frac {A^2} {T} } = \log_2 {\frac {B S_x} {K} }</math> When applied to the left-hand side of the exposure equation, <math>E_v</math> denoted combinations of camera settings; when applied to the right-hand side, <math>E_v</math> denoted combinations of [[luminance]] and [[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 camera with an <math>E_v</math> scale such as was included on some [[Hasselblad]] lenses. Adjustment of [[exposure (photography)|exposure]] was simple, because a change of 1 <math>E_v</math> corresponded to a change of 1 [[exposure step (photography)|exposure step]], i.e., either a halving or doubling of exposure. Use of the <math>E_v</math> scale on such cameras is discussed briefly by [[#CITEREFRAdams1981|Adams (1981, 39)]]. ==The additive (logarithmic) system==<!-- This section is linked from [[Light value]] --> Although some photographers [[#CITEREFRAdams1981|(Adams 1981, 66)]]<ref> Ansel Adams described the exposure equation in a slightly different form: &ldquo;To use the Exposure Formula, take the film speed number (on the ASA scale) and determine its approximate square root. This number is remembered as the ''key stop'' for that film. .&nbsp;.&nbsp;. ''At the key stop, the correct shutter speed is the reciprocal of the luminance expressed in c/ft<sup style="font-size: 70%">2</sup>''.&rdquo; The relationship to the ASA exposure equation may not be obvious; however, substituting for <math>A</math> and <math>T</math> gives :<math>\frac {A^2} {T} = LS</math> The calibration constant <math>K</math> might appear to be missing, but with luminance in c/ft<sup style="font-size: 70%">2</sup>, it was unity (greatly simplifying the calculation). With luminance in cd/m<sup style="font-size: 70%">2</sup>, <math>K</math>&nbsp;=&nbsp;10.8, slightly less than current recommendations. </ref> 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, [[#CITEREFR ASAZ38.2.2-1942|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: [[#CITEREFR ASAPH2.5-1960|ASA PH2.5-1960]] proposed extending the concept of [[exposure value]] to all [[exposure (photography)|exposure]] parameters. Taking base-2 [[logarithm]]s of both sides of the exposure equation and separating numerators and denominators reduces exposure calculation to a matter of addition: :<math>E_v = A_v + T_v = B_v + S_v</math> where * <math>A_v</math> is the aperture value: <math>A_v = 2</math> <math>\log_2</math> <math>A</math> * <math>T_v</math> is the time value: <math>T_v = \log_2 </math> <math>(1/T)</math> * <math>E_v</math> is the [[exposure value]]: <math>E_v = A_v + T_v</math>. * <math>S_v</math> is the speed value: <math>S_v = \log_2</math> <math>(N S_x)</math> * <math>B_v</math> is the luminance value: <math>B_v = \log_2</math> <math>(B / N K)</math> * <math>N</math> is a constant that establishes the relationship between the ASA arithmetic [[film speed]] <math>S_x</math> and the ASA [[speed value]] <math>S_v</math>. The value of <math>N</math> is approximately 0.30 (precisely, <math>2^{-7/4}</math>).<ref> The origin of the value of <math>2^{-7/4}</math> for <math>N</math> is arcane, apparently so much so that [[#CITEREFR ASAPH2.12-1961|ASA PH2.12-1961]] included an explanation of what [[#CITEREFR ASAPH2.5-1960|ASA PH2.5-1960]] had intended. </ref> ASA standards covered incident-light meters as well as reflected-light meters; the incident-light exposure equation is :<math> \frac {A^2} {T} = \frac {I S_x} {C} </math> where * <math>I</math> is the scene [[illuminance]] * <math>C</math> is the incident-light meter calibration constant The use of <math>I</math> for illuminance reflects photographic industry practice at the time of the 1961 ASA standard for exposure meters, [[#CITEREFR ASAPH2.12-1961|ASA PH2.12-1961]]; current [[SI]] practice prefers the symbol <math>E</math>. [[#CITEREFR ASAPH2.12-1961|ASA PH2.12-1961]] included incident-light metering in the APEX concept: :<math>E_v = A_v + T_v = I_v + S_v</math> where * <math>I_v</math> is the incident-light value: <math>I_v = \log_2</math> <math>(I / N C)</math> ==APEX in practice== APEX made [[exposure (photography)|exposure]] computation a relatively simple matter; the foreword of [[#CITEREFR ASAPH2.5-1960|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, [[#CITEREFR ANSIPH2.7-1973|ANSI PH2.7-1973]] and [[#CITEREFR ANSIPH2.7-1986|ANSI PH2.7-1986]], eliminated exposure calculator dials in favor of tabulated APEX values. However, the logarithmic markings for [[aperture]] and [[shutter speed]] required to set the computed exposure were never incorporated in consumer cameras. Accordingly, no reference to APEX was made in [[#CITEREFR ANSIPH3.49-1971|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 <math>v</math> originally was subscript, it sometimes was given simply