92:
processes that govern light emission are such that these photons are emitted from the laser at random times; but the many billions of photons needed to create a spot are so many that the brightness, the number of photons per unit of time, varies only infinitesimally with time. However, if the laser brightness is reduced until only a handful of photons hit the wall every second, the relative fluctuations in number of photons, i.e., brightness, will be significant, just as when tossing a coin a few times. These fluctuations are shot noise.
150:
20:
2308:
1058:
from point A to point B every nanosecond. During the first half of a nanosecond we would expect 50 electrons to arrive at point B on the average, but in a particular half nanosecond there might well be 60 electrons which arrive there. This will create a more negative electric charge at point B than average, and that extra charge will tend to
335:. However, shot noise is temperature and frequency independent, in contrast to Johnson–Nyquist noise, which is proportional to temperature, and flicker noise, with the spectral density decreasing with increasing frequency. Therefore, at high frequencies and low temperatures shot noise may become the dominant source of noise.
1643:, shot noise describes the fluctuations of the number of photons detected (or simply counted in the abstract) because they occur independently of each other. This is therefore another consequence of discretization, in this case of the energy in the electromagnetic field in terms of photons. In the case of photon
1062:
the further flow of electrons from leaving point A during the remaining half nanosecond. Thus the net current integrated over a nanosecond will tend more to stay near its average value of 100 electrons rather than exhibiting the expected fluctuations (10 electrons rms) we calculated. This is the case
1057:
While this is the result when the electrons contributing to the current occur completely randomly, unaffected by each other, there are important cases in which these natural fluctuations are largely suppressed due to a charge build up. Take the previous example in which an average of 100 electrons go
91:
Shot noise exists because phenomena such as light and electric current consist of the movement of discrete (also called "quantized") 'packets'. Consider light—a stream of discrete photons—coming out of a laser pointer and hitting a wall to create a visible spot. The fundamental physical
1655:
can the number of photons measured per unit time have fluctuations smaller than the square root of the expected number of photons counted in that period of time. Of course there are other mechanisms of noise in optical signals which often dwarf the contribution of shot noise. When these are absent,
83:
such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a
137:
The term can also be used to describe any noise source, even if solely mathematical, of similar origin. For instance, particle simulations may produce a certain amount of "noise", where because of the small number of particles simulated, the simulation exhibits undue statistical fluctuations which
326:
electrons per second; even though this number will randomly vary by several billion in any given second, such a fluctuation is minuscule compared to the current itself. In addition, shot noise is often less significant as compared with two other noise sources in electronic circuits,
1789:
358:, so that one sixth of the time less than 90 electrons would pass a point and one sixth of the time more than 110 electrons would be counted in a nanosecond. Now with this small current viewed on this time scale, the shot noise amounts to 1/10 of the DC current itself.
138:
don't reflect the real-world system. The magnitude of shot noise increases according to the square root of the expected number of events, such as the electric current or intensity of light. But since the strength of the signal itself increases more rapidly, the
1907:
1086:
In other situations interactions can lead to an enhancement of shot noise, which is the result of a super-poissonian statistics. For example, in a resonant tunneling diode the interplay of electrostatic interaction and of the density of states in the
1587:
1675:, and is directly measurable when it dominates the noise of the subsequent electronic amplifier. Just as with other forms of shot noise, the fluctuations in a photo-current due to shot noise scale as the square-root of the average intensity:
1074:
However this reduction in shot noise does not apply when the current results from random events at a potential barrier which all the electrons must overcome due to a random excitation, such as by thermal activation. This is the situation in
1025:
is characterized by an ideal transmission in all open channels, therefore it does not produce any noise, and the Fano factor equals zero. The exception is the step between plateaus, when one of the channels is partially open and produces
876:
728:
244:
1806:
of the quantised electromagnetic field, or to the discrete nature of the photon absorption process. However, shot noise itself is not a distinctive feature of quantised field and can also be explained through
1418:
617:
1681:
2312:
1164:
1477:
1243:
1351:
1094:
Shot noise is distinct from voltage and current fluctuations expected in thermal equilibrium; this occurs without any applied DC voltage or current flowing. These fluctuations are known as
338:
With very small currents and considering shorter time scales (thus wider bandwidths) shot noise can be significant. For instance, a microwave circuit operates on time scales of less than a
1102:
temperature of any resistive component. However both are instances of white noise and thus cannot be distinguished simply by observing them even though their origins are quite dissimilar.
1293:
170:
about its mean, and the elementary events (photons, electrons, etc.) are no longer individually observed, typically making shot noise in actual observations indistinguishable from true
435:
88:, one can show that the relative fluctuations reduce as the reciprocal square root of the number of throws, a result valid for all statistical fluctuations, including shot noise.
1007:
At finite temperature, a closed expression for noise can be written as well. It interpolates between shot noise (zero temperature) and
Nyquist-Johnson noise (high temperature).
1647:, 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
1470:
283:
932:
261:
due to other sources are more likely to dominate over shot noise. However, when the other noise source is at a fixed level, such as thermal noise, or grows slower than
882:
314:). Because the electron has such a tiny charge, however, shot noise is of relative insignificance in many (but not all) cases of electrical conduction. For instance 1
1002:
969:
758:
516:
146:(considering only shot noise) increases anyway. Thus shot noise is most frequently observed with small currents or low light intensities that have been amplified.
