# Photometry

With photometry or photometry ( oldgr. Φῶς phos 'light' and μετρεῖν meter ' to measure') measuring methods in the wavelength range of visible light are referred to with the help of a photometer .

## Sub-areas

Photometry was originally a branch of physics or chemistry , astronomy and photography , but is now a regular engineering science . For example, it is constantly being further developed in photovoltaics or in the production of displays for industrial measurement technology for quality assurance and quality control. It is the standard method in the development of optical technologies such as laser technology , as well as related colorimetry .

In addition, photometry is also used in (bio) chemical and medical analysis . It allows qualitative and quantitative evidence as well as tracking the dynamics of chemical processes of radiation-absorbing chemical compounds.

A measurement of the absorbance over different wavelengths is called spectroscopy , e.g. B. UV / VIS spectroscopy or infrared spectroscopy . A recorded measurement at different wavelengths is called a spectrum . With unfiltered irradiated light, UV fluorescence in a sample can lead to measurement errors in the visible range of the radiation, which is why a filter , prism or diffraction grating can be used to limit the wavelength ranges of the irradiated light. It is also important to know the radiation functions and spectral dependencies of materials. For this reason, spectral measurements are also carried out. The generalization of photometry to the entire electromagnetic spectrum (radio to gamma radiation ) is called radiometry .

### Transmission measurements

Photometric measurement of a red particle in a solution
Older photometer for medical purposes, but can also be used in chemical analysis

The absorption and color of a liquid or a transparent solid depend on the material composition and the concentration. With photometry, the concentrations of colored solutions are determined with the help of visible light. The measurement is carried out in a special sample vessel, the so-called cuvette .

If the solution of an absorbing substance is irradiated with light, the intensity that passes through (a detector that works as linearly as possible is required) depends on the generally wavelength-dependent absorption properties of the substance, the concentration and the length of the light path in the solution. This law is described by the Lambert-Beer law . To apply this law, the intensity signal I measured in a narrow wavelength range for various known and unknown concentrations is plotted logarithmically against the concentration c . A straight line is created from which the unknown concentrations can be read.

A photometer does this interpolation arithmetically: the intensities are divided by the intercept I ( c = 0) (→ transmittance) and logarithmized (→ extinction ). The extinction is proportional to the concentration.

If several absorbing species are present in the solution, a wavelength range is selected which is absorbed by the species to be determined, but not by other constituents. Some substances that show little or no absorption can be converted into well-absorbing substances by chemical means. For example, formaldoxime can be used to photometrically determine the concentration of numerous metal ions. Light with the selected wavelength is generated with filters, monochromators or lasers .

### Reflection measurements

Photometric examinations primarily concern the color evaluation of surfaces for quality assurance in coloring. Calibrated photosensors are used that measure at several wavelengths by means of filters .

From the possibly wavelength-dependent diffuse reflection, conclusions can also be drawn about the surface structure (e.g. DRIFTS ).

### Evaluation of light sources

The photometric evaluation of light sources is carried out using photometric parameters such as luminous intensity , luminous flux , illuminance and luminance . The sensitivity of the human eye is taken into account by means of light sensitivity curves . The V-lambda curves for photopic and scotopic vision can be used to calculate photometric units from radiometric units. In relation to the light intensity as the basic unit of photometry, its definition does not provide any reference to the spectral light sensitivity function.

Properties such as color rendering index , color temperature and light color are also used for the photometric evaluation of light sources. In addition, radiation characteristics and the degree of efficiency of luminaires , light sources and light-emitting diodes are a useful assessment parameter.

### astronomy

In astronomy there are other photometric systems that are not based on the sensitivity curve of the eye, but on the physical properties of the star spectra .

measures the strength of the radiation over a wide range of wavelengths . The most common methods measure through three or four filters (UBV: Ultraviolet, Blue, Visual, or uvby: ultraviolet, violet, blue, yellow) and use this to determine the parameters of a star ( spectral type ). The magnitude differences of the individual filter measurements are referred to as colors, UB or BV, which are often plotted as a color-brightness diagram (see also color index ).
In narrow band photometry
only areas of individual spectral lines are measured in order to determine their strengths without recording a spectrum , which would be far more complex. However, this only works with strong absorption lines and line emission spectra without a (strong) continuous component, such as the spectra of planetary nebulae .

