Sources classification Radiometry relates to the measurement of the energy radiated by one or more sources in any region of the electromagnetic spectrum. As an antenna, a source, whose largest dimension is D, at a given wavelength λ of the electromagnetic radiation it emits, can be considered a point source if viewed from a distance r which is D r. If the above condition is not verified, the source is an extended source. Consider an extended surface source (source whose emission is proportional to its surface). ds is an infinitesimal element of the emitting surface and consider the radiated power within the solid angle dω along a direction r that forms an angle θ with the unit vector n normal to ds. ds θ r dω n 1
Radiometric quantities The infinitesimal power dp emitted by the element ds is proportional to dω and to the visible surface (the surface projected onto the plane normal to r, equal to r n ds = cos θ ds): dp LddS cos The coefficient of proportionality L is called radiance or total brightness of the surface at the point under consideration and at the direction specified by the angle θ. Then the radiance or total brightness is the radiated power in a given direction per unit of solid angle, by the unit of emitting surface projected onto the plane normal to the direction of emission: L d P dds cos The specific brightness or simply the brightness is the radiance per unit of bandwidth : B dl d 3 d P ddds cos
Planck's radiation law All objects, at temperatures above absolute zero, absorb and radiate energy in the form of electromagnetic waves. A blackbody absorbs all the radiation falling upon it at all wavelengths and the brightness B (W m Hz 1 rad ) of the radiation it emits is given by the Planck's radiation law: where: B hν h = 6.63 10 34 J s = Planck s constant ν = radiation frequency (Hz) c = 3 10 8 m s 1 = velocity of light c 1 k = 1.38 10 3 J K 1 = Boltzmann s constant T = blackbody temperature ( K) A blackbody is a perfect absorber (it does not reflect radiation) and a perfect radiator. 3 e hν kt 1 3
Rayleigh-Jeans radiation law In the region of radio wavelengths hv << kt, so that the denominator of the second factor of the Planck s radiation law can be replaced by the Taylor series expansion around ν = 0 truncated at the first order term and expressed by: hν e kt hν 1 1 1 kt it follows: hν kt B hν c 3 kt hν ν c kt kt λ 4
Noise temperature - Nyquist relationship Consider an antenna with effective area A e (consequently the gain G = (4π/λ ) A e ) whose beam (aperture Ω A ) intercepts an unlimited surface at a temperature T. In the region of radio wavelengths the surface emits radiation according to the Rayleigh- Jeans law, then the noise power P received by the antenna is : 1 kt P A Ω kt since in this case Ae ΩA GΩA e A 1 λ λ 4 The factor 1/ is inserted because the antenna is responsive to only one of the two polarizations of the incident radiation. The noise power at the receiver input does not change if we replace the antenna with a resistor of value equal to its radiation resistance R (to comply with adaptation) that is at the temperature T. The received noise power is directly proportional to the surface temperature and to the receiver bandwidth Δν. Accordingly, the antenna and its receiver can measure temperatures of faraway regions. 5
Noise temperature of a two-port Consider a linear two-port device with power gain G and denote by: W GN 0 GkT Δ the output noise power of the two-port in the frequency range Δν due to the noise of R G (that is the resistance of the input generator and it is at the reference temperature T 0 ); W N the output noise power of the two-port within the frequency range Δν due to the noise generated within itself (which we consider ν independent). This power can be regarded generated, rather than the two-port, by an input resistor that is considered at a temperature T such that it is W N GkTΔ. This temperature is called (punctual) noise temperature of the two-port. We define noise figure F of the two-port: F WGN W W GN N T 1 T 0 it follows: T F 1T 0 The noise figure is frequently expressed in db. 6
Total power receiver Any receiver which measures the sum of the total out noise power from the antenna and from the receiver itself is called a total power receiver. The incoming noise power to be measured is firstly amplified by a radio frequency amplifier. Follows a mixer where the input signal is mixed with that generated by a local oscillator, to obtain an output signal at intermediate frequency (IF) whose power is directly proportional to the RF power (heterodyne receiver). The IF signal (like the RF signal) is similar to a randomly modulated carrier wave. A square law detector follows (its voltage output is proportional to the noise power at its input) and an integrator that averages the detected signal. 7
Implementation of a radiometer for human microwave electromagnetic field emission detection for demonstration and low-cost We want to implement a demo equipment to check the human emission, due to Planck's radiation law, of electromagnetic fields in the microwave region. The receiver will then be able to measure the difference between the temperature of the back wall (which is supposed to be at room temperature 300 K) and that of a warm body (37 C = 310 K) crossing the receiving antenna beam. The most critical block of an equipment for microwave radiometry is the receiver. It must be low noise so that the system is very sensitive and can measure small differences in electromagnetic field or temperature. For the implementation of the receiver front-end, expensive low-noise amplifiers (LNA) are thus necessary. Since the advent of commercial television, on the consumer market are easily available low cost devices dedicated to the reception of satellite TV called LNB = Low Noise Block. LNB uses, as front-end section, a low noise amplifier. 8
