Editing Light meter (section)

==Exposure meter calibration==

In most cases, an incident-light meter will cause a medium tone to be recorded as a medium tone, and a reflected-light meter will cause ''whatever is metered'' to be recorded as a medium tone.  What constitutes a "medium tone" depends on meter calibration and several other factors, including film processing or digital image conversion.

Meter calibration establishes the relationship between subject lighting and recommended camera settings. The calibration of photographic light meters is covered by [[#CITEREF ISO2720:1974|ISO 2720:1974]].

===Exposure equations===

For reflected-light meters, camera settings are related to ISO speed and subject luminance by the reflected-light exposure equation:

<math>
\frac {N^2} {t} = \frac {L S} {K}
</math>

where

* <math>N</math> is the relative [[aperture]] ([[f-number]])
* <math>t</math> is the exposure time ("[[shutter speed]]") in seconds
* <math>L</math> is the average scene [[luminance]]
* <math>S</math> is the ISO arithmetic [[film speed|speed]]
* <math>K</math> is the reflected-light meter calibration constant

For incident-light meters, camera settings are related to ISO speed and subject illuminance by the incident-light exposure equation:

:<math>
\frac {N^2} {t} = \frac {E S} {C}
</math>

where

* <math>E</math> is the [[illuminance]]
* <math>C</math> is the incident-light meter calibration constant

===Calibration constants===<!-- This section is linked from [[Exposure value]] -->

Determination of calibration constants has been largely subjective; [[#CITEREF ISO2720:1974|ISO 2720:1974]] states that

<blockquote>
The constants <math>K</math> and <math>C</math> shall be chosen by statistical analysis of the results of a large number of tests carried out to determine the acceptability to a large number of observers, of a number
of photographs, for which the exposure was known, obtained under various conditions of subject manner and over a range of luminances.
</blockquote>

In practice, the variation of the calibration constants among manufacturers is considerably less than this statement might imply, and values have changed little since the early 1970s.

[[#CITEREF ISO2720:1974|ISO 2720:1974]] recommends a range for <math>K</math> of 10.6 to 13.4 with
luminance in cd/m<sup>2</sup>.  Two values for <math>K</math> are in common use: 12.5 ([[Canon Inc.|Canon]], [[Nikon]], and
[[Sekonic]]<ref>Specifications for Sekonic light meters are available on the [http://www.sekonic.com/ Sekonic] web site under "Products."</ref>) and 14 ([[Minolta]],<ref name="KM_2006" /> [[Kenko (company)|Kenko]],<ref name="KM_2006">[[Konica Minolta]] Photo Imaging, Inc. left the camera business on March 31, 2006. Rights and tooling for Minolta exposure meters were acquired by Kenko Co, Ltd. in 2007.
Specifications for the Kenko meters are essentially the same as for the equivalent Minolta meters.</ref> and [[Pentax]]); the difference between the two values is approximately {{frac|6}} [[Exposure value|EV]].

The earliest calibration standards were developed for use with wide-angle averaging reflected-light meters
([[#CITEREF JonesCondit1941|Jones and Condit 1941]]).  Although wide-angle average metering has largely given way to other metering sensitivity patterns (e.g., spot, center-weighted, and multi-segment), the values for <math>K</math> determined for wide-angle averaging meters have remained.

The incident-light calibration constant depends on the type of light receptor.  Two receptor types are common: flat ([[cosine]]-responding) and hemispherical ([[cardioid]]-responding).  With a flat receptor, [[#CITEREF ISO2720:1974|ISO 2720:1974]] recommends a range for <math>C</math> of 240 to 400 with illuminance in [[lux]]; a value of 250 is commonly used.  A flat receptor typically is used for measurement of lighting ratios, for measurement of illuminance, and occasionally, for determining exposure for a flat subject.

For determining practical photographic exposure, a hemispherical receptor has proven more effective. [[Don Norwood]], inventor of incident-light exposure meter with a hemispherical receptor, thought that a sphere was a reasonable representation of a photographic subject. According to his patent ([[#CITEREF Norwood1938|Norwood 1938]]), the objective was

<blockquote>
to provide an exposure meter which is substantially uniformly responsive to light incident upon the photographic subject from practically all directions which would result in the reflection of light to the camera or other photographic register.
</blockquote>

and the meter provided for "measurement of the effective illumination obtaining at the position of the subject."

