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A large amount of
confusion about light measurements comes from the fact that
there are several different ways of measuring light. Many
terms are used to measure aspects of lighting, and a simple
cruise on the Internet will take you through a plethora of
terms such as: lumens, lux, candlepower, foot-candles, lamberts,
phot, nit, irradiance, illuminance, Color Rendition Index
(CRI), Kelvin and Photosynthetic Photon Flux Density (PPFD),
among others. Why are there so many measures to describe light?
This article will sort through this abundance of lighting
measures.
There are basically three categories of
light measures based on the particular application and interpretation,
each with its own set of terminology.
1. Recall that light is a form of radiation, and hence
can be measured as radiant energy using energy based measures.
These units of light measurement are termed radiometric
measures of light.
2. Light is also used to illuminate for visual purposes,
hence light can also be measured for this application based
on how the human eye perceives light. Measures of light
based on visual perception are called photometric measures,
and are by far the most commonly used and available metrics
because they are used by the large lighting industry.
3. The form of measurement that we, as reefkeepers, are
concerned about is the Photosynthetically Available Radiation
(PAR), which measures the number of photosynthetically
useful photons, and has been discussed in detail in Part
II.
There are two main ways light can be measured: 1) at the
source, and 2) at the surface of the object being illuminated.
The quantity of light at the source is termed flux, and is
measured as "quantity" per unit of time. This is
very similar to measuring the flow of a pump in gallons/hr
or liters/min. We can think of a light source as a pump emitting
radiation and measure this pumping capacity over time. It
represents the total light output from the source per unit
of time. What this measured "quantity" is depends
on whether the light is interpreted using radiometric, photometric
or photosynthetic standards.
The light radiating from the source ultimately falls onto
an object, and we can measure the amount of light falling
onto a given area of the object. This quantity is measured
per unit area, and measures the light's density on a unit
area.
The light emanates in several directions and we can either
measure this without regard to the direction from which it
comes, or measure it in a given direction. When measuring
light in a given direction, it's helpful to visualize the
light as radiating from all directions in a sphere. This sphere
can be broken down into cones whose apex is at the center
of the sphere with the cone specified by the solid angle at
the apex. Thus the light can be measured as the amount of
flux contained in such a cone and measured per unit angle.
The unit angle used is called a steradian (similar to a radian
in three dimensions). A complete sphere has 4p
steradians.
The different quantities used in light
measurements and their units of measure are summarized in
the table below, and will be discussed in further detail.
Radiometric Measurement of Light
Because light is radiant energy,
the energy is measured in typical units of energy - joules
(J).
Radiant Flux, also called radiant power, is
the flow rate of radiant energy. It is measured in terms of
power units called watts, which are basically a measure of
energy per unit time. 1 watt = 1 joule/sec.
Radiant Intensity is the radiant flux per unit
solid angle and is measured in watts/steradian. The radiant
intensity is independent of the distance because it measures
only the amount of radiant flux contained in the cone with
an angle at the apex equal to one steradian.
As we move further from the source, the cone's spread increases
so the radiant intensity falls onto a larger surface. Thus,
the density of light falling onto the surface decreases as
the area increases (following the inverse square law for a
point source), even when the angle at the cone's apex does
not change. This is measured as radiance. Radiance
is the radiant flux density per unit solid angle and is measured
in watts/m2/steradian.
If we do not care about the light's direction and want to
measure the light falling onto a source from all directions,
then we measure this as irradiance. Irradiance, also
known as radiant flux density, is the radiant flux per unit
area at a point on the surface. Hence, its units are expressed
in watts/m2 or joules/sec/m2.
It is denoted as E.
Spectral Irradiance is the irradiance per unit
wavelength interval at wavelength λ.
This is denoted as Eλ
and its units are expressed in watt/m2/nm.
Recall that the spectral power distribution plot discussed
in Part
II is plotted using spectral irradiance values.
Photometric Measurements
Photometric measurements are
geared toward how the human eye perceives light. The
sensitivity of human eyes is different for different
wavelengths. In the late 1920s the Commission Internationale
de L'Eclairage (CIE), based on experimentation using human
subjects, established how the human eye responds to light
at different wavelengths. The human eye is more sensitive
to light at 555 nm (green) and less sensitive to blues and
reds. This characteristic of human vision established the
standard observer response curve known as the luminous
efficiency function to represent how the human eye responds
to light at different wavelengths. Per this standard, detectors
in the eye respond differently to different regions of the
spectrum, and the response is scaled with respect to the peak
values.
The change in the eye's spectral response can be explained
by the presence of two types of receptors, rods and cones,
in the retina. Cones are active at high light levels and are
most densely situated in the central part of the field of
view. The cones' spectral response corresponds to the photopic
sensitivity curve. The rods are responsible for human vision
at low light levels and are prevalent in the peripheral field
of view, away from our direct line of sight. As light levels
are reduced, cones become less active and rods become active
with established spectral sensitivity gradually switching
toward the scotopic response curve. The peak spectral
sensitivity for photopic vision is 555 nm, and 507 nm for
scotopic vision. From this it is quite clear that the human
eye finds light at 555 nm to be the brightest, with the blues
and reds tending to be less bright. The luminous efficiency
functions are shown in Figure 1.
