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400 450 500 550 600 650 700 750
0 0.2 0.4 0.6 0.8 1
Wavelength in nm
Sensitivityina.u.
V(λ) V’(λ)
Figure2.8– Spectral sensitivity curves, V(λ) and V’(λ) for human vision during photopic illumination (red) and scotopic illumination (blue).
For scotopic vision, the maximum of the spectral sensitivity is at around 510 nm and it is obvious, that the vision in the lower wavelength range is significantly better while the vision in the higher wavelength range is significantly worse. For the mesopic range, the sensitivity curve shifts between the V(λ) and the V’(λ) functions [17,51].
Despite knowing, that for different brightness levels, different sensitivity curves are valid, all photometric measurements are done using the V(λ) function. This is either done by measur-ing the spectral distribution and then multiplymeasur-ing it by the V(λ) function or the measurement equipment is already filtered with the V(λ) function. Most often this is the case, since it is much faster, requires less space and does not include any further calculations. However, this is a highly complicated and very sensitive procedure and is, up to now, often done by hand.
The most accurate results are achieved by using partial filtering as shown in figure2.9.
Figure2.9– Image of a partial V(λ) filter. Each individual filter part is selected in size and thickness to, in total, and togeather with the spectral responsivity of the silicon detectot, to a transmission curve similar to the sensitivity of the human eye. (Image source:[52])
2.3 lighting parameters 19 In a partial filter setup, each individual filter part is selected in thickness, size and spectral transmittance in a way, that the integrated transmission of all filter parts and the sensitivity curve of the measurement sensor lead to a total sensitivity of the equipment, similar to the V(λ) curve. Final deviations are then compensated by an individual calibration file for every measurement head.
Since this method requires a large area, sensors with a small measurement area, cannot be equipped with partial filtering. Here a selected filter-glass is used to get the total sensi-tivity as similar to the human sensisensi-tivity as possible. Since the spectral responsivity of every photo diode is different, and the possibility to create different transmission spectra in glass is limited, the results of this method are significantly worse compared to partial filtering.
2.3.2 luminous flux
Luminous flux is probably the most intuitive of all photometric values. It describes the total amount of light (weighted by the V(λ) curve) emitted by a light source. The SI-unit for lumi-nous flux is lm and lumilumi-nous flux is indicated byφ.
Luminous flux is often used to objectively evaluate light sources by measuring the total light, that is emitted by a light source and is one of the photometric values often found on general lamps or headlamp lamps. In general public, luminous flux is often used to compare the brightness of different light sources. Per se, this is correct: a light bulb with 2000 lm is, overall brighter than one with only 500 lm. But since the luminous flux measures the total emitted light, any angular dependency is neglected. Therefore, a light source with a highly di-rected light distribution may lead to a brighter illuminated area, for example on a work desk, than a potentially higher rated light source, that distributes its light evenly into all directions.
There exist several possibilities to measure luminous flux. Small light sources, without any refracting optics, can be measured in a so called integrating (Ulbricht) sphere as shown in figure2.10a. An integrating sphere is a spherical optical component with its interior coated with a highly reflective (ρ > 0.8) and diffuse paint. In general, the principle is, that by scat-tering nearly all the light over and over, on average, light from all angles will be directed from the light source onto the light detector. By measuring with a standard light source with known luminous flux, one can now calculate the luminous flux of the new light source.
Light sources that are either too big to be placed into an Ulbricht sphere, or use any kind of optic, thus leading to a directed light distribution, need to be measured differently. The most common approach here is, to use a photo goniometer. Here either the light source is turned around 360° over all axis, or the sensor is turned around the light source. Which case is used, usually depends on the light source, since, for example, some fluorescent tube should not be operated under certain angles or burning positions.
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(a) (b)
Figure2.10– Measurement equipment to measure luminous flux.(a)shows an integrating sphere to for mea-suring small and unidirectional light sources (Image source:[53]),(b)shows an automotive goniophotometer to measure headlamps and other directed light sources (Image source:[52])
Therefore, turning the light source around its own axis is impossible, and the sensor will be used to cover all angles. On the other hand, light sources with a highly directed light distribution, such as automotive headlamps, require a large measurement distance of 25 m and therefore moving the sensor around the light source is unreasonable. Figure2.10bshows an automotive goniophotometer, where the light source will be turned around a defined axis.
2.3.3 luminous intensity
While the luminous flux gives the complete light emitted by a light source, the parameter used to describe the light emitted by luminaires under a given angle is the luminous intensity.