For historical reasons, astronomy uses magnitude as a unit .

## Photometric quantities

In photometry, light is not only evaluated according to its physical performance or energy, but rather the physiological perception of brightness of the human eye is taken as a basis. They are therefore photobiological quantities. The corresponding quantities in radiometry , on the other hand, describe electromagnetic radiation independently of physiology. If a radiometric quantity is given, the corresponding photometric quantity can be determined by weighting the radiometric quantity wavelength by wavelength with the light sensitivity curve of the human eye.

### Luminous flux

The luminous flux indicates how much visible light a light source emits or an illuminated object receives per unit of time. ${\ displaystyle \ Phi _ {\ mathrm {v}}}$

It corresponds to the radiation power (radiation flux) of the emitted electromagnetic radiation (measured in watts ), weighted with the sensitivity of the human eye. This sensitivity to light is strongly dependent on the wavelength of the radiation; it has its maximum in green light of λ = 555 nm. The conversion factor from radiant power to luminous flux is the photometric radiation equivalent . The luminous flux results from the radiant power according to ${\ displaystyle \ Phi _ {\ mathrm {e}}}$ ${\ displaystyle \ lambda}$ ${\ displaystyle K (\ lambda)}$

 ${\ displaystyle \ Phi _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle \ int K (\ lambda) \ {\ frac {\ mathrm {d} \ Phi _ {\ mathrm {e}} (\ lambda)} {\ mathrm {d} \ lambda}} \ \ mathrm {d } \ lambda}$ (general), ${\ displaystyle =}$ ${\ displaystyle K (\ lambda) \ cdot \ Phi _ {\ mathrm {e}}}$ (for monochromatic light, so only one wavelength).

In the international system of units, a separate unit of measurement is used for luminous flux , the lumen (lm) and not the watt , in order to make it clear that this is not an objective, physical, but an empirical, photobiological quantity.

### Light intensity

The luminous intensity describes the luminous flux that is emitted by the entire light source in a certain direction. It is defined as the luminous flux per element of the solid angle${\ displaystyle I _ {\ mathrm {v}}}$ ${\ displaystyle \ Omega}$

 ${\ displaystyle I _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ mathrm {d} \ Phi _ {\ mathrm {v}}} {\ mathrm {d} \ Omega}}}$ (general), ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ Phi _ {\ mathrm {v}}} {\ Omega}}}$ (with isotropic radiation).

It is given in the SI unit candela (1 cd = 1 lm / sr ). If the light beam covers the full solid angle, is . A light source that radiates the luminous flux isotropically into the full solid angle therefore has a luminous intensity of . If the luminous flux is emitted in a smaller solid angle, for example in a headlight , the light intensity in this direction is correspondingly greater. ${\ displaystyle \ Omega = 4 \ pi \, \ mathrm {sr}}$${\ displaystyle \ Phi _ {\ mathrm {v}} = 1 \, \ mathrm {lm}}$ ${\ displaystyle I _ {\ mathrm {v}} = {\ tfrac {1} {4 \ pi}} \, \ mathrm {cd}}$

### Illuminance

The illuminance is a variable on the receiver side. It describes the surface density of the luminous flux that falls on the illuminated surface - for example, the illumination of a workplace or a cinema screen. It is defined as the luminous flux through the surface element on the receiver side: ${\ displaystyle E _ {\ mathrm {v}}}$${\ displaystyle A}$

 ${\ displaystyle E _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ mathrm {d} \ Phi _ {\ mathrm {v}}} {\ mathrm {d} A}}}$ (general), ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ Phi _ {\ mathrm {v}}} {A}}}$ (with even distribution of the luminous flux over the illuminated area).

From this follows the photometric law of distance , according to which the illuminance decreases with the square of the distance from the light source:

 ${\ displaystyle E _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle {\ frac {I _ {\ mathrm {v}}} {r ^ {2}}}}$ (when the light hits the illuminated surface perpendicularly).