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Figure 1. Luminous Efficiency Functions.
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All photometric light measurements evaluate light in terms
of this standard visual response described by the luminous
efficiency function and, hence, all are weighted measures.
Not all of the wavelengths are treated equally. The wavelength
at 555 nm is assigned a weight of 1, and the others are scaled
according to this function. According to this function, light
at a wavelength of 450 nm is given a weight of 0.038. This
explains why a light source with large amounts of radiation
in the "blue" region will have a low reading when
using photometric units.
The quantities used for photometric measurements correspond
to those used for radiometric measurements, with the main
difference being that the measurements are evaluated with
respect to the human eye's response.
Luminous Flux is the amount of radiation
coming from a source per unit time, evaluated in
terms of a standard visual response. Unit: lumen (lm).
You will see most data from lighting companies refer to light
output in terms of lumens. Think of this as the amount of
light produced by the lamp as perceived by the human eye.
Luminous Intensity is the luminous flux per
unit solid angle in a given direction. Unit: candela (cd).
One candela is 1 lumen/steradian.
Illuminance is the luminous flux per unit area.
It is measured in lux (lumen/m2)
or footcandles (lumen/ft2).
The light emanating from a lamp is used to illuminate objects
and the amount of light (measured in lumens) falling onto
a specific area of the object, usually one square meter, is
termed lux. When we measure this same area in square feet,
the unit is footcandles. These units are often used in photography,
where we are interested in how much light is falling onto
the subject.
Conversion from Radiometric Units to Photometric Units
The following method is used to convert
between photometric units and radiometric units. As defined,
1 watt = 683 lumens at 555 nm (peak photopic response), and
it is scaled for other wavelengths based on the Luminous Efficiency
Function V (λ)
shown in Figure 1.
To determine a lamp's lux values, the spectral irradiance
at each wavelength (taken from the spectral power distribution)
in the spectral range (380-780nm) is multiplied by the luminous
efficiency function at the equivalent wavelengths. Then, all
of these multiplied values are summed and multiplied by 683
to find the total lux output. As you can see, the conversion
requires knowledge of the spectral power distribution and
cannot be done without it.
So far we have been dealing with metric units. To convert
to English units, or to other measurement systems, appropriate
conversions need to be made. These converted units are often
given different names (thereby adding to the confusion)! As
an example we can look at the different terms and units used
for measuring luminance.
LUMINANCE:
1 lm/m2/sr (lumens per sq.
meter per steradian)
=
1 candela/m2 (cd/m2)
=
1 nit
=
10-4 stilb (sb) (or 1 candela/cm2)
=
9.290 x 10-2 cd/ft2
=
π apostilbs (asb)
=
π x 10-4 lamberts (L)
=
2.919 x 10-1 foot-lamberts
(fL)
Units for Photosynthesis Measurements
In keeping corals and plants we should
not be concerned about light as humans see it, but rather
as the plants and corals see it. For the purpose of photosynthesis,
light is termed Photosynthetically Available Radiation
(PAR). This radiation's range is identical to what humans
can see in the 400-700 nm range, but each photon
is treated uniformly in this measurement (unlike the photometric
measurement, which weights the photons according to how the
human eye sees them).
The reason for expressing PAR as a number of photons instead
of energy units is that the photosynthetic reaction takes
place when a plant absorbs the photon, regardless of the photon's
wavelength (provided it lies in the range between 400 and
700 nm). That is, if a plant absorbs a given number of blue
photons, the amount of photosynthesis that takes place is
exactly the same as when the same number of red photons is
absorbed. Note, however, that the plant or coral may have
an absorption response that preferentially absorbs more photons
of certain wavelengths (more on this later).
Recall from Part
II, PAR is measured as PPFD, which are Einstein/m2/s
or µmoles/m2/s. One
Einstein = 1 mole of photons = 6.022×1023
photons, hence, 1 µEinstein = 6.022×1017
photons.
Conversion from Radiometric Units to PPFD
If we know the spectral irradiance at any given wavelength
(we can get this from the spectral power distribution), then
we can determine the PPFD for the given wavelength by multiplying
the spectral irradiance (watts/m2)
by the watts to Einstein conversion factor for each wavelength
(recall from Part
I how to convert energy at a given wavelength into the
number of photons). To compute the total PPFD over the range
of 400-700 nm, compute the PPFD for each wavelength and sum
over the range of 400-700 nm.
Summary:
There are three
basic forms of light measurement - radiometric, photometric
and photosynthetic - and these can be measured at the source
or at the object onto which the light falls. Photometric measurements
are derived from the radiometric measurements by factoring
in the human eye's response, and do not treat all radiation
equally. Photosynthetic measures, on the other hand, treat
all radiation equally. The starting point for all these measures
is the spectral power distribution, from which all other entities
can be derived. Conversion from one set of units to the others
is simply not possible unless the spectral power distribution
is known.
In addition to these lighting measures, additional measures
such as Color Rendition Index (CRI) and Correlated Color Temperature
(CCT) are used to describe light. These will be covered in
the next part of this series.
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