#32. Eighteen Percent Midtone Reflectance
True or False?
Eighteen percent reflectance is the midpoint of a five-stop exposure range.
When a photographer talks about 18% as a midtone reflectance, he or she is also implicitly talking about a range of reflectances that has a midtone, and about a maximum reflectance in the range of which the 18% midtone reflectance is a fraction (a percentage).
A photographer can picture a range of reflectances either as a bunch of tones from surfaces in some scene that reflect the ambient illumination or as the bunch of tones created by the surfaces in an image. The tones that the photographer can see–the reflectances–range from black (0% reflectance) through a bunch of grays to white (100% reflectance). (In practice, the photographer might see a narrower range of tones or reflectances, but to include the most general of situations, the photographer must consider the widest possible range of tones or reflectances.)
Since each reflectance can be associated with some luminance (using the Reflection Equation) and each luminance with some exposure (using the Illumination Equation), a midtone reflectance Rm can be related to the midtone and maximum luminances and exposures in the scene with the following equation:
1.00 / Rm = Lmax / Lm = Hmax / Hm
Since the midtone expsoure Hm is the midpoint in any exposure range with half the range above it and half the range below it, the last equation can be rewritten in terms of the width of the exposure range in stops using binary logarithms log2():
log2(1.00/Rm) = log2(Hmax) – log2(Hm) = [ log2(Hmax) – log2(Hmin) ]/2
log2(1.00/Rm) = Width of the Range/2
2 x log2(1.00/Rm) = Width of the Range
In other words, the width of the range in stops is twice the number of stops in the reciprocal of the midtone reflectance 1/Rm. Talking about a midtone reflectance of 18%, the photographer is talking about an exposure range of 5.0 stops.
1.00/0.18 = 5.56
log2(1.00/0.18) = log10(1.00/0.18)/log10(2)
= 0.745/0.301 = 2.47 stops
2 x log2(1.00/0.18) = 4.95 or 5.0 stops = Width of the Range
Copyright 2008 Michael G. Prais, Ph.D.
For a readable but in-depth analysis of this concept along with many other concepts associated with photographic exposure, take a look at the book Photographic Exposure Calculations and Camera Operation. This book provides insight into the equations that govern exposure, exposure meters, photosensitive arrays (both solid-state and emulsion) and the Zone System as well as concepts associated with resolution, dynamic range, and depth of field.
The book is available through Amazon.com (ISBN 978-1-4392-0641-6) where you can Search Inside!™.
Check http://michaelprais.info under Photography for the table of contents, an extensive list of the topics and subtopics covered, the preface describing the purpose of the book, and a diagram central to the concepts in the book.
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