**Where:**

(SPQ_{λn}) = Average value of the spectral radiometric quantity in wavelength interval number “n”

The smaller the wavelength interval, Δλ, and the slower the variation in SPQ_{λ}, the higher the accuracy.

Calculate the illuminance produced by the 6253 150 W Xe arc lamp, on a small vertical surface 1 m from the lamp and centered in the horizontal plane containing the lamp bisecting the lamp electrodes. The lamp operates vertically.

Curve values for this lamp (found at the end of this section) are for 0.5 m, and since irradiance varies roughly as r ^{-2}, divide the 0.5 m values by 4 to get the values at 1 m. These values are in mW m^{-2} nm^{-1} and are shown in Figure 4. With the appropriate irradiance curve you need to estimate the spectral interval required to provide the accuracy you need. Because of lamp-to-lamp variation and natural lamp aging, you should not hope for better than ca. ±10% without actual measurement, so don't waste effort trying to read the curves every few nm. The next step is to make an estimate from the curve of an average value of the irradiance and V(λ) for each spectral interval and multiply them. The sum of all the products gives an approximation to the integral.

We show the “true integration” based on the 1 nm increments for our irradiance spectrum and interpolation of V(λ) data, then an example of the estimations from the curve.

Figure 4 shows the irradiance curve multiplied by the V(λ) curve. The unit of the product curve that describes the radiation is the IW, or light watt, a hybrid unit bridging the transition between radiometry and photometry. The integral of the product curve is 396 mIWm^{-2}, where an IW is the unit of the product curve.