Principle and Optical Metrology of 222 nm uv light bulb Radiation Propagation
Properties and Electromagnetic Spectrum of Electromagnetic Waves
Light is an electromagnetic wave. According to Maxwell's electromagnetic theory, a time-varying electric field E (or magnetic field H) in a region of space will induce a varying magnetic field H (or electric field E) in adjacent regions. These alternating varying electric and magnetic fields continuously generate each other and propagate through space at a finite speed, forming electromagnetic waves. Electromagnetic waves exhibit the following properties:
(1) Both the electric field E and magnetic field H of an electromagnetic wave are perpendicular to the direction of propagation, and the three vectors (E, H, and propagation direction) are mutually perpendicular. Thus, electromagnetic waves are transverse waves. The vectors E, H, and the propagation direction form a right-handed screw system.
(2) For an electromagnetic wave propagating in a given direction, E and H oscillate in their respective planes-a characteristic known as polarization.
(3) At every point in space, E and H undergo periodic variations and are in phase, reaching maxima and minima simultaneously.
(4) At any point and any instant, the magnitude relationship between E and H is εE = μH.
(5) The propagation speed of electromagnetic waves in vacuum is c = 1/√(ε₀μ₀), and in a medium it is v = 1/√(εμ).
Electromagnetic waves span an extremely broad range, from radio waves and optical waves to X-rays and γ-rays-all belonging to the same category, differing only in wavelength. Currently discovered and widely utilized electromagnetic waves range from wavelengths longer than 10⁴ m to shorter than 10⁻⁵ nm. When arranged by frequency or wavelength, they form the electromagnetic spectrum. Optical radiation occupies only a tiny segment of this spectrum, with ultraviolet radiation being the primary focus of our study.
Optical Radiation
Energy that propagates in the form of electromagnetic waves or particles (photons), capable of being reflected, imaged, or dispersed by optical elements, along with its propagation process, is collectively referred to as optical radiation. It is generally considered to cover wavelengths from 10 nm to 1 mm (frequencies ~3×10¹¹ to 3×10¹⁶ Hz). Optical radiation is typically divided into three parts based on wavelength and human visual response: ultraviolet radiation, visible light, and infrared radiation. Wavelengths are usually expressed in nm for the visible-to-ultraviolet range, in μm for infrared, and wavenumbers are conventionally given in cm⁻¹.
Ultraviolet radiation has shorter wavelengths than violet light and is invisible to the human eye, spanning 1–390 nm. It is subdivided into near-UV, far-UV, and extreme-UV. Extreme-UV is almost completely absorbed by air and can only propagate in vacuum, hence it is also called vacuum ultraviolet (VUV). In solar UV studies, ultraviolet radiation is often classified into UVA, UVB, and UVC bands.
In particular, the far-ultraviolet light produced by a 222 nm uv light bulb (a KrCl* excimer lamp) has attracted considerable attention in recent years for unoccupied-space disinfection applications in public areas. Its high photon energy, strong absorption by oxygen in air, and extremely shallow penetration depth in human skin (limited to the stratum corneum) make it uniquely safe and effective.
To quantitatively describe optical radiation, specific physical quantities are required. Detection and measurement of optical radiation employ two distinct systems: radiometric units and photometric units.
The radiometric system uses radiant flux (or radiant power) and radiant energy as fundamental quantities, depending solely on the radiating object. Basic units are watt (W) and joule (J). Radiometry applies across the entire electromagnetic spectrum.
The photometric system reflects visual brightness perception. Its fundamental quantity is luminous intensity, with the basic unit candela (cd). Photometry is applicable only to the visible range.
Although the physical quantities in the two systems differ conceptually, their symbols correspond one-to-one. Radiometric quantities are denoted with subscript "e", photometric quantities with subscript "v".
A major conclusion of Maxwell's theory is the existence of electromagnetic waves, and light is an electromagnetic wave. Light is essentially no different from radio waves, microwaves, X-rays, or γ-rays except in wavelength range. Based on this theory, attenuation of light intensity in the atmosphere can be calculated. In this book, ultraviolet measurement distances are relatively short (only tens of meters), so the propagation medium can be regarded as uniform, and effects of refractive index and atmospheric turbulence are neglected. Subsequent measurements treat the medium as vacuum.
Basic Laws of Optical Radiation Measurement
A radiation source can be characterized by radiant intensity, radiant exitance (radiant flux density), and radiant flux to describe its strength and spatial energy distribution.
Radiant intensity is the radiant power emitted by a source per unit solid angle, reflecting the angular distribution of radiant energy.
Radiant exitance (radiant flux density) is the total radiant power emitted per unit area, reflecting surface emission density.
Radiant flux is the total power emitted by the entire source into space (time rate of radiant energy).
Radiance is defined as the radiant power emitted per unit projected area in the line-of-sight direction per unit solid angle. The relationships among radiant intensity, radiant exitance, radiant flux, and radiance are expressed as:
Integrating radiance over the source area yields radiant intensity: J = ∫ₐ N cosθ dA (3-1)
Integrating radiance over solid angle yields radiant exitance: M = ∫ₒ N cosθ dΩ (3-2)
Double integration over area and solid angle yields radiant flux: Φ = ∫ₐ ∫ₒ N cosθ dA dΩ (3-3)
Where: N - radiance of the source; dA - source area element; θ - angle between emission direction and surface normal; dΩ - solid angle element; cosθ dA - projected area in the emission direction.
Irradiance has the same dimensions as radiant exitance (W/cm²), but refers to power received per unit area at the detector. When an instrument receives radiation, irradiance at the entrance pupil is: E = ∫ₒ N cosθ dΩ (3-4)
Equation (3-4) is formally identical to (3-2), but uses the radiance at the receiver and integrates over the instrument's acceptance solid angle. If transmission losses are neglected, source radiance equals received radiance; with losses, calculation remains straightforward. Thus, determining source radiance is crucial in engineering applications.
In general, radiation or reflection from objects is directional, occurring only within limited solid angles, meaning radiance depends on direction. An ideal diffuse emitter (Lambertian radiator) emits uniformly into the hemispherical space with constant radiance. The radiant intensity from a Lambertian surface element follows Lambert's cosine law: dJ = N cosθ dA ∝ cosθ (3-5)
When observing a diffuse luminous object (e.g., the Sun) from different angles, the projected area seen by each retinal cell remains constant, as does the solid angle subtended at the pupil. Since Lambertian radiance is independent of viewing direction, received energy is constant, producing a uniformly bright disk.
For an ideal Lambertian emitter radiating into a hemisphere, the relationship between radiant exitance and radiance is: dΩ = sinθ dθ dφ M = ∫ N cosθ dΩ = N ∫₀²π dφ ∫₀π/₂ cosθ sinθ dθ = πN (3-6)
Notably, radiant exitance equals π times radiance, not 2π (the full hemispherical solid angle).
A perfect Lambertian radiator is an ideal model. In practice, many sources approximate Lambertian behavior only within limited angular ranges. For most electrical insulators, radiance can be considered approximately constant for angles ≤60° from the normal; for conductors, ≤50°. Certain sources, such as some 222 nm uv light bulb excimer discharge tubes, also exhibit near-Lambertian distribution over small angles, making them convenient as standard sources for ultraviolet radiometric calibration.
