#31. The Standard Width of a Photosensitive Exposure Range
True or False?
The standard width of a photosensitive exposure range for a photosensitive array can be calculated from the reference exposure Ho, which is found in the definition of the photosensitivity S = Ho / Hsp, and the location of the speed point exposure Hsp relative to the location of the minimum usable exposure Hmin.
The width of a photosensitive exposure range is the number of stops between the minimum usable exposure Hmin of the range and the maximum usable exposure Hmax of the range. Using the binary logarithm, log2(), of the exposures to get the number of stops. we have:
Width of a Range in stops = log2(Hmax) – log2(Hmin)
Since the midtone exposure Hm is the midpoint of the exposure range with half of the range on either side of it, we can also have:
Width of a Range in stops = 2 x [ log2(Hm) – log2(Hmin) ]
Recognizing that the speed point exposure Hsp is regularly defined as a shift in exposure δ from the minimum usable exposure Hmin,
log2(Hsp) = log2(Hmin) + log2(δ)
recognizing that the midtone exposure Hm is defined as a shift in exposure M from the speed point exposure Hsp,
log2(Hm) = log2(Hsp) + log2(M)
and combining these equations, we should be able to recognize that the midtone exposure Hm is a two-step shift in exposure from the minimum usable exposure Hmin.
log2(Hm) = log2(Hmin) + log2(δ) + log2(M)
This equation can be rearranged into expressions for the shift from Hmin to Hm in terms of quantities defined by the standards and substituted into the second equation for the width of a range in stops. The resulting equation for the width of a range indicates that the width of a range is twice the shift in exposure from the minimum usable exposure to the midtone exposure which is described by the shifts in exposure δ and M.
Width of a Range in stops = 2 x [ log2(δ) + log2(M) ]
The speed point shifts δ are given in terms of densities in the sensitometric (film speed) standards for emulsions and must be divided by log10(2) = 0.30… to convert them to stops. Taking monochrome negatives, for instance, the speed point exposure is associated with Dmin + 0.10. The speed point shift in stops is 0.10/0.30 = 0.33 stops, that is, a third of a stop.
The midtone shifts M are determined from the value of the reference exposures Ho given in the sensitometric (film speed) standards for emulsions using the implicit equation in the exposure meter standards.
Ho M = qo K
M = qo K / Ho
Therefore, the standard width of a photosensitive exposure range for a photosensitive array can be calculated with two pieces of information from the sensitometric standard for the array, δ and Ho, along with values for the conversion constant qo and the exposure meter constant K.
The diagrams that support the calculation of the standard width of the photosensitive exposure range for various types of photosensitive arrays can be found in the book Photographic Exposure Calculations and Camera Operation.
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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