Misplaced Pages

#576423

30-452: The procedure for conversion from spectral radiance to luminance is standardized by the CIE and ISO . Brightness is the term for the subjective impression of the objective luminance measurement standard (see Objectivity (science) § Objectivity in measurement for the importance of this contrast). The SI unit for luminance is candela per square metre (cd/m). A non-SI term for

60-551: A curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow . Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing . This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as

90-406: A surface , denoted L e,Ω,ν , is defined as where ν is the frequency. Spectral radiance in wavelength of a surface , denoted L e,Ω,λ , is defined as where λ is the wavelength. Radiance of a surface is related to étendue by where As the light travels through an ideal optical system, both the étendue and the radiant flux are conserved. Therefore, basic radiance defined by

120-578: A computer to propagate many rays. When applied to problems of electromagnetic radiation , ray tracing often relies on approximate solutions to Maxwell's equations such as geometric optics , that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength . Ray theory can describe interference by accumulating the phase during ray tracing (e.g., complex-valued Fresnel coefficients and Jones calculus ). It can also be extended to describe edge diffraction , with modifications such as

150-459: A function of frequency or wavelength. Radiance is the integral of the spectral radiance over all frequencies or wavelengths. For radiation emitted by the surface of an ideal black body at a given temperature, spectral radiance is governed by Planck's law , while the integral of its radiance, over the hemisphere into which its surface radiates, is given by the Stefan–Boltzmann law . Its surface

180-520: A lossless medium, the luminance does not change along a given light ray . As the ray crosses an arbitrary surface S , the luminance is given by L v = d 2 Φ v d S d Ω S cos ⁡ θ S {\displaystyle L_{\mathrm {v} }={\frac {\mathrm {d} ^{2}\Phi _{\mathrm {v} }}{\mathrm {d} S\,\mathrm {d} \Omega _{S}\cos \theta _{S}}}} where More generally,

210-446: A particular surface from a particular angle of view . Luminance is thus an indicator of how bright the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye's pupil . Luminance is used in the video industry to characterize the brightness of displays. A typical computer display emits between 50 and 300 cd/m . The sun has a luminance of about 1.6 × 10 cd/m at noon. Luminance

240-438: A surface will be received by an optical system looking at that surface from a specified angle of view. In this case, the solid angle of interest is the solid angle subtended by the optical system's entrance pupil . Since the eye is an optical system, radiance and its cousin luminance are good indicators of how bright an object will appear. For this reason, radiance and luminance are both sometimes called "brightness". This usage

270-617: A way similar to the way a digital camera records color images. The luminance of a specified point of a light source, in a specified direction, is defined by the mixed partial derivative L v = d 2 Φ v d Σ d Ω Σ cos ⁡ θ Σ {\displaystyle L_{\mathrm {v} }={\frac {\mathrm {d} ^{2}\Phi _{\mathrm {v} }}{\mathrm {d} \Sigma \,\mathrm {d} \Omega _{\Sigma }\cos \theta _{\Sigma }}}} where If light travels through

300-478: Is Lambertian , so that its radiance is uniform with respect to angle of view, and is simply the Stefan–Boltzmann integral divided by π. This factor is obtained from the solid angle 2π steradians of a hemisphere decreased by integration over the cosine of the zenith angle . Radiance of a surface , denoted L e,Ω ("e" for "energetic", to avoid confusion with photometric quantities, and "Ω" to indicate this

330-399: Is invariant in geometric optics . This means that for an ideal optical system, the luminance at the output is the same as the input luminance. For real, passive optical systems, the output luminance is at most equal to the input. As an example, if one uses a lens to form an image that is smaller than the source object, the luminous power is concentrated into a smaller area, meaning that

SECTION 10

#1732772060577

360-571: Is perpendicular to the light's wavefronts ; its tangent is collinear with the wave vector . Light rays in homogeneous media are straight. They bend at the interface between two dissimilar media and may be curved in a medium in which the refractive index changes. Geometric optics describes how rays propagate through an optical system. Objects to be imaged are treated as collections of independent point sources, each producing spherical wavefronts and corresponding outward rays. Rays from each object point can be mathematically propagated to locate

390-424: Is a directional quantity), is defined as where In general L e,Ω is a function of viewing direction, depending on θ through cos θ and azimuth angle through ∂Φ e /∂Ω . For the special case of a Lambertian surface , ∂ Φ e /(∂Ω ∂ A ) is proportional to cos θ , and L e,Ω is isotropic (independent of viewing direction). When calculating the radiance emitted by a source, A refers to an area on

420-686: Is a model of optics that describes light propagation in terms of rays . The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays: In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity , absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces, complicating analysis. Historically, ray tracing involved analytic solutions to

450-468: Is also conserved. In real systems, the étendue may increase (for example due to scattering) or the radiant flux may decrease (for example due to absorption) and, therefore, basic radiance may decrease. However, étendue may not decrease and radiant flux may not increase and, therefore, basic radiance may not increase. Light ray In optics , a ray is an idealized geometrical model of light or other electromagnetic radiation , obtained by choosing

