The question of how luminous flux is measured began to matter to lighting users only when types of lamps appeared whose brightness was not equal to the power consumption measured in watts.
Let's figure out how the concept of brightness is related to the concept of illumination, as well as how you can imagine the distribution of light flux throughout the room and choose the right lighting device.
What is luminous flux?
Light flux is the power of light radiation visible to the human eye; light energy emitted by a surface (luminous or reflective). Luminous flux energy is measured in lumen-seconds and corresponds to 1 lumen emitted or perceived in 1 second. This indicator describes the total flow, without taking into account the concentrating efficiency of the entire device. This assessment also includes scattered, useless light, so the same number of lumens may appear in sources of different designs.
It is necessary to distinguish between the luminous value and the energy value - the latter characterizes light regardless of its property of causing visual sensations. Each photometric light quantity has an analogue that can be expressed quantitatively in units of energy or power. For light energy, this analogue is radiant energy, measured in joules.
Luminous flux unit
1 lumen is the light emitted by a source with a luminous intensity of 1 candela within a solid angle of 1 steradian. A 100-watt incandescent lamp produces approximately 1,000 lumens of light. The brighter the light source, the more lumens it emits.
In addition to lumens, there are other units of measurement that allow us to characterize light. It is possible to measure the spatial and surface flux density - this is how we know the luminous intensity and illumination. Luminous intensity is measured in candelas, illuminance in lux. But it is more important for the consumer to understand in what units the brightness of light bulbs and other lighting devices is indicated when selling. Some manufacturers report the number of lumens divided by watt. This is how luminous efficiency (luminous output) is measured: how much light a lamp produces using 1 watt.
Defining formulas
Since any light source emits it unevenly, the number of lumens does not fully describe the lighting fixture. You can calculate the intensity of light in candelas by dividing its flux, expressed in lumens, by the solid angle, measured in steradians. Using this formula, it will be possible to take into account the totality of rays coming from the source when they intersect the surface of an imaginary sphere, forming a circle on it.
But the question arises what the number of candelas we find gives in practice; It is impossible to find a suitable LED or flashlight based only on the luminous intensity parameter; you also need to take into account the ratio of the scattering angle, which depends on the design of the device. When choosing lamps that shine evenly in all directions, it is important to understand whether they are suitable for the buyer's purposes.
If previously light bulbs for different rooms were selected based on the number of watts, then before purchasing LED lamps you will have to calculate their total brightness in lumens, and then divide this figure by the area of the room. This is how illumination is calculated, which is measured in lux: 1 lux is 1 lumen per 1 m². There are lighting standards for rooms for various purposes.
Luminous flux measurement
Before releasing a product to the market, the manufacturer determines and measures the characteristics of the lighting device in the laboratory. It is impossible to do this at home, without special equipment. But you can check the numbers indicated by the manufacturer using the above formulas using a compact lux meter.
The difficulty in accurately measuring light is that it comes from all possible directions of propagation. Therefore, laboratories use spheres with an inner surface that has a high reflectivity - spherical photometers; They are also used to measure the dynamic range of cameras, i.e. photosensitivity of their matrices.
In everyday life, it makes more sense to measure such important light parameters as room illumination and pulsation coefficient. High pulsation ratio and dim lighting cause people to overstrain their eyes, which causes fatigue faster.
The light flux pulsation coefficient is an indicator characterizing the degree of its unevenness. Acceptable levels of these coefficients are regulated by SanPiN.
It is not always possible to notice with the naked eye that the light bulb is flickering. However, even a slight excess of the pulsation coefficient affects the human central nervous system negatively and also reduces performance. Light, which can pulsate unevenly, is emitted by all screens: computer and laptop monitors, tablet and mobile phone displays, and TV screens. Ripple is measured with a lux meter-pulse meter.
What is candela?
Another important characteristic of the light source is the candela, which is one of the 7 units of the International System of Units (SI) adopted by the General Conference on Weights and Measures. Initially, 1 candela was equal to the radiation of 1 candle, taken as the standard. This is where the name of this unit of measurement came from. Now it is determined using a special formula.
Candela is the intensity of light measured exclusively in a given direction. The propagation of rays over a part of the sphere outlined by a solid angle allows one to calculate a value equal to the ratio of the luminous flux to this angle. Unlike lumens, this value is used to determine the intensity of rays. This does not take into account useless, scattered light.
A flashlight and a ceiling light will have a different cone of light because the rays fall at different angles. Candelas (more precisely, millicandelas) are used to indicate the luminous intensity of sources with a directional glow: indicator LEDs, flashlights.
