Digital Correlation Microwave Polarimetry : Analysis and Demonstration

The design, analysis, and demonstration of a digital-correlation microwave polarimeter for use in earth remote sensing is presented. We begin with an analysis of threelevel digital correlation and develop the correlator transfer function and radiometric sensitivity. A fifth-order polynomial regression is derived for inverting the digital correlation coefficient into the analog statistic. In addition, the effects of quantizer threshold asymmetry and hysteresis are discussed. A two-look unpolarized calibration scheme is developed for identifying correlation offsets. The developed theory and calibration method are verified using a 10.7 GHz and a 37.0 GHz polarimeter. The polarimeters are based upon 1-GS/s three-level digital correlators and measure the first three Stokes parameters. Through experiment, the radiometric sensitivity is shown to approach the theoretical as derived earlier in the paper and the two-look unpolarized calibration method is successfully compared with results using a polarimetric scheme. Finally, sample data from an aircraft experiment demonstrates that the polarimeter is highly-useful for ocean windvector measurement.


I Introduction
Recent advances in the interpretation of polarimetric microwave thermal emission from the Earth's oceans and atmosphere have prompted the study of new retrieval techniques for near-surface ocean wind vectors and mesospheric temperature profiles [1]. These techniques are facilitated by a more complete characterization of the polarization characteristics of the upwelling radiation field than obtainable using conventional single-or dual-polarization radiometers.
As an example of these techniques, polarimetric measurements have been shown to greatly facilitate the retrieval of ocean surface wind direction [2,3].
The quantity used to fully describe the second-order statistics of the quasi-monochromatic

The parameters
Tv and T h can be measured using standard linearly-polarized total power radiometers [5]. Detection of the third and fourth Stokes parameters, however, requires two additional measurements to effectively perform the correlations in (1). The various types of polarimetric radiometers fall into two basic categories: adding polarimeters (AP) and direct correlating polarimeters (DCP). The adding polarimeter uses measurements of the brightness temperature of 2 at leasttwo additional polarizationstatese.g.,45°slant-linearlypolarized(T45o) andeitherleftor fight-handcircularlypolarized(Tt or Tr). From the four measured brightness temperatures and using the Stokes parameter rotational transformation [6], the third and fourth Stokes parameters can be determined, e.g.: (2) The direct correlating polarimeter estimates Tu and Tv by cross-correlating the instantaneous voltage signals of the vertical and horizontal channels.
The actual correlation can be performed by either analog or digital multiplying circuitry.
If the time-varying voltages v. (t) and vh(t) are assumed to be stationary and ergodic [7], then the covariance estimate P_h is: where r is the integration time. Since the IF voltages are related to the incident field quantities by the receiving antenna's effective area and the receiver's signal transfer characteristics, measuring /_h is equivalent to measuring TLr: where _" = _ is the correlation coefficient and T,_,su_ are the system temperatures of the ra- Several mechanisms can contribute to calibration errors in (4) and (5). Antenna cross-amount of whichmustbeknown.Onemethodfor comprehensive calibrationof thefirstthreemodified Stokes parameters usesa rotatingpolarizedcalibrationstandard [8]. Thepolarizedstandard presents to the receivera stronglypolarizedbut preciselydetermined radiationfield andallows complete determination of thegainsandoffsetsfor the first threeStokesparameters. Calibration of thefourthStokes parameter channel canbeaccomplished by insertionof anappropriate 90°shift in theRFpathusing,e.g.,aquarter waveplate [9]. Useof thepolarized standard in space, however, requiresadditionalhardware beyondthe conventional ambient andcoldblackbodystandards that arecommonlyused.
In theimplementation of(4) and (5) it is desirable todesignasystemthatrequiresaminimal amount of calibrationhardware. Whileananalogcorrelator canbeusedto determine Tu or Tv, its response will generally require the in-situ identification of relatively large leakage gains 9u_ and 9Uh from T_ and Tn, viz.: vu = 9u,,Tv + gunTh + guuTv + 9uvTv + ou (6) as well as the offset term o_. While leakage gains can be minimized by proper tuning and balancing, elimination of long term drift in detection and video components -their root cause -can be prohibitively expensive.
A solution to the above problem above of precise measurement of either Ttr or Tv can be found through digital correlation.
Here the radio-frequency (RF) or intermediate-frequency (IF) signals are sampled at the Nyquist rate, the digital samples cross-correlated using fast multiplication circuitry, and the correlation integral (4) performed via digital accumulation. Provided that the digitized signal contains no DC component and the A/D conversion is linear and unbiased, the correlation coefficient/_ can be obtained without leakage or offset. A further advantage of using a digital correlator with more than one bit (or two levels) of discretization is that in-situ calibration can be performed using only conventional ambient and cold unpolarized views, for example, an ambient blackbody target and cold space.

