Microwave-Radiometer

Figure 1: History of cosmic background radiation measurements. Left: microwaveinstruments, right: background radiation as seen by the corresponding instrument.Picture: NASA/WMAP Science Team.

1 IntroductionThe term microwaves refers to alternating electromagnetic signals with frequen-cies between 300 MHz and 300 GHz (wavelengths 1 mm to 1 m). Because of thelong wavelengths, compared to the visible and infrared, microwaves have specialproperties that can be used for many applications. Thanks to the long wavelengthmicrowaves can penetrate through cloud cover, haze, dust, and even rain as theyare less susceptible to atmospheric scattering. In addition, various molecules andatoms resonances occur in the microwave range. The majority of microwave ap-plications can be found in communication systems, radar systems, environmentalremote sensing, and medical systems. An incomplete list of applications:

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Figure 2: Examples of microwave applications. Top left: A-Train, satellite instru-ments allow a comprehensive picture of Earth weather and climate (Picture: NASA).Top right: Cosmic background imager with its 13 radio antennas located in the At-acama dessert, Chile (Picture: CBI/Caltech/NSF). Middle left: Arctic ozone loss in2011 as measured by Aura MLS (Picture NASA). Middle right: Antenna of. Bottomleft: Stockhorn panorama seen in microwave range by SPIRA and in visible range.Bottom right: Example of an active millimeter wave scanner used to detect concealedobjects.

• Mobile communication (WLAN...)

• GPS

• Remote sensing of the atmosphere, the earth, space (astronomy)

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• Radar systems for military, commercial and scientific use

As an example of space applications the history of the measurement of the cosmicbackground radiation is illustrated in Fig. 1. Further examples are presented inFig. 2.

The main aims of this experiment are:

• Become familiar with the basics of radiative transfer, microwave radiometryand receiver techniques.

• Measure the brightness temperatures of the sky around the 22 GHz emis-sion line of water vapor, the brightness temperature of a person and thetransmission of different materials.

The student should write a report answering the theoretical questions, describ-ing the radiometer and the experiments as well as discussing the results.

2 Theory

2.1 RadiometryDescribe the receiver setup and working principle of the prakti microwave ra-diometer (Fig. 3 and 6) and discuss with help of the advised literature (mainly [1]ch. 1, [2] ch. 13) the following terms and questions:

• The mixing principle. Why is mixing necessary?

• Square-law detector. Which physical quantity is actually measured?

• Describe the relationship between noise power and noise temperature.

• Explain system noise temperature, receiver noise temperature, antenna tem-perature.

• Antenna pattern. Definition, Illustration? Explain that the directivity D =4πAe/λ

2 , with Ae the effective aperture area and λ the wavelength.

• Sensitivity. What determines the sensitivity of a radiometer (radiometerformula)?

• Calibration. How is a radiometer calibrated (hot-cold calibration)?

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A/D

detector

amplifierLow noise

synth

x2Freq. doubler/amplifier

Noise diode

Attenuator

LO

temp. sensorWaveguide load,

card

USB Analog

Antenna

Amplifier

Mixer Filter

RF IF

Mech. switch

Figure 3: Blockdiagram of the radiometer. The dashed lines indicate that the syn-thesizer is external. Together with an active frequency doubler it provides the LOsignal.

2.2 Radiative TransferShortly discuss the Radiative Transfer equation and its solution. The followingterms should be explained:

• Emission and absorption.

• Brightness temperature. Physical temperature. Emissivity.

• Optical depth/opacity (t = e−τ = e−kαl)

• Airmass factor. Assume a plane-parallel atmosphere with horizontally strat-ified temperature. Explain the relation between brightness temperature TBand cos(θ)−1 (see Fig. 4 for illustration).

Radiative transfer determines the signal measured with the prakti microwaveradiometer. Fig. 5 shows the frequency dependant brightness temperature in themicrowave region for two different situations, a humid and a dry one. An otherexample showing the dependence of the brightness temperature on frequency aswell as on the observation angle can be found in Fig. 13.6 of [2]. The praktiradiometer is operated in the vicinity of the 22.235 GHz water vapor line.

