direct detection (incoherent detection) heterodyne ... · x 1.3mm f=230ghz 0.1km/s Δf=0.1mhz...
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Direct detection (incoherent detection)
Radiation photon
Heterodyne detection (coherent detection)
Radiation wave
cm
direct detection/heterodyne detectionapplicable
X
1.3mm f=230GHz 0.1km/sΔf=0.1MHz 0.13km/s f/Δf 2,300,000
R
VLBI 1milliarcsec
Imaging 3D imaging
Focal plane array 10-100
imaging
Heterodyne receivers (frequency conversion) 200 GHz 300 GHz
I/V
2
V2
3
3
2
210 VaVaVaai
),sin( 11 tE )sin( 22 tE
ttEE
tE
tE
cos cos
)2cos(12
)2cos(12
212121
2
2
21
2
1
Filter
down converter
up converter 2 φ
Quantum limit of Coherent detection system ΔE Δt > h/4π Heisenberg uncertainty principle
ΔE = hνΔn photon
2πνΔ = Δφ
Δφ Δn > 1/2 photon
photon G n1 photon n2=G n1
φ1 φ2
Δn1 = Δn2/G Δφ1 Δn1 > 1/2G G>1
(G-1)hν
(1-1/G)hν hν G ∞
Coherent detection
Tmin = hν/k
100GHz 5.5K; ~10^4K
Receiver/detector
Noise temperature
Noise Figure
Noise Equivalent Power
signal
noise
Device noise
device
Thermal noise, Johnson noise
Shot noise
Flicker noise, 1/f noise
background
background
/
etc.
Nyquist (thermal noise)
T R
0
<I > 0 <I^2 >≠0
thermal noise , Johnson noise
T Rhν<< kT
Pν = kT Nyquist
H. Nyquist, Phys. Rev., 32, 110-113 (1928)
hν~kT or hν>kTPlank 0 hν/2k
T R
thermal noise (Johnson noise)
white noise
Nyquist 2 R T l impedance R
= transmission line
2
ν ν+dν
2l/c dν
Boltzmann
1 1/2 kT
<kinetic E> = <potential E> 1kT ν ν+dν
2l/c kT dν
Δt = l/c
P = ½ 1/Δt 2l/c kT = KT
T R
T R
l
R
c
2n
n
l C , n = 1,2,3,…..
Shot noise, Schottky noise
2 <i s^2> I
Noise temperature
etc.
G
Tin Tin Tout
Tnoise
G
Tout
Radiative transfer
Opacityτ radiation
η
Tin
T’noise
G
Tout
Ibg
τ
Tamb
Tamb (LTE)
e-τ = η
Iout=Ibg e-τ
+ Tamb (1 - e-τ)
Tout = Tin * η
+ Tamb (1-η)
Tout = (Tin + Tnoise) * η
Tnoise = Tamb ((1/η) – 1)
η Tn
Tn = Tamb (1-η)/η
290K 50 K η=Tamb/(Tn+Tamb) 0.85
70K 70 K * (1-η)/η = 12 K
i.e.,
3000K
0.088 10%
cascade
100 dB
Q1 D = 10 m ηa = 0.6 B = 200 MHz flux density S = 1 Jy (= 10-26 [W/Hz/m2])
W
W = ½ Aeff S B
= ½ ηa π(D/2)2 S B = ? [W]
Q3 Ta K
W = k B Ta
Q2 μW
20 30dBamp
Cascade
Tin G1, Tn1
G1(Tin+Tn1)
G2, Tn2
G2(G1(Tin+Tn1) + Tn2) = G2 G1 (Tin + Tn1 + Tn2/G1)
cascade
Tn = Tn1 + Tn2(1/ G1) + Tn3 (1/ G1 G2) + Tn4 (1/ G1 G2 G3) +
G1 G2 G3
Tn1 Tn2 Tn3
Tin
Cascade
Tn = Tn1 + Tn2(1/G1) + Tn3 (1/G1 G2) + Tn4 (1/G1G2 G3) +
amplifierTn1
ex. NRO 220 GHz radiometer for adoptive phase correction
= harmonic mixer, NF = 7.5 dB (Tn = (10^(NF/10)-1) * Tamb ~ 1340 K), CL = 9.2 dB conversion loss; gain
2 = low noise amp (LNA), NF = 0.5 dB (Tn = 35 K), G = 30 dB
3 = amp, NF = 2.0 dB (Tn = 170 K), G = 30 dB
Tn = 1340 + 35*10^(CL/10) + 170*(CL/10* 1/10^3)
2 hot cold
290K LN2 78K
Tn = (Thot – Tcold Y)/Y-1
Direct detection (incoherent detection)
Radiation photon
Heterodyne detection (coherent detection)
Radiation wave
cm
direct detection/heterodyne detectionapplicable
Bolometer photon radiation
Δf/f 0.3
0.3K 0.1K
TES Bolometer: /photon incoherent detection
Absorber( ): radiation (particle)
Thermometer( ):
Thermal link( ): ( -> -> )
TES bolometer: Transition Edge Sensor(TES) bolometer
TES
Thermal
link
SiN
Au
Ti TES
TES
Ω
1275μm
=360μm
~2μm
~10nm
350GHz (0.87mm)
270
SIS
10m
total power
W = kBG (Tn + Ta)
Tn
Heterodyne hν/k
10
Tsys
Tn TRX
RX: receiver
TX: transmitter
2 black body
absorber
Ta e-τ
Ta*
total power
W = kBG (Tsys + Ta) Ta:
Nyquist
Tsys, Ta
Tsys cm Tn K10K
10K 100K 1000K<1
Heterodyne
Ta<<Tsys Tsys Ta
Determination of Ta* based on the Chopper-Wheel method
W = kBG ( Trx
+ Tatm(1-exp(-tau))
+ Ta*)
Trx: receiver noise temperature
Tatm: physical temperature of atmosphere
Ta*: antenna temperature (added power) due to observing astronomical source
Beam switching + Chopper wheel
on-sourceoff-source
Load
On-source
Won = kGB (Ta* e-τ + TRX + Tatm (1– e-τ))
Off-source
Woff = kGB (TRX + Tatm (1– e-τ))
Load
Wroom = kGB (TRX + Troom)
Ta* = {(Won–Woff)/(Wroom–Woff)} Troom
vs
/