# Lighting FAQBy Mikhail Dubinovskiy
- What does "Candela", "Lumen", etc. mean?
- Footcandle to Lux Conversion
- What does "inverse square law"
- What does "cosine law" mean
- What is the difference between Lumen and Watt
- How to calculate beam angle
- How to calculate lumens output
# What does "Candela", "Lumen", etc. mean?
The formal definition can be found in many handbooks, so here are informal and, hopefully more useful, definitions:
**Luminous intensity** (or **candlepower**) is the light
density within a very small solid angle, in a specified direction. In
other words, this is the total number of lumens from a surface emitted
in a given direction. The unit of measure is candela. In modern
standards, the **candela** is the basic of all measurements of light
and all other units are derived from it. Candlepower measurements are
often taken at various angles around the source and the results plotted
to give a candlepower distribution curve. Such a curve shows luminous
intensity (how "bright" the source seems) in any direction.
**Luminous flux** is the time rate of flow of light. The unit of
measure is the Lumen. One lumen may be defined as the light flux emitted
in one unit solid angle by a one-candela uniform-point source. The **lumen**
differs from the candela in that it is a measure of light flux
irrespective of direction. The lumen is used to express a quantity of
light flux: total output of a source, output within a specific angular
zone, amount of absorbed light, etc. However, if you need to
calculate something which is not related to the human eye, for example
temperature increase due to absorbed light, do not use luminous flux,
instead we need to use the correct unit of power, the Watt (see below).
**Illumination** is the density of luminous flux on a surface This
parameter shows how "bright" the surface point appears to the human
eye. The appropriate units of measure are **Footcandle** and **Lux**.
One footcandle is the illumination produced by one lumen uniformly
distributed over one square foot of a surface, or conversely this is the
illumination at the point of a surface which is one foot from, and
perpendicular to, a uniform point source of one candela. So, footcandles
incident on a surface=Lumens/Area(sq.feet). Lux is used in the
International System. Both have a similar objective, but meters are used
for Lux and feet are used for Candelas. Therefore, one lux=0.0929
footcandles. Or, approximately, 1 Fc=10 Lux.
**Luminance** or **Brightness** is a luminous intensity of a
surface in a given direction per unit of projected area of the surface.
Luminance can be expressed in two ways: in candelas per unit area or in
lumens per unit area. I don't want do go too into this subject, because
it is so seldom used. There are many different standard units of
measurement. For example: **Candela per square inch (cd/in²) , Footlambert** (luminance of a surface emitting one lumen per square foot), **Lambert** (similar, but per square cm).
1 cd/in.² =452 Footlamberts
1 Lambert=929 Footlamberts=2.054 cd/in².
Actually, our eye sees brightness, not illumination. Every visible
object has brightness. Usually, brightness is proportional to the
object's illumination, so a well illuminated object seems brighter. For a
perfectly diffusing reflecting surface:
Footlamberts = Footcandles * Surface Reflectance
# Footcandle to Lux Conversion
One footcandle is the illumination produced by one lumen uniformly
distributed over one square foot of surface, and lux is the illumination
over one square meter of surface. Therefore, one lux=0.0929
footcandles. Or, approximately, 1 Fc=10 Lux.
# What does "inverse square law"
The
inverse square law tells is that the illumination is inversely
proportional to the square of the distance between the point source and
the surface, i.e.: If
you have a fixture (which can be treated as a point source if the
distance from the surface is large) and you measure the illumination at
20 feet as 2000 Fc at the beam center, then at 40 feet the illumination
is 500 Fc at the beam center.
# What does "cosine law" mean
Effective illumination is proportional to the cosine of the angle of
incidence of the light on the surface (angle between the direction of
the light and the perpendicular to the surface)
Illumination at the O point on surfaces 1 and 2:
Here are a few cases:
When the surface is tilted by an angle of 30º, the illumination is reduced by a factor of 0.87
45º - 0.71
60º - 0.5
# What is the difference between Lumen and Watt
Lumen is a unit of the photometric system and Watt belongs to the radiometry system.
Both characterize a power of light flow. However, lumen is power
"related" to the human eye sensitivity. Therefore, lights with the same
power in watts, but different colors have different luminous fluxes,
because the human eye has different sensitivity at different
wavelengths. At a wavelength of 555 nm (maximum eye sensitivity) 1 Watt
equals 683 Lm.
Very powerful sources of infrared radiation produce no lumen output,
because the human eye can’t see it. However, if you need to calculate
total power absorbed by a surface (to estimate temperature increase, for
example), you have to transfer lumen flux to watt. This can be done by
using a spectral luminous efficiency curve, which can be found in many
photometry handbooks.
# How to calculate beam angle
This is easy. If you know the distance from a fixture to the screen
(much larger than fixture length) and the image diameter, then:
In most practical cases the following approximation is true:
Of course, both measurements must be in the same units (meters, feet, inches, etc.)
(Example: distance = 20 feet, image diameter=5 feet. Exact formula gives 14.25 º, second – 14.32º)
In the case of "soft edge" light image diameter, usually, is measured
at point where illumination is 50% (beam angle) or 10% (field angle) of
the center illumination.
# How to calculate lumens output
The best way is to use a photometric sphere, however the number of
people who have one is much less than the number of people who want to
know total lumen output (luminous flux) of a fixture.
Another way is to measure illumination (which is the density of
luminous flux on a surface) at a number of points and then integrate the
resulting values.
Assuming that the beam has axial symmetry (if not – you’re in
trouble. You have to measure many points all over the beam) and fixture
beam angle is small (we can neglect cosine-cube coefficient from
cosine-law and inverse-square-law, that is less than 5% for the 20º beam
and 1% for the 10º beam), we have the following formula:
Beam
radius is divided into n equal part (radiuses and illumination reading
values are indexed from 0, at the beam center, to n-1, at the beam
edge).
**2 points (center and edge readings only):**
**3 points (center, middle, and edge):**
**4 points:**
**5 points:**
**8 points:**
Here:
*P* - total lumens
*R* - beam radius
*E* - illumination
There is nothing magical about these equations. They are obtained by using integrating rules over the beam.
In the case of "soft edge" fixture, where the image size is taken at
10% of the center illumination (field angle), the first formula becomes
very simple:
To get the result in lumens, you should use proper units. If you use
footcandles, then the radius must be in feet. If you use lux, then the
radius must be in meters.
And last, it doesn't make any sense to calculate luminous flux with
2-3 digits after the decimal point by this method. Assumptions which
were made (illumination distribution is perfectly symmetrical, etc.)
inevitably result in some error in the final calculation, so instead of
14231.41 Lm it is more practical to use 14KLm. |