The efficiency of this energy transfer is inversely proportional to the sixth power of the distance between donor and acceptor making FRET extremely sensitive to small distances.

Measurements of FRET efficiency can be used to determine if two fluorophores are within a certain distance of each other.

The FRET efficiency () is the quantum yield of the energy transfer transition, i. e. the fraction of energy transfer event occurring per donor excitation event:

The FRET efficiency depends on many parameters that can be grouped as follows:

The FRET efficiency is measured and used to identify interactions between the labeled complexes.

There are several ways of measuring the FRET efficiency by monitoring changes in the fluorescence emitted by the donor or the acceptor.

One method of measuring FRET efficiency is to measure the in acceptor emission intensity.

Since photobleaching consists in the permanent inactivation of excited fluorophores, resonance energy transfer from an excited donor to an acceptor fluorophore prevents the photobleaching of that donor fluorophore, and thus high FRET efficiency leads to a longer photobleaching decay time constant:

FRET efficiency can also be determined from the change in the fluorescence lifetime of the donor.

* Browser-based calculator to find the critical distance and FRET efficiency with known spectral overlap

* FRET Fluorescence resonance energy transfer is used to study protein interactions, detect specific nucleic acid sequences and used as biosensors, while fluorescence lifetime ( FLIM ) can give an additional layer of information.

There are also several quantitative protein phosphorylation methods, including fluorescence immunoassays, Microscale Thermophoresis, FRET, TRF, fluorescence polarization, fluorescence-quenching, mobility shift, bead-based detection, and cell-based formats.

Fluorophores can also be used to quench the fluorescence of other fluorescent dyes ( see article Quenching ( fluorescence )) or to relay their fluorescence at even longer wavelength ( see article FRET )

In fluorescence microscopy, fluorescence confocal laser scanning microscopy, as well as in molecular biology, FRET is a useful tool to quantify molecular dynamics in biophysics and biochemistry, such as protein-protein interactions, protein – DNA interactions, and protein conformational changes.

A limitation of FRET is the requirement for external illumination to initiate the fluorescence transfer, which can lead to background noise in the results from direct excitation of the acceptor or to photobleaching.

Fluorescence-lifetime imaging yields images with the intensity of each pixel determined by, which allows one to view contrast between materials with different fluorescence decay rates ( even if those materials fluoresce at exactly the same wavelength ), and also produces images which show changes in other decay pathways, such as in FRET imaging.

Since the fluorescence lifetime of a fluorophore depends on both radiative ( i. e. fluorescence ) and non-radiative ( i. e. quenching, FRET ) processes, energy transfer from the donor molecule to the acceptor molecule will decrease the lifetime of the donor.

In addition, there has been a flurry of activity extending FCS in various ways, for instance to laser scanning and spinning-disk confocal microscopy ( from a stationary, single point measurement ), in using cross-correlation ( FCCS ) between two fluorescent channels instead of autocorrelation, and in using Förster Resonance Energy Transfer ( FRET ) instead of fluorescence.

* Fluorescent methods: fluorescence resonance energy transfer ( FRET ), fluorescence correlation spectroscopy ( FCS ), total internal reflection fluorescence ( TIRF )

When the donor and acceptor are in proximity ( 1 – 10 nm ) due to the interaction of the two molecules, the acceptor emission will increase because of the intermolecular FRET from the donor to the acceptor.

When a twist or bend of the protein brings the change in the distance or relative orientation of the donor and acceptor, FRET change is observed.

FRET efficiencies can also be inferred from the photobleaching rates of the donor in the presence and absence of an acceptor.

In general, " FRET " refers to situations where the donor and acceptor proteins ( or " fluorophores ") are of two different types.

Obviously, spectral differences will not be the tool used to detect and measure FRET, as both the acceptor and donor protein emit light with the same wavelengths.

The efficiency of a heat engine relates how much useful work is output for a given amount of heat energy input.

It prevents heat loss, which in turn relates to energy loss, or decrease in the efficiency of the system.

The final theme of local government expenditures and taxes relates to urban economics as it analyzes the efficiency of the fragmented local governments presiding in metropolitan areas.

This is not to be confused with efficiency which is always a dimensionless ratio of output divided by input which for lighting relates to the watts of visible power as a fraction of the power consumed in watts.

* Optics, the electromagnetic impedance of a medium, or the quantum efficiency of detectors.

The fluorescence quantum yield gives the efficiency of the fluorescence process.

In this case one speaks of full radiative decay and this means that the quantum efficiency is 100 %.

The quantum efficiency ( QE ) is defined as the fraction of emission processes in which emission of light is involved:

where is the quantum efficiency ( the conversion efficiency of photons to electrons ) of the detector for a given wavelength, is the electron charge, is the frequency of the optical signal, and is Planck's constant.

In the case of photon detection, the relevant process is the random conversion of photons into photo-electrons for instance, thus leading to a larger effective shot noise level when using a detector with a quantum efficiency below unity.

With q as the electronic charge, is the wavelength of interest, h is Planck's constant, c is the speed of light, k is Boltzmann's constant, T is the temperature of the detector, is the zero-bias dynamic resistance area product ( often measured experimentally, but also expressible in noise level assumptions ), is the quantum efficiency of the device, and is the total flux of the source ( often a blackbody ) in photons / sec / cm².

The efficiency is due to the efficiency of the quantum Fourier transform, and modular exponentiation by squarings.

Recent research indicates that chlorophyll within plants appears to exploit the feature of quantum superposition to achieve greater efficiency in transporting energy, allowing pigment proteins to be spaced further apart than would otherwise be possible.

The efficiency of a quantum well laser is greater than that of a bulk laser because the density of states function of electrons in the quantum well system has an abrupt edge that concentrates electrons in energy states that contribute to laser action.

Further improvements in the laser efficiency have also been demonstrated by reducing the quantum well layer to a quantum wire or to a " sea " of quantum dots.

They exhibited a peak quantum efficiency of 0. 4 % at 800 nm.

The caesium-antimony photocathode had a dramatically improved quantum efficiency of 12 % at 400 nm, and was used in the first commercially successful photomultipliers manufactured by RCA ( i. e., the 931-type ) both as a photocathode and as a secondary-emitting material for the dynodes.

More recent developments in OLED architecture improves quantum efficiency ( up to 19 %) by using a graded heterojunction.

By using these phosphorescent materials, both singlet and triplet excitons will be able to decay radiatively, hence improving the internal quantum efficiency of the device compared to a standard PLED where only the singlet states will contribute to emission of light.

This results in almost double the quantum efficiency of existing OLEDs.

Considerable research has been invested in developing blue OLEDs with high external quantum efficiency as well as a deeper blue color.

External quantum efficiency values of 20 % and 19 % have been reported for red ( 625 nm ) and green ( 530 nm ) diodes, respectively.

Scintillation counters are widely used because they can be made inexpensively yet with good quantum efficiency.

The quantum efficiency of a gamma-ray detector ( per unit volume ) depends upon the density of electrons in the detector, and certain scintillating materials, such as sodium iodide and bismuth germanate, achieve high electron densities as a result of the high atomic numbers of some of the elements of which they are composed.