A Mean Statistics
The input signals to a correlator, va (t) and vb (t), are modeled as jointly-Gaussian stationary random processes with root mean square (RMS) voltages a_, and avb and correlation coefficient p = ._nzz_.
If the processes are sampled with period T at or below their Nyquist rate, then the sample sequences consist of independently and identically distributed pairs with the following joint Gaussian probability density function (pdf): The three-level quantization performed on the input signals by the A/D converter can be modeled by a nonlinear transfer function: where the quantities z_ZVtha are the threshold levels of the A/D converters (see also Figure 2), with the subscript t_ denoting either channel a or b. For typical CMOS or ECL logic, Vtha ,_ 0.05 to 0.50 volts, therefore, the necessary microwave signal power can range from -12 to +8 dBm in a standard 50 f_ system.
Thesethreestatistical parameters aremeasured by accumulation of theoutputs of a simple digital circuit such as shown in Figure 3.
The statistics of s,_^2, ,_, and r_b and their relationship to Ta, Tb, and Tu are obtained by integrating the right-hand sides of (9) and (10) against the pdf (7). The expected value of the digital variance is = 2[1- (11) where 0,_ =" vth,_ /a,,,, and is the normal cumulative distribution function. Figure 4 is a plot showing the relationship between the digital variance and RMS input voltage at a fixed threshold voltage. As will be shown in section B, for maximum sensitivity in Tv the value of 0,_ should be close to 0.61. Inverting (11) yields a simple estimate for the signal standard deviation for a measured digital signal variance: or, in terms of antenna brightness temperatures: V2ha where Ro is the system impedance, B is the bandwidth, Go is the system gain, and TaEc,_ is the receiver noise temperature. In general, the parameters (_ _kl_a,, } and TREC,,_ are slowly time varying and represent system gains and offsets that must be identified via periodic calibration. The relationship between the input correlation coefficient p and the expected value of the digital covariance rab is similarly straightforward and can be obtained by integrating the righthand side of (10) against the joint pdf over two dimensions. The problem can be reduced, however, to an integration over one-dimension using Price's theorem [17,18]. Price's theorem relates the covariance of theinputsignalsto thedigitalcorrelationcoefficient: = f(avoOa, avbOb; where J is the Dirac impulse function. The input covariance can be related to the input correlation coefficient using the chain rule of differentiation:

Or_b Orab OP_°_b Or_b
Op -OR,,.Vb Op = cr_ a,b oir_°_b (16) Thus, the digital correlation coefficient is a one-dimensional integral of the pdf over p: In practice 0_ and Ob are taken to be 0, and Ob from (13). The relationship between the input correlation coefficient and the digital covariance is plotted in Figure 5 for a fixed threshold level For a given r_b, the correlation estimate t5 is determined by nonlinear inversion of (17).
The inversion technique must be carefully chosen so that systematic errors arising from the approximation are not larger than the statistical uncertainty of the estimate. This requirement is quite stringent. For example, from (5), a radiometer with a system temperature of Tsy8 = 500 K and a noise requirement of ATrms = 0.1 K for the third or fourth Stokes parameter requires a measurement ofp with absolute error less than 0.1K/(2 • 500K) = 1 x 10 -4. The two existing inversion techniques for three-level correlators are based upon power series inversions of either the bivariate normal integral [19] or the one dimensional integral (17) [20]. In the former method [19] the inversion was derived for the cross-correlator, while for the latter method it was derived for the auto-correlator. Both sharesimilarconvergence characteristics, e.g.,third-orderexpansions are requiredto obtain0.1%accuracy or anabsolute errorof 10-4 for IPl< 0.6. Thelattertechnique, however, is mathematically simplerandpermitsananalysisof theeffectsof systemnonidealities (considered in sectionA). Sincethis expression wasoriginallyderivedfor the autocorrelator, a newandmoreaccurate expression tailoredto thecross-correlator is presented here(thederivation is presented in AppendixA). Firsttheintegrandof (17)is approximated by a Taylorseriesabout p' = 0. Next, the series is integrated to obtain: where Acceptable inversion errors for Earth-science polarimetry are attainable using this fifth-order power series.