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Figure 4: Geometry of sky observation. T0 is the background temperature, Tm is themean temperature of the atmosphere and θ is the zenith angle.

3 ExperimentThe measurements are performed with the radiometer shown in Fig. 6. Section3.1 presents practical hints on how to use the prakti radiometer and section 3.2 ex-plains how to do a tipping curve measurement for the calibration of the radiometer.The measurements to be performed are given in sections 3.3 to 3.5.

3.1 Information and practical hints• The measurements are made on the roof terrace of the building and should

be performed under clear sky conditions since clouds affect the measure-ments.

• The noise power of the microwave components and especially the gain ofthe amplifier is strongly temperature dependent. To reduce large gaindrifts,the radiometer should be switched on at least 1 hour before the actual mea-surements. This gives enough time for the radiometer to reach thermal equi-librium.

• An external synthesizer in combination with a frequency doubler and ampli-fier is used as a local oscillator (LO). The LO frequency is twice the selectedsynthesizer frequency. The measurements can be performed around 18,20, 22, 24 and 26 GHz.

• The mechanical waveguide switch allows to measure the signal from theantenna or to switch to an internal calibration load which acts as a blackbodysource. Two calibration loads are coupled to it. A noise diode, followedby an attenuator [no. 3 and 4 of Fig. 6], and a matched waveguide load[no. 5 of Fig. 6]. The matched waveguide load is a blackbody at ambient

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Figure 5: Intercomparison of brightness temperature spectra calculated from RS-92radiosonde measurements at Thun and coincident brightness temperatures observedby ground-based microwave radiometers at Bern (black plus symbols at 21, 22 and31 GHz and narrow O3 line profiles at 142 GHz). The red line denotes the bright-ness temperature spectrum of a humid summer day, while the blue line denotes thespectrum of a dry winter day. Values of integrated water vapor (IWV) and integratedliquid water (ILW) are given in the legend. Both figure and text taken from [3]

temperature, which is measured by the temperature sensor [and defined inthe measurement software as Tref].

• An inclinometer is installed inside the receiver box, to determine the eleva-tion of the radiometer. For observation angles close to zenith the inclinome-ter returns nan (not a number).

• The gain of the instrument changes over time. Therefore, it is important toassure that all measurements used for one calibration are performed consec-utively. Especially at 18 GHz the instrument has limited stability.

Measurement software:There is a Labview program on the laptop to facilitate the measurement and storethe data. First, initialize the data acquisition card by double clicking on the icon’RM Praktikum Init’ on the Desktop, and then ’Refresh’. Then, open in the folderPraktikum/Software the Labview program ’Praktikum.vi’. For the measurements:

1. Indicate the file path by pressing the yellow folder button and choosing thefile. ASCII files are generated.

2. Start the software by pressing on the white arrow on the top left.

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3. Start the measurement by pressing the START button.

4. To stop the measurement, press the STOP button long enough till the green’Measuring’ led switches off. Alternatively you can perform measurementswith fixed integration time by pressing the NEXT button.

5. To stop the software, press the End Program on the top right.

6. Do not save any changes.

7. To be able to see the elevation angle of the radiometer when not measuringyou can run ’elevation continuous.vi’.

In the ASCII file, tab-separated variables are stored, such as the detector output,the elevation, temperature of the waveguide load and time. On the front panel youcan choose antenna on/off (0/1 in the file), noise diode on/off (1/0 in the file) andthe LO-frequency. These values are not used to control but only written into thefile to make data analysis easier. Make sure that your choices are in agreementwith your measurement set up (that means the real switches should agree with theones in Labview)!

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Figure 6: The frontend of the microwave radiometer. The numbers are explained intable 1.

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Table 1: Numbers identifying the different components of the front end (Fig. 6).

1 : Antenna2 : Mechanical switch3 : Noise diode4 : Attenuator (not used)5 : Waveguide load + temperature sen-

sor6 : Amplifier at RF7 : Mixer8 : Filter9 : Amplifier at IF10 : Frequency doubler + amplifier11 : Input from synthesizer12 : Detector and amplifier13 : A/D card14 : Inclinometer

3.2 How to do a tipping curveYou need to calibrate the output voltage to get the brightness temperature of theatmosphere. The knowledge gained in the theoretical part should help you. Somehints on how to calibrate the instrument using tipping curve measurements aregiven here.