1671:
used in the Geiger mode, where individual photon detections are observed. However the same noise source is present with higher light intensities measured by any
640:
536:
478:
458:
379:
361:
The result by
Schottky, based on the assumption that the statistics of electrons passage is Poissonian, reads for the spectral noise density at the frequency
1091:
leads to a strong enhancement of shot noise when the device is biased in the negative differential resistance region of the current-voltage characteristics.
1067:, where shot noise is almost completely cancelled due to this anti-correlation between the motion of individual electrons, acting on each other through the
774:
890:
539:
1371:
886:
648:
2119:
2196:
Thermal and Shot Noise. Appendix C. Retrieved from class notes of Prof. Cristofolinini, University of Parma. Archived on
Wayback Machine.
1019:
is characterized by low transmission in all transport channels, therefore the electron flow is
Poissonian, and the Fano factor equals one.
192:
548:
2109:
Horowitz, Paul and
Winfield Hill, The Art of Electronics, 2nd edition. Cambridge (UK): Cambridge University Press, 1989, pp. 431–2.
2838:
2487:
893:(multi-channel case). This noise is white and is always suppressed with respect to the Poisson value. The degree of suppression,
2654:
1784:{\displaystyle (\Delta I)^{2}\ {\stackrel {\mathrm {def} }{=}}\ \langle \left(I-\langle I\rangle \right)^{2}\rangle \propto I.}
2317:
542:). In the simplest case, these transmission eigenvalues can be taken to be energy independent and so the Landauer formula is
2991:
1794:
The shot noise of a coherent optical beam (having no other noise sources) is a fundamental physical phenomenon, reflecting
480:
is the average current of the electron stream. The noise spectral power is frequency independent, which means the noise is
2093:
1119:
1202:
2848:
2730:
2644:
2283:
1984:
1304:
3047:
2231:
Carmichael, H. J. (1987-10-01). "Spectrum of squeezing and photocurrent shot noise: a normally ordered treatment".
1445:
2985:
2833:
2684:
2362:
2323:
1254:
3037:
2045:
V.J. Goldman, B. Su (1995). "Resonant
Tunneling in the Quantum Hall Regime: Measurement of Fractional Charge".
1037:
1029:
A metallic diffusive wire has a Fano factor of 1/3 regardless of the geometry and the details of the material.
3027:
2518:
1182:
768:. The correct result takes into account the quantum statistics of electrons and reads (at zero temperature)
387:
3032:
2894:
2801:
1582:{\displaystyle \mathrm {SNR} ={\frac {I\cdot QE\cdot t}{\sqrt {I\cdot QE\cdot t+N_{d}\cdot t+N_{r}^{2}}}},}
2206:
3052:
2649:
2371:
1656:
however, optical detection is said to be "photon noise limited" as only the shot noise (also known as "
765:
2996:
2944:
2574:
2467:
1828:
1095:
332:
68:
118:, which describes the occurrence of independent random events, are significant. It is important in
2123:
3042:
2858:
2447:
2144:
Iannaccone, Giuseppe (1998). "Enhanced Shot Noise in
Resonant Tunneling: Theory and Experiment".
1812:
1652:
489:
264:
2781:
2716:
2679:
1298:
would be generated. Coupling this noise through a capacitor, one could supply a noise power of
896:
1196:
For a current of 100 mA, measuring the current noise over a bandwidth of 1 Hz, we obtain
2970:
2815:
2659:
1808:
1668:
1022:
974:
941:
183:
143:
2879:
2396:
2240:
2163:
2056:
2001:
1949:
1889:
736:
494:
154:
115:
85:
106:
Shot noise may be dominant when the finite number of particles that carry energy (such as
8:
2639:
2634:
2452:
2355:
2340:
1795:
1048:. The first direct measurement of their charge was through the shot noise in the current.
167:
26:
2244:
2167:
2060:
2005:
1953:
1893:
2695:
2585:
2179:
2153:
2080:
1965:
1939:
1880:
1854:
1844:
1803:
1799:
1648:
1083:
is thus commonly used as a noise source by passing a particular DC current through it.
1004:) channels produce no noise, since there are no irregularities in the electron stream.
625:
521:
463:
443:
364:
347:
175:
123:
80:
1961:
2909:
2904:
2700:
2524:
2421:
2406:
2386:
2289:
2279:
2256:
2072:
2047:
2027:
1992:
1969:
1816:
1174:
871:{\displaystyle S={\frac {2e^{3}}{\pi \hbar }}\vert V\vert \sum _{n}T_{n}(1-T_{n})\ .}
761:
56:
2183:
2084:
3002:
2975:
2949:
2529:
2462:
2426:
2327:
2248:
2171:
2064:
2017:
2009:
1957:
1897:
1110:
485:
355:
307:
153:
The number of photons that are collected by a given detector varies, and follows a
127:
2068:
84:
few throws is repeated over and over, the outcomes will fluctuate a lot. From the
2980:
2934:
2899:
2889:
2767:
2457:
2416:
2097:
1926:
1664:
1435:
1106:
1045:
1016:
96:
64:
60:
45:
2175:
2609:
2554:
2534:
2348:
2090:
1672:
1427:
1041:
938:. Noises produced by different transport channels are independent. Fully open (
346:
that would amount to only 100 electrons passing every nanosecond. According to
303:
171:
3021:
2965:
2939:
2674:
2549:
2502:
2497:
2492:
2482:
2477:
2401:
2293:
2260:
2013:
1924:
Blanter, Ya. M.; BĂĽttiker, M. (2000). "Shot noise in mesoscopic conductors".