as lower case, and sometimes as uppercase. Treating these quantities as [[acronym]]s rather than quantity symbols probably is reasonable because several of the quantity symbols (<math>E</math>, <math>B</math>, and <math>I</math> for [[exposure]], [[luminance]], and [[illuminance]]) used at the time APEX was proposed are in conflict with current preferred [[SI]] practice. A few artifacts of APEX remain. Canon cameras use 'Av' and 'Tv' to indicate relative [[aperture]] and [[shutter speed]]. Some meters, such as [[Pentax]] [[spot meter]]s, directly indicate the [[exposure value]] for ISO 100 [[film speed]]. For a given [[film speed]], [[exposure value]] is directly related to luminance, although the relationship depends on the reflected-light meter calibration constant <math>K</math>. 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 step (photography)|exposure step]]s as "EV steps," as when adjusting [[exposure]] relative to what the light meter indicates. A compensation of +1 EV (or +1 step), for example, means to expose for a longer time or with a smaller <math>f</math>-number. This usage can be confusing, because an [[exposure compensation]] of +1&nbsp;EV actually calls 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 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 <math>N</math> given in the Exif 2.2 specification (&ldquo;Exif 2.2&rdquo;; [[#CITEREFR JEITA2002|JEITA 2002]]) differs slightly from the APEX value of <math>2^{-7/4}</math> (0.2973); with the Exif value, an ISO linear [[film speed]] of 100 corresponds exactly to a speed value<ref> Exif 2.2 refers to <math>S_\mathrm {v}</math> as &ldquo;film sensitivity.&rdquo; </ref> <math>S_\mathrm {v}</math> of 5. The relationship between <math>B_{\mathrm {v}}</math> and [[luminance]] depends on both the speed scaling constant <math>N</math> and the reflected-light meter calibration constant <math>K</math>: :<math>B_\mathrm {v} = \log_2 \frac {B} {NK}</math> Because Exif 2.2 records ISO linear speed rather than film sensitivity, the value of <math>N</math> affects the recorded value of <math>B_{\mathrm {v}}</math> but not the recorded film speed. Exif 2.2 does not recommend a range of values for <math>K</math>, presumably leaving the choice to the equipment manufacturer. The example data in Annex C of Exif 2.2 give 1 footlambert for <math>B_{\mathrm {v}}</math> = 0. This is in agreement with the APEX value for <math>B</math>, but would imply <math>K = 1/N</math>, or 3.125 with <math>B</math> in footlamberts. With <math>B</math> in cd/m<sup style="font-size: 70%">2</sup>, this becomes 10.7, which is slightly less than the value of 12.5 recommended by [[#CITEREFR ISO272:1974|ISO 2720:1974]] and currently used by many manufacturers. The difference possibly arises from rounding <math>B</math> in the example table; it also is possible that the example data simply were copied from an old ASA or ANSI standard. ==Notes== <references/> ==References== * <span id="CITEREFRAdams1981">Adams, Ansel. 1981. ''The Negative.'' Boston: New York Graphic Society.</span> ISBN 0-8212-1131-5 * <span id="CITEREFR_ANSIPH2.7-1973">ANSI PH2.7-1973. ''American National Standard Photographic Exposure Guide''. New York: American National Standards Institute.</span> Superseded by ANSI PH2.7-1986. * <span id="CITEREFR_ANSIPH2.7-1986">ANSI PH2.7-1986. ''American National Standard for Photography &mdash; Photographic Exposure Guide''. New York: American National Standards Institute.</span> * <span id="CITEREFR_ANSIPH3.49-1971">ANSI PH3.49-1971. ''American National Standard for general-purpose photographic exposure meters (photoelectric type)''. New York: American National Standards Institute.</span> After several revisions, this standard was withdrawn in favor of ISO 2720:1974. * <span id="CITEREFR_ASAPH2.5-1960">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.</span> * <span id="CITEREFR_ASAPH2.12-1961">ASA PH2.12-1961. ''American Standard, General-Purpose Photographic Exposure Meters (photoelectric type)''. New York: American Standards Association.</span> Superseded by ANSI PH3.49-1971. * <span id="CITEREFR_ASAZ38.2.2-1942">ASA Z38.2.2-1942. ''American Emergency Standard Photographic Exposure Computer''. New York: American Standards Association.</span> * <span id="CITEREFR_ISO2720:1974"> [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.</span> * <span id="CITEREFR_JEITA2002">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.</span> * JEITA. ''See'' Japan Electronics and Information Technology Industries Association. ==See also== * [[Light meter#Exposure meter calibration|Exposure meter calibration]] ==External links== * [http://doug.kerr.home.att.net/pumpkin/#APEX Doug Kerr's in-depth description of APEX] [[Category:Photographic techniques]]