# Exposure (in lux second) required for camera to yield middle gray image?

Started Aug 18, 2015 | Questions thread
Re: Exposure (in lux second) required for camera to yield middle gray image?

Well, I stand to be corrected by true experts on this subject, but this is my working knowledge on the subject based on this http://www.imatest.com/docs/sensitivity_ei/ and other items I've read in the past.

ISO is defined as

ISO = 10/H

where H (measure in lux-seconds) is the light captured at the sensor resulting in an 18% grey tone. So for an ISO of 100, H would correspond to 0.1 lux-seconds at the sensor surface.

To work out the corresponding scene luminance, it is necessary to account for lens transmission, vignetting, and geometry of lens/subject relationship. The imatest page shows how to work that out with some assumptions to give

H = 0.67*L*t/N^2

where L is luminance at the scene in cd per sq. meter, t is exposure time, and N is f-number. Putting these together

N^2/t = L*ISO / (10/0.67)

where the factor K = 10/0.67 = 15 is the reflected-light calibration constant that depends on the assumptions regarding lens transmission, etc. The wikipedia article claims Nikon and Canon use a value of 12.5 here, but I have no direct knowledge.

So for ISO = 100, N = 2.8, t = 1/100, and a calibration constant K = 12.5, the required luminance would be about

L = 2.8^2*100*12.5/100 = 98 cd per sq. meter

to produce a middle grey tone in your final image. Illumination is trickier, and a typical calibration constant is 250 for incident light measured in lux. So for this same example we would need

L = 2.8^2*100*250/100 = 1960 lux.

Hope that helps, and I stand to be corrected by the more knowledgeable folks that participate in this forum.

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