With a hemispherical receptor, [[#CITEREF ISO2720:1974|ISO 2720:1974]] recommends a range for <math>C</math> of 320 to 540 with illuminance in lux; in practice, values typically are between 320 (Minolta) and 340 (Sekonic).  The relative responses of flat and hemispherical receptors depend upon the number and type of light sources; when each receptor is pointed at a small light source, a hemispherical receptor with <math>C</math> = 330 will indicate an exposure approximately 0.40 step greater than that indicated by a flat receptor with <math>C</math> = 250.  With a slightly revised definition of illuminance, measurements with a hemispherical receptor indicate "effective scene illuminance."

===Calibrated reflectance===

It is commonly stated that reflected-light meters are calibrated to an 18% reflectance,<ref> Some authors ([[#CITEREF Ctein1997|Ctein 1997]], 29) have argued that the calibrated reflectance is closer to 12% than to 18%. </ref> but the calibration has nothing to do with reflectance, as should be evident from the exposure formulas.  However, some notion of reflectance is implied by a comparison of incident- and reflected-light meter calibration.

Combining the reflected-light and incident-light exposure equations and rearranging gives

:<math>\frac {L} {E} = \frac {K} {C}</math>

[[Reflectance]] <math>R</math> is defined as

:<math>R = \frac {\mbox {flux emitted from surface}} {\mbox {flux incident upon surface}}</math>

A uniform perfect diffuser (one following [[Lambert's cosine law]]) of luminance <math>L</math> emits a flux density of <math>\pi</math><math>L</math>; reflectance then is

:<math>R = \frac {\pi L} {E} = \frac {\pi K} {C}</math>

Illuminance is measured with a flat receptor.  It is straightforward to compare an incident-light measurement using a flat receptor with a reflected-light measurement of a uniformly illuminated flat surface of constant reflectance.  Using values of 12.5 for <math>K</math> and 250 for <math>C</math> gives

:<math>R = \frac {\pi \times 12.5} {250} \approx 15.7\%</math>

With a <math>K</math> of 14, the reflectance would be 17.6%, close to that of a standard 18% neutral test card.  In theory, an incident-light measurement should agree with a reflected-light measurement of a test card of suitable reflectance that is perpendicular to the direction to the meter.  However, a test card seldom is a uniform diffuser, so incident- and reflected-light measurements might differ slightly.

In a typical scene, many elements are not flat and are at various orientations to the camera, so that for practical photography, a hemispherical receptor usually has proven more effective for determining exposure.  Using values of 12.5 for <math>K</math> and 330 for <math>C</math> gives

:<math>R = \frac {\pi \times 12.5} {330} \approx 11.9\%</math>

With a slightly revised definition of reflectance, this result can be taken as indicating that the average scene reflectance is approximately 12%.  A typical scene includes shaded areas as well as areas that receive direct illumination, and a wide-angle averaging reflected-light meter responds to these differences in illumination as well as differing reflectances of various scene elements. Average scene reflectance then would be

:<math>\mbox{average scene reflectance} =
\frac {\mbox {average scene luminance} } {\mbox {effective scene illuminance }}
</math>

where "effective scene illuminance" is that measured by a meter with a hemispherical receptor.

[[#CITEREF ISO2720:1974|ISO 2720:1974]] calls for reflected-light calibration to be measured by aiming the receptor at a transilluminated diffuse surface, and for incident-light calibration to be measured by aiming the receptor at a point source in a darkened room.  For a perfectly diffusing test card and perfectly diffusing flat receptor, the comparison between a reflected-light measurement and an incident-light measurement is valid for any position of the light source.  However, the response of a hemispherical receptor to an off-axis light source is approximately that of a [[cardioid]] rather than a [[cosine]], so the 12% "reflectance" determined for an incident-light meter with a hemispherical receptor is valid only when the light source is on the receptor axis.

===Cameras with internal meters===

Calibration of cameras with internal meters is covered by [[#CITEREF ISO2721:1982|ISO 2721:1982]]; nonetheless, many manufacturers specify (though seldom state) exposure calibration in terms of <math>K</math>, and many calibration instruments (e.g., Kyoritsu-Arrowin multi-function camera testers<ref>Specifications for Kyoritsu testers are available on the [http://www.criscam.com/ C.R.I.S. Camera Services] web site under "kyoritsu test equipment."</ref> ) use the specified <math>K</math> to set the test parameters.