1901:
1815:
of shot noise. Shot noise also sets a lower bound on the noise introduced by
1657:
1068:
328:
114:
in an optical device) is sufficiently small so that uncertainties due to the
723:{\displaystyle S={\frac {2e^{3}}{\pi \hbar }}\vert V\vert \sum _{n}T_{n}\ ,}
2664:
2614:
2544:
2252:
2076:
2031:
1439:
1088:
1076:
764:
result in the sense that it does not take into account that electrons obey
289:(the DC current or light level, etc.) can lead to dominance of shot noise.
178:
of shot noise is equal to the square root of the average number of events
2690:
2669:
2604:
2596:
2539:
2472:
2411:
2333:
2158:
1944:
1849:
1839:
935:
481:
119:
100:
52:
1474:
The SNR for a CCD camera can be calculated from the following equation:
253:
is very large, the signal-to-noise ratio is very large as well, and any
2580:
2564:
2559:
2391:
1876:"Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern"
343:
339:
1802:, the shot noise in the photodetector can be attributed to either the
2884:
2022:
1834:
1044:
moving at the sample edge whose charge is a rational fraction of the
302:
Shot noise in electronic circuits consists of random fluctuations of
1908:
On spontaneous current fluctuations in various electrical conductors
1875:
239:{\displaystyle \mathrm {SNR} ={\frac {N}{\sqrt {N}}}={\sqrt {N}}.\,}
1935:
1365:
1248:
If this noise current is fed through a resistor a noise voltage of
1064:
311:
107:
1811:. What the semiclassical theory does not predict, however, is the
1413:{\displaystyle P={\frac {\Phi \,\Delta t}{\frac {hc}{\lambda }}}}
354:
number of electrons in any nanosecond would vary by 10 electrons
131:
2569:
1640:
1099:
612:{\displaystyle I={\frac {e^{2}}{\pi \hbar }}V\sum _{n}T_{n}\ ,}
315:
111:
23:
19:
149:
33:
increases from left to right and from upper row to bottom row.
2791:
2752:
2745:
2442:
1186:
1109:
due to the finite charge of an electron, one can compute the
1080:
30:
1985:"Suppression of shot noise in metallic diffusive conductors"
67:
in optical devices, where shot noise is associated with the
1033:
2370:
95:
The concept of shot noise was first introduced in 1918 by
733:
commonly referred to as the
Poisson value of shot noise,
166:
For large numbers, the
Poisson distribution approaches a
518:
of the contact through which the current is measured (
2278:. Wolf, Emil. Cambridge: Cambridge University Press.
1982:
1684:
1480:
1448:
1374:
1307:
1257:
1205:
1122:
977:
944:
899:
777:
739:
651:
628:
551:
524:
497:
466:
446:
390:
367:
267:
195:
2044:
1923:
1159:{\displaystyle \sigma _{i}={\sqrt {2qI\,\Delta f}}}
1098:or thermal noise and increase in proportion to the
1783:
1581:
1464:
1412:
1345:
1287:
1238:{\displaystyle \sigma _{i}=0.18\,\mathrm {nA} \;.}
1237:
1158:
996:
963:
926:
870:
752:
722:
634:
611:
530:
510:
472:
452:
429:
373:
277:
238:
3019:
1663:Shot noise is easily observable in the case of
1442:is calculated as the square root of the signal:
1819:which preserve the phase of an optical signal.
1368:is calculated as follows, in units of photons:
1660:" or "photon noise" in this context) remains.
1346:{\displaystyle P={\frac {1}{2}}qI\,\Delta fR.}
2356:
1113:current fluctuations as being of a magnitude
1063:in ordinary metallic wires and in metal film
889:(independently the single-channel case), and
488:, which relates the average current with the
157:, depicted here for averages of 1, 4, and 10.
44:is a type of noise which can be modeled by a
1769:
1755:
1749:
1734:
817:
811:
691:
685:
418:
412:
642:is the applied voltage. This provides for
142:proportion of shot noise decreases and the
2363:
2349:
2230:
2143:
2120:"Bryant, James, Analog Dialog, issue 24-3"
1919:
1917:
1915:
1288:{\displaystyle \sigma _{v}=\sigma _{i}\,R}
1231:
1052:
2157:
2021:
1943:
1387:
1330:
1281:
1222:
1147:
235:
2273:
1983:Beenakker, C.W.J.; BĂĽttiker, M. (1992).
