# V-lambda curve

Relative light sensitivity curves: day vision  V (λ) (red) compared to night vision  V '(λ) (blue). These curves have to be multiplied by the factors  K m and  K ' m in order to give the complete photometric radiation equivalents  K (λ) or  K' (λ) .

The luminosity curve (also: the relative spectral luminous efficiency ) describes the spectral light -Sensitivity the human eye in daylight ( photopic range ). ${\ displaystyle V (\ lambda)}$

## Light sensitivity level

Electromagnetic radiation in the wavelength range from around 380 to 780  nanometers (i.e. in the “ visible spectral range ”) triggers a sensation of brightness in the human eye - this radiation is perceived as light . However, the eye is not equally sensitive everywhere in this area. In the case of wavelengths at the edge of the visible range, a higher radiation intensity is necessary in order to produce the same perception of brightness than in the case of wavelengths in the middle of the visible range.

The sensitivity of the eye to the wavelength is described by the spectral photometric radiation equivalent . For example, the curve indicates ${\ displaystyle \ lambda}$ ${\ displaystyle K (\ lambda)}$${\ displaystyle K (\ lambda)}$

• which spectral luminance is perceived at the wavelength when a certain spectral radiance falls into the eye, or${\ displaystyle \ lambda}$
• which spectral light intensity is achieved at the wavelength when a certain spectral radiation intensity is present.${\ displaystyle \ lambda}$

General establishes the connection between the photometric quantities (luminance, luminous intensity) and the associated radiometric quantities (radiance, radiant intensity). ${\ displaystyle K (\ lambda)}$

It is common to write the curve as ${\ displaystyle K (\ lambda)}$

${\ displaystyle K (\ lambda) \, = \, K_ {m} \ cdot V (\ lambda)}$,

so to break them down into the product

• the numerical value in lumens per watt that it assumes at its maximum (the “maximum value of the photometric radiation equivalent”), and${\ displaystyle K_ {m}}$
• the curve varying between 0 and 1 , which describes the course of the sensitivity for different wavelengths relative to the curve maximum (the "relative spectral brightness sensitivity").${\ displaystyle V (\ lambda)}$

## Day vision

The curve was determined empirically and published in the "International Standard Observer " in 1924 ( International Commission on Illumination , Commission Internationale de l'Éclairage, CIE). A 1971 revision by the CIE was recommended and published by the International Committee for Weights and Measures in 1972 . There was a further revision in 1983 (CIE 018.2-1983). It is defined in the range from 360 nm to 830 nm in 1 nm steps for a 2 ° standard observer; the values ​​of are only valid for an observation in a 2 ° field of view , which corresponds to the central area of sharp vision in humans. In Germany it is  standardized under DIN 5031. ${\ displaystyle V (\ lambda)}$${\ displaystyle V (\ lambda)}$

The maximum 1 of the curve is at 555 nm. ${\ displaystyle V (\ lambda)}$

If the curve is multiplied by the factor , the result is the spectral photometric radiation equivalent for daytime vision. ${\ displaystyle V (\ lambda)}$${\ displaystyle \ textstyle K_ {m} \, = \, 683 \ {\ frac {\ mathrm {lm}} {\ mathrm {W}}}}$${\ displaystyle K (\ lambda)}$

## Twilight and night vision

The curve was defined for twilight vision ( mesopic region ) and the curve for night vision ( scotopic region ) . This attain z. B. in the context of glare assessment for automobile headlights in the dark is becoming increasingly important. The spectral shift between day and night vision is known as the Purkinje effect . ${\ displaystyle V_ {eq} (\ lambda)}$${\ displaystyle V '(\ lambda)}$

The maximum 1 of the curve is at 507 nm. ${\ displaystyle V '(\ lambda)}$

If the curve is multiplied by the factor , the result is the spectral photometric radiation equivalent for night vision. ${\ displaystyle V '(\ lambda)}$${\ displaystyle \ textstyle K '_ {m} \, = \, 1699 \ {\ frac {\ mathrm {lm}} {\ mathrm {W}}}}$${\ displaystyle K '(\ lambda)}$

## Brightness sensitivity curve and environment

The human eye's sensitivity to light lies in the focus of the terrestrial solar spectrum with the color green. An environment characterized by green plants probably plays a role here; The blue-green spectral range is also important in moonlight and in ( algae- rich) water.

The eyes of mammals are similar to those of humans. However, little research has been done into the color vision of animals . Birds and insects can see especially in the violet and also in the near ultraviolet spectral range.

Visual sensitivity cell types in humans and animals: