Intelligence of Engineering in Photography : The Binary Sequences
by Fattah Sakuldee
Photography is a science of arts as well as an arts of science. This wonderful fact exhibits a magnet bringing people from various areas into the same base-ground to experience the beauty of their unfamiliar pieces of knowledge. For me, as a physicist, I have always been very impressed by the modernistic design and the balance of arts and science in photography. One of the examples which I bring it today is one of the best representative of such claim : binary sequences in light exposure element.
From a kind of elementary photography one may say it's quite common that an exposure value (EV, or the index of exposure IE,) is usually indicated in base-2 logarithmic sequence. Namely, for instance, the luminosity of EV 16 will be exactly two time of that of EV 15. The base-10 logarithm, however, seems to be more common scale in contemporary science to represent the exponential quantities, e.g. the degree of sound intensity (dB), the degree of the magnitude of earthquake (Richter scale), the luminosity of star or the power of Hydrogen ions (pH) in the chemical solution. It is quite frustrated at the first glance that why the degree of exposure in photography need to be in base-2 instead of base-10 or other numbers.
In my opinion, such base-2 suits many aspect of practicals in photography. For examples, according to inverse square law of light intensity*, it is easy to keep in mind that doubling the distance of the object from light source will decrease the incident light intensity by 2 EV. The similar rule of thump can also be applied for bellow extension in large format or macro photography. While the former case is related to the light adjustment in studio the bellow adjustment in older day photography seems to be an actual reason making the base-2 more advantageous over other scale. Another convenience in older photography is shutter design, where the speeds are labeled by a sequence of doubling numbers, e.g. 1, 1/2, 1/4, ...
In the similar fashion, the sequence of f-stop is also increased doubly corresponding to the doubling in diameter of diaphragm aperture (f/2, f/4, ...). The film speed increment is also in the same sequence. At this point, one can also find another advantage of the base-2. That is, it makes the calculation of film speed is quite easy in practical. For examples, since 2^(1/3)=1.26, 2^(2/3)=1.60 and 2^(1/2)=1.41, one may use film speed ASA 160 if one wants the scene brighter by roughly 1/2 or 2/3 stop. One can also approximate that ASA 100 is brighter than ASA 80 by about 1/3 stop while ASA 100 can be either 1/2 or 2/3 stop over ASA 64. As seen, the small difference in base-2 sub-scale allows us to control the light in flexible way which will be extremely useful in practical.
To be honest, I could find the real reason for the appearance of the base-2 in photography but if you allow me the guess, I would say that the the light exposure is not in a wide range of number and base-2 is the smallest scale can be used in this kind of measurement. Let's say if the ratio between maximum and minimum intensity applicable is about 100000 one will have just five or six numbers to represent the intensity in base-10 scale while it ranges from 0 to about 16 in base-2. This delicate scale give us a very practical instrument in a fine adjustment in photography as discussed. Nowadays, in the digital age where every quantity is described in binary digit, the base-2 has also done the greater job to join the understanding of film photography and the digital scheme during the transition of camera technology. Of course, the emergence of the binary scale may be an optimal accident. It proofs the intelligence of the contemporary engineering of photography. Also, it exemplifies the beauty of arts and science in this area.
*The light intensity is proportional to the inverse square of the distance from the light source.
by Fattah Sakuldee
Photography is a science of arts as well as an arts of science. This wonderful fact exhibits a magnet bringing people from various areas into the same base-ground to experience the beauty of their unfamiliar pieces of knowledge. For me, as a physicist, I have always been very impressed by the modernistic design and the balance of arts and science in photography. One of the examples which I bring it today is one of the best representative of such claim : binary sequences in light exposure element.
From a kind of elementary photography one may say it's quite common that an exposure value (EV, or the index of exposure IE,) is usually indicated in base-2 logarithmic sequence. Namely, for instance, the luminosity of EV 16 will be exactly two time of that of EV 15. The base-10 logarithm, however, seems to be more common scale in contemporary science to represent the exponential quantities, e.g. the degree of sound intensity (dB), the degree of the magnitude of earthquake (Richter scale), the luminosity of star or the power of Hydrogen ions (pH) in the chemical solution. It is quite frustrated at the first glance that why the degree of exposure in photography need to be in base-2 instead of base-10 or other numbers.
In the similar fashion, the sequence of f-stop is also increased doubly corresponding to the doubling in diameter of diaphragm aperture (f/2, f/4, ...). The film speed increment is also in the same sequence. At this point, one can also find another advantage of the base-2. That is, it makes the calculation of film speed is quite easy in practical. For examples, since 2^(1/3)=1.26, 2^(2/3)=1.60 and 2^(1/2)=1.41, one may use film speed ASA 160 if one wants the scene brighter by roughly 1/2 or 2/3 stop. One can also approximate that ASA 100 is brighter than ASA 80 by about 1/3 stop while ASA 100 can be either 1/2 or 2/3 stop over ASA 64. As seen, the small difference in base-2 sub-scale allows us to control the light in flexible way which will be extremely useful in practical.
To be honest, I could find the real reason for the appearance of the base-2 in photography but if you allow me the guess, I would say that the the light exposure is not in a wide range of number and base-2 is the smallest scale can be used in this kind of measurement. Let's say if the ratio between maximum and minimum intensity applicable is about 100000 one will have just five or six numbers to represent the intensity in base-10 scale while it ranges from 0 to about 16 in base-2. This delicate scale give us a very practical instrument in a fine adjustment in photography as discussed. Nowadays, in the digital age where every quantity is described in binary digit, the base-2 has also done the greater job to join the understanding of film photography and the digital scheme during the transition of camera technology. Of course, the emergence of the binary scale may be an optimal accident. It proofs the intelligence of the contemporary engineering of photography. Also, it exemplifies the beauty of arts and science in this area.
*The light intensity is proportional to the inverse square of the distance from the light source.
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