Development and Characterization of Fully Polarimetric Noise Injection Radiometer for MIRAS Andreas Colliander∗ , Simo Tauriainen∗ , Tuomo Auer∗ , Juha Kainulainen∗ , Josu Uusitalo† , Martti Toikka‡ and Martti Hallikainen∗ ∗ Laboratory
of Space Technology, Helsinki University of Technology P.O.Box 3000, FIN-02015 HUT, Finland, Email: andreas.colliander@hut.fi † Ylinen Electronics Ltd, Teollisuustie 9A, FIN-02700 Kauniainen, Finland, Email: josu.uusitalo@ylinen.fi ‡ Toikka Engineering Ltd, Hannuntie 18, FIN-02360 Espoo, Finland, Email:
[email protected].fi is the Boltzmann’s constant; η is the impedance of the medium and Ev and Eh are the vertically and horizontally polarised electric fields. The brackets stand for infinite time average. II. O PERATION OF NIR NIR has several operational modes, but the most important for the object of this paper are the following: total power mode (NIR-TP), antenna measurement mode (NIR-A) and reference channel calibration mode (REF-CAL). Figure 1 presents a schematic diagram of the power detector output of one recever in NIR-A and REF-CAL modes. Noise temperature
Abstract— An L-band noise injection radiometer (NIR) has been designed and implemented by Helsinki University of Technology Laboratory of Space Technology for the SMOS (Soil Moisture and Ocean Salinity) mission of ESA [1]. The work is performed as a part of ESA’s MIRAS Demonstrator Pilot Project-2 (MDPP-2) under a subcontract for EADS-CASA. Other partners in the MDPP-2 NIR project are Toikka Engineering Ltd. and Ylinen Electronics Ltd. NIR will work as a part of the MIRAS (Microwave Imaging Radiometer Using Aperture Synthesis) instrument. Its main purpose is (1) to provide precise measurement of the average brightness temperature scene for absolute calibration of the MIRAS image map and (2) to measure the noise temperature level of the internal active calibration source for individual receiver calibration. The performance of NIR is a decisive factor of the MIRAS performance. The challenge in the implemented, so-called blind correlation, method is the fact that there is additional noise in the correlated signal due to using the noise injection method. The main objective of this paper is to demonstrate the feasibility of this technique.
Tna
Tna Tref
Ta Tr
Tnr Tref
Ta Tr
I. I NTRODUCTION
1/fD
1/fD
The precision of a noise injection radiometer is based on comparing the measured signal to two reference sources, the noise temperatures of which are known. This will remove the effect of the receiver gain and offset variations. The length of the noise pulse is then proportional to the antenna temperature [2]. NIR will also be used in the MIRAS array as a regular receiver unit for interferometric image creation. In addition to measuring the horizontally and vertically polarized antenna noise temperature and the calibration network noise temperature, the MDPP-2 NIR was designed to provide fully polarimetric measurement capability. The Stokes parameters are retrieved using the same correlator, which the MIRAS uses for solving the correlation for the interferometric image creation. The so-called modified Stokes parameters are defined under the Rayleigh-Jeans approximation as [3] |Ev |2 Tv 2 Th λ2 |E h| (1) T= T3 = k η 2 Ev Eh∗ , B T4 2 Ev Eh∗
NIR-A mode
REF-CAL mode
where Tv , Th , T3 and T4 are the brightness temperatures of the vertically and horizontally polarised radiation and third and fourth Stokes parameter, respectively; λ is the wavelength; kB
Fig. 1. NIR operational modes for one receiver: NIR-A mode is for measuring the antenna temperature and REF-CAL mode is for calibration of the reference channel noise-injection (which is used for MIRAS calibration network measurement). One Dicke cycle is the period 1/fD . See text for explanation of other symbols.
The NIR-A mode operation is based on the following equation Tref = τ (Ta + Tna ) + (1 − τ )Ta , (2) where Tref is the Dicke reference load noise temperature, Ta is the antenna temperature of the receiver, Tna is the noise temperature of the noise injection of the receiver and τ is the length of the noise injection as a fraction of the Dicke cycle. The REF-CAL mode follows the next rule Ta + Tna = τ (Tref + Tnr ) + (1 − τ )Tref ,
(3)
where Tnr is the noise temperature of the reference noise injection of the receiver, which is to be solved. Note that in the REF-CAL mode noise is injected during the entire antenna measurement time. This property will be used in the subsequent measurement.
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III. S OLVING S TOKES PARAMETERS A. Stokes Parameters in Total Power Measurement MIRAS measures the normalized complex correlation of two receivers using 1-bit/2-level digital correlators, which are assumed to operate on the basis of the following equations [4]
π Zk , µk = sin (4) 2 where µk is the measured correlation coefficient, k = 1 in total power mode, and Nk
1 sign x(ti ) sign y(ti ) , Zk = Nk i=1
(5)
in which x(ti ) and y(ti ) are the input signal samples of the two receivers and Nk is the number of the samples being correlated. The ideal correlation coefficient is retrieved from the measured one using the subsequent relation (e.g. [5]) Tv Th g˜1 = gF W , (6) µk = g˜k µ0 , Tv + Trv Th + Trh where Trv and Trh are the receiver noise temperatures of the v- and h-receiver, respectively, g˜1 is called the modulus term, µ0 is the ideal correlation coefficient and gF W is the fringewashing function, which describes the frequency response properties of the receivers. The third and fourth Stokes parameter can be solved using the ideal complex correlation coefficient as follows (7) T3 + jT4 = 2 Tv Th (µii + jµqi ), where the real part of the nominal correlation coefficient, µii , is the correlation between the in-phase outputs of the receivers, and the imaginary part, µqi , is the correlation between the quadrature output of the h-receiver and the in-phase output of the v-receiver. Thus the third and fourth Stokes parameters can be solved from the measured correlation coefficients as follows 2 Tv + Trv Th + Trh (µii + jµqi ) (8) T3 + jT4 = gF W Redundant correlation coefficient, the complex conjugate of the nominal, is the one in which the real part, µqq , is the correlation between the quadrature outputs and the imaginary part, µiq , is the correlation between the in-phase output of the h-receiver and the quadrature output of the v-receiver. B. Solving Stokes Parameters with Noise Injection When the Stokes parameters are to be measured during a noise injection measurement the modulus term is written so that the injected noise is taken into account in the receiver noise temperature. Thus in noise injection measurement equations (4), (5) and (6) are written with k = 1, 2, 3, 4, where indices 1 through 4 are the time steps in the Dicke cycle (see Figure 1) and are defined here as follows:
1. Antenna measurement without noise injection 2. Antenna measurement with noise injection to one channel 3. Antenna measurement with noise injection to both channels 4. Measurement of the Dicke load (zero correlation) Since µk is written for every time step, it yields with (4)
4 Nk −1 µ = sin sin (˜ gk µ0 )) (9) N k=1
from which µ0 can be solved numerically or by approximating sin−1 (˜ gk µ0 ) ≈ g˜k µ0
(10)
since µ0 is often small. The modulus terms are written for the noise injection time steps as follows Tv Th (11) g˜2 = gF W Tv + Trv + Tnv Th + Trh Tv Th g˜3 = gF W (12) Tv + Trv + Tnv Th + Trh + Tnh where Tnv and Tnh are the noise temperatures of the noise injections of the v- and h-receiver, respectively. The equations hold when the noise injection is longer in the v-receiver. If the noise injection is longer in the horizontal receiver, the subscript v is interchanged with the subscript h in (11). IV. M EASUREMENT R ESULTS The correlation measurements were carried out using the measurement setup presented in Figure 2. The idea is to be able to create a situation where NIR can see different Stokes parameters in any of its operational modes. Matched load in liquid N2
Controllable phase shifters
ϕ
H
ϕ
V
NIR
Power divider
Fig. 2. Schematic diagram of the measurement setup for the correlation measurements.
A. Calibration The MIRAS correlator has the property with which the input signals can be correlated with zeros in order to solve the correlator offset error. The quadrature error is solved using the correlation between the in-phase and quadrature channel of the receiver and the in-phase error using the correlated noise. The noise temperature emitted by the cold load was determined by measuring the cable temperature distribution with five temperature sensors. Also the physical temperatures of the power divider and phase shifters were measured. In this way the antenna temperature could be determined at all times during the measurements.