Description of a LNB It is composed by a corrugated truncated cone illuminator, two orthogonal dipoles, a double low noise amplifier front-end (for the two linear polarizations), an active mixer, a very stable local oscillator (with dielectric resonator - DRO), a band pass filter, an intermediate frequency (IF) amplifier and a regulator for applied voltage. The LNB amplifies the input signal (that it is in the frequency band between 11 GHz and 1 GHz - Ku band) and converts it into the intermediate frequency (1 GHz); the overall gain of the block is about 60 db and the bandwidth Δν is about 1 GHz. 9
Features and use of the equipment At the frequency ν = 1 GHz corresponds the wavelenght (c = velocity of light): 8 c 310 λ 5 mm ν 9 1 10 By enforcing the project choice about using as front-end receiver a LNB with parabolic mirror (of diameter D = 60 cm) usually employed in satellite TV, the resulting equipment will have a spatial resolution, according to the Rayleigh criterion given by the first minimum diffraction pattern of the paraboloid: 3 λ 510 α 1. 1. 0.05 rad 3. D 6010 The Fraunhofer zone begins at a distance from the paraboloid above: D r 0.6 30 m. 0.05 10
Features and use of the equipment The manufacturer of the LNB block provides a noise figure equal to 0.5 db, corresponding to: 0. 5 10 10 F 1.1 then the receiver noise temperature T R is: 6 T K (T 0 = ambient temperature 300 K). 0 F 1 300 1.1 1 36. In absence of a person in front of the antenna, it receives the radiation emitted T R by the back wall, which is supposed at ambient temperature. Therefore, the minimum temperature detectable by the receiver is: TR TBackwall 36.6 300 ΔT K (τ = integrator time constant) min 0.1 9 Δν τ 10 10 The receiver is then able to detect the difference between the wall temperature and the temperature of the person who is in front of the paraboloid (ΔT observing system). 11
Diagram of the Planck's radiation law at 310 K the equipment operating area is shown with red dotted lines Brightness (W m - Hz -1 rad - ) 10-14 10-15 10-16 10-17 10-18 10-19 10-0 10-1 10-10 -3 10-4 10 6 10 7 10 8 10 9 10 10 10 11 10 1 10 13 10 14 10 15 10 16 Frequency (Hz) 1
System general description - A.F. section The measurement of the noise power received by the antenna is obtained by detecting the RF signal using a diode detector. The used detector was designed according to a diagram with temperature compensation. 100 pf HP 508-810 4.7 kω LNB Antenna cable (1 GHz) Input (IF signal) 100 Ω 7 pf 4.7 kω 100 pf HP 508-810 Output (DC signal) Incident radiation at 1 GHz Satellite TV line amplifier G = 0 db Detector + DC Circuit ADC PC 13
System general description - I.F. section Since the equipment must provide an only qualitative output indication, the detector can easily operate out of the quadratic region. It is then possible to increase the gain of the intermediate frequency section via a line amplifier (gain 0 db) in order to minimize the necessary D.C. amplification. This amplifier also provides the power supply to the LNB block via the antenna cable. The line amplifier is a low cost component. LNB Antenna cable (1 GHz) Incident radiation at 1 GHz Satellite TV line amplifier G = 0 db + Detector DC Circuit ADC PC 14
System general description - D.C. section The output of the detector transits first through an integrator that eliminates the rapidly varying components of the detected signal. A long time constant for this block improves the minimum detectable temperature of the receiver but does not allow the appreciation of the rapid changes in the noise power. The value of compromise was determined experimentally as 0.01 s. LNB Antenna cable (1 GHz) Incident radiation at 1 GHz Satellite TV line amplifier G = 0 db Detector + DC Circuit ADC PC 15
System general description - D.C. section The level translator, connected to the output of the integrator, consists of an adder circuit and allows to subtract (or to add), through a manual adjustment, a voltage level to the detected signal. When the equipment is detecting only the back wall radiation, it is possible to subtract to the detected output an equal level, leading to zero the indication of the measuring instrument ( off-set operation). In this way, the radiometer will measure the difference between the emission of the object that the antenna is pointing and the electromagnetic background radiation. LNB Antenna cable (1 GHz) Incident radiation at 1 GHz Satellite TV line amplifier G = 0 db Detector + DC Circuit ADC PC 16
Diagram of D.C. section +1 V From the detector 100 k 0.1 μf 3 + 100 k LM 358 5 + 1 7 6 4 8 0.1 nf 10 k To the noninverting input of the ADC 15 k Low-pass filter G = 6.6 00 k 100 k 4V7 +1 V Offset circuit G = 1.5 600 80 1 k LM336 5 V 100 0.1 nf 17
System general description - D.C. section The integrator and the off-set circuit are also used to amplify the D.C. signal before sending it to the analog-to-digital converter. LNB Antenna cable (1 GHz) Incident radiation at 1 GHz Satellite TV line amplifier G = 0 db Detector + DC circuit ADC PC 18
Display The digitized signal is displayed on PC. LNB Antenna cable (1 GHz) Incident radiation at 1 GHz Satellite TV line amplifier G = 0 db + Detector DC circuit ADC PC 19
Use as a radio telescope The receiver can also be used as a demo radio telescope. In this case, considering the cold sky at a temperature of about 40 K, we can compute the minimum detectable temperature as: ΔT min T R T ColdSky Δν τ 36.6 40 10 9 10 0.0 K Because of the small size of the paraboloid, only the largest celestial radio sources are observable, i.e. Sun, Moon and Milky Way, not yet resolved. Moreover, since the detector does not always work in the quadratic region, a quantitative measure of the temperatures is not reliable. 0