B Sensitivity
A radiometer's fundamental sensitivity is limited by the available bandwidth, observation time, and receiver noise temperature. The radiometric sensitivity of a polarization correlating radiometer is: wherea_is the standard deviation of the estimate _. For continuous (analog) correlation using N independent samples and small values ofp it can be shown that limp__0 a_-= 1/x,/-N [11]. Thus, using (5) and (21) For the three level system with balanced channels (0a = Ob = 0), the sensitivity for vanishingly small correlation is (see Appendix A): The impact of quantization noise can be minimized by proper selection of the threshold voltages Vth,_. The optimal value of 0 (determined numerically) is 0.61 with a corresponding sensitivity of: ATu,_, = 2.47 v/Tv"u'Th"u" (25) Comparing this expression to (22) we find that the 1.6-bit digital correlator achieves 81% of the sensitivity available from an ideal analog correlator.
The total power channels are useful for normalized threshold level estimation as well as measurements of the first two Stokes parameters. The sensitivity of a total power channel can be calculated in a similar fashion by aM (26) AT,_,_,-0(_)/0"F_ With the threshold levels 0a = 0o = 0.61 (i.e., set for optimal cross-correlator sensitivity), the total power channels have a fundamental sensitivity of (see appendix B) AT,_,rm8 = 2.20 TS_'''_ (27) vW Theideal(analog) totalpowerradiometer hasa sensitivityof Tsus/x/N. Thus, a three-level digital total power radiometer can achieve 41% of the sensitivity of an ideal analog radiometer when the threshold voltages are optimized for the cross-correlation channel.
It is noted that in (27) the optimal sensitivity for the total power channels is not used because the threshold voltages were chosen to optimize the cross-correlation channel. In otherwords, the threshold level value of 0.61 is the optimum value for small cross correlations; however, this value is not optimal for the total power channels. This choice is acceptable, however, because in the polarization correlating radiometer the total power channels are primarily used to measure the relative threshold level values. If the thresholds were to be set for optimum total-power sensitivity, the digital total-power radiometer could 78% of the sensitivity of the analog radiometer with 0,_ = 1.58.

Systematic Errors
Two sources of systematic errors in a polarimetric radiometer are analyzed in this section: (1) Figure 6): otherwise Relations (9) and (10) can now be recomputed to reveal the effects of threshold offsets.