Lumens and Luxes
The amount of light flux is measured in lumens; this is a characteristic of its source. The number of rays that reach any surface (reflecting or absorbing) will already depend on the distance between the source and this surface.
The level of illumination is measured in lux (lx) with a special device - a lux meter. The simplest lux meter consists of a selenium photocell that converts light into electric current energy, and a dial microammeter that measures this current.
The spectral sensitivity of a selenium photocell differs from the sensitivity of the human eye, so correction factors have to be used in different conditions. The simplest lux meters are designed to measure one type of illumination, for example, daylight. Without using coefficients, the error can be more than 10%.
High-class lux meters are equipped with light filters, special spherical or cylindrical attachments (for measuring spatial illumination), devices for measuring brightness and checking the sensitivity of the device. Their error level is about 1%.
Poor indoor lighting contributes to the development of myopia, has a bad effect on performance, causes fatigue, and decreased mood.
The minimum illumination of the surface of a computer desk according to SanPiN is 400 lux. School desks must have an illumination level of at least 500 lux.
Lumen and Watt
Energy-saving lamps with the same light output consume 5-6 times less electrical energy than incandescent lamps. LED – 10-12 times less. The power of the light flux no longer depends on the number of watts. But manufacturers always indicate watts, since the use of too powerful light bulbs in sockets not intended for such a load leads to damage to electrical appliances or a short circuit.
If you arrange the most common types of light bulbs in order of increasing light output, you can get the following list:
- Incandescent lamp – 10 lumens/watt.
- Halogen – 20 lumens/watt.
- Mercury – 60 lumens/watt.
- Energy saving – 65 lumens/watt.
- Compact fluorescent lamp - 80 lumens/watt.
- Metal halide - 90 lumens/watt.
- Light-emitting diode (LED) – 120 lumens/watt.
But most people are accustomed to looking at the number of watts specified by the manufacturer when purchasing light bulbs. To calculate how many watts per square meter you need, you first need to decide how bright the light in the room should be. 20 watts of incandescent lamp per 1 m² - this lighting is suitable for a workplace or living room; for a bedroom 10-12 watts per 1 m² will be enough. When purchasing energy-saving lamps, these numbers are divided by 5. It is also important to take into account the height of the ceiling: if it is higher than 3 m, the total number of watts should be multiplied by 1.5.
In the system of energy photometric quantities, the analogue of luminous intensity is radiation intensity. In relation to radiant intensity, luminous intensity is a reduced photometric quantity obtained using the relative spectral luminous efficiency values of monochromatic radiation for daytime vision:
where is the maximum value of the spectral luminous efficiency of monochromatic radiation (photometric equivalent of radiation), equal to 683 lm / W, and is the spectral density of the radiation force, defined as the ratio of the value per small spectral interval enclosed between and to the width of this interval:
Examples
Light intensity of various sources:
Notes
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- Brightness
- Quantity of substance
See what “Power of Light” is in other dictionaries:
the power of light- luminous intensity: A physical quantity determined by the ratio of the luminous flux propagating from a light source inside a small solid angle containing the direction in question to this angle. [GOST 26148 84, article 42] Source...
THE POWER OF LIGHT- one of the main light quantities, characterizing the glow of a source of visible radiation in a certain direction. Equal to the ratio of the luminous flux propagating from the source inside the element. solid angle containing a given direction to this... ... Physical encyclopedia
THE POWER OF LIGHT- LIGHT POWER, luminous flux propagating inside a solid angle equal to 1 steradian. The unit of measurement for luminous intensity is the candela (cd), equal to the luminous intensity of a source emitting monochromatic radiation in a given direction with a frequency... ... Modern encyclopedia
The power of light- LIGHT POWER, luminous flux propagating inside a solid angle equal to 1 steradian. The unit of measurement of luminous intensity is the candela (cd), equal to the luminous intensity of a source emitting monochromatic radiation in a given direction with a frequency ... ... Illustrated Encyclopedic Dictionary
the power of light- (Iν) A physical quantity determined by the ratio of the luminous flux propagating from a light source inside a small solid angle containing the direction in question to this angle. [GOST 26148 84] Topics: optics, optical... ... Technical Translator's Guide
