Fano noise
Encyclopedia
Fano noise is a fluctuation of an electric charge obtained in a detector (in spite of constant value of the measured quantity, which is usually an energy), arising from processes in the detector.
It was first described by Ugo Fano
in 1947 (Phys. Rev. 72, p. 26–29), as a fluctuation of amount of ion pairs produced by a charged particle of high energy in a gas. The amount of the ion pairs is proportional to the energy the particle loses in the gas, but with some error - due to the Fano noise. Surprisingly, the noise is usually smaller than a Poisson distribution
noise (in which the variance
is equal to the value - note the variance is average squared distance from the expected value), showing there is an interaction between ionization acts. A Fano factor was introduced to describe it, and the factor is almost independent of the energy measured (Fano computed it to change from 0.43 to 0.47 for ionization of atomic hydrogen by electrons of energy from 1keV to 100keV). Fano expected it to be between 1/3 and 1/2 for gases, for moderate energies of ionizing particles.
The Fano noise applies as well to other processes in which an energy is converted to an electric charge - solid state detectors of charged particles and gamma radiation, and even semiconductor light detectors like image sensors. E.g. it is a limiting factor in the noise characteristics of CCD
s and CMOS
image sensor
s. The Fano factor achieveable is an important parameter of the detector material — the smaller it is the better.
It was first described by Ugo Fano
Ugo Fano
Ugo Fano was an Italian American physicist, a leader in theoretical physics in the 20th century.- Biography :Ugo Fano was born into a wealthy Jewish family in Turin, Italy...
in 1947 (Phys. Rev. 72, p. 26–29), as a fluctuation of amount of ion pairs produced by a charged particle of high energy in a gas. The amount of the ion pairs is proportional to the energy the particle loses in the gas, but with some error - due to the Fano noise. Surprisingly, the noise is usually smaller than a Poisson distribution
Poisson process
A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
noise (in which the variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
is equal to the value - note the variance is average squared distance from the expected value), showing there is an interaction between ionization acts. A Fano factor was introduced to describe it, and the factor is almost independent of the energy measured (Fano computed it to change from 0.43 to 0.47 for ionization of atomic hydrogen by electrons of energy from 1keV to 100keV). Fano expected it to be between 1/3 and 1/2 for gases, for moderate energies of ionizing particles.
The Fano noise applies as well to other processes in which an energy is converted to an electric charge - solid state detectors of charged particles and gamma radiation, and even semiconductor light detectors like image sensors. E.g. it is a limiting factor in the noise characteristics of CCD
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...
s and CMOS
CMOS
Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...
image sensor
Image sensor
An image sensor is a device that converts an optical image into an electronic signal. It is used mostly in digital cameras and other imaging devices...
s. The Fano factor achieveable is an important parameter of the detector material — the smaller it is the better.