Lumen
Lumen is 1/683 watt of monochromatic light, i.e. strictly single-color radiation with a wavelength of 555 nm, corresponding to the maximum of the eye's spectral sensitivity curve. The value of 1/683 appeared historically, when the main source of light was ordinary candles, and the radiation of newly emerging electric light sources was compared with the light of such candles. At present, this value is legalized by many international agreements and accepted everywhere.
Solid angle
The luminous flux from light sources - be it a simple match or a state-of-the-art electric lamp - is usually distributed more or less evenly in all directions. However, with the help of mirrors or lenses, light can be directed in the way we need, concentrating it in some part of space. A part or share of space is characterized by a solid angle. The concept of "solid angle" has no direct relation to light, but is used in lighting engineering so widely that without it, it is impossible to explain many lighting terms and quantities.
The whole world
Luminous intensity is the ratio of the luminous flux contained in a solid angle to the size of that angle. Luminous intensity is measured in candelas (abbreviated Russian notation cd, foreign — cd). The word candela is translated into Russian as a candle, and the unit of luminous intensity in the USSR was called a candle until 1963.
Candela
One candela is the luminous intensity of a source emitting a luminous flux in a solid angle. A regular stearin candle has approximately this luminous intensity (hence it is clear that the luminous flux of such a candle is approximately 12.56 lumens). Light from a source is usually needed to illuminate a specific place - a desk, a shop window, streets, etc. To characterize the illumination of specific places, another luminous quantity is introduced - illumination.
Illumination
Illumination is the value of the luminous flux per unit area of the illuminated surface. If the luminous flux Ф falls on some area S, then the average illumination of this area (denoted by the letter E) is equal to: E = Ф/S. The unit of illumination is called lux (abbreviated in Russian literature as lx). One lux is the illumination at which the luminous flux of 1 lm falls on an area of 1 square meter: 1 lx = 1 lm/1 m2. To imagine this value, let us say that illumination of about 1 lx is created by a stearin candle on a plane perpendicular to the direction of light, from a distance of 1 meter. For comparison: illumination from the full Moon on the Earth's surface in winter at the latitude of Moscow does not exceed 0.5 lx; direct illumination from the Sun at midday in summer at the latitude of Moscow can reach 100,000 lx. Let's assume that the illumination on the desktop is 100 lux. On the desk are sheets of white paper, a black folder, and a book in a gray cover. The illumination of all these objects is the same, but the eye sees that the sheets of paper are lighter than the book, and the book is lighter than the folder. That is, our eye evaluates the lightness of objects not by their illumination, but by some other value. This "other value" is called brightness.
Brightness
The brightness of a surface S is the ratio of the luminous intensity emitted by this surface in any direction to the area of the projection of this surface onto a plane perpendicular to the selected direction. As is known, the area of the projection of any flat surface onto another plane is equal to the area of this surface multiplied by the cosine of the angle between the planes. While there are special units of measurement for luminous flux, luminous intensity and illumination (lumen, candela and lux), there is no special name for the unit of measurement of brightness. True, in old (before 1963) textbooks on physics, lighting engineering, optics and other technical literature there were several names for the units of measurement of brightness: in Russian - nit and stilb, in English - foot-lambert, apostilb, etc. The international SI system has not adopted any of these units, and has not come up with a special name for the adopted unit of measurement of brightness. The unit of measurement of brightness in all countries is now the brightness of a flat surface emitting a luminous intensity of 1 cd from one square meter in the direction perpendicular to the luminous surface, i.e. 1 cd/m2. What does the brightness of objects depend on? First of all, of course, on the amount of light falling on them. But in the given example, the same amount of light falls on all objects lying on the table. This means that brightness also depends on the properties of the objects themselves, namely, on their ability to reflect incident light.