THE POWER OF LIGHT- luminous flux propagating inside a solid angle equal to 1 steradian. SI unit candela (cd) ... Big Encyclopedic Dictionary
the power of light- šviesos stipris statusas T sritis fizika atitikmenys: engl. light intensity vok. Lichtstärke, f rus. luminous intensity, f; source luminous intensity, f pranc. intensity lumineuse, f; intensité lumineuse de la source, f … Fizikos terminų žodynas
the power of light- luminous flux propagating inside a solid angle equal to 1 steradian. The SI unit of measurement is the candela (cd). * * * LIGHT INTENSITY LIGHT INTENSITY, luminous flux propagating within a solid angle equal to 1 steradian. Unit... ... encyclopedic Dictionary
the power of light- šviesos stipris statusas T sritis Standartizacija ir metrologija apibrėžtis Vienas pagrindinių SI dydžių, apibūdinantis regimosios šviesos šaltinio švytėjimą kuria nors kryptimi. Jis išreiškiamas šviesos srauto ir erdvinio kampo, kuriame sklinda… … Penkiakalbis aiškinamasis metrologijos terminų žodynas
luminous intensity I V- 2.16 luminous intensity IV: The ratio of the luminous flux ФV, cd, emanating from the source and propagating inside the solid angle ω, IV = ФV/ω. Unit of measurement cd. Source … Dictionary-reference book of terms of normative and technical documentation
Books
- The power of the ancestors. Unknown nature (number of volumes: 2), Rainbow Mikhail. The following books are included in the package. "Unknown nature". According to the author, there is nothing more mysterious and mysterious than the phenomena that we encounter in everyday life. Our world, in key... Buy for 470 RUR
- Color Power and Color Therapy: Harness the Transformative Powers of Light and Color for Health and Well-Being, Lilly Simon and Sue. Color is the energy of light and the universal language of communication of all beings. Any color causes changes in us for all beings. Any color causes changes in us on all levels - physical,...
From the definition it follows that the value for the frequency 540⋅10 12 Hz is equal to 683 lm / W = 683 cd sr / W exactly.
The selected frequency corresponds to a wavelength of 555.016 nm in air under standard conditions and is close to the maximum sensitivity of the human eye, located at a wavelength of 555 nm. If the radiation has a different wavelength, then more luminous energy is required to achieve the same luminous intensity.
Detailed consideration[ | ]
All light quantities are reduced photometric quantities. This means that they are formed from the corresponding energy photometric quantity using a function representing the dependence of the spectral luminous efficiency of monochromatic radiation for daytime vision on the wavelength. This function is usually represented as K m ⋅ V (λ) (\displaystyle K_(m)\cdot V(\lambda)), where is a function normalized so that at its maximum it is equal to unity, and is the maximum value of the spectral luminous efficiency of monochromatic radiation. Sometimes K m (\displaystyle K_(m)) also called the photometric equivalent of radiation.
Calculation of light magnitude X v , (\displaystyle X_(v),) the corresponding energy value is produced using the formula
X v = K m ∫ 380 nm 780 nm X e , λ (λ) V (λ) d λ , (\displaystyle X_(v)=K_(m)\int \limits _(380~(\text(nm) ))^(780~(\text(nm)))X_(e,\lambda )(\lambda)V(\lambda)\,d\lambda ,)Where X e , λ (\displaystyle X_(e,\lambda ))- spectral density of quantity X e , (\displaystyle X_(e),) defined as the ratio of the quantity d X e (λ) , (\displaystyle dX_(e)(\lambda),) falling on a small spectral interval concluded between and λ + d λ , (\displaystyle \lambda +d\lambda ,) to the width of this interval:
X e , λ (λ) = d X e (λ) d λ . (\displaystyle X_(e,\lambda )(\lambda)=(\frac (dX_(e)(\lambda))(d\lambda )).)It may be noted that under X e (λ) (\displaystyle X_(e)(\lambda)) here we mean the flux of that part of the radiation whose wavelength is less than the current value λ (\displaystyle \lambda).
Function V (λ) (\displaystyle V(\lambda)) determined empirically and given in tabular form. Its values do not depend in any way on the choice of light units used.
Contrary to what was said about V (λ) (\displaystyle V(\lambda)) meaning K m (\displaystyle K_(m)) is entirely determined by the choice of the main light unit. Therefore, to establish a relationship between light and energy quantities in the SI system, it is necessary to determine the value K m (\displaystyle K_(m)), corresponding to the SI unit of luminous intensity, the candela. With a strict approach to defining K m (\displaystyle K_(m)) it is necessary to take into account that the spectral point 540⋅10 12 Hz, which is discussed in the definition of candela, does not coincide with the position of the maximum of the function V (λ) (\displaystyle V(\lambda)).