With the illuminance I, given by
I = dφ
dΩ1 (2.1)
where Ω1is the solid angle under which the light is emitted. Again as with all other photo-metric values, an illuminance measurement head is used. The angular opening of this head is limited by a tubus so that no stray light can affect the measurement head and the distance to the light source is set to a known value. Then the luminous intensity is calculated by
I =E·r2 (2.2)
with E being the illuminance. The measurement of single luminous intensity values can typically be done manually with a simple setup as described above. However, the luminous intensity of a light source, like street lights or an automotive headlamp, needs to be measured
2.3 lighting parameters 21 angle dependent. Therefore, automated measurement equipment was developed, that moves either the measurement arm around the light source and measures the luminous intensity with a set resolution, or, in cases the measurement distance needs to be much larger, the light source is turned as seen in figure 2.10b. For automotive headlamps, this angular measure-ment is necessary due to the different photometric requiremeasure-ments under different angles like, for example, to ensure detection in the right-hand side and avoid glare for oncoming traffic at the same time.
2.3.4 illuminance
Illuminance,E, describes the amount of luminous flux incident on a specific area:
E = dφ
dA (2.3)
where A is the area at which the light is measured. Illuminance was often referred to as brightness, but since this often lead to confusion with other photometric terms like lu-minance, it was defined that "brightness" should not be used in a quantitative manner. In SI-units, illuminance is given in lux (lx).
To measure the illuminance, typically a silicon-based photo-diode with an added V(λ) fil-ter is used. The need for the additional filfil-ter arises in the significant difference in sensitivity per wavelength between the human eye and a silicon based semiconductor. While the human eye follows the described V(λ) function, a typical silicon chip will have an absorption curve starting at about 350 nm and reaching over 1100 nm. Both sensitivity curves are shown in figure 2.11. The spectral sensitivity of silicon is shown in blue, while the V(λ) function is shown in black. Both functions are normalized.
Figure2.11– Spectral sensitivity curves of a silicon-based semiconductor (blue) and the V(λ) curve (black) (image source:[54]).
On top of the filter, a Lambert diffuser is added to ensure a homogeneous mixing of the incoming light over the whole sensor area, as well as defining the measurement area. The so-called cosine-adaptation is a geometric appliance added to the semiconductor to ensure that any angle between the light source and the system, actually leads to a cosine behaviour on
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the measured illuminance. This adaptation is often done as one part including the diffuser.
In many automotive studies, the measurement of the illuminance is the only feasible method of characterizing the photometric properties for dynamic situations [55–60]. This leads to the current state, where most evaluations on automotive headlamps are based upon illuminance measurements and Adrian, Flannagan, Holladay,Lehnert, Locher, Stiles, Völker, Vos and Zydekall derived similar correlations between the illuminance and the glare perception of subjects. Nevertheless, illuminance does not take any properties of the illuminated surface into account but only describes the incident light. However, since most of all materials in nature do not reflect all wavelengths equally, different materials may appear differently when illuminated with similar illuminance values. The photometric value taking this into account is the luminance.
2.3.5 luminance
While illuminance measures the light coming onto a specific area, luminance measures the light leaving a specific area. This is described by the following equation
L = dφ
dA1·dΩ1 (2.4)
with Lbeing the luminance.
It therefore does not describe the amount of light shining onto a surface but rather the emit-ted or reflecemit-ted light of a given area under a solid angle. Luminance is measured in SI units as cd m−2 or in non SI units in nit. Since luminance is a photometric value, the amount of light measured is, once again, weighted by the V(λ) function. The luminance is the photomet-ric value associated with the brightness perception of humans. This brightness perception, however, is not a linear function but rather follows a logarithmic behaviour.
As mentioned above, the only photometric value, that is actually measurable is illuminance.
But since the geometric relations between illuminance(E)and luminance(L)are known, the luminance can be calculated by
L= I
A1 (2.5)
= E·r2
A1 (2.6)
= E
A1/r2 (2.7)
= E
Ω with Ω= A1
r2 (2.8)
where Ω describes the solid angle and is given by dividing the visible area (A) by the distance to the measurement area (r) squared. Therefore, a conventional luminance meter, is a illuminance head, which is equipped with a specific geometry, to limit the solid angle under which light can be measured.
If a diffusely reflecting (lambertian) surface is measured, the luminance L can be directly calculated from the illuminance E at the surface according to
L = ρ
π ·E (2.9)