The illuminance is given in the SI unit lux (1 lx = 1 lm / m 2 ).

### Specific light emission

The specific light emission is the surface density of the luminous flux on the side of the transmitter. It makes a statement about which luminous flux is emitted by a given part of the light source surface in all directions: ${\ displaystyle M _ {\ mathrm {v}}}$

 ${\ displaystyle M _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ mathrm {d} \ Phi _ {\ mathrm {v}}} {\ mathrm {d} A}}}$ (general), ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ Phi _ {\ mathrm {v}}} {A}}}$ (with uniform radiation of the luminous flux from the surface of the light source).

Like the illuminance, it is given in the SI unit lm / m 2 . The name "Lux" may not be used in this context.

### Luminance

The definition of luminance essentially corresponds to that of luminous intensity. While the light intensity directed in a certain direction includes all light rays sent by the light source in this direction, the luminance only takes into account the rays emitted in this direction and by a certain surface element. ${\ displaystyle L _ {\ mathrm {v}}}$

The luminance is defined as the quotient of the luminous flux passing through the surface in the direction (or incident) and the product of the solid angle penetrated by the beam and the projection of the surface onto a plane perpendicular to the direction of emission: ${\ displaystyle L _ {\ mathrm {v}}}$${\ displaystyle A}$${\ displaystyle \ varepsilon}$${\ displaystyle \ Phi _ {\ mathrm {v}}}$${\ displaystyle \ Omega}$${\ displaystyle A \ cdot \ cos \ varepsilon}$

 ${\ displaystyle L _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ mathrm {d} I _ {\ mathrm {v}}} {\ mathrm {d} A \ cos \ varepsilon}} = {\ frac {\ mathrm {d ^ {2}} \ Phi _ {\ mathrm {v}}} {\ mathrm {d} A \ cos \ varepsilon \ cdot \ mathrm {d} \ Omega}}}$ (general), ${\ displaystyle =}$ ${\ displaystyle {\ frac {\ Phi _ {\ mathrm {v}}} {A \ cos \ varepsilon \ cdot \ Omega}}}$ (with uniform radiation from the surface of the light source isotropic in a solid angle).

The luminance determines the impression of brightness that the eye gains from the observed surface. A very small, almost point-like light source appears more “glistening” than a flat light source that emits the same luminous flux.

Luminance is a very useful calculation variable because, like luminous intensity, it remains constant on the way from the transmitter to the receiver (while, for example, the resulting illuminance decreases quadratically). If the luminance emitted from point A in the direction of point B is known, then the luminance arriving at B from the direction of A is also known, namely it is the same. For details, see the explanations on the basic photometric law .

The SI unit of luminance is cd / m 2 .

### Amount of light

The amount of light is the electromagnetic radiation energy , weighted with the light sensitivity curve , which was emitted by a light source or absorbed by an object within a certain period of time. It is therefore added up (integrated) equal to the luminous flux over the considered time interval : ${\ displaystyle Q _ {\ mathrm {v}}}$ ${\ displaystyle Q _ {\ mathrm {e}}}$${\ displaystyle \ Phi _ {\ mathrm {v}}}$${\ displaystyle \ Delta t}$

 ${\ displaystyle Q _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle \ int _ {\ Delta t} \ Phi _ {\ mathrm {v}} \ cdot \ mathrm {d} t}$ (general), ${\ displaystyle =}$ ${\ displaystyle \ Phi _ {\ mathrm {v}} \ cdot \ Delta t}$ (with constant lighting over time).

The amount of light is given in lumen seconds (lm · s).