Luminous efficiency of radiation with a frequency of 540⋅10 12 Hz[ | ]
In general, the luminous intensity is related to the radiation intensity I e (\displaystyle I_(e)) ratio
I v = K m ⋅ ∫ 380 nm 780 nm I e , λ (λ) V (λ) d λ , (\displaystyle I_(v)=K_(m)\cdot \int \limits _(380~(\text (nm)))^(780~(\text(nm)))I_(e,\lambda )(\lambda)V(\lambda)\,d\lambda ,)Where I e , λ (\displaystyle I_(e,\lambda ))- spectral density of radiation force equal to d I e (λ) d λ (\displaystyle (\frac (dI_(e)(\lambda))(d\lambda ))).
For monochromatic radiation with wavelength λ (\displaystyle \lambda) formula relating the power of light I v (λ) (\displaystyle I_(v)(\lambda)) with radiation power I e (λ) (\displaystyle I_(e)(\lambda)), simplifies, taking the form
I v (λ) = K m ⋅ I e (λ) V (λ) (\displaystyle I_(v)(\lambda)=K_(m)\cdot I_(e)(\lambda)V(\lambda)), or, after moving from wavelengths to frequencies, I v (ν) = K m ⋅ I e (ν) V (ν) . (\displaystyle I_(v)(\nu)=K_(m)\cdot I_(e)(\nu)V(\nu).)From the last relation for ν 0 = 540⋅10 12 Hz it follows
K m ⋅ V (ν 0) = I v (ν 0) I e (ν 0) . (\displaystyle K_(m)\cdot V(\nu _(0))=(\frac (I_(v)(\nu _(0)))(I_(e)(\nu _(0))) ).)Taking into account the definition of candela, we get
K m ⋅ V (ν 0) = 683 c d ⋅ s r W (\displaystyle K_(m)\cdot V(\nu _(0))=683~\mathrm (\frac (cd\cdot sr)(W)) ), or what is the same 683 l m W . (\displaystyle 683~\mathrm (\frac (lm)(W)) .)Work K m ⋅ V (ν 0) (\displaystyle K_(m)\cdot V(\nu _(0))) represents the value of the spectral luminous efficiency of monochromatic radiation for a frequency of 540⋅10 12 Hz. As follows from the production method, this value is equal to 683 cd sr/W = 683 lm/W exactly.
Maximum luminous efficiency K m (\displaystyle (\boldsymbol (K))_(m))[ | ]
For determining K m (\displaystyle K_(m)) It should be taken into account that, as stated above, a frequency of 540⋅10 12 Hz corresponds to a wavelength of ≈555.016 nm. Therefore, from the last equality it follows
K m = 683 V (555.016) l m W . (\displaystyle K_(m)=(\frac (683)(V(555(,)016)))~\mathrm (\frac (lm)(W)) .)Normalized function V (λ) (\displaystyle V(\lambda)) given in tabular form with an interval of 1 nm, it has a maximum equal to unity at a wavelength of 555 nm. Interpolation of its values for a wavelength of 555.016 nm gives a value of 0.999997. Using this value we get
K m = 683.002 l m W . (\displaystyle K_(m)=683(,)002~\mathrm (\frac (lm)(W)) .)In practice, a rounded value is used with sufficient accuracy for all cases K m = 683 l m W . (\displaystyle K_(m)=683~\mathrm (\frac (lm)(W)) .)
Thus, the connection between an arbitrary light quantity X v (\displaystyle X_(v)) and its corresponding energy value X e (\displaystyle X_(e)) in the SI system it is expressed by the general formula
X v = 683 ∫ 380 nm 780 nm X e , λ (λ) V (λ) d λ . (\displaystyle X_(v)=683\int \limits _(380~(\text(nm)))^(780~(\text(nm)))X_(e,\lambda )(\lambda)V( \lambda)\,d\lambda .)History and prospects[ | ]
Hefner lamp - the standard of the “Hefner candle”
Examples [ | ]
The luminous intensity emitted by a candle is approximately equal to one candela, so this unit of measurement was formerly called a "candle", a name that is now obsolete and not used.
For household incandescent lamps, the luminous intensity in candelas is approximately equal to their wattage.
