Calculation of camera exposure. Moon, P. and Spencer, D. E. Journal of the Franklin Institute, 258(2):113--139, 1954. 00000
Calculation of camera exposure [link]Paper  abstract   bibtex   
The practical results on photographic exposure may be summarized in the simple equation, t f$^{\textrm{2}}$=6U,$_{\textrm{Q}}$ H$_{\textrm{p}}$ This equation relates the helios H$_{\textrm{P}}$ of a scene detail (Fig. 1) to the incident phosage U$_{\textrm{Q}}$ on the film. Knowing the characteristic curve for the film, the photographer decides what value of U$_{\textrm{Q}}$ is to correspond to a given value of H$_{\textrm{P}}$. Then Eq. 9 determines the camera exposure ( t f$^{\textrm{2}}$). The photographer makes two decisions: 1. (a) What are H$_{\textrm{max}}$ and H$_{\textrm{min}}$for the range in which gradation is desired? These limits rarely coincide with the true maximum and minimum helios of the scene: they depend on what the photographer wishes to emphasize and what he wishes to ignore. 2. (b) Where should the U$_{\textrm{max}}$ and U$_{\textrm{min}}$ (corresponding to H$_{\textrm{max}}$ and H$_{\textrm{min}}$) be placed on the characteristic curve of the film? We advocate the two-helios method of calculating camera exposure. H$_{\textrm{max}}$ and H$_{\textrm{min}}$ are measured, and these two values are related to U$_{\textrm{max}}$ and U$_{\textrm{min}}$ on the characteristic curve. Equation 9 then determines exposure time t for any aperture f. The slide rule of Fig. 7 allows easy visualization of the relations. The constant 6 in Eq. 9 is an average value based on representative lens transmittance and a point 15° from the lens axis. This constant may be re-evaluated for the particular lens being used, though such refinement is not ordinarily necessary. One should also remember that when photographing at short distances, the f of Eq. 9 is not the number engraved on the lens barrel. Various one-helios methods have been advocated (28) to simplify the calculation of exposure: 1. (1) Calculation based on H$_{\textrm{av}}$, 2. (2) On H$_{\textrm{min}}$, 3. (3) On H$_{\textrm{max}}$. These schemes are inferior to the two-helios method because they do not allow the photographer to visualize how his highlights and shadows will be reproduced. In (1), some sort of average helios is measured for the scene, and the camera exposure is t f$^{\textrm{2}}$ If H$_{\textrm{av}}$ is the geometric mean of H$_{\textrm{max}}$ and H$_{\textrm{min}}$: H$_{\textrm{av}}$ = H$_{\textrm{max}}$H$_{\textrm{min,}}$ and if both H$_{\textrm{max}}$ and H$_{\textrm{min}}$ are known and their ratio H$_{\textrm{max}}$ H$_{\textrm{min}}$ has a value that can be reproduced, then Eq. 9a offers a good method of calculating exposure. But if H$_{\textrm{av}}$ is taken as the reading of an ordinary photoelectric exposure meter, the results are practically worthless, as has been shown by Jones and Condit (8) and by Berg (14). For (2), the film is exposed for the shadows: t f$^{\textrm{2}}$ = 6U$_{\textrm{min}}$ H$_{\textrm{min}}$ Used without additional information, this method tells nothing about what will happen to the highlights. For (3), t f$^{\textrm{2}}$ = 6U$_{\textrm{max}}$ H$_{\textrm{max}}$ which tells nothing about the shadows. These schemes are usable, but only if the ratio H$_{\textrm{max}}$ H$_{\textrm{min}}$ is known to be within allowable limits. The paper concludes with a consideration of flash exposure based on the same methods. © 1954.
@article{moon_calculation_1954,
	title = {Calculation of camera exposure},
	volume = {258},
	shorttitle = {Calculation of camera exposure},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-50449150080&partnerID=40&md5=c65cbe9d11043a98192345ffb5993f72},
	abstract = {The practical results on photographic exposure may be summarized in the simple equation, t f$^{\textrm{2}}$=6U,$_{\textrm{Q}}$ H$_{\textrm{p}}$ This equation relates the helios H$_{\textrm{P}}$ of a scene detail (Fig. 1) to the incident phosage U$_{\textrm{Q}}$ on the film. Knowing the characteristic curve for the film, the photographer decides what value of U$_{\textrm{Q}}$ is to correspond to a given value of H$_{\textrm{P}}$. Then Eq. 9 determines the camera exposure ( t f$^{\textrm{2}}$). The photographer makes two decisions: 1. (a) What are H$_{\textrm{max}}$ and H$_{\textrm{min}}$for the range in which gradation is desired? These limits rarely coincide with the true maximum and minimum helios of the scene: they depend on what the photographer wishes to emphasize and what he wishes to ignore. 2. (b) Where should the U$_{\textrm{max}}$ and U$_{\textrm{min}}$ (corresponding to H$_{\textrm{max}}$ and H$_{\textrm{min}}$) be placed on the characteristic curve of the film? We advocate the two-helios method of calculating camera exposure. H$_{\textrm{max}}$ and H$_{\textrm{min}}$ are measured, and these two values are related to U$_{\textrm{max}}$ and U$_{\textrm{min}}$ on the characteristic curve. Equation 9 then determines exposure time t for any aperture f. The slide rule of Fig. 7 allows easy visualization of the relations. The constant 6 in Eq. 9 is an average value based on representative lens transmittance and a point 15° from the lens axis. This constant may be re-evaluated for the particular lens being used, though such refinement is not ordinarily necessary. One should also remember that when photographing at short distances, the f of Eq. 9 is not the number engraved on the lens barrel. Various one-helios methods have been advocated (28) to simplify the calculation of exposure: 1. (1) Calculation based on H$_{\textrm{av}}$, 2. (2) On H$_{\textrm{min}}$, 3. (3) On H$_{\textrm{max}}$. These schemes are inferior to the two-helios method because they do not allow the photographer to visualize how his highlights and shadows will be reproduced. In (1), some sort of average helios is measured for the scene, and the camera exposure is t f$^{\textrm{2}}$ If H$_{\textrm{av}}$ is the geometric mean of H$_{\textrm{max}}$ and H$_{\textrm{min}}$: H$_{\textrm{av}}$ = H$_{\textrm{max}}$H$_{\textrm{min,}}$ and if both H$_{\textrm{max}}$ and H$_{\textrm{min}}$ are known and their ratio H$_{\textrm{max}}$ H$_{\textrm{min}}$ has a value that can be reproduced, then Eq. 9a offers a good method of calculating exposure. But if H$_{\textrm{av}}$ is taken as the reading of an ordinary photoelectric exposure meter, the results are practically worthless, as has been shown by Jones and Condit (8) and by Berg (14). For (2), the film is exposed for the shadows: t f$^{\textrm{2}}$ = 6U$_{\textrm{min}}$ H$_{\textrm{min}}$ Used without additional information, this method tells nothing about what will happen to the highlights. For (3), t f$^{\textrm{2}}$ = 6U$_{\textrm{max}}$ H$_{\textrm{max}}$ which tells nothing about the shadows. These schemes are usable, but only if the ratio H$_{\textrm{max}}$ H$_{\textrm{min}}$ is known to be within allowable limits. The paper concludes with a consideration of flash exposure based on the same methods. © 1954.},
	number = {2},
	journal = {Journal of the Franklin Institute},
	author = {Moon, P. and Spencer, D. E.},
	year = {1954},
	note = {00000},
	keywords = {Lighting, Photography},
	pages = {113--139}
}
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