Definitions photometric quantities of the light series and the mathematical relationships between them are similar to the corresponding quantities and relationships of the energy series. That's why light flow, propagating within the solid angle equals . unit of measurement luminous flux (lumen). For monochromatic light relationship between energy and light quantities given by the formulas:
where is a constant called the mechanical equivalent of light.
The luminous flux falling on the interval of wavelengths from l before ,
, (30.8)
where j is the distribution function of energy over wavelengths (see Fig. 30.1). Then the total luminous flux carried by all spectrum waves,
. (30.9)
illumination
The luminous flux can also come from bodies that do not themselves glow, but reflect or scatter the light falling on them. In such cases, it is important to know what light flux falls on a particular area of the body surface. For this it serves physical quantity, called illumination
. (30.10)
illumination numerically equals the ratio of the total luminous flux incident on the surface element to the area of \u200b\u200bthis element (see Fig. 30.4). For an even light output
Illumination unit 
(lux). Suite equals the illumination of a surface with an area of 1 m 2 when a luminous flux of 1 lm falls on it. Energy illumination is defined similarly
Unit of energy illumination.
Brightness
For many lighting calculations, some sources can be considered as point sources. However, in most cases, the light sources are placed close enough to distinguish their shape, in other words, the angular dimensions of the source lie within the ability of the eye or optical instrument to distinguish an extended object from a point. For such sources, a physical quantity called brightness is introduced. The concept of brightness is not applicable to sources whose angular dimensions are less than the resolution of the eye or an optical instrument (for example, to stars). Brightness characterizes the radiation of a luminous surface in a certain direction. The source can glow with its own or reflected light.
Let's single out a light flux propagating in a certain direction in a solid angle from a section of a luminous surface. The axis of the beam forms an angle with the normal to the surface (see Fig. 30.5).
Projection of a section of a luminous surface onto a site perpendicular to the selected direction,
(30.14)
called visible surface source site element (see Figure 30.6).
The value of the luminous flux depends on the area of the visible surface, on the angle and on the solid angle:
The proportionality factor is called brightness, It depends on optical properties radiating surface and may be different for different directions. From (30.5) brightness
. (30.16)
In this way, brightness is determined by the luminous flux emitted in a certain direction by a unit of visible surface per unit solid angle. Or in other words: the brightness in a certain direction is numerically equal to the intensity of light created by a unit area of the visible surface of the source.
AT general case the brightness depends on the direction, but there are light sources for which the brightness does not depend on the direction. Such sources are called Lambertian or cosine, because Lambert's law is valid for them: the light intensity in a certain direction is proportional to the cosine of the angle between the normal to the source surface and this direction:
where is the light intensity in the direction of the normal to the surface, is the angle between the normal to the surface and the selected direction. To ensure the same brightness in all directions, technical lamps are equipped with milk glass shells. Lambertian sources emitting diffused light include a surface coated with magnesium oxide, unglazed porcelain, drawing paper, and freshly fallen snow.
Unit of brightness 
(nit). Here are the brightness values of some light sources:
Moon - 2.5 knt,
fluorescent lamp - 7 knt,
light bulb filament - 5 Mnt,
the surface of the Sun is 1.5 Gnt.
The lowest brightness perceived by the human eye is about 1 micronth, and the brightness exceeding 100 knt causes pain in the eye and can damage vision. The brightness of a sheet of white paper when reading and writing should be at least 10 nits.
Energy brightness is defined similarly
. (30.18)
Unit of measurement of radiance.
Luminosity
Let us consider a light source of finite dimensions (shining with its own or reflected light). luminosity source is called surface density luminous flux emitted by a surface in all directions within a solid angle. If a surface element emits a luminous flux, then
For uniform luminosity, we can write:
Luminosity unit.
Energy luminosity is defined similarly
Unit of energy luminosity.
Laws of illumination
Photometric measurements are based on two laws of illumination.
1. The illumination of a surface by a point light source varies in inverse proportion to the square of the distance of the source from the illuminated surface. Consider a point source (see Figure 30.7) that emits light in all directions. Let us describe around the source concentric spheres with the source with radii and . Obviously, the luminous flux through the surface areas and is the same, since it propagates in one solid angle. Then the illumination of the areas and will be, respectively, and . Expressing the elements spherical surfaces through the solid angle , we get:
. (30.22)
2. The illumination created on an elementary section of the surface by a light flux incident on it at a certain angle is proportional to the cosine of the angle between the direction of the rays and the normal to the surface. Let's consider a parallel beam of rays (see Fig. 29.8) falling on areas of surfaces and . Rays are incident on the surface along the normal, and on the surface at an angle to the normal. The same light flux passes through both sections. The illumination of the first and second sections will be, respectively, and 
. But, therefore,
Combining these two laws, we can formulate basic law of illumination: the illumination of a surface by a point source is directly proportional to the luminous intensity of the source, the cosine of the angle of incidence of the rays, and inversely proportional to the square of the distance from the source to the surface
. (30.24)
Calculations using this formula give a fairly accurate result if the linear dimensions of the source do not exceed 1/10 of the distance to the illuminated surface. If the source is a disk with a diameter of 50 cm, then at a point on the normal to the center of the disk relative error in calculations for a distance of 50 cm it reaches 25%, for a distance of 2 m it does not exceed 1.5%, and for a distance of 5 m it decreases to 0.25%.
If there are several sources, then the resulting illumination is equal to the sum of the illuminations created by each individual source. If the source cannot be considered as a point source, its surface is divided into elementary sections and, having determined the illumination created by each of them, according to the law 
, then integrate over the entire surface of the source.
There are lighting standards for workplaces and premises. On the tables classrooms illumination should be at least 150 lux, for reading books you need illumination, and for drawing - 200 lux. For corridors, illumination is considered sufficient, for streets -.
The most important source of light for all life on Earth - the Sun creates on upper bound atmosphere energy illumination, called the solar constant - and illumination of 137 klx. The energy illumination created on the Earth's surface by direct rays in summer is two times less. The illumination created by direct sunlight at noon at the middle latitude of the area is 100 klx. The change of seasons on Earth is explained by the change in the angle of incidence of the sun's rays on its surface. In the northern hemisphere, the largest angle of incidence of rays on the Earth's surface is in winter, and the smallest - in summer. Illumination on open space with a cloudy sky is 1000 lux. Illumination in a bright room near the window - 100 lux. For comparison, we present the illumination from full moon- 0.2 lux and from the night sky on a moonless night - 0.3 mlk. The distance from the Sun to the Earth is 150 million kilometers, but due to the fact that the force sunlight equals, the illumination created by the Sun on the surface of the Earth is so great.