Reflection
Reflectivity is the ratio of the amount of luminous flux reflected from a surface to the amount of luminous flux incident on that surface from a light source or lamp. The higher the reflection coefficient of an object, the brighter it appears to us. In the example with the desk, the reflection coefficient of the sheets of paper is higher than that of the book binding, and that of the binding is higher than that of the folder. The reflection coefficient of materials depends on both the properties of the materials themselves and the nature of their surface treatment. Reflection can be directed in one direction or scattered in a certain solid angle. Let's take a sheet of ordinary white writing paper or Whatman paper. No matter which side or angle we look at such a sheet, it appears to us to be equally bright, that is, its brightness is the same in all directions. Such reflection is called diffuse or scattered; accordingly, surfaces with such a reflection character are also called diffuse. This is not glossy paper, most fabrics, matte paints, whitewash, rough metal surfaces and much more. But if we start to polish a rough metal surface, the nature of its reflection will begin to change. If the surface is polished very well, then all the light falling on it will be reflected in one direction. In this case, the angle at which the incident light is reflected is exactly equal to the angle at which it falls on the surface. Such reflection is called specular, and the equality of the angles of incidence and reflection of light is one of the basic laws of lighting engineering: all methods of calculating spotlights and lamps with a mirror optical part are based on this law. In addition to specular and diffuse reflection, there is directional-scattered (for example, from poorly polished metal surfaces, silk fabrics or glossy paper), as well as mixed (for example, from milky glass). The curve characterizing the angular distribution of the reflection coefficient is called the reflection indicatrix. For surfaces with diffuse reflection, brightness is related to illumination by a simple ratio: the brightness of a mirror surface is equal to the brightness of objects reflected in it (light sources, ceiling, walls, etc.), multiplied by the reflection coefficient. To assess the brightness of objects and surfaces with directional diffuse and mixed reflection, it is necessary to know the reflection indicatrices. The four named light quantities - luminous flux, luminous intensity, illumination and brightness - are the most important concepts, without knowledge of which it is impossible to explain the operation of light sources and lighting devices. However, for such an explanation, it is also necessary to know the lighting characteristics of materials. We have already become familiar with one of these characteristics - the reflection coefficient. But in nature, there are no materials that reflect all the light falling on them. The share of light that is not reflected from the material is generally divided into two parts: one part passes through the material, the other is absorbed in it.
Transmission and absorption coefficients
The proportion of light that passes through a material is characterized by the transmittance coefficient, and the proportion that is absorbed is characterized by the absorption coefficient. The relationships between these three coefficients - reflection, absorption and transmission - can be very different, but in all cases without exception, the sum of the three coefficients is equal to one. There is not a single material in nature in which at least one of the three coefficients is equal to 1. The greatest diffuse reflection is found in freshly fallen snow, chemically pure barium sulfate and magnesium oxide. The greatest specular reflection is found in pure polished silver and specially treated aluminum.
The value of the transmission coefficient is indicated in reference literature for a certain thickness of the material (usually for 1 cm). The most transparent materials include ultra-pure quartz and some brands of polymethyl methacrylate (organic glass), in which a hypothetical (in reality non-existent!) substance with an absorption coefficient equal to 1 is called an "absolutely black body". Like reflection, light transmission can be directional (in silicate or organic glasses, polycarbonate, polystyrene, quartz, etc.), diffuse or scattered (milky glass), directional-scattered (frosted glass), and mixed.
The vast majority of materials reflect, transmit or absorb light of different wavelengths, i.e. different colors, in different ways. It is this property of materials that determines their color and creates the multicolored world around us. To fully characterize the lighting properties of materials, it is necessary to know not only the absolute values of their reflection, transmission and absorption coefficients, but also the distribution of these coefficients in space (indicatrices) and by wavelength. The distribution of coefficients by wavelength is called spectral characteristics (reflection, transmission or absorption). All three of these coefficients are relative (dimensionless) quantities and are measured in fractions of a unit or in percentages (in the same fractions multiplied by 100).