Light intensity of various sources| Source | Power, W | Approximate luminous intensity, cd |
|---|---|---|
| Candle | 1 | |
| Modern (2010) incandescent lamp | 100 | 100 |
| Regular LED | 0,015..0,1 | 0,005..3 |
| Super bright LED | 1 | 25…500 |
| Ultra-bright LED with collimator | 1 | 1500 |
| Modern (2010) fluorescent lamp | 22 | 120 |
| Sun | 3,83⋅10 26 | 2,8⋅10 27 |
Light quantities[ | ]
Information about the main light photometric quantities is given in the table.
| Name | Quantity designation | Definition | SI units notation | Energy analogue |
|---|---|---|---|---|
| Light energy | Q v (\displaystyle Q_(v)) | K m ∫ 380 nm 780 nm Q e , λ (λ) V (λ) d λ (\displaystyle K_(m)\int _(380~(\text(nm)))^(780~(\text(nm )))Q_(e,\lambda )(\lambda)V(\lambda)\,d\lambda ) | lm · | Radiation energy |
| Light flow | Φ v (\displaystyle \Phi _(v)) | d Q v d t (\displaystyle (\frac (dQ_(v))(dt))) | lm | Radiation flux |
| The power of light | I v (\displaystyle I_(v)) | d Φ v d Ω (\displaystyle (\frac (d\Phi _(v))(d\Omega ))) | cd | Radiation intensity (luminous energy intensity) |
| U v (\displaystyle U_(v)) | d Q v d V (\displaystyle (\frac (dQ_(v))(dV))) | lm s −3 | ||
| Luminosity | M v (\displaystyle M_(v)) | d Φ v d S 1 (\displaystyle (\frac (d\Phi _(v))(dS_(1)))) | lm m−2 | Energetic luminosity |
| Brightness | L v (\displaystyle L_(v)) | d 2 Φ v d Ω d S 1 cos ε (\displaystyle (\frac (d^(2)\Phi _(v))(d\Omega \,dS_(1)\,\cos \varepsilon ))) | cd m−2 |
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Initial value
Converted value
candela candle (German) candle (British) decimal candle pentane candle pentane candle (10 light output) Hefner candle Carcel unit candle decimal (French) lumen/steradian candle (international)
More about the power of light
General information
Luminous intensity is the power of the luminous flux within a certain solid angle. That is, the intensity of light does not determine all the light in space, but only the light emitted in a certain direction. Depending on the light source, the luminous intensity decreases or increases as the solid angle changes, although sometimes this value is the same for any angle if the source distributes the light evenly. Luminous intensity is a physical property of light. In this way, it differs from brightness, since in many cases, when they talk about brightness, they mean a subjective sensation, and not a physical quantity. Also, brightness does not depend on the solid angle, but is perceived in the general space. The same source with a constant luminous intensity can be perceived by people as light of different brightness, since this perception depends on environmental conditions and on the individual perception of each person. Also, the brightness of two sources with the same luminous intensity may be perceived differently, especially if one produces diffuse light and the other directed light. In this case, the directional source will appear brighter, even though the luminous intensity of both sources is the same.
Luminous intensity is considered as a unit of power, although it differs from the usual concept of power in that it depends not only on the energy emitted by the light source, but also on the wavelength of the light. The sensitivity of people to light depends on the wavelength and is expressed by the function of relative spectral luminous efficiency. The luminous intensity depends on the luminous efficiency, which reaches a maximum for light with a wavelength of 550 nanometers. This is green. The eye is less sensitive to light of longer or shorter wavelengths.
In the SI system, luminous intensity is measured in candela(kd). One candela is approximately equal to the intensity of light emitted by one candle. Sometimes the obsolete unit is also used, candle(or international candle), although in most cases this unit is replaced by candelas. One candle is approximately equal to one candela.
If you measure the luminous intensity using a plane that shows the spread of light, as in the illustration, you can see that the magnitude of the luminous intensity depends on the direction towards the light source. For example, if the direction of maximum emission of an LED lamp is taken to be 0°, then the measured luminous intensity in the 180° direction will be much lower than for 0°. For diffuse sources, the luminous intensity for 0° and 180° will not be much different, and may be the same.
In the illustration, light emitted by two sources, red and yellow, covers an equal area. Yellow light is diffused, like candle light. Its strength is approximately 100 cd, regardless of direction. Red is the opposite, directional. In the direction of 0°, where the radiation is maximum, its strength is 225 cd, but this value quickly decreases with deviations from 0°. For example, the luminous intensity is 125 cd when directed at a source of 30° and only 50 cd when directed at 80°.
The power of light in museums
Museum staff measure the light intensity in museum spaces to determine the optimal conditions for visitors to view the works on display, while at the same time providing gentle light that causes as little damage as possible to museum exhibits. Museum exhibits containing cellulose and dyes, especially those made from natural materials, deteriorate from prolonged exposure to light. Cellulose provides strength to fabric, paper and wood products; Often in museums there are many exhibits made from these materials, so the light in the exhibition halls poses a great danger. The stronger the light intensity, the more museum exhibits deteriorate. In addition to destruction, light also discolors or yellows cellulose-containing materials such as paper and fabrics. Sometimes the paper or canvas on which the paintings are painted deteriorates and breaks down faster than the paint. This is especially problematic since the paint on a painting is easier to restore than the base.