For sources whose light intensity depends on direction, sometimes use average spherical luminous intensity, where is the total luminous flux of the lamp. Lumen ratio electric lamp to its electrical power is called light output lamps: . For example, a 100 W incandescent lamp has an average spherical luminous intensity of about 100 cd. The total luminous flux of such a lamp is 4 × 3.14 × 100 cd = 1260 lm, and the luminous efficiency is 12.6 lm / W. The luminous efficiency of fluorescent lamps is several times greater than that of incandescent lamps, and reaches 80 lm / W. In addition, the service life of fluorescent lamps exceeds 10 thousand hours, while for incandescent lamps it is less than 1000 hours.
Over millions of years of evolution human eye adapted to sunlight, and therefore it is desirable that the spectral composition of the light of the lamp be as close as possible to the spectral composition of sunlight. This requirement is best met by fluorescent lamps. That is why they are also called fluorescent lamps. The brightness of the filament of a light bulb causes pain in the eye. To prevent this, milky glass shades and lampshades are used.
With all their advantages, fluorescent lamps also have a number of disadvantages: the complexity of the switching circuit, the pulsation of the light flux (with a frequency of 100 Hz), the impossibility of starting in the cold (due to mercury condensation), the buzz of the throttle (due to magnetostriction), environmental hazard (mercury from a broken lamp poisons environment).
In order for the spectral composition of the radiation of an incandescent lamp to be the same as that of the Sun, it would be necessary to heat its filament to the temperature of the surface of the Sun, i.e., up to 6200 K. But tungsten, the most refractory of metals, melts already at 3660 K.
A temperature close to that of the solar surface is reached in an arc discharge in mercury vapor or in xenon at a pressure of about 15 atm. The light intensity of an arc lamp can be brought up to 10 Mcd. Such lamps are used in film projectors and spotlights. Lamps filled with sodium vapor are distinguished by the fact that in them a significant part of the radiation (about a third) is concentrated in the visible region of the spectrum (two intense yellow lines at 589.0 nm and 589.6 nm). Although the emission of sodium lamps is very different from the usual sunlight for the human eye, they are used to illuminate motorways, as their advantage is a high luminous efficiency, up to 140 lm / W.
Photometers
Devices designed to measure the intensity of light or light fluxes from different sources are called photometers. According to the principle of registration, photometers are of two types: subjective (visual) and objective.
The principle of operation of a subjective photometer is based on the ability of the eye to fix the same illumination (more precisely, brightness) of two adjacent fields with a sufficiently high accuracy, provided that they are illuminated with light of the same color.
Photometers for comparing two sources are designed so that the role of the eye is reduced to establishing the same illumination of two adjacent fields illuminated by the compared sources (see Fig. 30.9). The observer's eye examines a white trihedral prism installed in the middle of a blackened tube inside. The prism is illuminated by and sources. By changing the distances and from the sources to the prism, it is possible to equalize the illumination of the surfaces and . Then , where and are the light intensities, respectively, of the sources and . If the luminous intensity of one of the sources is known (reference source), then the luminous intensity of the other source in the selected direction can be determined. By measuring the luminous intensity of the source in different directions, they find the total luminous flux, illumination, etc. The reference source is an incandescent lamp, the luminous intensity of which is known.
The impossibility of changing the ratio of distances within a very wide range forces the use of other methods of attenuating the flow, such as light absorption by a filter of variable thickness - a wedge (see Fig. 30.10).
One of the varieties visual method photometry is a method of blanking based on the use of a constant threshold sensitivity of the eye for each individual observer. The threshold sensitivity of the eye is the lowest brightness (about 1 micron) to which the human eye reacts. Having previously determined the sensitivity threshold of the eye, in some way (for example, with a calibrated absorbing wedge), the brightness of the source under study is reduced to the sensitivity threshold. Knowing how many times the brightness is weakened, it is possible to determine the absolute brightness of the source without a reference source. This method is extremely sensitive.
Direct measurement of the total luminous flux of the source is carried out in integral photometers, for example, in a spherical photometer (see Fig. 30.11). The source under study is suspended in the inner cavity of a sphere whitewashed inside with a matte surface. As a result of multiple reflections of light inside the sphere, illumination is created, determined by the average luminous intensity of the source. The illumination of the hole, protected from direct rays by the screen, is proportional to the luminous flux: , where is the constant of the device, depending on its size and color. The hole is covered with milky glass. The brightness of milk glass is also proportional to the light output. It is measured by the photometer described above or by another method. In technology, automated spherical photometers with photocells are used, for example, to control incandescent lamps on the conveyor of an electric lamp plant.
Objective Methods Photometry is divided into photographic and electrical. Photographic methods are based on the fact that the blackening of the photosensitive layer in a wide range is proportional to the density of light energy that fell on the layer during its illumination, i.e. exposure (see Table 30.1). This method determines the relative intensity of two closely spaced spectral lines in one spectrum or compare the intensities of the same line in two adjacent (taken on the same photographic plate) spectra by blackening certain sections of the photographic plate.
Visual and photographic methods are gradually being replaced by electrical ones. The advantage of the latter is that they are quite easy to automatically register and process the results, up to the use of a computer. Electric photometers make it possible to measure the intensity of radiation beyond the visible spectrum.
CHAPTER 31
31.1. Characteristics thermal radiation
Bodies heated to sufficiently high temperatures glow. The glow of bodies due to heating is called thermal (temperature) radiation. Thermal radiation, being the most common in nature, occurs due to energy thermal motion atoms and molecules of a substance (i.e., due to its internal energy) and is characteristic of all bodies at temperatures above 0 K. Thermal radiation is characterized by a continuous spectrum, the position of the maximum of which depends on temperature. At high temperatures, short (visible and ultraviolet) electromagnetic waves, at low - predominantly long (infrared).
The quantitative characteristic of thermal radiation is spectral density of energy luminosity (radiance) of a body- radiation power per unit area of the body surface in the frequency range of unit width:
Rv,T =, (31.1)
where is energy electromagnetic radiation emitted per unit time (radiation power) per unit surface area of the body in the frequency range v before v+dv.
Unit spectral density energy luminosity Rv,T- joule per square meter (J / m 2).
The written formula can be represented as a function of the wavelength:
=Rv,Tdv= R λ ,T dλ. (31.2)
Because c = λvυ, then dλ/ dv = - c/v 2 = - λ 2 /With,
where the minus sign indicates that as one of the values increases ( λ or v) the other value decreases. Therefore, in what follows, the minus sign will be omitted.
In this way,
R υ,T =Rλ,T . (31.3)
Using formula (31.3), one can go from Rv,T to Rλ,T and vice versa.
Knowing the spectral density of energy luminosity, we can calculate integral energy luminosity(integral emissivity), summing over all frequencies:
R T = . (31.4)
The ability of bodies to absorb radiation incident on them is characterized by absorbance
And v,T =(31.5)
showing what fraction of the energy brought per unit time per unit area of the body surface by electromagnetic waves incident on it with frequencies from v before v+dv is absorbed by the body.
Spectral absorbance is a dimensionless quantity. Quantities Rv,T and A v,T depend on the nature of the body, its thermodynamic temperature, and at the same time differ for radiations with different frequencies. Therefore, these values are classified as T and v(or rather, to a fairly narrow frequency range from v before v+dv).
A body capable of absorbing completely at any temperature all radiation of any frequency incident on it is called black. Therefore, the spectral absorbance of a black body for all frequencies and temperatures is identically equal to unity ( A h v, T = one). There are no absolutely black bodies in nature, however, such bodies as soot, platinum black, black velvet and some others are close to them in a certain frequency range in their properties.
ideal model the black body is a closed cavity with a small hole, the inner surface of which is blackened (Fig. 31.1). A beam of light that got inside Fig.31.1.
of such a cavity experiences multiple reflections from the walls, as a result of which the intensity of the emitted radiation turns out to be practically zero. Experience shows that when the hole size is less than 0.1 of the cavity diameter, the incident radiation of all frequencies is completely absorbed. Thereby open windows houses from the side of the street appear black, although inside the rooms it is quite light due to the reflection of light from the walls.
Along with the concept of a black body, the concept is used gray body- a body whose absorptive capacity less than one, but is the same for all frequencies and depends only on the temperature, material and state of the body surface. Thus, for the gray body A with v,T< 1.
Kirchhoff's law
Kirchhoff's law: the ratio of the spectral density of energy luminosity to the spectral absorbance does not depend on the nature of the body; it is a universal function of frequency (wavelength) and temperature for all bodies:
= rv,T(31.6)
For black body A h v, T=1, so it follows from Kirchhoff's law that Rv,T for a black body is rv,T. Thus, the universal Kirchhoff function rv,T is nothing but the spectral density of the energy luminosity of a black body. Therefore, according to Kirchhoff's law, for all bodies the ratio of the spectral density of the energy luminosity to the spectral absorptivity is equal to the spectral density of the energy luminosity of a black body at the same temperature and frequency.
It follows from Kirchhoff's law that the spectral density of the energy luminosity of any body in any region of the spectrum is always less than the spectral density of the energy luminosity of a black body (for the same values T and v), because A v,T < 1, и поэтому Rv,T < r v υ,T. In addition, from (31.6) it follows that if the body at a given temperature T does not absorb electromagnetic waves in the frequency range from v, before v+dv, then it is them in this frequency range at a temperature T and does not radiate, since A v,T=0, Rv,T=0
Using the Kirchhoff law, the expression for the integral energy luminosity of a black body (31.4) can be written as
R T = .(31.7)
For the gray body R with T = A T = A T R e, (31.8)
where R e= -energy luminosity of the black body.
Kirchhoff's law describes only thermal radiation, being so characteristic of it that it can serve as a reliable criterion for determining the nature of radiation. Radiation that does not obey Kirchhoff's law is not thermal.
For practical purposes, it follows from Kirchhoff's law that bodies with a dark and rough surface have an absorption coefficient close to 1. For this reason, dark clothes are preferred in winter, and light in summer. But bodies with an absorption coefficient close to unity also have a correspondingly higher energy luminosity. If you take two identical vessels, one with a dark, rough surface, and the walls of the other are light and shiny, and pour the same amount of boiling water into them, then the first vessel will cool faster.
31.3. Stefan-Boltzmann laws and Wien displacements
It follows from Kirchhoff's law that the spectral density of the energy luminosity of a black body is a universal function, so finding its explicit dependence on frequency and temperature is important task theories of thermal radiation.
Stefan, analyzing experimental data, and Boltzmann, applying thermodynamic method, solved this problem only partially by establishing the dependence of the energy luminosity R e from temperature. According to Stefan-Boltzmann law,
R e \u003d σ T 4, (31.9)
i.e., the energy luminosity of a black body is proportional to the quarters of the power of its thermodynamic temperature; σ
- Stefan-Boltzmann constant: its experimental value is 5.67×10 -8 W/(m 2 ×K 4).
Stefan - Boltzmann's law, defining dependence R e on temperature, does not give an answer regarding the spectral composition of black body radiation. From the experimental curves of the dependence of the function rλ,T from the wavelength λ (r λ,T =´ ´ r ν,T) at various temperatures(Fig.30.2) Fig.31.2.
it follows that the distribution of energy in the spectrum of a black body is uneven. All curves have a pronounced maximum, which shifts towards shorter wavelengths as the temperature rises. Area bounded by the dependency curve rλ,T from λ and the abscissa axis, is proportional to the energy luminosity R e black body and, therefore, according to the Stefan-Boltzmann law, the quarters of the degree of temperature.
V. Vin, relying on the laws of thermo- and electrodynamics, established the dependence of the wavelength λ max corresponding to the maximum of the function rλ,T, on temperature T. According to Wien's displacement law,
λ max \u003d b / T, (31.10)
i.e. wavelength λ
max corresponding maximum value spectral
energy luminosity density rλ,T blackbody is inversely proportional to its thermodynamic temperature. b - constant fault its experimental value is 2.9×10 -3 m×K.
Expression (31.10) is called Wien's displacement law, it shows the displacement of the maximum position of the function rλ,T as the temperature increases to the region of short wavelengths. Wien's law explains why, as the temperature of heated bodies decreases, their spectrum is increasingly dominated by long-wave radiation (for example, the transition white heat turns red when the metal cools).
Rayleigh-Jeans and Planck formulas
From the consideration of the Stefan-Boltzmann and Wien laws, it follows that the thermodynamic approach to solving the problem of finding universal function Kirchhoff did not give the desired results.
A rigorous attempt at theoretical dependency inference rλ,T belongs to Rayleigh and Jeans, who applied the methods of statistical physics to thermal radiation, using classical law uniform distribution energy in degrees of freedom.
The Rayleigh-Jeans formula for the spectral density of the energy luminosity of a black body has the form:
r ν , T = <E> = kT, (31.11)
where <Е>= kT– average energy oscillator with natural frequency ν .
As experience has shown, expression (31.11) is consistent with experimental data only in the region of sufficiently low frequencies and high temperatures. In the region of high frequencies, this formula disagrees with the experiment, as well as with the Wien displacement law. And getting the Stefan-Boltzmann law from this formula leads to absurdity. This result is called " ultraviolet catastrophe". Those. within classical physics failed to explain the laws of energy distribution in the spectrum of a black body.
In the region of high frequencies, good agreement with experiment is given by Wien's formula (Wien's radiation law):
r ν, T \u003d Сν 3 A e -Аν / T, (31.12)
where rv, T- spectral density of the energy luminosity of the black body, FROM and BUT – constants. In modern notation using
Planck's constant Wien's radiation law can be written as
r ν, T = . (31.13)
The correct expression consistent with experimental data for the spectral density of the energy luminosity of a black body was found by Planck. According to the quantum hypothesis, atomic oscillators do not radiate energy continuously, but in certain portions - quanta, and the quantum energy is proportional to the frequency of oscillations
E 0 =hν = hс/λ,
where h\u003d 6.625 × 10 -34 J × s - Planck's constant. Since the radiation is emitted in portions, the oscillator energy E can only take on certain discrete values , multiples of an integer number of elementary portions of energy E 0
E = nhv(n= 0,1,2…).
AT this case average energy<E> oscillator cannot be taken equal to kT.
In the approximation that the distribution of oscillators over possible discrete states obeys the Boltzmann distribution, the average energy of the oscillator is
<E> = , (31.14)
and the spectral density of energy luminosity is determined by the formula
r ν , T = . (31.15)
Planck derived the formula for the universal Kirchhoff function
rv, T = , (31.16)
which agrees with the experimental data on the distribution of energy in the radiation spectra of a black body over the entire range of frequencies and temperatures.
From Planck's formula, knowing the universal constants h,k and With, we can calculate the Stefan-Boltzmann constants σ and wine b. And vice versa. Planck's formula is in good agreement with experimental data, but it also contains particular laws of thermal radiation, i.e. is complete solution problems of thermal radiation.
Optical pyrometry
The laws of thermal radiation are used to measure the temperature of incandescent and self-luminous bodies (for example, stars). Methods for measuring high temperatures that use the dependence of the spectral density of energy luminosity or the integral energy luminosity of bodies on temperature are called optical pyrometry. Devices for measuring the temperature of heated bodies by the intensity of their thermal radiation in the optical range of the spectrum are called pyrometers. Depending on which law of thermal radiation is used when measuring the temperature of bodies, radiation, color and brightness temperatures are distinguished.
1. Radiation temperature is the temperature of a black body at which its energy luminosity R e equal to energy luminosity R t body under study. In this case, the energy luminosity of the body under study is recorded and, according to the Stefan-Boltzmann law, its radiation temperature is calculated:
T p =.
Radiation temperature T p body is always less than its true temperature T.
2.Colorful temperature. For gray bodies (or bodies close to them in properties), the spectral density of energy luminosity
R λ,Τ = A Τ r λ,Τ,
where A t = const < 1. Consequently, the distribution of energy in the emission spectrum of a gray body is the same as in the spectrum of a black body having the same temperature, therefore Wien's displacement law applies to gray bodies. Knowing the wavelength λ m ah, corresponding to the maximum spectral density of energy luminosity Rλ,Τ of the body under study, its temperature can be determined
T c = b/ λ m ah,
which is called color temperature. For gray bodies, the color temperature coincides with the true one. For bodies that are very different from gray (for example, those with selective absorption), the concept of color temperature loses its meaning. In this way, the temperature on the surface of the Sun is determined ( T c=6500 K) and stars.
3.Brightness temperature T i, is the temperature of a black body at which, for a certain wavelength, its spectral density of energy luminosity is equal to the spectral density of the energy luminosity of the body under study, i.e.
rλ,Τ = Rλ,Τ,
where T –true temperature body, which is always higher than the brightness.
A disappearing filament pyrometer is usually used as a brightness pyrometer. In this case, the image of the pyrometer thread becomes indistinguishable against the background of the surface of the hot body, i.e., the thread, as it were, “disappears”. Using a blackbody calibrated milliammeter, the brightness temperature can be determined.
Thermal light sources
The glow of hot bodies is used to create light sources. Black bodies should be the best thermal light sources, since their spectral energy luminosity density for any wavelength is greater than the spectral energy luminosity density of non-black bodies, taken at the same temperatures. However, it turns out that for some bodies (for example, tungsten), which have selectivity of thermal radiation, the fraction of energy attributable to radiation in the visible region of the spectrum is much larger than for a black body heated to the same temperature. Therefore, tungsten, having also a high melting point, is the best material for making lamp filaments.
The temperature of the tungsten filament in vacuum lamps should not exceed 2450K, since at higher temperatures its strong sputtering occurs. The maximum radiation at this temperature corresponds to a wavelength of 1.1 μm, i.e., it is very far from the maximum sensitivity of the human eye (0.55 μm). Filling lamp bulbs with inert gases (for example, a mixture of krypton and xenon with the addition of nitrogen) at a pressure of 50 kPa makes it possible to increase the filament temperature to 3000 K, which leads to an improvement in the spectral composition of the radiation. However, the light output does not increase in this case, since additional energy losses occur due to heat exchange between the filament and the gas due to thermal conductivity and convection. To reduce energy losses due to heat transfer and increase the light output of gas-filled lamps, the filament is made in the form of a spiral, the individual turns of which heat each other. At high temperature a fixed layer of gas is formed around this spiral and heat exchange due to convection is excluded. Energy efficiency incandescent lamps currently does not exceed 5%.
1. Radiation flux. The concept of the spectrum of electromagnetic radiation. The principle of measuring the flow distribution over the spectrum. Energy quantities.
Flux (power) of radiation (F) yavl. the main quantity in the energy system of measurements. The power (or flux) of radiation is taken to be the energy transferred per unit time. The value of F is expressed in watts (W).
Electromagnetic wave range hesitation, n. in nature, is quite wide and extends from fractions of an angstrom to a kilometer.
Spectrum of electromagnetic radiation, microns
Gamma rays _____________________________________ less than 0.0001
X-rays _______________________________ 0.01-0.0001
Ultraviolet rays ____________________________ 0.38-0.01
Visible light __________________________________________ 0.78-0.38
Infrared rays ________________________________1000-0.78
Radio waves ____________________________________________ more than 1000
Only a part of electromagnetic radiation with a wavelength interval from λmin = 0.01 μm to λmax = 1000 μm belongs to the optical region of the spectrum. Such radiation is created as a result of electromagnetic excitation of atoms, vibrational and rotary motion molecules.
AT optical spectrum three main areas can be distinguished: ultraviolet, visible, infrared.
Ultraviolet radiation produces the most powerful photons and has a strong photochemical effect.
The emission of visible light, despite the rather narrow interval, allows us to see all the diversity of the world around us. So the human eye practically does not perceive radiation with extreme wavelength ranges (they have a weak effect on the eye), in practice visible light it is customary to consider radiation with a wavelength range of 400-700 nm. This radiation has a significant photophysical and photochemical effect, but less than ultraviolet.
Photons have the minimum energy from the entire optical region of the spectrum infrared radiation. For this radiation har-but thermal action and, to a large extent lesser degree, photophysical and photochemical. action.
2. The concept of the radiation receiver . Receiver reactions. Classification of radiation receivers. Linear and non-linear receivers. Spectral sensitivity of the radiation receiver.
bodies in which such transformations take place under the action of optical radiation, received in lighting engineering common name "radiation receivers"
Conventionally, radiation receivers are divided into:
1. The natural receiver of radiation is the human eye.
2. Light-sensitive materials used for optical recording of images.
3. Receivers are also photosensitive elements measuring instruments(densitometers, colorimeters)
Optical radiation has a high energy and therefore affects many substances and physical bodies.
As a result of the absorption of light in media and bodies, whole line phenomena (Figure 2.1, Sir 48)
A body that has absorbed radiation begins to radiate itself. In this case, the secondary radiation may have a different spectral range compared to the absorbed one. N-r, under lighting ultraviolet light body emits visible light.
The energy of the absorbed radiation is converted into electrical energy, as in the case of the photoelectric effect, or produces a change electrical properties material that occurs in photoconductors. Such transformations are called photophysical.
Another type of photophysical transformation is the transition of radiation energy into thermal energy. This phenomenon has found application in thermoelements used to measure radiation power.
The radiation energy is converted into chemical energy. A photochemical transformation of a substance that absorbs light takes place. This conversion occurs in most photosensitive materials.
The bodies in which such transformations occur under the action of optical radiation have received a common name in lighting engineering. "radiation receivers"
Linear non-linear receivers??????????????????
Spectral sensitivity of the radiation receiver.
Under the action of optical radiation in the receiver, a photochemical and photophysical transformation takes place, which in a given way changes the properties of the receiver.
This change is called the useful response of the receiver.
However, not all the energy of the incident radiation is spent on a useful reaction.
Part of the energy of the receivers is not absorbed and therefore cannot cause a reaction. The absorbed energy is also not completely converted to useful. For example, in addition to photochemical transformation, heating of the receiver can occur. Practically used part of the energy called. useful, and the practically used part of the radiation power (radiation flux Ф) is the effective flux Ref.
The ratio of the effective flux Ref to the radiation flux incident on the receiver
called sensitivity of the receiver.
For most receivers, the spectral sensitivity depends on the wavelength.
Sλ= сРλ eff/Фλ and Рλ eff=КФλSλ
The quantities are called Фλ and Рλ, respectively, the monochromatic radiation flux and the monochromatic effective flux, and Sλ is the monochromatic spectral sensitivity.
Knowing the power distribution over the spectrum Ф(λ) for the radiation incident on the receiver and the spectral sensitivity of the receiver S(λ), it is possible to calculate the effective flux by the formula – Реф=К ∫ Ф(λ)S(λ)dλ
The measurement refers to a range of ∆λ limited either by the spectral response of the receiver or by the spectral range of the measurement.
3.Features of the eye as a receiver. Light flow. Its connection with the radiation flux. visibility curve. The difference between light and energy flows in the range of 400-700 nm.
Features of the eye as a receiver.
The visual apparatus consists of a radiation receiver (eyes), optic nerves and visual areas of the brain. In these zones, the signals that form in the eyes and enter through the optic nerves are analyzed and converted into visual images.
The radiation receiver consists of two eyeballs, each of which, with the help of six external muscles, can easily rotate in the orbit both in the horizontal and vertical planes. When examining an object, the eyes move abruptly, alternately fixing on various points object. This movement is vector in nature, i.e. the direction of each jump is determined by the object under consideration. The jump speed is very high, and the fixation points, where the eye stops for 0.2-0.5 s, are located mainly at the borders of details, where there are brightness differences. During "stops" the eye is not at rest, but makes quick micro-movements relative to the point of fixation. Despite these microsaccades, at the points of fixation, the observed area of the object is focused on the fovea of the light-sensitive retina from the eyes.
Fig.2.4 (Horizontal section of the eye) p.56
Light flow(F) By luminous flux, in general, understand the power of radiation, estimated by its effect on the human eye. The unit of luminous flux is lumen (lm).
The action of the light flux on the eye causes its certain reaction. Depending on the level of action of the light flux, one or another type of light-sensitive eye receivers, called rods or cones, works. In conditions low level illumination (eg, in the light of the moon), the eye sees the surrounding objects due to rods. At high levels of illumination, the daytime vision apparatus, for which the cones are responsible, begins to work.
In addition, cones are divided into three groups according to their light-sensitive substance with different sensitivity in various areas spectrum. Therefore, unlike rods, they react not only to the light flux, but also to its spectral composition.
In this regard, we can say that the light action is two-dimensional. Quantitative characteristic eye reactions associated with the level of illumination, called. light. The quality characteristic associated with different levels reactions of three groups of cones, called chromaticity.
An important characteristic yavl distribution curve of the relative spectral sensitivity of the eye (relative spectral luminous efficiency) in daylight νλ =f(λ) Fig.1.3 p.9
In practice, it has been established that in daylight conditions the human eye has the maximum sensitivity to radiation with Lamda = 555 nm (V555 = 1). At the same time, each unit of luminous flux with F555 has a radiation power Ф555 = 0.00146W. The ratio of the luminous flux F555 to Ф555 is called spectral light efficiency.
K= F555/F555=1/0.00146=680 (lm/W)
Or for any wavelength of radiation in the visible range K=const:
K \u003d 1 / V (λ) * F λ / Ф λ \u003d 680. (one)
Using formula (1), it is possible to establish a relationship between the luminous flux and the radiation flux.
Fλ = 680 * Vλ * Фλ
For integrated radiation
F= 680 ∫ Vλ Фλ dλ
4. Photoactive flow. General information about efficient flow. Monochromatic and integral streams. Actinism .
Two types of effective fluxes are used in lighting engineering and reproduction technology: light F and photoactinic A.
The luminous flux is related to the power (radiation flux Ф) by the following expression:
F=680 ∫ Ф(λ) V(λ) dλ
400 nm
where Ф(λ) is the distribution of radiation power over the spectrum, V(λ) is the relative spectral luminous efficiency curve (visibility curve), and 680 is the coefficient that allows you to go from watts to lumens. It is called the luminous flux equivalent and is expressed in lm/W.
If the luminous flux falls on any surface, its surface density is called illuminance. Illumination E is related to the luminous flux by the formula
Where Q is the area in m The unit of illumination is lux (kl)
For light-sensitive materials and photodetectors of measuring devices, use photoactinic flowA.
This is the efficient flow defined by the expression
A = ∫ Ф (λ) S (λ) dλ
If the spectral range in which the measurement is made is limited by the wavelengths λ1 and λ2, then the expression for photoactinic flow will take the form
A \u003d ∫ F (λ) * S (λ) dλ
λ1
The unit of measurement A depends on the unit of measurement of the spectral sensitivity. If Sλ is relative value, and is measured in watts. If Sλ has dimension, e.g.
m /J, then this will affect the dimension of the photoactinic flux
Surface density of the photoactinic flux on the illuminated surface naz radiation actinicitya, a= dA/ dQ
If the surface of the receiver is illuminated evenly, then a=A/Q.
For monochromatic radiation.
Fλ = 680 * Vλ * Фλ
For integrated radiation
F= 680 ∫ Vλ Фλ dλ
Actinism- lighting analogue. Its unit of measurement depends on the dimension A
If A - W, then a-W / m
Fig.2.2 page 52
The greater the actinicity of the radiation, the more efficiently the radiation energy is used and the more, with other equal conditions, the response of the receiver will be useful.
To achieve maximum actinicity, it is desirable that the maximum spectral sensitivity of the receiver and the maximum radiation power fall on the same spectrum zones. This consideration guides the selection of a light source for obtaining images on a particular type of light-sensitive materials.
For example, the copy process.
The copy layers used to make printing plates are sensitive to ultraviolet and blue-violet radiation. They do not react to the radiation of other zones of the visible spectrum. Therefore, to carry out the copying process, they use
Metal halide lamps, rich in ultraviolet and blue spectrum radiation.
FIG 2.3. Page 53 manual
5. Color temperature. Luminosity curves of an absolute black body at different temperatures. The concept of a normalized curve. Definition of the term "color temperature". Direction change in the color of the radiation with a change in color temperature.
Color temperature means the temperature in kelvins of a completely black body, at which the radiation has the same color as the one under consideration. For incandescent lamps with a tungsten filament, the spectral distribution of radiation is proportional to the spectral distribution of radiation from a completely black body in the wavelength range of 360-1000 nm. To calculate the spectral composition of black body radiation for a given absolute temperature heating it, you can use the Planck formula:
e -5 s 2 / λ t
Rλ \u003d C1 λ (e -1)
uh
Where Rλ is the spectral energy luminosity, C1 and C2 are constants, e is the base natural logarithms, T-absolute temperature, K
Experimentally, the color temperature is determined by the value of the blue-red ratio of actinicities. Actinicity-illuminance, effective in relation to the photodetector:
Аλ = Фλ Sλ / Q = Eλ Sλ
Where Ф is the radiant flux, Sλ is the sensitivity of the photodetector, Qλ is its area
If a light meter is used as a photodetector, then the actinicity is the illumination determined when the photocell is shielded with blue and red light filters.
Technically, the measurement is made as follows.
The photocell of the light meter is alternately shielded by specially selected blue and red light filters. Light filters must be zonal and have the same multiplicity in the transmission zone. Luxmeter galvanometer determines the illumination from the measured source for each of the filters. Calculate the blue-red ratio using the formula
K \u003d Ac / Ak \u003d Es / Ek
SCHEDULE page 6 lab slave
Фλ. To do this, according to the Planck formula, the values of the spectral energy luminosity are calculated. Next, the resulting function is normalized. Rationing consists in a proportional decrease or increase in all values in such a way
so that the function passes through a point with coordinates λ= 560nm, lg R560 =2.0
or λ= 560 nm, R560 rel = 100 In this case, it is assumed that each value refers to the spectral interval ∆λ corresponding to the calculation step.
∆λ=10 nm, luminosity 100 W*m correspond to a wavelength of 560 nm in the wavelength range of 555-565 nm.
Fig 1.2 Page 7 lab slave
Using the spectral dependence function Rλ = f λ, one can find the functions E λ = Фλ = f λ To do this, use the formulas
E- illumination, R-luminosity, F- energy flow, Q- area
6. Light source. their spectral characteristics. Classification of light sources according to the type of radiation. Planck and Wien formula.
7. Photometric properties of radiation sources. Classification by geometric quantities: point and extended light sources, photometric body.
Depending on the ratio of the dimensions of the emitter and its distance to the studied point of the field, radiation sources can be divided into 2 groups:
1) point sources of radiation
2) a source of finite dimensions (linear source) A radiation source whose dimensions are significantly less distance to the point under study are called point. In practice, a point source is taken to be one whose maximum size is at least 10 times smaller than the distance to the radiation receiver. For such radiation sources, the inverse square law of distance is observed.
E=I/r 2 cosine alpha, where alpha=angle between the light beam and the perpendicular to surface C.
If from the point at which the point source of radiation is located to put aside in various directions space are vectors of unit radiation strength and draw a surface through their ends, then we get a PHOTOMETRIC BODY of the radiation strength of the source. Such a body completely characterizes the distribution of the radiation flux of a given source in the surrounding space
8. Conversion of radiation by optical media. Characteristics of radiation conversion: light coefficients, multiplicities, optical densities, the relationship between them. Filters Definition of the term. Spectral curve as a universal filter characteristic.
When the radiation flux Ф0 hits the real body(optical medium), part of its Ф(ro) is reflected by the surface, part of Ф(alpha) is absorbed by the body, and part of Ф(tau) passes through it. body ability ( optical environment) to such a transformation is characterized by the reflection coefficient ro=Fro/Ф0, the coefficient tau=Ftau/Ф0.
If the coefficients are determined by the conversion of light fluxes (F, lm), then they are called light (photometric)
Rosv \u003d Fo / Fo; Alphasw=Falpha/Fо; tausv=Ftau/Fо
For optical and light coefficients, the statement is true that their sum is 1.0 (po + alpha + tau \u003d 1)
There are two more kinds of coefficients - monochromatic and zonal. The former evaluate the effect of the optical medium on monochromatic radiation with a wavelength of lambda.
The zonal coefficients estimate the conversion of radiation borrowing from the spectrum zones (blue with delta lambda = 400-500 nm, green with delta lambda = 500-600 nm and red with delta lambda = 600-700 nm)
9. Law of Bouguer-Lambert-Beer. Quantities bound by law. Additivity of optical densities as the main conclusion from the Bouguer-Lambert-Beer law. Light scattering indicatrices, turbidity of media. Types of light scattering.
F 0 /F t =10 kl , k-absorption rate. Beer found that the absorption index also depends on the concentration of the light-absorbing substance c, k \u003d Xc, x is the molar absorption index, expressed as the reciprocal of the thickness of the layer, attenuating light by 10 times at a concentration of light-absorbing substance in it 1 mol / l.
The final equation expressing the Bouguer-Lambert-Beer law looks like this: F0 / Ft \u003d 10 to the power of Xc1
The luminous flux transmitted by the layer is related to the decreased flux exponentially through the molar absorption index, the layer thickness and the concentration of the light-absorbing substance. It follows from the considered law physical meaning concepts of optical density. By integrating the expression Ф0/Фт=10 to the power Xc1
We get D \u003d X * s * l, those. Optical density environment depends on its nature, is proportional to its thickness and the concentration of light-absorbing in-va. Since the Bouguer-Lambert-Beer law characterizes the fraction of absorbed light through the fraction of transmitted light, it does not take into account the reflected and scattered light. In addition, the resulting relation expressing the Bouger-Lambert-Beer law is valid only for homogeneous media and does not take into account the loss of light reflection from the surface of bodies. Deviation from the law leads to non-additivity of optical media.
Luminous flux - the power of light energy, an effective value, measured in lumens:
Ф = (JQ/dt. (1.6)
The unit of luminous flux is lumen (lm); 1 lm corresponds to the luminous flux emitted in a unit solid angle by a point isotropic source with a light intensity of 1 candela (the definition of a capdela will be given below).
Monochromatic light output
F(A. dk) = Kt. m Fe, (L, dk) Vx = 683 Fe, (A, dk) Vx.
Luminous flux of complex radiation: with a linear speckir
Ф=683£Ф,(Л„ dk)VXh
continuum
where n is the number of lines in the spectrum; F<>D,(A.) is a function of the spectral density of the radiation flux.
sshs studying ( energy force light) le(x^ - spatial density of the radiation flux, numerically equal to the ratio of the radiation flux c1Fe to the solid angle t/£2, within which the flux propagates and is uniformly distributed:
>ea v=d The strength of the radiation determines the spatial density of the radiation of a point source located at the top of the solid angle (Fig. 1.3). The direction 1ef is taken as the axis of the solid angle dLl. oriented by angles a and P in the longitudinal and transverse planes. The unit of radiation strength, W/sr, has no name. The spatial distribution of the radiation flux of a point source is uniquely determined by its photometric body - a part of space bounded by a surface drawn through the ends of the radius-vectors of the radiation force. The cross section of a photometric gel by a plane passing through the origin and a point source determines the luminous intensity curve (CLC) of the source for the given section plane. If the photometric body has an axis of symmetry, the radiation source characterizes the KSS in the longitudinal plane (Fig. 1.4). Radiation flux of a point round-symmetrical radiation source F? \u003d jle (a) dLi \u003d 2l J le (a) sin ada, where Dj is the zonal solid angle within which the source radiation propagates; is determined in the longitudinal plane by the angles "| and a „. Light intensity of a point source - spatial density of the light flux laf,=dФ/dQ. (1.8) Candela (cd) is a unit of luminous intensity (one of the basic units of the SI system). The candela is equal to the intensity of light emitted in the perpendicular direction from an area of 1/600,000 m2 of a black body at the solidification temperature of platinum T = 2045 K and a pressure of 101325 Pa. The luminous flux IS is determined by the CSS, if the photometric body has an axis of symmetry. If KSS / (a) is given by a graph or table, the calculation of the luminous flux of the source is determined by the expression F \u003d £ / shdts-, + i, where /w - srslnss value of light intensity in the zonal solid angle; Dj, (+| = 2n(cos a, - cos a, _|) (see Table 1.1). Energy luminosity (radiance) - the ratio of the radiation flux emanating from the considered small surface area to the area of the logo area: M e \u003d (1Fe / dA; Mex\u003e \u003d Fe / A, (1.9) where d$>e and Ф(. - radiation fluxes emitted by a surface area dA or surface A. The unit of energy luminosity (W/m2) is the radiance flux. emitted from 1 m2 of surface; This unit has no name. Luminosity - the ratio of the luminous flux emanating from the small surface area under consideration to the area of this area: M =
where ёF and Ф - light fluxes emitted by a surface area dA or surface A. Luminosity is measured in lm / m2 - this is the luminous flux emitted from 1 m2. Energy illumination (irradiance) - the density of the radiant flux but the irradiated surface Ee \u003d (1Fe / s1A; Ecp \u003d Fe / A, (1.11) where Ee, Eср - respectively, the irradiance of the surface area dA and the average irradiance of the surface A. Per unit of measurement of irradiance. Wg/m2. take such an irradiance at which 1 W of the radiant flux falls and is evenly distributed over the surface of 1 m2; This unit has no name. Illumination - the density of the luminous flux over the illuminated surface dF.=d<>/dA Еср - F/L, (1.12) where dE and Еср are the illumination of the surface area dA and the average illumination of the surface A. Lux (lx) is the unit of illumination. An illumination of 1 lux has a surface, on 1 m2 of which a luminous flux of 1 lm falls and is evenly distributed over it. The energy brightness of a body or a section of its surface in the direction a is the ratio of the radiation strength in nanoparticles a to the projection of the radiating surface onto a plane perpendicular to this direction (Fig. 1.5): ~ dIshch / (dA cos ss), ~ ^ey. ^" (1-13) where Leu and Lcr are the energy radiances of the surface area dA and surface A in the direction a, the projections of which onto a plane perpendicular to this direction are equal to dAcosa and a, respectively; dleu and ea are, respectively, the radiation strengths emitted by dA and A in the a direction. The energy brightness of a flat surface B 1 M is taken as a unit of radiance. having a radiation force of 1 Vg/sr in the perpendicular direction. This unit (W/srm2) has no name. The brightness in the direction a of a body or a section of its surface is equal to the ratio of the luminous intensity in this direction to the projection of the surface: La = dIa/(dAcosa); /.acp = /a/a, (1.14) where /u and Lacp are the brightnesses of the surface area dA and the surface A in the a direction. whose projections onto a plane perpendicular to this direction are respectively equal to dA cos a and a; dla. 1a - respectively, the light intensity emitted by the surfaces dA, and A in the direction a. The unit of measurement of brightness (cd/m2) is the brightness of such a flat surface, which in the perpendicular direction emits a luminous intensity of 1 cd from an area of 1 m2. equivalent brightness. Under conditions of twilight vision, the relative spectral luminous efficiency of the organ of vision depends on the level of adaptation Y (X, /.) and occupies an intermediate position between K (A) and Y "(X), shown in Fig. 1.2. Under these conditions, their study of various spectral composition, the same brightness for daytime vision, but different brightness for the eye (Purkins effect), for example, blue will be brighter than red.In the field of twilight vision, the concept of equivalent brightness is used. You can choose the radiation of a certain spectral composition, for which the brightness at all levels is assumed to be proportional to the radiation power. A. A. Gershun [1] suggested that they be considered as such. called reference, to use black body radiation at the solidification temperature of platinum. Their study of a different spectral composition, equal in brightness with the reference one, will have the same equivalent brightness with it, although the standard radiation brightnesses will be different. Equivalent brightness makes it possible to compare different radiations by their luminous effect even under conditions of uncertainty of the relative spectral sensitivity function. To quantify radiation, a fairly wide range of quantities is used, which can be conditionally divided into two systems of units: energy and light. In this case, the energy quantities characterize the radiation related to the entire optical region of the spectrum, and the lighting quantities characterize the visible radiation. The energy quantities are proportional to the corresponding lighting quantities. The main quantity in the energy system, which makes it possible to judge the amount of radiation, is radiation flux Ph, or radiation power, i.e. amount of energy W, radiated, carried or absorbed per unit time: The Fe value is expressed in watts (W). - energy unit In most cases, they do not take into account the quantum nature of the appearance of radiation and consider it continuous. A qualitative characteristic of radiation is the distribution of the radiation flux over the spectrum. For radiations having a continuous spectrum, the concept is introduced spectral density of the radiation flux (
)
- the ratio of the radiation power attributable to a certain narrow section of the spectrum to the width of this section (Fig. 2.2). For a narrow spectral range d
the radiation flux is dФ
.
The ordinate shows the spectral densities of the radiation flux
= dФ
/d
,
therefore, the flow is represented by the area of an elementary section of the graph, i.e. Figure 2.2 - Dependence of the spectral flux density
radiation from wavelength
E Under luminous flux F, in the general case, understand the power of the radiation, estimated by its effect on the human eye. The unit of luminous flux is lumen (lm). – lighting unit The action of the light flux on the eye causes its certain reaction. Depending on the level of action of the light flux, one or another type of light-sensitive eye receivers, called rods or cones, works. In low light conditions (for example, in the light of the moon), the eye sees the surrounding objects due to rods. At high levels of illumination, the daytime vision apparatus, for which the cones are responsible, begins to work. In addition, cones are divided into three groups according to their light-sensitive substance with different sensitivity in different regions of the spectrum. Therefore, unlike rods, they react not only to the light flux, but also to its spectral composition. In this regard, it can be said that light action two-dimensional. The quantitative characteristic of the reaction of the eye associated with the level of illumination is called lightness. The qualitative characteristic associated with the different level of reaction of the three groups of cones is called chromaticity. The power of light
(I).
In lighting technology, this value is taken as basic. This choice does not have a fundamental basis, but is made for reasons of convenience, since The intensity of light does not depend on distance. The concept of luminous intensity refers only to point sources, i.e. to sources whose dimensions are small compared to the distance from them to the illuminated surface. The luminous intensity of a point source in a certain direction is per unit solid angle
light flow F emitted by this source in a given direction: I=F / Ω Energy luminous intensity is expressed in watts per steradian ( Tue/Wed). Per lighting unit of luminous intensity is accepted candela(cd) is the luminous intensity of a point source that emits a luminous flux of 1 lm, distributed evenly within a solid angle of 1 steradian (sr). A solid angle is a part of space bounded by a conical surface and a closed curvilinear contour that does not pass through the vertex of the angle (Fig. 2.3). When a conical surface is compressed, the dimensions of the spherical area o become infinitely small. The solid angle in this case also becomes infinitesimal: Figure 2.3 - To the definition of the concept of "solid angle" Illumination (E).
Under energetic illumination E uh understand the flow of radiation on area unit illuminated surface Q:
Energy illumination is expressed in W/m 2
.
Light illumination E
expressed by the light flux density F on the surface it illuminates (Fig. 2.4): For the unit of light illumination is taken luxury, i.e. the illumination of a surface receiving a luminous flux of 1 lm uniformly distributed over it over an area of 1 m 2. Among other quantities used in lighting engineering, important are energy radiation Wuh
or light energy W,
as well as energy Ne or light H
exposure. The values We and W are determined by the expressions where Under energy H uh or light exposure understand the surface energy density of radiation W
uh
or light energy W respectively on the illuminated surface. That is lightsand Iexposure H is the product of illumination E, created by the radiation source, for a time t action of this radiation.
If the emission spectrum lies within the limits of
1
before
2
, then the magnitude of the radiation flux
are, respectively, the functions of changing the radiation flux and the luminous flux in time. We is measured in joules or Ws, a W
–
in lm s.