1873:
1189:over which the noise is considered, and
148:
18:
2839:Signal-to-interference-plus-noise ratio
2091:Description on the researcher's website
1912:
430:{\displaystyle S(f)=2e\vert I\vert \ ,}
342:and if we were to have a current of 16
99:who studied fluctuations of current in
3020:
2655:Equivalent pulse code modulation noise
1364:The flux signal that is incident on a
2344:
1619:= dark current (electrons/pixel/sec),
1596:= photon flux (photons/pixel/second),
1438:. Following Poisson statistics, the
297:
2778:(energy per symbol to noise density)
2276:Optical coherence and quantum optics
310:being the flow of discrete charges (
13:
2849:Signal-to-quantization-noise ratio
1723:
1720:
1717:
1688:
1488:
1485:
1482:
1388:
1384:
1331:
1227:
1224:
1148:
203:
200:
197:
161:
29:simulation. Number of photons per
14:
3064:
2763:(energy per bit to noise density)
2731:Carrier-to-receiver noise density
2645:Effective input noise temperature
1798:in the electromagnetic field. In
805:
679:
574:
2374:(physics and telecommunications)
2311: This article incorporates
2306:
1079:, for instance. A semiconductor
881:It was obtained in the 1990s by
484:. This can be combined with the
2986:Block-matching and 3D filtering
2834:Signal-to-noise ratio (imaging)
2685:Noise, vibration, and harshness
2324:General Services Administration
2267:
2224:
1651:below unity. Only in an exotic
1040:electric current is carried by
55:shot noise originates from the
2199:
2190:
2137:
2112:
2103:
2038:
1976:
1867:
1695:
1685:
1038:fractional quantum Hall effect
859:
840:
400:
394:
1:
2519:Additive white Gaussian noise
2069:10.1126/science.267.5200.1010
1962:10.1016/S0370-1573(99)00123-4
1860:
1608:= integration time (seconds),
1465:{\displaystyle S={\sqrt {P}}}
318:of current consists of about
292:
2895:Interference (communication)
2802:Signal-to-interference ratio
2792:Signal, noise and distortion
1359:
460:is the electron charge, and
110:in an electronic circuit or
63:. Shot noise also occurs in
7:
2650:Equivalent noise resistance
2176:10.1103/physrevlett.80.1054
1822:
1193:is the DC current flowing.
1010:
278:{\displaystyle {\sqrt {N}}}
10:
3069:
1800:optical homodyne detection
2958:
2945:Total variation denoising
2927:
2918:
2872:
2709:
2625:
2511:
2435:
2379:
2274:Leonard., Mandel (1995).
1634:
1630:= read noise (electrons).
927:{\displaystyle F=S/S_{P}}
74:
2014:10.1103/PhysRevB.46.1889
1906:English translation in:
1902:10.1002/andp.19183622304
490:transmission eigenvalues
16:Type of electronic noise
3048:Poisson point processes
2859:Contrast-to-noise ratio
2207:"Signal-to-Noise Ratio"
2146:Physical Review Letters
1804:zero point fluctuations
1653:squeezed coherent state
1053:Effects of interactions
997:{\displaystyle T_{n}=0}
964:{\displaystyle T_{n}=1}
2782:Modulation error ratio
2717:Carrier-to-noise ratio
2680:Noise spectral density
2319:Federal Standard 1037C
2313:public domain material
2253:10.1364/JOSAB.4.001588
1785:
1583:
1466:
1414:
1347:
1289:
1239:
1160:
1105:Since shot noise is a
998:
965:
928:
872:
766:Fermi–Dirac statistics
754:
724:
636:
613:
532:
512:
474:
454:
431:
375:
279:
240:
158:
81:statistical experiment
34:
3038:Electrical parameters
2997:Denoising autoencoder
2971:Anisotropic diffusion
2816:Signal-to-noise ratio
2660:Impulse noise (audio)
2575:Johnson–Nyquist noise
2463:Government regulation
2332: (in support of
2211:Teledyne Photometrics
1874:Schottky, W. (1918).
1829:Johnson–Nyquist noise
1786:
1669:avalanche photodiodes
1602:= quantum efficiency,
1584:
1467:
1415:
1348:
1290:
1240:
1161:
1096:Johnson–Nyquist noise
1023:Quantum point contact
999:
966:
929:
873:
755:
753:{\displaystyle S_{P}}
725:
637:
614:
533:
513:
511:{\displaystyle T_{n}}
475:
455:
432:
376:
333:Johnson–Nyquist noise
280:
241:
184:signal-to-noise ratio
152:
144:signal-to-noise ratio
22:
3028:Electronics concepts
2880:List of noise topics
1809:semiclassical theory
1796:quantum fluctuations
1682:
1478:
1446:
1372:
1305:
1255:
1203:
1181:is the single-sided
1120:
975:
971:) and fully closed (
942:
897:
775:
737:
649:
626:
549:
522:
495:
464:
444:
388:
365:
265:
193:
155:Poisson distribution
116:Poisson distribution
86:law of large numbers
3033:Noise (electronics)
2640:Circuit noise level
2635:Channel noise level
2245:1987JOSAB...4.1588C
2168:1998PhRvL..80.1054I
2061:1995Sci...267.1010G
2055:(5200): 1010–1012.
2006:1992PhRvB..46.1889B
1954:2000PhR...336....1B
1894:1918AnP...362..541S
1572:
1356:to a matched load.
186:(SNR) is given by:
168:normal distribution
3053:Mesoscopic physics
2696:Pseudorandom noise
2586:Quantization error
2397:Noise cancellation
2096:2008-08-28 at the
1934:(1–2). Dordrecht:
1881:Annalen der Physik
1855:Quantum efficiency
1845:Contact resistance
1817:quantum amplifiers
1781:
1649:quantum efficiency
1579:
1558:
1462:
1410:
1343:
1285:
1235:
1177:of an electron, Δ
1156:
994:
961:
934:, is known as the
924:
868:
829:
750:
720:
703:
632:
609:
592:
540:transport channels
528:
508:
470:
450:
427:
371:
348:Poisson statistics
306:, which is due to
298:Electronic devices
275:
236:
176:standard deviation
159:
130:, and fundamental
124:telecommunications
35:
3015:
3014:
3011:
3010:
2950:Wavelet denoising
2910:Thermal radiation
2905:Spectrum analyzer
2701:Statistical noise
2525:Atmospheric noise
2422:Noise temperature
2407:Noise measurement
2387:Acoustic quieting
2239:(10): 1588–1603.
