**5.2 Intensity and irradiance/illuminance**

These two geometric quantities are often considered together since the measurement configuration, shown in Figure 12, is the same for both. The analysis of the measurement equations is based upon the observation that the output of a radiation detector is directly dependant upon the total flux that is incident upon the sensitive area of the detector, which will be assumed in this chapter to be the area of the input aperture. Therefore, the basic equation relating the two detector signals and the radiation from the sources is simply:

$$\frac{\dot{q}^T}{\dot{q}^S} = \frac{\Phi^T}{\Phi^S} \tag{35}$$

The geometric resolution components placed before the detector, such as shown in Figure 13, are designed to ensure that only the desired flux is input to the detector. In the case of intensity and irradiance/illuminance measurements, the geometrical factors are the distance *d* and the aperture area *A*. Although the intensity of a (point) source does not change with distance, the flux that is incident upon a detector with a fixed input aperture A varies with the square of the distance as we discussed in Section 4.1.7.1. Therefore any comparison of two intensity sources (or irradiance/illuminance sources) will depend upon the distance at which we measure their output using a detector. If we allow the distances of the test and standard intensity sources from the detector aperture to be different, <sup>T</sup> *d* and <sup>S</sup> *d* respectively, the detector signal ratio is given by:

$$\frac{\dot{\mathbf{d}}^{\mathrm{T}}}{\dot{\mathbf{d}}^{\mathrm{S}}} = \frac{\boldsymbol{\Phi}^{\mathrm{T}}}{\boldsymbol{\Phi}^{\mathrm{S}}} = \frac{\boldsymbol{I}^{\mathrm{T}} \cdot \boldsymbol{A}}{(\boldsymbol{d}^{\mathrm{T}})^{2}} \cdot \frac{(\boldsymbol{d}^{\mathrm{S}})^{2}}{\boldsymbol{I}^{\mathrm{S}} \cdot \boldsymbol{A}} = \frac{\boldsymbol{I}^{\mathrm{T}}}{\boldsymbol{I}^{\mathrm{S}}} \cdot \left(\frac{\boldsymbol{d}^{\mathrm{S}}}{\boldsymbol{d}^{\mathrm{T}}}\right)^{2} \tag{36}$$

from which we obtain the test source intensity as

$$I^T = I^S \cdot \left(\frac{d^T}{d^S}\right)^2 \cdot \frac{\dot{i}^T}{\dot{i}^S} \tag{37}$$

To reduce errors and uncertainties, we usually try to set up our measurements such that T S *d d* and that this distance is large enough that the inverse square law is valid.

If we combine Equations (8) and (9) together with Figure 12, we see that an intensity source may be used to calibrate an irradiance/illuminance meter:

$$E^{\mathbb{S}} = \frac{\Phi^{\mathbb{S}}}{A} = \frac{I^{\mathbb{S}}}{(d^{\mathbb{S}})^2} \tag{38}$$

The input aperture area of the detector has cancelled out of the equations.

#### **5.3 Radiance/luminance**

A very convenient method used to produce a standard radiance or luminance source uses an isotropic diffusing reflecting surface to produce a known radiance from a known irradiance incident upon the surface, as discussed in Section 4.1.7.3 above. A schematic for the measurements is given in Figure 14. Note that the known irradiance at the diffuser may be produced by either a standard radiant intensity source (Equation (38)) or a standard irradiance source. For luminance, the known sources may also be either a standard luminous intensity source or a standard illuminance source.

basic equation relating the two detector signals and the radiation from the sources is

T T S S *i i*

The geometric resolution components placed before the detector, such as shown in Figure 13, are designed to ensure that only the desired flux is input to the detector. In the case of intensity and irradiance/illuminance measurements, the geometrical factors are the distance *d* and the aperture area *A*. Although the intensity of a (point) source does not change with distance, the flux that is incident upon a detector with a fixed input aperture A varies with the square of the distance as we discussed in Section 4.1.7.1. Therefore any comparison of two intensity sources (or irradiance/illuminance sources) will depend upon the distance at which we measure their output using a detector. If we allow the distances of the test and standard intensity sources from the detector aperture to be different, <sup>T</sup> *d* and <sup>S</sup> *d*

> <sup>2</sup> T T T S2 T S S S T2 S S T ( )

> > <sup>2</sup> T T

S S

*d i*

( ) *i I Ad I d i d IAI d* 

T S

T S *d d* and that this distance is large enough that the inverse square law is valid.

S

The input aperture area of the detector has cancelled out of the equations.

*d i I I*

 

To reduce errors and uncertainties, we usually try to set up our measurements such that

If we combine Equations (8) and (9) together with Figure 12, we see that an intensity source

*<sup>I</sup> <sup>E</sup> A d*

A very convenient method used to produce a standard radiance or luminance source uses an isotropic diffusing reflecting surface to produce a known radiance from a known irradiance incident upon the surface, as discussed in Section 4.1.7.3 above. A schematic for the measurements is given in Figure 14. Note that the known irradiance at the diffuser may be produced by either a standard radiant intensity source (Equation (38)) or a standard irradiance source. For luminance, the known sources may also be either a standard

S S

S 2 ( )

respectively, the detector signal ratio is given by:

from which we obtain the test source intensity as

may be used to calibrate an irradiance/illuminance meter:

luminous intensity source or a standard illuminance source.

**5.3 Radiance/luminance** 

(35)

(36)

(37)

(38)

simply:

Fig. 14. Radiance source derived from an irradiance source with diffuser
