Microwave RadiometryMicrowave Radiometry

Ch6 Ulaby & LongINEL 6669Dr. X-Pol

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OutlineOutline Introduction Thermal Radiation Black body radiation

– Rayleigh-Jeans Power-Temperature correspondence Non-Blackbody radiation

– TB, brightness temperature– TAP, apparent temperature– TA, antenna temperature

More realistic Antenna– Effect of the beam shape– Effect of the losses of the antenna

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Thermal RadiationThermal Radiation

All matter (at T>0K) radiates electromagnetic energy!

Atoms radiate at discrete frequencies given by the specific transitions between atomic energy levels. (Quantum theory)– Incident energy on atom can be absorbed by it to move

an e- to a higher level, given that the frequency satisfies the Bohr’s equation.

– f = (E1 - E2) /hwhere, h = Planck’s constant = 6.63x10-34 J

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Thermal RadiationThermal Radiation

absorption => e- moves to higher level emission => e- moves to lower level

(collisions cause emission)Absortion Spectra = Emission SpectraAbsortion Spectra = Emission Spectra

atomic gases have (discrete) line spectra according to the allowable transition energy levels.

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Molecular Radiation SpectraMolecular Radiation Spectra

Molecules consist of several atoms. They are associated to a set of vibrational and

rotational motion modes.

Each mode is related to an allowable energy level.

Spectra is due to contributions from; vibrations, rotation and electronic transitions.

Molecular Spectra = many lines clustered together; not discrete but continuous.

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Atmospheric WindowsAtmospheric Windows

Absorbed(blue area)

Transmitted(white)

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Radiation by bodies Radiation by bodies (liquids - solids)(liquids - solids)Liquids and solids consist of many

molecules which make radiation spectrum very complex, continuous; all frequencies radiate.

Radiation spectra depends on how hot is the object as given by Planck’s radiation law.

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CommonTemperature -CommonTemperature -conversionconversion

90oF = 305K = 32oC 80oF = 300K = 27oC

70oF = 294K = 21oC

32oF = 273K=0oC

0oF = 255K = -18oC -280oF = 100K = -173oC

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Spectral brightness intensitySpectral brightness intensityIIff [Planck’s Law] [Planck’s Law]

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SunSun

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Solar Radiation Solar Radiation TTsunsun= = 5,800 K5,800 K

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Properties of PlanckProperties of Planck’’s Laws Law

fm = frequency at which the maximum radiation occurs

fm = 5.87 x 1010 T [Hz]where T is in Kelvins Maximum spectral Brightness Bf (fm)

If (fm) = c1 T3

where c1 = 1.37 x 10-19 [W/(m2srHzK3)]

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Problem 4.1Problem 4.1Solar emission is characterized by a blackbody

temperature of 5800 K. Of the total brightness radiated by such a body, what percentage is radiated over the frequency band between fm/2 and 2 fm, where fm is the frequency at which the spectral brightness Bf is maximum?

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Stefan-Boltzmann Stefan-Boltzmann Total brightness of body at Total brightness of body at TTTotal brightness is

20M W/m2 sr

13M W/m2 sr67%

where the Stefan-Boltzmannconstant is= 5.67x10-8 W/m2K4sr

http://energy.sdsu.edu/testcenter/testhome/javaapplets/planckRadiation/blackbody.html

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Solar powerSolar power How much solar power could ideally be

captured per square meter for each Steradian?

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Blackbody Radiation -Blackbody Radiation -given by Planckgiven by Planck’’s Laws Law

Measure spectral brightness If [Planck]

For microwaves, Rayleigh-Jeans Law, condition hf/kT<<1 (low f ) , then ex-1 x

At T<300K, the error < 1% for f<117GHz),and error< 3% for f<300GHz)

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Rayleigh-Jeans ApproximationRayleigh-Jeans Approximation

Rayleigh-Jeansf<300GHz>2.57mm)T< 300K

Mie Theory

frequency

If

Wien

KJk

sBoltzmann

/1038.1

'23

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Total power measured due Total power measured due to objects Brightness, to objects Brightness, IIff

I=Brightness=radiance [W/m2 sr]If = spectral brightness (B per unit Hz)I = spectral brightness (B per unit cm)

Fn= normalized antenna radiation pattern= solid angle [steradians]Ar=antenna aperture on receiver

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Power-Temperature correspondencePower-Temperature correspondence

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Analogy with a resistor noise Analogy with a resistor noise

Antenna Pattern

T

R

T

Analogous to Nyquist;noise power from R

Direct linear relationpower and temperature

*The blackbody can be at any distance from the antenna.