1993:Physical Review B
1733:
1728:
1706:
1574:
1573:
1460:
1408:
1407:
1322:
1175:elementary charge
1154:
864:
820:
809:
716:
694:
683:
635:{\displaystyle V}
605:
583:
578:
531:{\displaystyle n}
473:{\displaystyle I}
453:{\displaystyle e}
423:
374:{\displaystyle f}
273:
230:
220:
219:
128:optical detection
3060:
3003:Deep Image Prior
2992:Shrinkage Fields
2976:Bilateral filter
2925:
2924:
2530:Background noise
2427:Phase distortion
2365:
2358:
2351:
2342:
2341:
2337:
2331:
2326:. Archived from
2310:
2309:
2298:
2297:
2271:
2265:
2264:
2228:
2222:
2221:
2219:
2217:
2203:
2197:
2194:
2188:
2187:
2161:
2159:cond-mat/9709277
2152:(5): 1054–1057.
2141:
2135:
2134:
2132:
2131:
2122:. Archived from
2116:
2110:
2107:
2101:
2088:
2042:
2036:
2035:
2025:
2000:(3): 1889–1892.
1989:
1980:
1974:
1973:
1947:
1945:cond-mat/9910158
1921:
1910:
1905:
1871:
1831:or thermal noise
1790:
1788:
1787:
1782:
1768:
1767:
1762:
1758:
1731:
1730:
1729:
1727:
1726:
1714:
1709:
1704:
1703:
1702:
1665:photomultipliers
1588:
1586:
1585:
1580:
1575:
1571:
1566:
1548:
1547:
1517:
1516:
1496:
1491:
1471:
1469:
1468:
1463:
1461:
1456:
1419:
1417:
1416:
1411:
1409:
1403:
1395:
1394:
1382:
1352:
1350:
1349:
1344:
1323:
1315:
1294:
1292:
1291:
1286:
1280:
1279:
1267:
1266:
1244:
1242:
1241:
1236:
1230:
1215:
1214:
1165:
1163:
1162:
1157:
1155:
1137:
1132:
1131:
1111:root mean square
1003:
1001:
1000:
995:
987:
986:
970:
968:
967:
962:
954:
953:
933:
931:
930:
925:
923:
922:
913:
877:
875:
874:
869:
862:
858:
857:
839:
838:
828:
810:
808:
800:
799:
798:
785:
759:
757:
756:
751:
749:
748:
729:
727:
726:
721:
714:
713:
712:
702:
684:
682:
674:
673:
672:
659:
641:
639:
638:
633:
618:
616:
615:
610:
603:
602:
601:
591:
579:
577:
569:
568:
559:
537:
535:
534:
529:
517:
515:
514:
509:
507:
506:
486:Landauer formula
479:
477:
476:
471:
459:
457:
456:
451:
436:
434:
433:
428:
421:
380:
378:
377:
372:
325:
323:
308:electric current
284:
282:
281:
276:
274:
269:
257:fluctuations in
245:
243:
242:
237:
231:
226:
221:
215:
211:
206:
3068:
3067:
3063:
3062:
3061:
3059:
3058:
3057:
3018:
3017:
3016:
3007:
2981:Non-local means
2954:
2935:Low-pass filter
2920:
2914:
2900:Noise generator
2890:Colors of noise
2868:
2775:
2771:
2760:
2756:
2705:
2627:
2621:
2601:Coherent noise
2577:(thermal noise)
2507:
2431:
2417:Noise reduction
2375:
2369:
2316:
2307:
2305:
2302:
2301:
2286:
2272:
2268:
2229:
2225:
2215:
2213:
2205:
2204:
2200:
2195:
2191:
2142:
2138:
2129:
2127:
2118:
2117:
2113:
2108:
2104:
2098:Wayback Machine
2043:
2039:
1987:
1981:
1977:
1927:Physics Reports
1922:
1913:
1888:(23): 541–567.