The damage caused to museum exhibits depends on the wavelength of light. For example, light in the orange spectrum is the least harmful, and blue light is the most dangerous. That is, light with longer wavelengths is safer than light with shorter wavelengths. Many museums use this information and control not only the total amount of light, but also limit blue light using light orange filters. At the same time, they try to choose filters that are so light that, although they filter out blue light, they allow visitors to fully enjoy the works exhibited in the exhibition hall.
It is important not to forget that exhibits deteriorate not only from light. Therefore, it is difficult to predict, based only on the intensity of light, how quickly the materials from which they are made will degrade. Long-term storage in museum spaces requires not only low lighting, but also low humidity and low oxygen levels, at least within display cases.
In museums where flash photography is prohibited, they often refer specifically to the harm of light to museum exhibits, especially ultraviolet light. This is practically unfounded. Just as limiting the entire spectrum of visible light is much less effective than limiting blue light, banning flash has little effect on the extent of light damage to exhibits. During the experiments, the researchers noticed slight damage to the watercolors caused by professional studio flash only after more than a million flashes. A flash every four seconds at a distance of 120 centimeters from the exhibit is almost equivalent to the light that is usually found in exhibition halls, where the amount of light is controlled and blue light is filtered. Those who take photographs in museums rarely use such powerful flashes, since most visitors are not professional photographers and take photos with phones and compact cameras. Flashes in the halls rarely work every four seconds. The damage from the ultraviolet rays emitted by the flash is also in most cases small.
Luminous intensity of lamps
The properties of lamps are usually described using luminous intensity, which differs from the luminous flux - a value that determines the total amount of light and shows how bright this source is in general. It is convenient to use luminous intensity to determine the luminous properties of lamps, for example, LED lamps. When purchasing them, information about the light intensity helps determine with what strength and in what direction the light will spread, and whether such a lamp is suitable for the buyer.
Light intensity distribution
In addition to the luminous intensity itself, luminous intensity distribution curves help to understand how the lamp will behave. Such diagrams of the angular distribution of light intensity are closed curves on a plane or in space, depending on the symmetry of the lamp. They cover the entire range of light propagation of this lamp. The diagram shows the magnitude of the light intensity depending on the direction of its measurement. The graph is usually plotted in either a polar or rectangular coordinate system, depending on the light source for which the graph is being plotted. It is often placed on lamp packaging to help the buyer imagine how the lamp will perform. This information is important for designers and lighting engineers, especially those who work in the field of cinema, theater, and the organization of exhibitions and performances. Luminous intensity distribution also affects driving safety, which is why engineers designing vehicle lighting use luminous intensity distribution curves. They must comply with strict regulations governing the distribution of light intensity in headlights to ensure maximum safety on the roads.
The example in the figure is in the polar coordinate system. A is the center of the light source, from where the light spreads in different directions, B is the luminous intensity in candelas, and C is the angle of measurement of the direction of the light, with 0° being the direction of the maximum luminous intensity of the source.
Measuring the intensity and distribution of light intensity
Light intensity and its distribution are measured with special instruments, goniophotometers And goniometers. There are several types of these devices, for example with a movable mirror, which allows you to measure light intensity from different angles. Sometimes, instead of a mirror, the light source itself moves. Typically these devices are large, with a distance of up to 25 meters between the lamp and the sensor that measures light intensity. Some devices consist of a sphere with a measuring device, a mirror and a lamp inside. Not all goniophotometers are large; there are also small ones that move around the light source during measurement. When purchasing a goniophotometer, the decisive factors, among other factors, are its price, size, power, and the maximum size of the light source that it can measure.
Half Brightness Angle
Half-brightness angle, sometimes also called luminosity angle, is one of the quantities that helps describe a light source. This angle indicates how directional or diffuse the light source is. It is defined as the angle of the light cone at which the luminous intensity of the source is equal to half its maximum intensity. In the example in the figure, the maximum luminous intensity of the source is 200 cd. Let's try to determine the half-brightness angle using this graph. Half the luminous intensity of the source is 100 cd. The angle at which the luminous intensity of the beam reaches 100 cd., that is, the angle of half brightness, is equal to 60 + 60 = 120 ° on the graph (half the angle is depicted in yellow). For two light sources with the same total amount of light, a narrower half-brightness angle means that its luminous intensity is greater, compared to the second source, for angles between 0° and the half-brightness angle. That is, directional sources have a narrower half-brightness angle.
