EXPOSURE EQUATION
and LIGHT METER CALIBRATION

Version 2


(An earlier version of this article recommended sacrificing the calibration of the meter's Absolute read-out for the calibration of its Exposure read-out. This version uses the meter's "Compensation" setting in addition to its "Calibration" settings so that there is no sacrifice):

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Main Exposure Equation:

(N^2)/t = L*S/K

Where:
N is F-numbers
t is exposure time
L is average scene luminance
S is ISO speed
K is calibration constant

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Per Lambert's Cosine Law if we have a perfect diffuser, then:

Reflectance R is:

R = pi*L/E = pi * K/C

Where:
L is luminance
E is illuminance.

K is the calibration constant for a reflected meter and
C is calibration constant for an incident meter
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For an 18% gray card:

R = .18
if we set E to 1.0 (for 100%) then:

L = .18 / pi

So, the reflected measurement in cd/m^2 should be

The incident lux multiplied by .18/pi (or .0573).
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Sekonic's Calibration Constants are:

K = 12.5 (for spot mode)

C = 250 (for incident mode)

(Sekonic's manual says that it uses 340 instead of 250 when the lumisphere is out, but changing the lumisphere position actually changes the absolute calibration, not the relationship of the absolute calibration to the exposure read-out. So, the relationship of aboslute reading to exposure actually stays static with calibration constant of 250 with sphere in both positions.)

Using these values, we can see that incident and spot should NOT agree on an 18% gray card, but on a 15.7% gray card, becuase:
pi*12.5/250=.157

Given that I've conditioned myself to think of 18% gray as middle gray and as "neutral" exposure, I wish the incident and spot would agree at 18% gray, which would require the ratio of their two calibration constants to one another to be pi/.18 rather than pi/.157.
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RECOMMENDATION FOR CALIBRATING SEKONIC DUALMASTER
FOR PRACTICAL ON-SET USE


First, I calibrate the absolute reading for both the spot and incident modes properly to spec (unlike in a previous version of this document in which I was intentionally throwing off the spot calibration). Since I've discovered that changing the lumisphere poistion changes not only the exposure calculation but also the absolute reading, I have to decide whether to calibrate for sphere-in or sphere-out. So, I choose sphere-out which is the mode I usually use in actual practice. And I know that it will read a bit off with sphere-in.

Next, in order to effectively alter the meter's calibration constants, I can use the meter's "Compensation" parameters and leave the "Calibration" parameters properly calibrated. 18% gray is .1972 stops brighter than 15.7% gray because log2(18/15.7)=.1972. So I need to brighten the incident exposure read-out by two tenths or darken the spot read-out by two tenths or do a combo of the two.

I choose to brighten the incident read-out because the spot meter's 12.5 calibration constant seems very accurate for real world prediction of actual photographic results (such as an 18% gray card coming out .18 in Linear Light in a camera file). So, I set the incident mode's "Compensation" so it reads two tenths brighter (this might be "+.2" or "-.2" in your meter, depending on the setup in your menus). I also make sure the spot "Compensation" is zero.

I've now left both the spot and incident correctly calibrated for absolute readings (i.e. in footcandles, lux, cd/m^2, footlamberts), and I've also maintained the spot meter's 12.5 calibration constant (for calculating the exposure based on the absolute reading), but I've altered how the incident meter calculates exposure from its absolute reading in lux. That is: I've effectively altered the incident calibration constant by two tenths of a stop: bringing it from 250 to 218, because 250/(2^.2)=217.6.

Reality check: I now check the incident meter in exposure mode (rather than absolute mode) against the spot meter (also in exposure mode) with an 18% gray card (using a near-collimated light source) and they match!

Of course, if you want to leave the "Compensation" parameter available for other things (like filter compensation) and if you also don't expect to use the absolute read-out of the meter (lux, cd/m^2, etc), then you can alternatively do as I recommended in the previous version of this document and throw off the "Calibration" parameter instead of the "Compensation" parameter by two tenths to effectively change the calibration constant. In which case, as per the above logic, I would now recommend throwing off the incident calibration (having it read .2 brighter than spec) rather than throwing off the spot calibration (having it read .2 darker than spec).

SHORT VERSION

The short version of this recommendation, boiled down to its essence is this: In calculating the exposure (f/stop, shutter time, ISO) from the absolute reading (amount of light in lux or cd/m^2), the calibration constant is the only parameter which is ambiguous and can be selected to taste. For my personal method of lighting, I like using 12.5 as the spot calibration constant (same as Sekonic's built in constant). And for incident, I like using 218 as the calibration constant, which is .2 stops off from Sekonic's built in constant.