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ciespec2unit

The ciespec2unit function weights given spectra with the provided reference weighting functions and returns the integrated values, see equation 1. The function uses a linear interpolation if the wavelength steps are smaller than in the weighting function reference, \Delta\lambda is derived from the input wavelength vector. The weighting functions are derived from the ciespec function. Any errors in the data set or in results generated with the Lighting Toolbox are not in the liability of the CIE nor me, see licence.

(1) \qquad X = K_{\text{m}} \cdot \sum{\left( X_{\text{e,}\lambda} \cdot S_{\lambda}\cdot\Delta\lambda\right)}

Where:

Parameter Description
XIs the spectrally weighted and integrated value.
K_{\text{m}}Is the luminous efficacy.
X_{\text{e,}\lambda}Is the spectral power distribution of the input unit.
S_{\lambda}Is the spectral weighting function.
\Delta\lambdaIs the wavelength step width.

Usage:

value = ciespec2unit(lam,spec,'reference',k)

Where:

ParameterDescription
valueIs/are the spectrally weighted and integrated return value(s).
lamIs a vector speciefying the wavelength steps.
specIs a vector or matrix contains the spectral power distribution(s) (SPD), row-wise.
'reference'Defines the weighting function, as in the following table, or as vector. Note: one can actually use all references given in the ciespec function.
k
(optional)
Is the luminous efficacy K_{\text{m}}, for photopic values K_{\text{m}} equals 683.002~\frac{\text{lm}}{\text{W}} for scotopic values K_{\text{m}} equal 1700.13~\frac{\text{lm}}{\text{W}}. Note that scotopic ‘V-L’ and rhodopic ‘rh’ are treated differently because ‘rh’ is evaluated as in CIE S 026.

Weighting references

ReferenceDescription
'x'2° tristimulus function \bar{x}
'y'2° tristimulus function \bar{y}, equals ’VL’
'z'2° tristimulus function \bar{z}
'xyz'2° tristimulus functions \bar{x}, \bar{y} and \bar{z}
'x10'10° tristimulus function \bar{x}_{10}
'y10'10° tristimulus function \bar{y}_{10}
'z10'10° tristimulus function \bar{z}_{10}
'xyz10'10° tristimulus function \bar{x}_{10}, \bar{y}_{10} and \bar{z}_{10}
'r'CIE \bar{r} function, note: source only 380 nm – 780 nm in 5 nm steps
'g'CIE \bar{g} function, note: source only 380 nm – 780 nm in 5 nm steps
'b'CIE \bar{b} function, note: source only 380 nm – 780 nm in 5 nm steps
'rgb'CIE \bar{r}, \bar{g} and \bar{b} function, note: source only 380 nm – 780 nm in 5 nm steps
'VL'V(\lambda), equals tristimulus function ’y’
'V-L'V'(\lambda), NOTE: equals rhodopic ’rh’ but the calculation is executed with K_{\text{m}}= 1700.13~\frac{\text{lm}}{\text{W}}.
'sc'retinal ganglion cells: s-cone-opic s_{\text{sc}} or cyanopic
'mc'retinal ganglion cells: m-cone-opic s_{\text{mc}} or chloropic
'lc'retinal ganglion cells: l-cone-opic s_{\text{lc}} or erythropic
'rh'retinal ganglion cells: rhodopic s_{\text{rh}}, or scotopic, NOTE: equals scotopic ‘V-L’ but the calculation is executed with K_{\text{m}}=1~\frac{\text{lm}}{\text{W}} according to CIE S 026.
'mel'retinal ganglion cells: melanopic s_{\text{mel}}
'a-opic'all retinal ganglion cells: s_{\text{sc}}, s_{\text{mc}}, s_{\text{lc}}, s_{\text{rh}} and s_{\text{mel}}
'BLH'Blue Light Hazard weighting function, see also: cieblh

Examples

Derive Tristimulus values X, Y and Z from the spectral power distribution of standard illuminant ‘D65’:

lam = 360:830;
spec = ciespec(lam,'D65');
XYZ = ciespec2unit(lam,spec,'xyz')

See also: ciespec, ciespec2xyz

Result:

XYZ =

   6.8599e+06   7.2173e+06   7.8584e+06

Derive α-opic values from the spectral power distribution of standard illuminants ‘D65’ and ‘D75’:

lam = 360:830;
spec = ciespec(lam,{'D65','D75'});
aopic = ciespec2unit(lam,spec,'a-opic')

See also: ciespec

Result:

aopic =

   5.8986e+03   1.0507e+04   1.1756e+04   1.0463e+04   9.5717e+03
   6.7283e+03   1.0830e+04   1.1855e+04   1.1180e+04   1.0376e+04

References:

ISO/CIE 23539:2023: Photometry - The CIE system of physical photometry. Commission International de l’Éclairage (CIE), Vienna Austria, 2023.

ISO/CIE 11664-1:2019(E): Colorimetry - Part 1: CIE standard colorimetric observers. Commission International de l’Éclairage (CIE), Vienna Austria, 2019.

CIE 15:2018: Colorimetry, 4th Edition. Commission International de l’Éclairage (CIE), Vienna Austria, 2018, ISBN: 978-3-902842-13-8 , (DOI: 10.25039/TR.015.2018).

CIE S 026/E:2018: CIE System for Metrology of Optical Radiation for ipRGC-Influenced Responses to Light. Commission International de l’Éclairage (CIE), Vienna Austria, 2018, (DOI: 10.25039/S026.2018).

IEC 62471:2006/CIE S 009:2002: Photobiological safety of lamps and lamp systems / Sécurité photobiologique des lampes et des appareils utilisant des lampes (bilingual edition). Commission Internationale de l'Éclairage (CIE), Vienna Austria, 2002.

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