1872:
1868:
1863:
1825:
1763:
1742:
1738:
1737:
1716:
1715:
1710:
1708:
1707:
1698:
1694:
1683:
1680:
1679:
1637:
1629:
1618:
1567:
1562:
1543:
1539:
1497:
1495:
1481:
1479:
1476:
1475:
1455:
1447:
1444:
1443:
1436:Planck constant
1396:
1383:
1381:
1373:
1370:
1369:
1362:
1314:
1306:
1303:
1302:
1275:
1271:
1262:
1258:
1256:
1253:
1252:
1223:
1210:
1206:
1204:
1201:
1200:
1136:
1127:
1123:
1121:
1118:
1117:
1107:Poisson process
1055:
1046:electron charge
1017:Tunnel junction
1013:
982:
978:
976:
973:
972:
949:
945:
943:
940:
939:
918:
914:
909:
898:
895:
894:
891:Markus BĂĽttiker
853:
849:
834:
830:
824:
801:
794:
790:
786:
784:
776:
773:
772:
744:
740:
738:
735:
734:
708:
704:
698:
675:
668:
664:
660:
658:
650:
647:
646:
627:
624:
623:
597:
593:
587:
570:
564:
560:
558:
550:
547:
546:
523:
520:
519:
502:
498:
496:
493:
492:
465:
462:
461:
445:
442:
441:
389:
386:
385:
366:
363:
362:
321:
319:
300:
295:
268:
266:
263:
262:
225:
210:
196:
194:
191:
190:
164:
162:Signal-to-Noise
97:Walter Schottky
77:
69:particle nature
65:photon counting
61:electric charge
57:discrete nature
46:Poisson process
17:
12:
11:
5:
3066:
3056:
3055:
3050:
3045:
3043:Quantum optics
3040:
3035:
3030:
3013:
3012:
3009:
3008:
3006:
3005:
3000:
2994:
2989:
2983:
2978:
2973:
2968:
2962:
2960:
2956:
2955:
2953:
2952:
2947:
2942:
2937:
2931:
2929:
2922:
2916:
2915:
2913:
2912:
2907:
2902:
2897:
2892:
2887:
2882:
2876:
2874:
2873:Related topics
2870:
2869:
2867:
2866:
2856:
2846:
2836:
2831:
2813:
2799:
2789:
2779:
2773:
2769:
2764:
2758:
2754:
2749:
2742:
2728:
2713:
2711:
2707:
2706:
2704:
2703:
2698:
2693:
2688:
2682:
2677:
2672:
2667:
2662:
2657:
2652:
2647:
2642:
2637:
2631:
2629:
2623:
2622:
2620:
2619:
2618:
2617:
2612:
2610:Gradient noise
2607:
2599:
2594:
2589:
2583:
2578:
2572:
2567:
2562:
2557:
2555:Gaussian noise
2552:
2547:
2542:
2537:
2535:Brownian noise
2532:
2527:
2522:
2515:
2513:
2512:Class of noise
2509:
2508:
2506:
2505:
2500:
2498:Transportation
2495:
2490:
2485:
2480:
2475:
2470:
2465:
2460:
2455:
2450:
2445:
2439:
2437:
2433:
2432:
2430:
2429:
2424:
2419:
2414:
2409:
2404:
2399:
2394:
2389:
2383:
2381:
2377:
2376:
2368:
2367:
2360:
2353:
2345:
2339:
2338:
2330:on 2022-01-22.
2300:
2299:
2284:
2266:
2223:
2198:
2189:
2136:
2111:
2102:
2037:
1975:
1911:
1865:
1864:
1862:
1859:
1858:
1857:
1852:
1847:
1842:
1837:
1832:
1824:
1821:
1792:
1791:
1780:
1777:
1774:
1771:
1766:
1761:
1757:
1754:
1751:
1748:
1745:
1741:
1736:
1725:
1722:
1719:
1713:
1701:
1697:
1693:
1690:
1687:
1673:photo detector
1636:
1633:
1632:
1631:
1625:
1620:
1614:
1609:
1603:
1597:
1578:
1570:
1565:
1561:
1557:
1554:
1551:
1546:
1542:
1538:
1535:
1532:
1529:
1526:
1523:
1520:
1515:
1512:
1509:
1506:
1503:
1500:
1494:
1490:
1487:
1484:
1459:
1454:
1451:
1428:speed of light
1406:
1402:
1399:
1393:
1390:
1386:
1380:
1377:
1361:
1358:
1354:
1353:
1342:
1339:
1336:
1333:
1329:
1326:
1321:
1318:
1313:
1310:
1296:
1295:
1284:
1278:
1274:
1270:
1265:
1261:
1246:
1245:
1234:
1229:
1226:
1221:
1218:
1213:
1209:
1167:
1166:
1153:
1150:
1146:
1143:
1140:
1135:
1130:
1126:
1054:
1051:
1050:
1049:
1042:quasiparticles
1030:
1027:
1020:
1012:
1009:
993:
990:
985:
981:
960:
957:
952:
948:
921:
917:
912:
908:
905:
902:
887:Gordey Lesovik
879:
878:
867:
861:
856:
852:
848:
845:
842:
837:
833:
827:
823:
819:
816:
813:
807:
804:
797:
793:
789:
783:
780:
747:
743:
731:
730:
719:
711:
707:
701:
697:
693:
690:
687:
681:
678:
671:
667:
663:
657:
654:
631:
620:
619:
608:
600:
596:
590:
586:
582:
576:
573:
567:
563:
557:
554:
527:
505:
501:
469:
449:
438:
437:
426:
420:
417:
414:
411:
408:
405:
402:
399:
396:
393:
370:
299:
296:
294:
291:
272:
247:
246:
234:
229:
224:
218:
214:
209:
205:
