Lighting Fundamentals

Spectral sensitivity of the eye

The sensitivity of the eye is not uniform over the visible spectrum, but varies with wavelength.� The spectral sensitivity is shown in the V(l) curve, with maximum sensitivity at 555nm.� There are three types of vision; photopic, scotopic and mesopic, which correspond to how the eye reacts under different luminance levels

Photopic vision

This is in effect when the surroundings have luminances of greater then 10 cdm^-2.� Vision is mediated entirely by the cone receptors, and is maximal in the blue-green end of the spectrum.

Scoptopic vision

This comes into operation when the luminance is less than 10^-2 cdm^-2 and they eye has had time to become dark adapted (typically around 30 minutes).� The spectral sensitivity curve for this, V ^�(l), is represented by a shift towards the blue end of the spectrum with maximal sensitivity at 507nm.� Since this mode of vision is mediated by the rod detectors, you have equal sensitity over the entire vsual field, and it is quite lke you see things �out of the corner of your eye�.� Unlike cones, rod detectors do not detect colour, and the scotopic view of the world is monochromatic.

Mesopic vision

In the intermediate range, three effects can be noted, in addition to a general increase in luminance;

� foveal detection becomes as easy as peripheral detection, and then easier

� a sense of colour can be appreciated

� the relative luminosity of different colours change;� in particular the luminosity of the eds increase more strongly than the blues.

The overall response of the eye lies some w(ere between V(l) and V ^�(l), moving from left to right, as the general luminance increases.

Basic Definitions

Luminous Flux,F;

The total visible light energy emitted by a source per unit time.�

Unit - Lumens (lm)

One lumen is by definition equal to 1/673W at the wavelength l=555nm where the eye has its maximum sensitivity.

Luminous Intensity,I;

The luminous flux from a source, F, in a specified direction inside a small solid angle,w.

Unit: lumen per steradian or candela (cd)

Illuminance, E;

The amount of luminous flux, F, incident per unit area of surface, A.

Unit: lumen pr square metre of lux (lx)

Luminance, L;

The intensity, I_u, per apparent unit area of the surface of the actual light source.

Unit: candela per square metre (cdm^-2)

Reflectance,r;

The ratio of reflected flux to incident flux (either luminous or radiant)

DERIVATION ???

Perfect Diffuse Reflector

This is a surface for which the luminance is independant of the angle of view.

Light Output Ratio

The ratio of the light output of a luminaire to the sum of the light outputs of the lamps it contains.

Luminous Efficacy, h;

For a light source with a total power input W watts the luminous efficacy, denoted by h_V, is given by

where F_V is the total light output of the source.

Unit: lumen per Watt ( lmW^-1)

Typical Efficacys:

GLS 9-20; TuHa 15-5; MCF 40-75; MBF 40-60; MBI 60-90; SOX 130-180; SON 95-130

L01(3). Fundamentals II - Propagation of Light

Methods of light emission (L&L pp. 101)

Light can be seen as either a wave or a particle.� It is a form of electromagnetic radiation, and is generally involved in the transfer of energy between particles.� There are many forms of energy transfer which emit light. Generally distinguished by the source of the input energy.

Incandescence Solids and liquids emit visible radiation when hey are heated to temperatures about 1000K.� The intensity increases and the appearance becomes whiter as the temperature increases.

Electric Discharge When an electric current is passed through a gas the atoms and molecules emit radiation whose spectrum is characteristic of the elements present.

Electroluminescence� Light is generated when electric current is passed through certain solids such as semiconductor or phosphor materials.

Photoluminescence� Radiation at one wavelength is absorbed, usually by a solid, and re-emitted at a different wavelength.� When the re-emitted radiation is visible the phenomenon may be termed either fluorescence or phosphorescence.

Generation of radiation (L&L pp. 102)

Quantum physics says that the outermost electron in a an atom may have one of discrete energies. Normally it resides in the state of lowest energy, or ground state.� When it absorbs energy, it is exited, and jumps to a higher energy state.� Eventually it is de-excited, and falls back to the ground state, emitting energy in the form of a photon.� The frequency of the light is given by Planck�s equation;

where

Q = difference in energy between the levels

= Planck�s Constant (6.6626176 x 10^-34 Js)

v = frequency of light radiated

Thermal radiation

When a body is heated to a high temperature its constituent atoms become excited by numerous interactions between them and energy is radiated in a continuous spectrum.� The continuous spectrum arises because the energy levels of the electrons in solids are broadened to the point of merging in a continuous band.� Thermodynamics have defined a perfect black body or full radiator.� By definition, a black body absorbs all energy falling upon it, provided it is held at a constant temperature.� Only a few materials such as carbon black and platinum black approach this ideal in reality.�

Planck also derived a relationship for the spectral distribution of thermal radiation for a full radiator;

where �is the spectral radiant exitance (Wm^-3)

DIAGRAM ???