480-469: Is now discouraged (see the article Brightness for a discussion). The nonstandard usage of "brightness" for "radiance" persists in some fields, notably laser physics . The radiance divided by the index of refraction squared is invariant in geometric optics . This means that for an ideal optical system in air, the radiance at the output is the same as the input radiance. This is sometimes called conservation of radiance . For real, passive, optical systems,

510-403: Is the watt per steradian per square metre ( W·sr ·m ). It is a directional quantity: the radiance of a surface depends on the direction from which it is being observed. The related quantity spectral radiance is the radiance of a surface per unit frequency or wavelength , depending on whether the spectrum is taken as a function of frequency or of wavelength. Historically, radiance

540-516: The illuminance is higher at the image. The light at the image plane, however, fills a larger solid angle so the luminance comes out to be the same assuming there is no loss at the lens. The image can never be "brighter" than the source. Retinal damage can occur when the eye is exposed to high luminance. Damage can occur because of local heating of the retina. Photochemical effects can also cause damage, especially at short wavelengths. The IEC 60825 series gives guidance on safety relating to exposure of

570-421: The light waves propagate through and around objects whose dimensions are much greater than the light's wavelength . Ray optics or geometrical optics does not describe phenomena such as diffraction , which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model. A light ray is a line ( straight or curved ) that

600-572: The candela per square metre. Luminance is essentially the same as surface brightness , the term used in astronomy. This is measured with a logarithmic scale, magnitudes per square arcsecond (MPSAS). Radiance In radiometry , radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiation , and to quantify emission of neutrinos and other particles. The SI unit of radiance

630-476: The corresponding point on the image. A slightly more rigorous definition of a light ray follows from Fermat's principle , which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. There are many special rays that are used in optical modelling to analyze an optical system. These are defined and described below, grouped by the type of system they are used to model. Geometrical optics , or ray optics,

SECTION 20

#1732772060577

660-462: The eye to lasers, which are high luminance sources. The IEC 62471 series gives guidance for evaluating the photobiological safety of lamps and lamp systems including luminaires. Specifically it specifies the exposure limits, reference measurement technique and classification scheme for the evaluation and control of photobiological hazards from all electrically powered incoherent broadband sources of optical radiation, including LEDs but excluding lasers, in

690-454: The integral covers all the directions of emission Ω Σ , In the case of a perfectly diffuse reflector (also called a Lambertian reflector ), the luminance is isotropic, per Lambert's cosine law . Then the relationship is simply L v = E v R π . {\displaystyle L_{\text{v}}={\frac {E_{\text{v}}R}{\pi }}.} A variety of units have been used for luminance, besides

720-759: The luminance along a light ray can be defined as L v = n 2 d Φ v d G {\displaystyle L_{\mathrm {v} }=n^{2}{\frac {\mathrm {d} \Phi _{\mathrm {v} }}{\mathrm {d} G}}} where The luminance of a reflecting surface is related to the illuminance it receives: ∫ Ω Σ L v d Ω Σ cos ⁡ θ Σ = M v = E v R , {\displaystyle \int _{\Omega _{\Sigma }}L_{\text{v}}\mathrm {d} \Omega _{\Sigma }\cos \theta _{\Sigma }=M_{\text{v}}=E_{\text{v}}R,} where

750-439: The output radiance is at most equal to the input, unless the index of refraction changes. As an example, if you form a demagnified image with a lens, the optical power is concentrated into a smaller area, so the irradiance is higher at the image. The light at the image plane, however, fills a larger solid angle so the radiance comes out to be the same assuming there is no loss at the lens. Spectral radiance expresses radiance as

780-475: The ray's trajectories. In modern applied physics and engineering physics , the term also encompasses numerical solutions to the Eikonal equation . For example, ray-marching involves repeatedly advancing idealized narrow beams called rays through the medium by discrete amounts. Simple problems can be analyzed by propagating a few rays using simple mathematics. More detailed analysis can be performed by using

810-515: The same unit is the nit . The unit in the Centimetre–gram–second system of units (CGS) (which predated the SI system) is the stilb , which is equal to one candela per square centimetre or 10 kcd/m. Luminance is often used to characterize emission or reflection from flat, diffuse surfaces. Luminance levels indicate how much luminous power could be detected by the human eye looking at

840-442: The surface of the source, and Ω to the solid angle into which the light is emitted. When calculating radiance received by a detector, A refers to an area on the surface of the detector and Ω to the solid angle subtended by the source as viewed from that detector. When radiance is conserved, as discussed above, the radiance emitted by a source is the same as that received by a detector observing it. Spectral radiance in frequency of

870-509: The wavelength range from 200 nm through 3000 nm . This standard was prepared as Standard CIE S 009:2002 by the International Commission on Illumination. A luminance meter is a device used in photometry that can measure the luminance in a particular direction and with a particular solid angle . The simplest devices measure the luminance in a single direction while imaging luminance meters measure luminance in

900-407: Was called "intensity" and spectral radiance was called "specific intensity". Many fields still use this nomenclature. It is especially dominant in heat transfer , astrophysics and astronomy . "Intensity" has many other meanings in physics , with the most common being power per unit area . Radiance is useful because it indicates how much of the power emitted, reflected, transmitted or received by

#576423