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Non-blackbody radiationNon-blackbody radiation

But in nature, we find variationswith direction, I()Isothermal medium at physical

temperature T

TB()

=>So, define a radiometric temperature (bb equivalent) TB

For Blackbody,

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Emissivity, Emissivity, ee

The brightness temperature of a material relative to that of a blackbody at the same temperature T. (it’s always “cooler”)

TB is related to the self-emitted radiation from theobserved object(s).

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Quartz versus BB at same TQuartz versus BB at same T

Emissivity depends alsoon the frequency.

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Ocean (color) visible Ocean (color) visible radiationradiation Pure Water is turquoise blue The ocean is blue because it absorbs all the other

colors. The only color left to reflect out of the ocean is blue.

“Sunlight shines on the ocean, and all the colors of the rainbow go into the water. Red, yellow, green, and blue all go into the sea. Then, the sea absorbs the red, yellow, and green light, leaving the blue light. Some of the blue light scatters off water molecules, and the scattered blue light comes back out of the sea. This is the blue you see.”

Robert Stewart, Professor

Department of Oceanography, Texas A&M University

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Apparent Temperature, Apparent Temperature, TTAPAP

Is the equivalent T in connection with the power incident upon the antenna

TB()

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Antenna Temperature, Antenna Temperature, TTAA

Noise power received at antenna terminals.

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Antenna Temperature Antenna Temperature (cont…)(cont…)Using we can rewrite as

for discrete source such as the Sun.

sunA

sunA TT

ArA

2

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Antenna Beam EfficiencyAntenna Beam Efficiency, , MM

Accounts for sidelobes & pattern shape

TA= b TML +(1- b)TSL

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Radiation Efficiency, Radiation Efficiency, ll

Heat loss on the antenna structure produces a noise power proportional to the physical temperature of the antenna, given as

TN= (1-)To

The l accounts for losses in a real antenna

TA’= TA +(1-)To

TATA’

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Combining both effectsCombining both effects

Combining both effectsTA’= b TML + (1- b)TSL+(1-)To

*where, TA’ = measured, TML = to be estimateda= scaling factorb= bias term

TML= 1/( b) TA’ + [(1- M)/ b]TSL+(1-)To/ B

TML= aTA+b

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Ej. Microwave RadiometerEj. Microwave Radiometer

K-band radiometer measures blackbody radiation from object at 200K. The receiver has a bandwidth of 1GHz. What’s the maximum power incident on the radiometer antenna?

dBW6.115108.2

)10)(200)(1038.1(

:

12

923

max

K

kTBPPAnswer

bb

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Ej. The Arecibo Observatory…Ej. The Arecibo Observatory……measured an antenna temperature of 245K when

looking at planet Venus which subtends a planar angle of 0.003o. The Arecibo antenna used has an effective diameter is 290m, its physical temperature is 300K, its radiation efficiency is 0.9 and it’s operating at 300GHz (=1cm).

what is the apparent temperature of the antenna?

what is the apparent temperature of Venus?

If we assumed lossless, what’s the error?

TA=239K

TVenus= 130K

TVenus= 136K (4% error)

)()003(.

/

)1('

:

2

2

steradians

A

TTT

Answer

venus

rA

olAlA

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Demo of Rayleigh-JeansDemo of Rayleigh-Jeans Let’s assume T=300K, f=5GHz, f=200MHz

8.0

7.7

7.4

5.0 f

Bf