202:
199:
172:Gaussian noise
163:
160:
76:
73:
15:
9:
6:
4:
3:
2:
3065:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3025:
3023:
3004:
3001:
2998:
2995:
2993:
2990:
2987:
2984:
2982:
2979:
2977:
2974:
2972:
2969:
2967:
2966:Gaussian blur
2964:
2963:
2961:
2957:
2951:
2948:
2946:
2943:
2941:
2940:Median filter
2938:
2936:
2933:
2932:
2930:
2926:
2923:
2917:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2877:
2875:
2871:
2864:
2860:
2857:
2854:
2850:
2847:
2844:
2840:
2837:
2835:
2832:
2829:
2825:
2821:
2817:
2814:
2811:
2807:
2803:
2800:
2797:
2793:
2790:
2787:
2783:
2780:
2777:
2776:
2765:
2762:
2761:
2750:
2748:
2747:
2743:
2740:
2736:
2732:
2729:
2726:
2722:
2718:
2715:
2714:
2712:
2708:
2702:
2699:
2697:
2694:
2692:
2689:
2686:
2683:
2681:
2678:
2676:
2675:Noise shaping
2673:
2671:
2668:
2666:
2663:
2661:
2658:
2656:
2653:
2651:
2648:
2646:
2643:
2641:
2638:
2636:
2633:
2632:
2630:
2624:
2616:
2613:
2611:
2608:
2606:
2603:
2602:
2600:
2598:
2595:
2593:
2590:
2588:(or q. noise)
2587:
2584:
2582:
2579:
2576:
2573:
2571:
2568:
2566:
2563:
2561:
2558:
2556:
2553:
2551:
2550:Flicker noise
2548:
2546:
2543:
2541:
2538:
2536:
2533:
2531:
2528:
2526:
2523:
2520:
2517:
2516:
2514:
2510:
2504:
2501:
2499:
2496:
2494:
2493:Sound masking
2491:
2489:
2486:
2484:
2481:
2479:
2476:
2474:
2471:
2469:
2466:
2464:
2461:
2459:
2456:
2454:
2451:
2449:
2446:
2444:
2441:
2440:
2438:
2434:
2428:
2425:
2423:
2420:
2418:
2415:
2413:
2410:
2408:
2405:
2403:
2402:Noise control
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2384:
2382:
2378:
2373:
2366:
2361:
2359:
2354:
2352:
2347:
2346:
2343:
2335:
2329:
2325:
2321:
2320:
2314:
2304:
2303:
2295:
2291:
2287:
2285:9780521417112
2281:
2277:
2270:
2262:
2258:
2254:
2250:
2246:
2242:
2238:
2234:
2227:
2212:
2208:
2202:
2193:
2185:
2181:
2177:
2173:
2169:
2165:
2160:
2155:
2151:
2147:
2140:
2126:on 2016-09-29
2125:
2121:
2115:
2106:
2099:
2095:
2092:
2086:
2082:
2078:
2074:
2070:
2066:
2062:
2058:
2054:
2050:
2049:
2041:
2033:
2029:
2024:
2019:
2015:
2011:
2007:
2003:
1999:
1995:
1994:
1986:
1979:
1971:
1967:
1963:
1959:
1955:
1951:
1946:
1941:
1937:
1933:
1929:
1928:
1920:
1918:
1916:
1909:
1903:
1899:
1895:
1891:
1887:
1884:(in German).
1883:
1882:
1877:
1870:
1866:
1856:
1853:
1851:
1848:
1846:
1843:
1841:
1838:
1836:
1833:
1830:
1827:
1826:
1820:
1818:
1814:
1810:
1805:
1801:
1797:
1778:
1775:
1772:
1764:
1759:
1752:
1746:
1743:
1739:
1711:
1699:
1691:
1678:
1677:
1676:
1674:
1670:
1666:
1661:
1659:
1658:quantum noise
1654:
1650:
1646:
1642:
1628:
1624:
1621:
1617:
1613:
1610:
1607:
1604:
1601:
1598:
1595:
1592:
1591:
1590:
1576:
1568:
1563:
1559:
1555:
1552:
1549:
1544:
1540:
1536:
1533:
1530:
1527:
1524:
1521:
1518:
1513:
1510:
1507:
1504:
1501:
1498:
1492:
1472:
1457:
1452:
1449:
1441:
1437:
1433:
1429:
1425:
1420:
1404:
1400:
1397:
1391:
1378:
1375:
1367:
1357:
1340:
1337:
1334:
1327:
1324:
1319:
1316:
1311:
1308:
1301:
1300:
1299:
1282:
1276:
1272:
1268:
1263:
1259:
1251:
1250:
1249:
1232:
1219:
1216:
1211:
1207:
1199:
1198:
1197:
1194:
1192:
1188:
1184:
1180:
1176:
1172:
1151:
1144:
1141:
1138:
1133:
1128:
1124:
1116:
1115:
1114:
1112:
1108:
1103:
1101:
1097:
1092:
1090:
1084:
1082:
1078:
1077:p-n junctions
1072:
1070:
1069:coulomb force
1066:
1061:
1047:
1043:
1039:
1035:
1031:
1028:
1024:
1021:
1018:
1015:
1014:
1008:
1005:
991:
988:
983:
979:
958:
955:
950:
946:
937:
919:
915:
910:
906:
903:
900:
892:
888:
884:
865:
854:
850:
846:
843:
835:
831:
825:
821:
814:
802:
795:
791:
787:
781:
778:
771:
770:
769:
767:
763:
745:
741:
717:
709:
705:
699:
695:
688:
676:
669:
665:
661:
655:
652:
645:
644:
643:
629:
606:
598:
594:
588:
584:
580:
571:
565:
561:
555:
552:
545:
