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Full Article | PDF Article**Journal of the Optical Society of America**- Vol. 7,
- Issue 6,
- pp. 407-414
- (1923)
- •doi: 10.1364/JOSA.7.000407

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- E. B. Rosa, Bur. Standards Bull., 6, pp. 343–373; 1910.

- See Report of the Committee on Nomenclature and Standards of the Illuminating Engineering Society for 1921.

- In the published treatments of this subject, there exist many ambiguities and misstatements due chiefly to a lack of precisely denned and generally understood fundamental photometric units. The treatment here given is believed to be entirely free from ambiguity. The advantage of a treatment based on flux vergency density (brightness) is obvious. No general relation between flux density in object and image exists but between the flux vergency densities, the relation is simple and free from all assumptions.

E. B. Rosa, Bur. Standards Bull., 6, pp. 343–373; 1910.

E. B. Rosa, Bur. Standards Bull., 6, pp. 343–373; 1910.

See Report of the Committee on Nomenclature and Standards of the Illuminating Engineering Society for 1921.

In the published treatments of this subject, there exist many ambiguities and misstatements due chiefly to a lack of precisely denned and generally understood fundamental photometric units. The treatment here given is believed to be entirely free from ambiguity. The advantage of a treatment based on flux vergency density (brightness) is obvious. No general relation between flux density in object and image exists but between the flux vergency densities, the relation is simple and free from all assumptions.

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$$dF=Cd\omega $$

$$B=\frac{dC}{dS}=\frac{dD}{d\omega}$$

$$\frac{d{D}^{\prime}}{dD}=\frac{{B}^{\prime}d{\omega}^{\prime}}{Bd\omega}=\frac{{u}^{2}T}{{\upsilon}^{2}}$$

$${B}^{\prime}{\upsilon}^{2}d{\omega}^{\prime}=TB{u}^{2}d\omega $$

$${B}^{\prime}{P}^{\prime}=TBP$$

$$d{D}^{\prime}={B}^{\prime}d{\omega}^{\prime}=\frac{{u}^{2}}{{\upsilon}^{2}}TBd\omega $$

$${D}^{\prime}=\frac{{u}^{2}}{{\upsilon}^{2}}TB\omega =TBP/{\upsilon}^{2}$$

$${D}^{\prime}=0.51\phantom{\rule{0.2em}{0ex}}BP\phantom{\rule{0.2em}{0ex}}\text{lumens}/{\text{cm}}^{2}$$

$$E={D}^{\prime}t=TBPt/{\upsilon}^{2}$$

$$Bd\omega \phantom{\rule{0.2em}{0ex}}\text{cos}\theta =2\pi B\phantom{\rule{0.2em}{0ex}}\text{cos}\theta \phantom{\rule{0.2em}{0ex}}\text{sin}\theta \phantom{\rule{0.2em}{0ex}}d\theta $$

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