Radiometry deals with radiant energy (i.e., electromagnetic radiation) of any wavelength.
The wavelength field includes the Ultra-Violt (UV), Visible Light and Infra-Red (IR).
Generally, radiometry explore the characteristics of electromagnetic wavelength in the range from 10 nm to 106 nm [Fig. 2-1] Two out of many typical units encountered are radiant energy by quantity of Joule (J) and radiant power (or radiant flux) by Watt (W). Due to the
scale of measured energy is not too large, the units are expressed by mJ and mW (m represent the value of 1×10-3) customarily.
Photometry is the measurement of visible light based on the response of the average human observer.The visible spectrum covers the wavelengths from approximately 390 to 800 nm. Photometry is like radiometry except that everything is weighted by the spectral response of the eye. Visual photometry uses the eye as a comparison detector, while physical photometry uses either optical radiation detectors constructed to mimic the spectral response of the eye, or spectroradiometry coupled with appropriate calculations to do the eye response weighting. Figure 2-2 shows the definition of typical photometric units and Table 2-1 expresses the quantities in lumen (lm), lux (lx), and candela (cd).
The only real difference between radiometry and photometry is that radiometry includes the entire optical radiation spectrum, while photometry is limited to the visible spectrum as defined by the response of the eye [2-5].
Fig. 2-2 Definition of radiometric and photometric quantities [3].
Table 2-1 SI photometry units.
Quantity Symbol SI unit Abbr.
Luminous flux Φv lumen lm
Luminous intensity Iv Candela (lm/sr) cd
Luminance Lv
candela per square meter
(lm/sr．m2 or cd/m2) nits
Illuminance Ev Lux (lm/m2) lx
Luminous exitance Mv lm/m2
Luminous efficacy lumen per watt (lm/W)
Fig. 2-3 Example of a typical spectral power distribution (SPD) [6].
2.1.1 Spectral Power Distribution
Incandescent, fluorescent, and high-intensity discharge (HID) lamps radiate across the visible spectrum, but with varying intensity in the different wavelengths. The spectral power distribution (SPD) for a given light source shows the relative radiant power emitted by the light source at each wavelength. Incandescent sources have a continuous SPD, but relative
power is low in the blue and green regions. The typically "warm" color appearance of incandescent lamps is due to the relatively high emissions in the orange and red regions of the spectrum as Fig. 2-3 shown.
2.1.2 Eye Sensitivity Functions
The eye sensitivity functions or the luminosity functions or the luminous efficiency functions describe the different visual spectral efficiency of human eye to different wavelength of visible light. There are two kinds of eye sensitivity functions in common usage [Fig. 2-4]. For bright day-light level, the photopic luminosity function approximates the response of the human eye. For dark night-light level, the response of the human eye changes and the scotopic curve applies. Radiometric quantities can be converted into photometric quantities and vice versa by the equation (photometric quantity, Fl(λ)) = K(λ) × (radiometric quantity, Fr(λ)). The equations can be written explicitly as
λ λ λ
λ) K F 683 SPD( )V( )d (
Fl = m⋅ r = ⋅
∫
⋅ (2.1.1)λ λ λ
λ) K F 1700 SPD( )V( )d (
Fl' = 'm⋅ r = ⋅
∫
⋅ ' (2.1.2)where Fl(λ), Fl'(λ) represents the quantity of day-light and night-light luminous efficacies, Km, Km' represents the maximum luminous efficacies and V(λ), V'(λ) represents the standard luminosity function, SPD(λ) is the spectral power distribution of the radiation and λ is wavelength in metric unit.
The standard day-light luminosity function is normalized to a peak value of unity at 555 nm and the maximum luminous efficacy of radiation for photopic vision is 683 lm/W.
Comparatively, the standard night-light luminosity function is normalized to a peak value of unity at 507 nm and the maximum luminous efficacy of radiation for photopic vision is 1700 lm/W. It is a standard function established by the Commission Internationale de l'Éclairage
(CIE) and may be used to convert radiant energy into luminous (i.e., visible) energy in 1983.