544:
543:
541:
525:
503:
499:
491:
487:
483:
467:
447:
424:
415:
409:
406:
403:
397:
391:
384:
383:
382:
368:
359:
357:
353:
349:
345:
341:
336:
334:
330:
329:flicker noise
317:
313:
309:
305:
290:
288:
285:, increasing
270:
260:
256:
252:
232:
227:
222:
216:
212:
207:
189:
188:
187:
185:
181:
177:
173:
169:
156:
151:
147:
145:
141:
135:
133:
129:
125:
121:
117:
113:
109:
104:
102:
98:
93:
89:
87:
82:
72:
70:
66:
62:
58:
54:
49:
47:
43:
42:Poisson noise
39:
32:
28:
25:
21:
2862:
2852:
2842:
2827:
2823:
2819:
2809:
2805:
2795:
2785:
2766:
2751:
2744:
2738:
2734:
2724:
2720:
2665:Noise figure
2626:Engineering
2615:Worley noise
2591:
2545:Cosmic noise
2468:Human health
2328:the original
2318:
2275:
2269:
2236:
2232:
2226:
2214:. Retrieved
2210:
2201:
2192:
2149:
2145:
2139:
2128:. Retrieved
2124:the original
2114:
2105:
2052:
2046:
2040:
1997:
1991:
1978:
1931:
1925:
1885:
1879:
1869:
1793:
1662:
1644:
1638:
1626:
1622:
1615:
1611:
1605:
1599:
1593:
1473:
1440:photon noise
1431:
1423:
1421:
1363:
1355:
1297:
1247:
1195:
1190:
1178:
1170:
1168:
1104:
1093:
1089:quantum well
1085:
1073:
1059:
1056:
1006:
883:Viktor Khlus
880:
760:. This is a
732:
621:
439:
360:
351:
337:
301:
286:
258:
254:
250:
248:
179:
174:. Since the
165:
139:
136:
105:
101:vacuum tubes
94:
90:
78:
50:
41:
37:
36:
2691:Phase noise
2670:Noise floor
2605:Value noise
2597:White noise
2540:Burst noise
2458:Environment
2453:Electronics
2436:Noise in...
2412:Noise power
2334:MIL-STD-188
1850:Image noise
1840:Burst noise
1036:exhibiting
936:Fano factor
344:nanoamperes
120:electronics
53:electronics
3022:Categories
2959:2D (Image)
2592:Shot noise
2581:Pink noise
2565:Infrasound
2560:Grey noise
2392:Distortion
2130:2008-07-24
1861:References
340:nanosecond
304:DC current
293:Properties
249:Thus when
71:of light.
38:Shot noise
2885:Acoustics
2448:Buildings
2294:855969014
2261:1520-8540
2089:See also
2023:1887/1116
1970:119432033
1938:: 1–166.
1835:1/f noise
1813:squeezing
1773:∝
1770:⟩
1756:⟩
1750:⟨
1747:−
1735:⟨
1689:Δ
1645:detection
1550:⋅
1531:⋅
1522:⋅
1511:⋅
1502:⋅
1405:λ
1389:Δ
1385:Φ
1360:Detectors
1332:Δ
1273:σ
1260:σ
1208:σ
1183:bandwidth
1149:Δ
1125:σ
1065:resistors
847:−
822:∑
806:ℏ
803:π
762:classical
696:∑
680:ℏ
677:π
585:∑
575:ℏ
572:π
312:electrons
108:electrons
2919:Denoise
2184:52992294
2094:Archived
2085:45371551
2077:17811442
2032:10003850
1936:Elsevier
1823:See also
1366:detector
1011:Examples
255:relative
140:relative
2928:General
2921:methods
2826:,
2380:General
2241:Bibcode
2216:8 March
2164:Bibcode
2057:Bibcode
2048:Science
2002:Bibcode
1950:Bibcode
1890:Bibcode
1589:where:
1434:is the
1426:is the
1173:is the
538:labels
132:physics
112:photons
2988:(BM3D)
2710:Ratios
2570:Jitter
2521:(AWGN)
2473:Images
2292:
2282:
2259:
2233:JOSA B
2182:
2083:
2075:
2030:
1968:
1732:
1705:
1641:optics
1635:Optics
1430:, and
1422:where
1169:where
1100:Kelvin
1026:noise.
863:
715:
622:where
604:
440:where
422:
352:actual
316:ampere
182:, the
75:Origin
24:Photon
2999:(DAE)
2796:SINAD
2746:dBrnC
2687:(NVH)
2628:terms
2503:Video
2488:Ships
2483:Rooms
2478:Radio
2443:Audio
2372:Noise
2315:from
2180:S2CID
2154:arXiv
2081:S2CID
1988:(PDF)
1966:S2CID
1940:arXiv
1187:hertz
1081:diode
1060:repel
482:white
79:In a
31:pixel
27:noise
2853:SQNR
2843:SINR
2290:OCLC
2280:ISBN
2257:ISSN
2218:2022
2073:PMID
2028:PMID
1667:and
1220:0.18
1034:2DEG
350:the
331:and
320:6.24
2863:CNR
2828:SNR
2786:MER
2249:doi
2172:doi
2065:doi
2053:267
2018:hdl
2010:doi
1958:doi
1932:336
1898:doi
1886:362
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1185:in
1032:In
356:rms
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1914:^
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