Measurements Applying Spectral Weighting Functions

Recommended products: specbos 1211-2

There are many effects of optical radiation on materials and processes, especially in biology, medicine, horticulture, but also in technical applications. Typical examples are the browning of human skin during sun exposure or in sun beds, the photosynthesis and the human vision. It is typical for such effects that the impact of the radiation on the process is wavelength dependent. Such dependencies are called action spectra or weighting functions (s(λ)). Mainly such functions have a maximum of 1 at the wavelength with the highest impact on the effect.
A well known weighting function is the V(λ) curve, the sensitivity curve of the human eye. It is a relative curve with its maximum of 1 at 555 nm and in combination with the factor of 683 lm/ W at this wavelength it can be transformed into an absolute curve.
Other photobiological weighting functions are listed in the following table and in the diagram [1]:

Name of effect Wavelength range
Erythemal action spectrum describing the reddening of the human skin 200 - 400 nm
De activation of Escherichia coli bacteria 200 - 350 nm
Pyrimidin dimerisation of DNS 280 - 360 nm
Rapid pigmentation of human skin 300 - 440 nm
Delayed pigmentation of human skin 285 - 440 nm
Vitamin D generation 255 - 320 nm
Photoisomerisation of bilirubin 405 - 545 nm
Different weighting functions
Some selected weighting functions

The following diagram shows the radiometric spectrum of a Metal halide lamp MT4000DL/BH of Iwasaki, which is used as green house lamp, the action spectrum of photosynthesis and the weighted spectrum of the illumination.

The integral value of the radiation effect Xeffect can be calculated according to the following formula:

X(λ) – non weighted radiation, s (λ) – action spectrum and λ1, λ2 – wavelength range of the action spectrum

Xeffect is used to compare the impact of different irradiance spectra on a certain effect.

This integral value can be measured with a detector which sensitivity is adapted to the specific action spectrum. A well known example for this technique is the luxmeter. But the instrument can always be used only for one effect.

Spectroradiometers are much more flexible to apply for such measurements. The action spectrum will be stored in the software and can be changed easily. There will be no matching error as in case of integral detectors. Furthermore the full weighted spectrum as well as the integral value will be measured. The measurement procedure is as follows:

  • The radiometric spectrum X(λ) will be measured in steps of  1 nm (mainly in Irradiance mode).
  • The spectrum will be multiplied with the corresponding value of the weighting function at each wavelength. The result is the weighted spectrum, in case of an Irradiance measurement it is the weighted spectral Irradiance.
  • The spectrum will be integrated, in practice this is the addition of all values if a step width of 1 nm is used. The result in case of an Irradiance measurement is the weighted Irradiance value.
Application of specbos 1211 in a greenhouse
Application of specbos 1211 in a greenhouse

A typical application of such measurements is the characterization of the illuminance in green houses. The plants react different on different illumination spectra and the aim of research is to find the best lighting conditions for the growing of the plant. Due to very different white spectra created by different lamp technologies the weighted values may be quite different although the radiometric values are equal.

If the weighting function range from 0 to 1, this mean that the effectivity can vary between 0 and 100%. In this case the weighted spectrum has the same unit as the non weighted illumination spectrum. The spectroradiometer specbos 1211 can be used for the measurement of such weighted values. The software JETI LiVal contains the special menu point Spectral calculations which allows to read a weighting function and to proceed the spectral and integral calculation.

Measured spectrum and inserted weighted spectrum
Measured spectrum and inserted weighted spectrum

The following issues have to be considered to get precise results for the weighting procedure:

  • Validity and precision of the weighting function
  • Wavelength range of the weighting function, the source and the spectroradiometer
  • Optical resolution and stray light of the spectroradiometer
  • Modulation of the source and time behaviour of the spectroradiometer

[1] DIN 5031-10: Optical radiation physics and illuminating engineering – Part 10: Photobiologically effective radiation, quantities, symbols and actions

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