There are advantages to both wide and narrow half-brightness angles, and which one should be preferred depends on the application of the light source. For example, for scuba diving, you should choose a flashlight with a narrow angle of half brightness if there is good visibility in the water. If visibility is poor, then there is no point in using such a flashlight, since it only wastes energy. In this case, a flashlight with a wide angle of half brightness, which diffuses the light well, is a better choice. Also, such a flashlight will help during photo and video shooting, because it illuminates a wider area in front of the camera. Some dive lights can be manually adjusted to half brightness, which is useful since divers can't always predict what the visibility will be like where they're diving.
Post a question in TCTerms and within a few minutes you will receive an answer.1. Luminous flux
Luminous flux is the power of radiant energy, assessed by the light sensation it produces. Radiation energy is determined by the number of quanta that are emitted by the emitter into space. Radiation energy (radiant energy) is measured in joules. The amount of energy emitted per unit time is called radiation flux or radiant flux. The radiation flux is measured in watts. The luminous flux is designated Fe.
where: Qе - radiation energy.
The radiation flux is characterized by the distribution of energy in time and space.
In most cases, when talking about the distribution of radiation flux over time, they do not take into account the quantum nature of the occurrence of radiation, but understand this as a function that gives a change in time of instantaneous values of the radiation flux Ф(t). This is acceptable because the number of photons emitted by the source per unit time is very large.
According to the spectral distribution of the radiation flux, sources are divided into three classes: with line, stripe and continuous spectra. The radiation flux of a source with a line spectrum consists of monochromatic fluxes of individual lines:
where: Фλ - monochromatic radiation flux; Fe - radiation flux.
For sources with a striped spectrum, radiation occurs within fairly wide areas of the spectrum - bands separated from one another by dark intervals. To characterize the spectral distribution of the radiation flux with continuous and striped spectra, a quantity called spectral flux density
where: λ - wavelength.
The spectral radiation flux density is a characteristic of the distribution of the radiant flux over the spectrum and is equal to the ratio of the elementary flux ΔФeλ corresponding to an infinitesimal area to the width of this area:
Spectral radiation flux density is measured in watts per nanometer.
In lighting engineering, where the main receiver of radiation is the human eye, the concept of luminous flux is introduced to assess the effective action of the radiation flux. Luminous flux is the flux of radiation, assessed by its effect on the eye, the relative spectral sensitivity of which is determined by the average spectral efficiency curve approved by the CIE.
In lighting technology, the following definition of luminous flux is used: luminous flux is the power of light energy. 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 luminous intensity of 1 candela.
Table 1. Typical luminous values of light sources:
| Types of lamps | Electrical energy, W | Luminous flux, lm | Luminous efficiency lm/w |
| 100 W | 1360 lm | 13.6 lm/W | |
| Fluorescent Lamp | 58 W | 5400 lm | 93 lm/W |
| High pressure sodium lamp | 100 W | 10000 lm | 100 lm/W |
| Low pressure sodium lamp | 180 W | 33000 lm | 183 lm/W |
| High pressure mercury lamp | 1000 W | 58000 lm | 58 lm/W |
| Metal halide lamp | 2000 W | 190000 lm | 95 lm/W |
The light flux Ф falling on a body is distributed into three components: reflected by the body Фρ, absorbed by Фα and transmitted Фτ. When using the following coefficients: reflection ρ = Фρ /Ф; absorption α =Фα/Ф; transmission τ = Фτ / Ф.
Table 2. Light characteristics of some materials and surfaces
| Materials or surfaces | Odds | Character of reflection and transmission | ||
| reflections ρ | absorption α | transmission τ | ||
| Chalk | 0,85 | 0,15 | - | Diffuse |
| Silicate enamel | 0,8 | 0,2 | - | Diffuse |
| Mirror aluminum | 0,85 | 0,15 | - | Directed |
| Glass mirror | 0,8 | 0,2 | - | Directed |
| Frosted glass | 0,1 | 0,5 | 0,4 | Directional-scattered |
| Organic milk glass | 0,22 | 0,15 | 0,63 | Directional-scattered |
| Opal silicate glass | 0,3 | 0,1 | 0,6 | Diffuse |
| Silicate milk glass | 0,45 | 0,15 | 0,4 | Diffuse |
2. Light power
The distribution of radiation from a real source in the surrounding space is not uniform. Therefore, the luminous flux will not be an exhaustive characteristic of the source if the distribution of radiation in different directions of the surrounding space is not simultaneously determined.