The maximal radiant exitance increases with temperature, and the wavelength at maximum power is inversely proportional to the temperature T. This is known as Wiens Displacement Law;

This law corresponds to the observation that a heated body first glows red, then yellow, and the bluish.

The total radiant exitance of a black body surface is found by integrating �over all wavelengths.� The result is suprisingly simple, known as the Stefan-Boltzmann law;

where s is the Stefan-Boltzmann constant.

Propagation of Light (L&L pp. 4-8)

Light as a wave travel through vacuums at a constant velocity, approx. 3 x 10⁸ ms^-1.� In a material medium e.g. air or glass, velocity of propagation is less than in a vacuum by a factor known as the Refractive Index.

Refraction

Light passing through a smooth boundary surface into the second medium suffers a change of direction according to the following laws;

� The incident ray, the refracted ray, and the perpendicular to the surface at the point of incidence all lie in one plane

� If the incident ray is in a medium of refractive index n₁ and makes an angle q₁ with the perpendicular to the surface, and the refracted ray is in a medium of refractive index n₂ and makes an angle q₂ with the perpendicular, then;

���� where q₁ and q₂ lie on opposite sides of the perpendicular (Snell�s Law).

When a ray passes from a high to a low refractive index material, such as glass to air, a refracted ray exists only if q₁ is less than the critical angle, which is equal to .

If the ray is incident at an angle greater than the critical angle, no refracted ray is present and all of the incident light energy appears in the reflected ray; the term total reflection is used for this condition.

Reflection

At a bounding surface that is smooth compared with the wavelength of the incident light, specular reflection is said to occur.� A single incident ray produces a single reflected ray and the following relations occur;

� the incident ray, the reflected ray and the perpendicular to the bounding surface at the point of incidence all lie on one plane

� the incident ray and the reflected ray make equal angles with the perpendicular and are on opposite sides of it.

Reflection is the main way of directing light inside a luminaire.

Absorption and Scattering

A light ray passing through a vacuum loses no energy, although the energy make become more spread out.� In their progression through material media however, light usually loses energy through absorption and scattering effects.

Absorption is caused by the conversion of light into some other form of energy, usually heat, but it could be changed into radiation of a different wavelenth (fluorescence), into electrical energy in a photocell, or chemical energy as in the photosynthesis that occurs in plants.

MORE ???

Scattering occurs in non-homogeneous media and is caused by multiple refraction and reflection at numerous, randomly oriented, boundary surfaces within the media.� Fog and cloud are examples of scattering conditions in air due to the presence of suspended water droplets.� Scattering can be wavelength selective due to a contribution from diffracting light, and this can also impart colour onto a media.� All material media scatter light to some extent because of the molecular structure of matter.� Scattering by very small particles, such as molecules, is greater for the shorter wavelengths of light; the blue sky is accounted for in this way.

Diffuse Reflectance and transmission; cosine diffusers

When a light ray meets a surface which has irregularities comparable with or greater than the wavelength of incident light there is no longer a single reflected or refracted ray, but the light spreads out in all directions from the point of incidence, as in scattering.� The light which returns to the medium from which the incident ray emerged is said to be diffusely reflected and the light which passes through into to the second medium is said to be diffusely refracted.

In general the precise angular distribution of the reflected and tramitted light depends on the angle of incidence and of the nature of the surface.� With very fine grained roughness the reflection may almost be specular at angles of incidence approaching 90^o.


Uniform Diffuser In order to allow for simple calculations to be made, the concept of a uniform or cosine diffuser is often used.� A uniform diffuser is one in which the reflected light distribution is independant of the angle of the incident light, and the intensity of the reflected light in a direction making an angle q with the perpendicular to the surface is proportional cos q. This is also known as a Lambertian Reflector.� No real surface completely satisfies the conditions for a uniform diffuser, but some surfaces make a good approximation, for example a layer of magnesium oxide powder.

Inverse square and cosine laws of illumination (L&L pp. 15)

We consider a point source, S, illuminating a plane surface, P.� We know the illuminance on a small area dA, illuminated by a luminous flux dF is

Similarly, the luminous Intensity I is given by

where dw is the angle subtended by the element dA at the source.�

The illuminance produced at a point source at a distance r from a plane is obtained by first eliminating dF from the above two equations to give;

�

and since

substituting for dw gives

This expresses both the inverse square and cosine laws of illumination from a point source.

Luminance(L&L pp.15)

Luminance is related to the sensation of brightness, although the two are not equal.� The concept of luminance can be applied to any surface which is emitting or reflecting light, and can be generalized to include any imaginary surface in space through which light is passing, e.g. a portion of the sky.� It can be shown that the luminance of any such surface in a non-emitting, non-absorbing, and non-scattering medium is constant along a ray passing through the surface.� In less formal terms, this corresponds to the observation that in clear air the brightness of a surface does not depend on its distance from the observer.�

A uniform diffuse source is one which has the same luminance over its entire surface for all viewing directions.

An element of area A emitting a total flux F in all directions (i.e. over a solid angle of 2p sr) has a luminous exitance given by

For a unform dif