For all of the optics measurement equipments, the characteristics of optical detector should make calibration follow the curve of luminous efficiency functions rules by CIE standard to meet the actual eye sensitivity of human eye.
Fig. 2-4 Eye sensitivity function of two types of vision can be described by photopic and scotopic response curves [3].
2.1.3 Solid Angle
A solid angle is used in photometry to measure the portion of a sphere bounded by some irregular surface [Fig. 2-5]. The sphere is defined by the vertex (the center of a luminous body) and the center of the surface (an aperture). An entire sphere has a solid angle of 4π steradians (sr).
Fig. 2-5 The definition of solid angle [7].
2.1.4 Luminous Intensity
Luminous intensity is the perceived power per unit solid angle. Luminous intensity is a measure of the wavelength weighted power emitted by a light source in a particular direction per unit solid angle, based on the spectral luminous efficiency curve of the human eye sensitivity. The SI unit of luminous intensity is the candela (cd). The concept of luminous intensity requires the assumption of a point source, or at least a source small enough for its dimensions to be negligible compared to the distance between light source and detector and, in principle at least, there is also a requirement that the measurement should be made over a very small element of solid angle.
2.1.5 Luminous Flux
In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light.
The SI unit of luminous flux is the lumen (lm). One lumen is defined as the luminous flux of light produced by a light source that emits one candela of luminous intensity over a solid angle of one steradian (sr).
2.1.6 Luminance
Luminance is used for measuring the brightness of a light source on a surface. It's defined by the luminous flux emitted from a surface per unit solid angle per unit area of the source where the area is calculated by projecting it onto a plane normal to the direction of propagation. Luminance is invariant under transformation by a lens and also gives the same results when measured at any distance from the source.
2.1.7 Illuminance
Illuminance is the luminance flux incident on a surface from all directions. The luminous flux comes from one or several sources. What happens to the light at the surface (where if it is reflected or absorbed) does not matter. Illuminance is measured with a detector placed on the surface pointing toward the light source.
2.1.8 Lambert's Cosine Law and Lambertian Surface
A surface that diffuses light perfectly produces luminous intensity (IV) in all directions that obeys Lambert's Cosine Law [Fig. 2-6 & Eq. 2.1.3], where the intensity (IV) varies as the cosine of the angle between normal and the direction of the intensity measurement. The direction of the light incident on the surface has no effect on the luminous intensity (IV) pattern.
θ I cos
θ
I = normal (2.1.3)
Fig. 2-6 Lambert's Cosine Law [7-8].
Fig. 2-7 Lambertian surface [7-8].
However, the luminance (LV) of the surface does not obey Lambert's Cosine Law and it is constant when viewed from any angle. Lambertian surface is a perfectly diffuse surface [Fig. 2-7 & Eq. 2.1.4]. This is because projected area viewed through the luminance aperture varies as the cosine of the angle between the normal and the luminance measurement angle, thus offsetting the cosine effect of the luminous intensity.
normal principles. Through electromagnetic theory, light is a wave varies electric and magnetic fields to comply with time. The light takes a spherical form when radiated from a point, and then behaves like plane waves when propagating. The path of a hypothetical point on the wave front of light is called a ray. Such a ray is an extremely convenient fiction for the ray-tracing.
It provides a way to discuss the behavior of light and analyze the optics of lighting systems.
Several optical software, such as LightToolsTM, OSLOTM, et al., can support the ray-tracing function to build optical module for a simulated environment.
2.2.1 Law of Refraction (Snell's Law)
Snell's law, a law of refraction, defines the refraction of light in the plane of incidence.
Snell's law describes the ratio of the incidence angle (θi) by the refraction angle (θt) equals to a constant which depends on the opposite ratio of the refractive indices of two optical media as: