To assess the radiation energy and its effect on radiation receivers, which include photoelectric devices, thermal and photochemical receivers, as well as the eye, energy light quantities.
The energy quantities are the characteristics optical radiation related to the entire optical range.
Eye for a long time was the only receiver of optical radiation. Therefore, it has historically developed so that for the quality and quantification For the visible part of the radiation, light (photometric) quantities are used that are proportional to the corresponding energy quantities.
Above, the concept of the radiation flux referring to the entire optical range was given. The value that in the system of light quantities corresponds to the radiation flux,
is the luminous flux Ф, i.e., the radiation power estimated by a standard photometric observer.
Let's consider light quantities and their units, and then we will find the connection of these quantities with energy ones.
To evaluate two sources of visible radiation, their luminescence is compared in the direction of the same surface. If the glow of one source is taken as unity, then by comparing the glow of the second source with the first one, we obtain a value called the luminous intensity.
AT international system SI units for the unit of luminous intensity is the candela, the definition of which was approved by the XVI General Conference (1979).
Candela - the power of light in given direction a source emitting monochromatic radiation with a frequency of Hz, energy force whose light in this direction is
Light intensity, or angular density luminous flux,
where is the luminous flux in a certain direction inside a solid angle
A solid angle is a part of space bounded by an arbitrary conical surface. If a sphere is described from the top of this surface as from the center, then the area of the sphere section cut off by the conical surface (Fig. 85) will be proportional to the square of the sphere radius:
The coefficient of proportionality is the value of the solid angle.
The unit of the solid angle is the steradian, which is equal to the solid angle with the vertex at the center of the sphere, which cuts out an area on the surface of the sphere, equal to the area square with side equal to the radius spheres. full sphere forms a solid angle
Rice. 85. Solid angle
Rice. 86. Radiation in a solid angle
If the radiation source is at the top of the line circular cone, then the solid angle allocated in space is limited by the internal cavity of this conical surface. Knowing the value of the plane angle between the axis and the generatrix of the conical surface, it is possible to determine the corresponding solid angle.
Let us single out in the solid angle an infinitely small angle that cuts out an infinitely narrow annular section on the sphere (Fig. 86). This case belongs to the most frequently encountered axisymmetric distribution of luminous intensity.
The area of the annular section where the distance from the axis of the cone to the narrow ring of width
According to fig. where is the radius of the sphere.
Therefore, where
Solid angle corresponding to a flat angle
For a hemisphere, the solid angle for a sphere is
From formula (160) it follows that the luminous flux
If the intensity of light does not change when moving from one direction to another, then
Indeed, if a light source with luminous intensity is placed at the vertex of a solid angle, then the same luminous flux enters any areas bounded by a conical surface that singles out this solid angle in space. . Then, as experience shows, the degree of illumination of these areas is inversely proportional to the squares of the radii of these spheres and is directly proportional to the size of the areas.
Thus, the following equality holds: i.e., formula (165).
The above justification of formula (165) is valid only when the distance between the light source and the illuminated area is sufficiently large compared to the size of the source and when the medium between the source and the illuminated area does not absorb or scatter light energy.
The unit of luminous flux is the lumen (lm), which is the flux within a solid angle when the luminous intensity of a source located at the top of the solid angle is equal to
The illumination of the area normal to the incident rays is determined by the ratio which is called the illumination E:
Formula (166), as well as formula (165), takes place under the condition that the luminous intensity I does not change when moving from one direction to another within a given solid angle. Otherwise, this formula will be valid only for an infinitely small area
If the incident rays form angles with the normal to the illuminated area, then formulas (166) and (167) will change, since the illuminated area will increase. As a result, we get:
When the site is illuminated by several sources, its illumination
where the number of radiation sources, i.e. the total illumination is equal to the sum of the illuminations received by the site from each source.
The unit of illumination is the illumination of the site when the light flux falls on it (the site is normal to the incident rays). This unit is called a lux
If the dimensions of the radiation source cannot be neglected, then to solve a number of problems it is necessary to know the distribution of the light flux of this source over its surface. The ratio of the luminous flux emanating from a surface element to the area of this element is called luminosity and is measured in lumens per square meter Luminosity also characterizes the distribution of the reflected light flux.
So the luminosity
where is the surface area of the source.
The ratio of the luminous intensity in a given direction to the projection area of a luminous surface onto a plane perpendicular to this direction is called brightness.
Therefore, the brightness
where is the angle between the normal to the site and the direction of the light intensity
Substituting into formula (172) the value [see formula (160)), we obtain that the brightness
From formula (173) it follows that the brightness is the second derivative of the flux with respect to the solid angle to the area.
The unit of brightness is the candela per square meter.
The surface density of the light energy of the incident radiation is called the exposure:
AT general case the illumination included in formula (174) can change over time
The exposition has a great practical value, for example, in photography and is measured in lux-seconds
Formulas (160) - (174) are used to calculate both light and energy quantities, firstly, for monochromatic radiation, i.e. radiation with a certain wavelength, and secondly, in the absence of consideration for the spectral distribution of radiation, which, as a rule, takes place in visual optical devices.
The spectral composition of radiation - the distribution of radiation power over wavelengths has great importance for calculating energy quantities when using selective radiation receivers. For these calculations, the concept of the spectral density of the radiation flux was introduced [see. formulas (157)-(159)].
In a limited range of wavelengths, respectively, we have:
The energy quantities defined by the formulas also apply to the visible part of the spectrum.
Basic photometric and energy quantities, defining their formulas and units according to the SI system are given in Table. 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 part of the spectrum belongs to the optical region electromagnetic radiation with a wavelength interval from λmin= 0.01 µm to λmax=1000 µm. 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 occur 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, changing the properties of the receiver in a given way.
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 distribution of power 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 central 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 illumination, the daytime vision apparatus begins to work, for which the cones are responsible.
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 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. To the radiation of other zones visible spectrum they don't react. 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. For calculation spectral composition 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. 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 considered 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 that attenuates 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.
Enough is used to quantify radiation. wide circle quantities, 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 - to visible radiation. The energy quantities are proportional to the corresponding lighting quantities.
The main quantity in 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 (j l)- 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 dl the radiation flux is dФ l . The ordinate shows the spectral densities of the radiation flux j l = dФ l /dl, therefore, the flow is represented by the area of an elementary section of the graph, i.e.
If the emission spectrum lies within the limits of l 1 before l 2, then the magnitude of the radiation flux
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.
Light intensity(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 W 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, not passing through the vertex of the corner (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 e 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 We or light energy W, as well as energy Ne or light H exposure.
The values We and W are determined by the expressions
where are, respectively, the functions of changes in the radiation flux and luminous flux in time. We is measured in joules or Ws, a W- in lm s.
Under energy H e or light exposure understand surface density radiation energy We or light energy W respectively on the illuminated surface.
That is light exposure H is the product of illumination E, created by the radiation source, for a time t action of this radiation.
Question 2. Photometric quantities and their units.
Photometry is a branch of optics that deals with the measurement of the energy characteristics of optical radiation in the processes of propagation and interaction with matter. Photometry uses energy quantities that characterize the energy parameters of optical radiation, regardless of its effect on radiation receivers, and also uses light quantities that characterize the physiological effects of light and are evaluated by the effect on the human eye or other receivers.
Energy quantities.
Energy flowF e is the value, numerically equal to energy W radiation passing through a section perpendicular to the direction of energy transfer, per unit time
F e = W/ t, watt (Tue).
The flow of energy is equivalent to the power of energy.
The energy radiated by a real source into the surrounding space is distributed over its surface.
Energy luminosity(radiance) R e is the radiation power per unit surface area in all directions:
R e = F e / S, (Tue/m 2),
those. is the surface radiation flux density.
Energy power of light (radiation force) I e is defined using the concept of a point source of light - a source whose dimensions compared to the distance to the observation point can be neglected. Energy power of light I e value, equal to the ratio radiation flux F e source to solid angle ω , within which this radiation propagates:
I e= F e / ω , (Tue/Wed) - watt per steradian.
A solid angle is a part of space bounded by some conical surface. Particular cases of solid angles are trihedral and polyhedral angles. Solid angle ω measured by area ratio S that part of the sphere centered at the vertex of the conical surface, which is cut out by this solid angle, to the square of the radius of the sphere, i.e. ω = S/r 2. A complete sphere forms a solid angle equal to 4π steradians, i.e. ω = 4π r 2 /r 2 = 4π Wed.
The light intensity of the source often depends on the direction of radiation. If it does not depend on the direction of radiation, then such a source is called isotropic. For an isotropic source, the luminous intensity is
I e= F e /4π.
In the case of an extended source, we can talk about the luminous intensity of an element of its surface dS.
Energy Brightness (radiance) AT e is a value equal to the ratio of the energy intensity of light Δ I e element of the radiating surface to the area ∆S projections of this element onto a plane perpendicular to the direction of observation:
AT e = Δ I e / ∆ S. [(Tue/(sr.m 2)].
Energy illumination (irradiance) E e characterizes the degree of illumination of the surface and is equal to the magnitude of the radiation flux from all directions incident on the unit of the illuminated surface ( Tue/m 2).
In photometry, the inverse square law (Kepler's law) is used: the illumination of a plane from a perpendicular direction from a point source with a force I e in the distance r from it is equal to:
E e = I e/ r 2 .
Deviation of the beam of optical radiation from the perpendicular to the surface by an angle α leads to a decrease in illumination (Lambert's law):
E e = I e cos α /r 2 .
Important role when measuring the energy characteristics of radiation, the temporal and spectral distribution of its power play. If the duration of optical radiation is less than the observation time, then the radiation is considered pulsed, and if it is longer, it is considered continuous. Sources can emit radiation various lengths waves. Therefore, in practice, the concept of radiation spectrum is used - the distribution of radiation power on a wavelength scale λ (or frequencies). Almost all sources radiate differently in different parts of the spectrum.
For an infinitely small interval of wavelengths dλ the value of any photometric quantity can be specified using its spectral density. For example, the spectral density of energy luminosity
R eλ = dW/dλ,
where dW is the energy radiated from a unit surface area per unit time in the wavelength range from λ before λ + dλ.
Light quantities. In optical measurements, various radiation receivers are used, the spectral characteristics of the sensitivity of which to light of different wavelengths are different. The spectral sensitivity of an optical radiation photodetector is the ratio of the value characterizing the level of the receiver's reaction to the flux or energy of monochromatic radiation that causes this reaction. Distinguish between the absolute spectral sensitivity, expressed in named units (for example, BUT/Tue if the receiver response is measured in BUT), and the dimensionless relative spectral sensitivity is the ratio of the spectral sensitivity at a given radiation wavelength to maximum value spectral sensitivity or to spectral sensitivity at a certain wavelength.
The spectral sensitivity of a photodetector depends only on its properties; it is different for different receivers. Relative spectral sensitivity human eye V(λ ) is shown in Fig. 5.3.
The eye is most sensitive to radiation with a wavelength λ =555 nm. Function V(λ ) for this wavelength is taken equal to unity.
With the same energy flux, the visually estimated light intensity for other wavelengths is less. The relative spectral sensitivity of the human eye for these wavelengths turns out to be less than one. For example, the value of the function means that light of a given wavelength must have an energy flux density 2 times greater than light for which , so that the visual sensations are the same.
The system of light quantities is introduced taking into account the relative spectral sensitivity of the human eye. Therefore, light measurements, being subjective, differ from objective, energy ones, and light units are introduced for them, which are used only for visible light. The basic unit of light in the SI system is luminous intensity - candela (cd), which is equal to the intensity of light in a given direction of a source emitting monochromatic radiation with a frequency of 5.4 10 14 Hz, the energy intensity of which in this direction is 1/683 W/sr. All other light quantities are expressed in terms of the candela.
The definition of light units is similar to energy units. To measure light quantities, special techniques and devices are used - photometers.
Light flow . The unit of luminous flux is lumen (lm). It is equal to the luminous flux emitted by an isotropic light source with a power of 1 cd within a solid angle of one steradian (with uniform radiation field inside the solid angle):
1 lm = 1 cd·one Wed.
Experienced it was found that the luminous flux of 1 lm, formed by radiation with a wavelength λ = 555nm corresponds to an energy flux of 0.00146 Tue. Luminous flux in 1 lm, formed by radiation with a different wavelength λ , corresponds to the energy flow
F e = 0.00146/ V(λ ), Tue,
those. one lm = 0,00146 Tue.
illumination E- value wound by the ratio of the luminous flux F incident on the surface, to the area S this surface:
E = F/S, luxury (OK).
1 OK– surface illumination, per 1 m 2 which the luminous flux falls in 1 lm (1OK = 1 lm/m 2). For measurements of illumination, devices are used that measure the flux of optical radiation from all directions - luxmeters.
Brightness R C (luminosity) of a luminous surface in some direction φ is a quantity equal to the ratio of the luminous intensity I in this direction to the square S projection of a luminous surface onto a plane perpendicular to this direction:
R C= I/(S cos φ ), (cd/m 2).
In general, the brightness of light sources is different for different directions. Sources whose brightness is the same in all directions are called Lambertian or cosine, since the luminous flux emitted by an element of the surface of such a source is proportional to cosφ. Strictly satisfies this condition only absolutely black body.
Any photometer with a limited viewing angle is essentially a luminance meter. Spectral and spatial distribution brightness and illumination allows you to calculate all other photometric quantities by integration.
1. What is the physical meaning absolute indicator
refraction of the medium?
2. What is relative indicator refraction?
3. Under what condition is observed total reflection?
4. What is the principle of operation of light guides?
5. What is Fermat's principle?
6. What is the difference between energy and light quantities in photometry?