To characterize the distribution of light flux, the concept of spatial density of light flux in different directions of the surrounding space is used. The spatial density of the luminous flux, determined by the ratio of the luminous flux to the solid angle with the vertex at the point where the source is located, within which this flux is evenly distributed, is called luminous intensity:
where: F - luminous flux; ω - solid angle.
The unit of luminous intensity is the candela. 1 cd.
This is the luminous intensity emitted in a perpendicular direction by a blackbody surface element with an area of 1:600000 m2 at the solidification temperature of platinum.
The unit of luminous intensity is the candela, cd is one of the basic quantities in the SI system and corresponds to a luminous flux of 1 lm, uniformly distributed within a solid angle of 1 steradian (avg). A solid angle is a part of space enclosed inside a conical surface. Solid angleω is measured by the ratio of the area it cuts out from a sphere of arbitrary radius to the square of the latter.
3. Illumination
Illuminance is the amount of light or luminous flux incident on a unit surface area. It is designated by the letter E and measured in lux (lx).
The unit of illumination lux, lux has the dimension lumen per square meter (lm/m2).
Illumination can be defined as the density of luminous flux on an illuminated surface:
Illumination does not depend on the direction of propagation of the light flux onto the surface.
Here are some generally accepted illumination indicators:
Summer, day under a cloudless sky - 100,000 lux
Street lighting - 5-30 lux
Full moon on a clear night - 0.25 lux
4. The relationship between luminous intensity (I) and illuminance (E).
Inverse square law
Illumination at a certain point on a surface perpendicular to the direction of propagation of light is defined as the ratio of luminous intensity to the square of the distance from this point to the light source. If we take this distance as d, then this relationship can be expressed by the following formula:
For example: if a light source emits light with an intensity of 1200 cd in a direction perpendicular to the surface at a distance of 3 meters from this surface, then the illuminance (Ep) at the point where the light reaches the surface will be 1200/32 = 133 lux. If the surface is at a distance of 6 m from the light source, the illumination will be 1200/62 = 33 lux. This relationship is called "inverse square law".
Illumination at a certain point on a surface not perpendicular to the direction of light propagation is equal to the luminous intensity in the direction of the measurement point, divided by the square of the distance between the light source and the point on the plane multiplied by the cosine of the angle γ (γ is the angle formed by the direction of incidence of the light and the perpendicular to this plane).
Hence:
This is the law of cosine (Figure 1).
Rice. 1. To the law of cosine
To calculate horizontal illumination, it is advisable to change the last formula by replacing the distance d between the light source and the measurement point with the height h from the light source to the surface.
In Figure 2:
Then:
We get:
Using this formula, the horizontal illumination at the measurement point is calculated.
Rice. 2. Horizontal illumination
6. Vertical illumination
Illumination of the same point P in a vertical plane oriented towards the light source can be represented as a function of the height (h) of the light source and the angle of incidence (γ) of luminous intensity (I) (Figure 3).
luminosity:
For surfaces of finite dimensions:
Luminosity is the density of the luminous flux emitted by a luminous surface. The unit of luminosity is the lumen per square meter of luminous surface, which corresponds to a surface of 1 m2 that uniformly emits a luminous flux of 1 lm. In the case of general radiation, the concept of energetic luminosity of the radiating body (Me) is introduced.
The unit of energetic luminosity is W/m2.
Luminosity in this case can be expressed through the spectral energy luminosity density of the emitting body Meλ(λ)
For a comparative assessment, we reduce the energy luminosities to the luminosities of some surfaces:
Sun surface - Me=6 107 W/m2;
Incandescent lamp filament - Me=2 105 W/m2;
The surface of the sun at the zenith is M=3.1 109 lm/m2;
Fluorescent lamp bulb - M=22 103 lm/m2.
This is the intensity of light emitted per unit surface area in a specific direction. The unit of measurement for brightness is candela per square meter (cd/m2).
The surface itself can emit light, like the surface of a lamp, or reflect light that comes from another source, like the surface of a road.
Surfaces with different reflective properties under the same illumination will have different degrees of brightness.
The brightness emitted by a surface dA at an angle Ф to the projection of this surface is equal to the ratio of the intensity of light emitted in a given direction to the projection of the emitting surface (Fig. 4).
Rice. 4. Brightness
Both the luminous intensity and the projection of the emitting surface do not depend on distance. Therefore, brightness is also independent of distance.
Some practical examples:
Sun surface brightness - 2000000000 cd/m2
Brightness of fluorescent lamps - from 5000 to 15000 cd/m2
Full moon surface brightness - 2500 cd/m2
Artificial road lighting - 30 lux 2 cd/m2