Inhaltsverzeichnis
UV-Strahlung: Unterteilung, Breitband Messgeräte, Spektrometer

UV Broadband Meters

Broadband meters are among the most used UV meters, as they can be purchased at an affordable price (starting from about 150€). They stand out due to the high reproducibility of the measured values, a high signal to noise ratio, and very easy handling.

All the advantages of broadband meters over spectrometers make them popular for reptile keepers. The interpretation of the measured values is, however, comparably complicated: Broadband meters measure the irradiance weighted with their own sensitivity spectrum, which do not agree with the correspondent name of the broadband meter. Measured values of different lamps or different brodband meters are fundamentally not comparable. Especially a lamp with a lower measured value at one braodband meter can nevertheless have higher physical uvb irradiance or a higher ability to facilitate vitamin D production.

Without knowledge of

the informative value of a broadband meter is quite limited.

In the case of reptile lamps one has also to consider, that not only the irradiance in a single point is relevant but the spatial distribution over an area that is at least as large as the size of the animal.

Construction and Function of a Broadbandmeter

A broadband meter consists mainly of two components: A detector and a filter. Additionally a diffuser is mounted above the filter to make the angle to which the meter responses bigger (Cosine correction). Without the diffuser the signal would depend too much on the angle between light source and meter.

Photodiodes, consisting of a semiconductor, are generally used as detectors. A photon with energy fitting to the band-gap of the semiconductor will create an electron-hole-pair and in the end an electrical current. The short circuit current is a linear function of the number of photons over a several orders of magnitude. Photodiodes are therefore an excellent device to measure the irradiance. For the visible region, usually silicon semiconductors are used. To match the band-gap for the uv range other semiconductors, for example SiC, GaN, diamond or GaAsP are needed.

In most cases the spectral sensitivity of the photodiode does not match the desired form, so that it can be further confined by filters.

The current from the photodiode then needs to be converted to a usable value. Many broadband meters give the irradiance in µW/cm² or W/m². Others use a weighted irradiance like UV index or vitamin D (international units per minute).
To do this, a lamp with known spectrum is measured with this meter and the calibration factor converting current into the wanted unit determined (Calibration).

There are three ways of calibration: Usage of a line source, Usage of a broadband source or measurement of the spectral sensitivity of the broadband meter [120].

A mercury vapour lamp is generally used (lines at 254 nm, 313 nm, 365 nm) as a line source. To determine the correct value the lamp can be measured with a simple power meter. This method is quick, simple and reproducible. When a broadband meter is calibrated using a line source, measuring a broadband light source often gives a too small value, measuring a line source a too high value [119].

For application in the field of medicine, calibration with a broad band light source is used. Here the broad band calibration light source must be characterized with a spectrometer, to find the correct value.

The most substantiated but laborious calibration method is determining the spectral response of the broadband meter.

Accuracy

The accuracy of every measurement is limited by several statistical and systematic errors [112]. For broadband meters these are:

Apart from these errors, the spectral sensitivity of the meter compared to the biological or physical effect that is to be measured, have a big influence on how to interpret the measured value.

Correction Factor

Even though braodband meters are often labelled „UVB“ meters or „UV index“ meters, it is technically not possible to match the spectral sensitivity of the broadband meter perfectly to the desired application.

A broadband meter evaluated the radiation from the light source (S_\mathrm{L}(\lambda)) strictly by its on spectral sensitivity (s_\mathrm{M}(\lambda)) and gives a reading proportional to M = F_\mathrm{Kalibr.}\int\limits_0^\infty \mathrm{d}\lambda S_\mathrm{L}(\lambda) \cdot s_\mathrm{M}(\lambda).

Part (red) of the spectrum of the light source (orange) that is seen by a uvb broadband meter (blue)

The person performing the measurement is usually more interested in the biological or chemical effect of the radiation or the physical range of the spectrum of the lamp, given by the spectral sensitivity S_\mathrm{B}(\lambda). He is interested in a value B = \int\limits_0^\infty \mathrm{d}\lambda S_\mathrm{L}(\lambda) \cdot s_\mathrm{B}(\lambda).

Part (red) of the spectrum of the light source (orange) that is to be measured (UVB, 280-320nm, blue)

When the spectrum of the light source S_\mathrm{L}(\lambda), the spectrum of the lamp used for calibration S_\mathrm{K}(\lambda), the spectral sensitivity of the meter s_\mathrm{M}(\lambda) and the spectral sensitivity of the process of interest (e.g. UVB, vitamin D …) s_\mathrm{B}(\lambda) are known, a correction factor can be calculated [38], [119], that relates the two values:

a = \frac{\int\limits_0^\infty\mathrm{d}\lambda S_\mathrm{K}(\lambda)\cdot s_\mathrm{B}}{\int\limits_0^\infty\mathrm{d}\lambda S_\mathrm{K}(\lambda)\cdot s_\mathrm{M}}\frac{\int\limits_0^\infty\mathrm{d}\lambda S_\mathrm{L}(\lambda)\cdot s_\mathrm{M}}{\int\limits_0^\infty\mathrm{d}\lambda S_\mathrm{L}(\lambda)\cdot s_\mathrm{B}} \quad = \quad \frac{F_\mathrm{Kalibr.}\int\limits_0^\infty\mathrm{d}\lambda S_\mathrm{L}(\lambda)\cdot s_\mathrm{M}}{\int\limits_0^\infty\mathrm{d}\lambda S_\mathrm{L}(\lambda)\cdot s_\mathrm{B}} \quad = \quad \frac{M}{B} \qquad\qquad B = aM

This correction factor is only a=1 in two cases, and only then measured value and value of interest are the same:

The more these pairs of variates depart from each other, the more the measured value departs from the correct value.

The correction factor must be calculated for every broadband meter (s_\mathrm{M}(\lambda) and S_\mathrm{K}(\lambda)) and every application (s_\mathrm{B}(\lambda) and S_\mathrm{L}(\lambda)). Global predictions of the error of a broadband meter are unsound.

Some publications examined correction factors of broadband meters:

Regression analysis

The value from one single broadband meter M=F_\mathrm{Kalibr.}\int\mathrm{d}\lambda S_\mathrm{L}(\lambda)s_\mathrm{M}(\lambda) contains hardly any information about the spectrum of the light-source. By adjusting the distance to the lamp, one can measure the same value from every single uv lamp.

But by comparing the readings from two broadband meters with different spectral sensitivity the knowledge about the lamps spectrum can be expanded. The ratio of the two measured values depends on the form (but not the intensity) of the lamps spectrum and the sensitivity of the two broadband meters.

\frac{M_1}{M_2} = \frac{F_1\int\mathrm{d}\lambda S_\mathrm{L}(\lambda)s_\mathrm{M1}(\lambda)}{F_2\int\mathrm{d}\lambda S_\mathrm{L}(\lambda)s_\mathrm{M2}(\lambda)} = f\left(S_\mathrm{L}^\mathrm{norm.}(\lambda),s_\mathrm{M1}(\lambda),s_\mathrm{M2}(\lambda)\right)

This value can be determined from measurements at various distances from the lamp, if the spectrum does not depend on the distance and the cosine correction of both meters are sufficiently equal. For the statistical evaluation regression analysis offers various methods.

To me the asumption of a line through the origin with errors \sigma_{xi}\propto\sqrt{x_i} and \sigma_{yi}\propto\sqrt{y_i} makes most sens.