A tipping curve is a series of measurements of the sky Uk under differentzenith angles θk. The aim of a tipping curve is to determine the opacity. Withthis information it is possible to determine the brightness temperature of the skyat zenith direction which can be used as a cold calibration target. Starting fromthe radiative transfer equation in the microwave region under the assumption of aone layered atmosphere with a mean temperature Tm, the brightness temperatureunder an zenith angle θ is given by

Tb(θ) = T0e−τ(θ) + (1 − e−τ(θ))Tm. (1)

T0 is the cosmic background radiation (= 2.7 K) and Tm is the mean temperatureof the atmosphere. Tm can be estimated from the ground temperature Tground

Tm ≈ Tground − 10K. (2)

In addition to the sky measurement the hot calibration target is measured (Uhot,switch to noise diode, turn noise diode off (measure Tamb)). As cold calibration

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target (Ucold) the sky at a high elevation angle is measured. The opacity can befound by iteration. The iteration starts with an initial estimation of the opacity τi(e.g. τi = 0.3). The iteration process works as follows:

• Tb,cold is calculated using equation (1) and inserting τi

• For zenith angles θ the tipping measurements are calibrated.

Tb,θ =Uθ − UhotUhot − Ucold

(Thot − Tb,cold) + Thot (3)

• With the calibrated measurements the opacities can be calculated solvingequation (1):

τθ = ln

(Tm − T0Tm − Tb,θ

)(4)

• The slope of a linear regression of the opacities τθ against the airmass factorsis equal to the new zenith opacity τ since it airmass A(90◦ ) = 1. τ is takenas the new τi.

The iteration steps are repeated until the offset of the linear regression is smallerthan 10−2. The linear fit has to pass through the origin because the opacity forzero airmass has to be zero.

The zenith opacity found by iteration is used to calculate the brightness tem-perature of the cold calibration load Tb,cold. With the brightness temperatures ofthe hot and the cold calibration load a hot-cold calibration can be performed.

3.3 Airmass and brightness temperature of the skyVerify the relation between brightness temperature of the atmosphere and cos(θ)−1

by performing an elevation scan (making measurements of the atmosphere underdifferent zenith angles). Plot the brightness temperature versus airmass. Adjustthe elevation angle step size in order to get a uniform spacing in airmass. Usetipping curve calibration. The antenna HPBW is 10◦ .

Determine the brightness temperatures of the sky at one elevation and 5 dif-ferent frequencies (18, 20, 22, 24 and 26 GHz) and plot them against frequency.Discuss the relation of the measured Tb with physical temperatures of the atmo-sphere (Hint: use RTE). Repeat the measurements with a perspex (plexiglas), astyrofoam and a glass plate in front of the antenna. Discuss the characteristicsof the materials (transmittance, opacity). In addition, determine the brightnesstemperature of a person.

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3.4 Calibration of the noise diodeThe noise diode in combination with the attenuator is an internal load with un-known noise temperature.

Determine the brightness temperature of the noise diode by a tipping curvecalibration (at 18, 20, 22, 24 and 26 GHz).

3.5 Receiver Noise Temperature and Radiometer noise formulaDetermine the receiver noise temperature of the radiometer (Trec). Describe yourcalculations in detail. Prove the sensitivity relation by performing a series ofmeasurements and compare the noise levels with different integration times tintby plotting ∆T/T versus tint (T = Tsys). Hint: choose 1/16 s integration time.

References[1] Michael A. Janssen, ed.: Atmospheric remote sensing by microwave radiom-

etry, Wiley & Sons, New York, 1993, XKF 201

[2] David M. Pozar: Microwave Engineering, Wiley & Sons, 2005

[3] Klemens Hocke et al.: A complete long-term series of integrated watervapour from ground-based microwave radiometers, International Journal ofRemote Sensing, Vol. 32, No. 3, 10 February 2011, 751-765

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