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Nominal Correlation Coefficient
Stokes Parameters (nominal) 200
0.2 0.15 8
0.1
6
0.05 qi
9 Cal
0
5
−0.05
4
−0.1 3
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1
Brightness Temperature [K]
7
T3 sim T sim 4 T3 TP T TP 4 T3 A T A 4 T3 RC T4 RC
150 100 50 0 −50
Cos Sin
−100 −150
2
−0.2 −0.2
−0.1
0 ii
0.1
−200
0.2
Fig. 3. Nominal correlation coefficient measured at different phase shifts between horizontal and vertical channels. The measurement used for offset and phase calibration is marked with text Cal. The coefficients on the outmost circle are measured in the NIR-TP mode, those on the innermost in the REFCAL mode and the ones between in the NIR-A mode.
−100 0 100 Phase Difference [deg]
Fig. 5. The measured third and fourth Stokes parameters in NIR-TP (TP), NIR-A (A) and REF-CAL (RC) operational modes and the simulated Stokes parameters (sim) with Sin and Cos functions for illustration. Stokes Parameters (redundant) 200 Brightness Temperature [K]
Redundant Correlation Coefficient 0.2 7
0.15 8
0.1
6 9
0.05 −iq
Cal
0
5
4
−0.05 −0.1
1
−0.2
50 0 −50
−0.1
Cos Sin
−100
−200
2
−0.2
Fig. 4.
100
T3 sim T sim 4 T3 TP T4 TP T3 A T4 A T RC 3 T RC 4
−150
3
−0.15
150
0 qq
0.1
−100 0 100 Phase Difference [deg]
0.2
Redundant correlation coefficient presented as in Figure 3.
B. Simulating Correlation Coefficient The results were also compared to the simulated correlation coefficient values calculated using the thoery presented in [6]. In order to do the simulation the scattering parameters of the connecting network were measured with a vector network analyser and the phase shifts of the phase shifters were determined using the correlator in-phase calibration. C. Measured Stokes Parameters Correlation coefficient was measured in different measurement modes as presented in Figures 3 and 4. The magnitudes (i.e. the radiuses) of the correlation coefficients depend on the ratio of the correlated noise and the total noise. The effect of the so-called blind correlation can be clearly seen. Furthermore the Stokes parameters were solved using the above equations yielding the results presented in Figures 5 and 6. The simulations, NIR-TP mode and NIR-A mode measurement results are close to each other, but the REF-CAL mode, in which noise is injected during the whole antenna measurement, results were more deviated. This is probably resulted in the modulus term determination. V. C ONCLUSIONS The feasibility of the so-called blind correlation method was demonstrated with measurements. The measurement technique
Fig. 6. The measured Stokes parameters using the redundant correlation coefficient. The results are presented as in Figure 5
makes the Stokes parameters highly sensitive to the modulus terms which have to be measured very accurately. Further measurements will be carried out in order to improve the accuracy of the results and to retrieve sensitivity estimates. ACKNOWLEDGMENTS The authors would like to thank Mr. Manuel Mart´ın-Neira from ESA and Mr. Joan Capdevila from EADS-CASA for valuable comments. Also Mr. Pekka Rummukainen and Mr. Kimmo Rautiainen from HUT Laboratory of Space Technology are acknowledged for help and comments. R EFERENCES [1] M. Mart´ın-Neira, J. M. Goutoule, MIRAS - A Two-dimensional Aperturesynthesis Radiometer for Soil Moisture and Ocean Salinity Observations, ESA Bull., No. 92, pp. 95-104, Nov. 1997 [2] F. Ulaby, R. Moore, A. Fung, Microwave Remote Sensing, Active and Passive, Vol.1, Fundamentals and Radiometry, Addison-Wesley Publishing Co. 1981 [3] L. Tsang, J. A. Kong R. T. Shin, Theory of Microwave Remote Sensing, John Wiley & Sons, Inc., 1999. [4] J. B. Hagen, D. T. Farley, Digital-correlation Techniques in Radio Science, Radio Science, Vol. 8, No. 8-9, pp.775-784, 1973 [5] F. Torres, A. Camps, J. Bar´a, I. Corbella, R. Ferrero, On-board Phase and Modulus Calibration of Large Aperture Synthesis Radiometers: Study Applied to MIRAS, IEEE Trans. Geosci. Remote Sensing, Vol. 34, pp. 1000-1009, July 1996 [6] I. Corbella, A. Camps, F. Torres, J. Bar´a, Analysis of Noise-Injection Networks for Interferometric Radiometer Calibration, IEEE Trans. Microwave Theory and Techniques, Vol. 48, No. 4, April 2000
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