Reduced photometric quantity

The reduced photometric quantity is the photometric quantity formed by the mathematical model of a linear spectrally additive receiver for the phenomenon under consideration ^[1] :

X_{r}=K\cdot \int _{0}^{\infty }X_{e,\,\lambda }(\lambda )\,S'\left(\lambda \right)\,d\lambda ,

{\ displaystyle X_ {r} = K \ cdot \ int _ {0} ^ {\ infty} X_ {e, \, \ lambda} (\ lambda) \, S '\ left (\ lambda \ right) \, d \ lambda,}

{\ displaystyle X_ {r} = K \ cdot \ int _ {0} ^ {\ infty} X_ {e, \, \ lambda} (\ lambda) \, S '\ left (\ lambda \ right) \, d \ lambda,}

Where $K$ ${\ displaystyle K}$ $K$ - the conversion factor from units of energy quantities to units used in this system of reduced quantities, $S'\left(\lambda \right)$ ${\ displaystyle S '\ left (\ lambda \ right)}$ ${\ displaystyle S '\ left (\ lambda \ right)}$ - the relative spectral sensitivity of a real or model photodetector, and $X_{e,\lambda }(\lambda )$ ${\ displaystyle X_ {e, \ lambda} (\ lambda)}$ $X _ {{e, \ lambda}} (\ lambda)$ - spectral density of the energy quantity $X_{e}$ ${\ displaystyle X_ {e}}$ $X_ {e}$ defined as the ratio of $dX_{e}(\lambda )$ ${\ displaystyle dX_ {e} (\ lambda)}$ $dX_ {e} (\ lambda)$ per small spectral interval between $\lambda$ ${\ displaystyle \ lambda}$ $\ lambda$ and $\lambda +d\lambda$ ${\ displaystyle \ lambda + d \ lambda}$ $\ lambda + d \ lambda$ , to the width of this interval.

Depending on the type of spectral sensitivity curve, several systems of reduced photometric quantities can be constructed. Among them, the most popular and widely used is the system of light quantities . It is officially recognized at the international level, units of light units are included in the International System of Units (SI) .

Relative spectral luminous efficiency of monochromatic radiation for daytime vision

The system of light values is based on the use of the dependence of the relative sensitivity of the human eye, adapted to daytime vision, on the radiation wavelength. This dependence in photometry is called the relative spectral luminous efficiency of monochromatic radiation for daytime vision. $V(\lambda )$ ${\ displaystyle V (\ lambda)}$ $V (\ lambda)$ ^[2] . The SI conversion factor $K$ ${\ displaystyle K}$ $K$ equal to 683 lm / W ^[3] .

For monochromatic radiation with a wavelength $\lambda$ ${\ displaystyle \ lambda}$ $\ lambda$ relation relating an arbitrary light value $X_{v}(\lambda )$ ${\ displaystyle X_ {v} (\ lambda)}$ $X_ {v} (\ lambda)$ with the corresponding energy value $X_{e}(\lambda )$ ${\ displaystyle X_ {e} (\ lambda)}$ $X_ {e} (\ lambda)$ , in SI has the form:

X_{v}(\lambda )=683\cdot X_{e}(\lambda )V(\lambda ).

{\ displaystyle X_ {v} (\ lambda) = 683 \ cdot X_ {e} (\ lambda) V (\ lambda).}

X_ {v} (\ lambda) = 683 \ cdot X_ {e} (\ lambda) V (\ lambda).

In the general case, when there are no restrictions on the distribution of radiation energy over the spectrum, this ratio takes the form:

X_{v}=683\cdot \int \limits _{380~nm}^{780~nm}X_{e,\lambda }(\lambda )V(\lambda )d\lambda .

{\ displaystyle X_ {v} = 683 \ cdot \ int \ limits _ {380 ~ nm} ^ {780 ~ nm} X_ {e, \ lambda} (\ lambda) V (\ lambda) d \ lambda.}

{\ displaystyle X_ {v} = 683 \ cdot \ int \ limits _ {380 ~ nm} ^ {780 ~ nm} X_ {e, \ lambda} (\ lambda) V (\ lambda) d \ lambda.}

It is also possible to determine systems of reduced photometric quantities for bactericidal action, plant growth, carcinogenic effect of radiation, or, for example, for animal vision - since in many animals the spectral sensitivity curves of the eyes do not coincide with the sensitivity curve of human eyes. For this reason, measuring the amount of light using conventional light meters in experiments, for example, in rats, should be done with caution - the light meter, by the principle of its action, uses the spectral sensitivity curve of the human eye and the amount of light received by the rats will not coincide with the readings.

Notes

↑ GOST 26148-84. Photometry. Terms and Definitions.
↑ GOST 8.332-78. State system for ensuring uniformity of measurements. Light measurements. The values of the relative spectral light efficiency of monochromatic radiation for daytime vision.
↑ The number 683 lm / W is an approximate value $K$ ${\ displaystyle K}$ adopted for practical use, a more accurate value is 683,002 lm / W. Details are in Candela's article.

[1] GOST 26148-84. Photometry. Terms and Definitions.

[2] GOST 8.332-78. State system for ensuring uniformity of measurements. Light measurements. The values of the relative spectral light efficiency of monochromatic radiation for daytime vision.

[3] The number 683 lm / W is an approximate value $K$ ${\ displaystyle K}$ adopted for practical use, a more accurate value is 683,002 lm / W. Details are in Candela's article.

Reduced photometric quantity

Notes

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