The troland (symbol Td), named after Leonard T. Troland, is a unit of conventional retinal illuminance. It is meant as a method for correcting photometric measurements of luminance values impinging on the human eye by scaling them by the effective pupil size. It is equal to retinal illuminance produced by a surface whose luminance is one nit when the apparent area of the entrance pupil of the eye is 1 square millimeter. [1]
The troland unit was proposed in 1916 by Leonard T. Troland, who called it a photon. [2]
The troland typically refers to the ordinary or photopic troland, which is defined in terms of the photopic luminance:
where L is the photopic luminance in cd m−2 and p is pupil area in mm2.
A scotopic troland is also sometimes defined:
where L′ is the scotopic luminance in cd m−2 and p is pupil area in mm2.
Although named "retinal illuminance" (and originally named "photon" by Troland), trolands do not measure the actual photon flux incident on the retina; that quantity depends on the specific wavelengths of light that constitute the luminance used in the calculation.
Troland does not directly convert to other units, being a retinal luminance per unit area of a pupil.
However Troland is linked to retinal illuminance in lux=lm/m2 as follows. Assuming the corneal luminance L from an extended source, the pupil diameter p and the focal length of the eye F, the retinal luminance is:
Lr [lm / m^2] = pi * L / 4 / (f/#)^2 ~ pi * L * p^2 / 4 / F^2.
Multiplying by the pupil area :
Alternatively, the retinal illuminance
As provided by a more accurate optical calculations, the conversion factor is 278 rather than 289 as demonstrated by simplified considerations above.
Sometimes (by convention only, although not rigorously accurate by definition), retinal luminance is expressed in . Assuming a Lambertian surface, 1 cd/m^2 = pi lm/m^2 = pi lux. That is, 1 [cd/m^2] = 289/pi [Troland] ~ 92 [Troland]
centimeter-gram-second (cgs) [3]
[length]^(-2) [luminous intensity] [3]
The candela is the base unit of luminous intensity in the International System of Units (SI); that is, luminous power per unit solid angle emitted by a point light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the standard luminosity function. A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given solid angle.
In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the direction of the incident light and the surface normal. The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his Photometria, published in 1760.
The Kruithof curve describes a region of illuminance levels and color temperatures that are often viewed as comfortable or pleasing to an observer. The curve was constructed from psychophysical data collected by Dutch physicist Arie Andries Kruithof, though the original experimental data is not present on the curve itself. Lighting conditions within the bounded region were empirically assessed as being pleasing or natural, whereas conditions outside the region were considered uncomfortable, displeasing or unnatural. The Kruithof curve is a sufficient model for describing pleasing sources that are considered natural or closely resemble Planckian black bodies, but its value in describing human preference has been consistently questioned by further studies on interior lighting.
In photography, exposure value (EV) is a number that represents a combination of a camera's shutter speed and f-number, such that all combinations that yield the same exposure have the same EV. Exposure value is also used to indicate an interval on the photographic exposure scale, with a difference of 1 EV corresponding to a standard power-of-2 exposure step, commonly referred to as a stop.
A luminosity function or luminous efficiency function describes the average spectral sensitivity of human visual perception of brightness. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It should not be considered perfectly accurate, but it is a good representation of visual sensitivity of the human eye and it is valuable as a baseline for experimental purposes. Different luminosity functions apply under different lighting condition, varying from photopic in brightly lit conditions through mesotopic to scotopic under low lighting conditions. Without qualification, the luminosity function generally refers to the photopic luminosity function.
In photometry, 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 luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.
In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per unit area emitted from a surface. Luminous emittance is also known as luminous exitance.
Riccò's law, discovered by astronomer Annibale Riccò, is one of several laws that describe a human's ability to visually detect targets on a uniform background. This law explains the visual relationship between a target angular area A and target luminance increment required for detection when that target is unresolved. The law is given by:
Photopic vision is the vision of the eye under well-lit conditions (luminance level 10 to 108cd/m2). In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher visual acuity and temporal resolution than available with scotopic vision.
Scotopic vision is the vision of the eye under low-light levels. The term comes from Greek skotos, meaning "darkness", and -opia, meaning "a condition of sight". In the human eye, cone cells are nonfunctional in low visible light. Scotopic vision is produced exclusively through rod cells, which are most sensitive to wavelengths of around 498 nm (green–blue) and are insensitive to wavelengths longer than about 640 nm. This condition is called the Purkinje effect.
A foot-lambert or footlambert is a unit of luminance in United States customary units and some other unit systems. A foot-lambert equals 1/π or 0.3183 candela per square foot, or 3.426 candela per square meter. The foot-lambert is named after Johann Heinrich Lambert (1728–1777), a Swiss-German mathematician, physicist and astronomer. It is rarely used by electrical and lighting engineers, in favor of the candela per square foot or candela per square meter.
In photometry, luminous energy is the perceived energy of light. This is sometimes called the quantity of light. Luminous energy is not the same as radiant energy, the corresponding objective physical quantity. This is because the human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions, the eye is most sensitive to light at a wavelength of 555 nm. Light with a given amount of radiant energy will have more luminous energy if the wavelength is 555 nm than if the wavelength is longer or shorter. Light whose wavelength is well outside the visible spectrum has a luminous energy of zero, regardless of the amount of radiant energy present.
Mesopic vision is a combination of photopic vision and scotopic vision in low but not quite dark lighting situations. Mesopic light levels range from luminances of approximately 0.01 cd/m2 to 3 cd/m2. Most nighttime outdoor and street lighting scenarios are in the mesopic range.
The Stiles–Crawford effect is a property of the human eye that refers to the directional sensitivity of the cone photoreceptors.
Photon transport in biological tissue can be equivalently modeled numerically with Monte Carlo simulations or analytically by the radiative transfer equation (RTE). However, the RTE is difficult to solve without introducing approximations. A common approximation summarized here is the diffusion approximation. Overall, solutions to the diffusion equation for photon transport are more computationally efficient, but less accurate than Monte Carlo simulations.
In crystallography, the Laue equations relate the incoming waves to the outgoing waves in the process of diffraction by a crystal lattice. They are named after physicist Max von Laue (1879–1960). They reduce to Bragg's law.
The stilb (sb) is the CGS unit of luminance for objects that are not self-luminous. It is equal to one candela per square centimeter or 104 nits (candelas per square meter). The name was coined by the French physicist André Blondel around 1920. It comes from the Greek word stilbein (στίλβειν), meaning 'to glitter'.
Leonard Thompson Troland (1889–1932) was an American physicist, psychologist and psychical researcher.