### exposure

The exposure describes the surface density of the total amount of light that fell on the illuminated surface during a given lighting period (or: exposure time). For example, it is decisive for the extent to which a photographic film is blackened in the exposed area: halving the illuminance can be compensated for by doubling the exposure time. ${\ displaystyle H _ {\ mathrm {v}}}$

The exposure is defined as the product of the illuminance and the duration of the lighting process: ${\ displaystyle H _ {\ mathrm {v}}}$${\ displaystyle E _ {\ mathrm {v}}}$${\ displaystyle \ Delta t}$

 ${\ displaystyle H _ {\ mathrm {v}}}$ ${\ displaystyle =}$ ${\ displaystyle \ int _ {\ Delta t} {\ frac {\ mathrm {d} \ Phi _ {\ mathrm {v}}} {\ mathrm {d} A}} \ cdot \ mathrm {d} t = \ int _ {\ Delta t} E _ {\ mathrm {v}} \ cdot \ mathrm {d} t}$ (general), ${\ displaystyle =}$ ${\ displaystyle E _ {\ mathrm {v}} \ cdot \ Delta t}$ (with constant lighting over time), ${\ displaystyle =}$ ${\ displaystyle {\ frac {Q _ {\ mathrm {v}}} {A}}}$ (with uniform exposure of area A).

It is given in the SI unit lux second (lx s).

The following table compares the radiometric quantities and the corresponding photometric quantities:

 radiometric quantity Symbol a) SI unit description photometric equivalent b) symbol SI unit Radiant flux radiant power, radiant flux, radiant power ${\ displaystyle \ Phi _ {\ mathrm {e}}}$ W ( watt ) Radiant energy through time Luminous flux luminous flux, luminous power ${\ displaystyle \ Phi _ {\ mathrm {v}}}$ lm ( lumens ) Radiant intensity irradiance, radiant intensity ${\ displaystyle I _ {\ mathrm {e}}}$ W / sr Radiation flux through solid angles Luminous intensity luminous intensity ${\ displaystyle I _ {\ mathrm {v}}}$ cd = lm / sr ( candela ) Irradiance irradiance ${\ displaystyle E _ {\ mathrm {e}}}$ W / m 2 Radiation flux through the receiver surface Illuminance illuminance ${\ displaystyle E _ {\ mathrm {v}}}$ lx = lm / m 2 ( lux ) Specific radiation emission current density, radiant exitance ${\ displaystyle M _ {\ mathrm {e}}}$ W / m 2 Radiation flux through the transmitter surface Specific light emission luminous exitance ${\ displaystyle M _ {\ mathrm {v}}}$ lm / m 2 Radiance radiance, radiance, radiance ${\ displaystyle L _ {\ mathrm {e}}}$ W / m 2 sr Radiant intensity through effective transmitter area Luminance luminance ${\ displaystyle L _ {\ mathrm {v}}}$ cd / m 2 Radiant energy amount of radiation, radiant energy ${\ displaystyle Q _ {\ mathrm {e}}}$ J ( joules ) by radiation transmitted energy Amount of light luminous energy, quantity of light ${\ displaystyle Q _ {\ mathrm {v}}}$ lm · s Irradiation irradiation, radiant exposure ${\ displaystyle H _ {\ mathrm {e}}}$ J / m 2 Radiant energy through the receiver surface Exposure luminous exposure ${\ displaystyle H _ {\ mathrm {v}}}$ lx s Radiation yield radiant efficiency ${\ displaystyle \ eta _ {\ mathrm {e}}}$ 1 Radiation flux through absorbed (mostly electrical) power Luminous efficiency (overall) luminous efficacy ${\ displaystyle \ eta _ {\ mathrm {v}}}$ lm / W
a)The index "e" is used to distinguish it from the photometric quantities. It can be omitted.
b)The photometric quantities are the radiometric quantities, weighted with the photometric radiation equivalent K , which indicates the sensitivity of the human eye.

### other sizes

Other quantities used in photometry are

## Historical

The Visual photometry is forerunner of today photometry.

## literature

• Lange, Zdeněk: Photometric analysis . Verlag Chemie, Weinheim 1980, ISBN 3-527-25853-1 .
• Noboru Ohta, Alan R. Robertson: Colorimetry: Fundamentals and Applications , Wiley-IS & T Series, West Sussex 2006, ISBN 978-0-470-09473-0 .
• DIN 5032-1: Light measurement - Part 1: Photometric methods . Beuth Verlag, Berlin 1999.
• Michael K. Shepard: Introduction to Planetary Photometry. Cambridge University Press, Cambridge 2017, ISBN 978-1-107-13174-3 .