A.1 Correlation channel
The digital correlation coefficient (17) including offsets becomes: Equation 29 can be considered equivalent to (17) but with small gain and offset perturbations of order 6_ and _b-We show here that the gain error is negligible if the input correlation coefficient is small. In contrast, the offset error is found to be an order of magnitude larger than the gain error.
This correlation offset, however, is parameterized in terms of the threshold level offset and may be compensated via calibration using two unpolarized standards.
The correlator offset error arises from the constant of integration rabla=o in (29). This constant was not explicitly shown in (17) because ideally it is zero. The constant can be evaluated by taking the expected value of (10) with p = 0 and using the modified definition of h(v -v6,,) in (28): Clearly, when either threshold level is ideal (i.e., _,_ = 0) the above term vanishes. A shift in both threshold levels, however, causes the offset error to become non-zero, the expected value of which can be separated into a product of two expected values since v,_ and vb are statistically independent when p = 0. The resulting correlation offset is: Assuming 6a and 65 are small allows (3 1) to be approximated using Taylor series expansions about +0. and +0b. The first term in the product is: where the 6_ terms cancel to leave an odd-valued function. The linear behavior of (32) makes the threshold asymmetry a significant source of error. The constant of integration in (29) is the product of two such terms: where is the normalized threshold offset product. The threshold asymmetries thus affect the digital correlation offset by an amount proportional to the normalized offset product. Expressed using voltages: The above product is generally a slowly time varying hardware constant, but as will be shown in section IV, it can be estimated using a conventional two-look unpolarized calibration.
The correlator gain perturbation is found by expanding the integrand of (29) in a threedimensional power series in p', 6_ and 6b, then integrating the resulting expansion with respect to p'. The algebra involved (see Appendix C) is cumbersome, although the result can be expressed as a sum of two series. The first series rabl&=tb=o is the ideal relationship between p and r given by (17).Thesecond seriesis anerror series 5rab (Sa, 5b, p) caused by nonzero threshold offsets 5,_ and 5b. Collecting these terms we have: The above series is truncated at O(p 4) and 0(53). Assuming that the nominal threshold levels are equal to the optimal value (0,_ = 0.61) the error series becomes: The error series is a sum of components that are 0(52p), O(6ZpZ), and O(o_pa), respectively.
To determine which components of the series are significant we assume that p = 0.1 and To render these error terms insignificant, the quantity 52 must be sufficiently small.
Using the previous criterion that all errors in p of magnitude _ 10 -s are negligible, the normalized threshold offsets should be no larger than 10 -2, that is, v_,, _< 10-2av,,. This is readily attainable using precision electronics for av,, "_ 0.5 V. If threshold offsets are not small enough, then the offsets should at least be controlled to render insignificant the higher-order terms (e.g., p2, p3... ), in which case only a correctable gain error occurs. For this latter case, it is sufficient that v6, _< 10-1av,_ to cause the magnitude of the p2 and pa terms to be less than 10 -5. The remaining error is linear in p and can be modeled as an effective change in the correlator gain: Notethattheidealcorrelator outputr_b16.=6_=o is implicitly included in (39). Typically the threshold offsets are small enough so that the gain perturbation is a only few percent.

A.2 Total power channel
The effect of threshold asymmetry on the total power channels is a perturbed system gain and offset along with a residual nonlinearity that we show to be negligible. Consider the expected value of the total power output: This expression is a simple extension of (1 1) but includes the threshold asymmetry.
series expansion then (40) can be written [ 7 ] ] (44) 1 2 There is a gain term affecting the total power channel output by a factor of (1 -_6a) and an offset 1 2 of approximately _6_. This additional system gain and offset is easily identified via a standard two-look calibration. The nonlinear residual is ( 41 Assuming the optimal value for the threshold levels (0,_ = 0.6D, the above residual is found to be ,,_ 10-_. If 6,_ <_ 10 -2, then the nonlinear residual term becomes ,-_ 10 -6, which is insignificant for either total power or threshold estimation.

B
Other correlator gain attenuating sources Analog-to-digital converter hysteresis acts to reduce the correlation output by an amount proportional to the magnitude of the hysteresis. This effect has been modeled by D'Addario, et al. [19] assuming a uniformly distributed region of uncertainty about the nominal threshold.
However, this statistical model underestimates the attenuation effect because the hysteresis is treated as a process that is statistically independent from the signal. Rather hysteresis is a nonstationary process in which the current threshold level is dependent upon the previous value of the input signal.
To make a more accurate assessment of hysteresis a Monte-Carlo simulator was constructed to demonstrate the effect on the gain of the correlation channel. The simulator is based upon an A/D converter transfer function of the form: where Vnys,,_ is the hysteresis voltage.
The transfer function is graphically illustrated in Figure   7. Input correlation coefficients in the range -0.1 < p < 0.1 were tested with varying levels of hysteresis using 214 Monte-Carlo samples for each case. In Figure 8 where v°(t), v°(t), and v_(t) are mutually uncorrelated and wide-sense stationary, and At is an additional path delay or timing skew. If vc (t) is bandlimited then the cross-correlation function is: where B is the bandwidth or bandlimiting cutoff frequency of v_(t), and the function sinc(z) Forexample, a 10°or 20°phase difference will cause a 1.5% or 6% reduction in the correlation coefficient, respectively.

IV Calibration
Calibration of a digital polarimeter entails the periodic identification of slowly time-varying system hardware parameters. For the total power channels, these constants are the system gain and offset.
For the polarization correlating channel, the threshold-offset product (36) in section A. 1 as well as any other additive offsets (such as those originating from correlated LO noise) must be identified. As shown below, these parameters can be estimated using the simple hot and cold views of unpolarized blackbody standards as obtained during conventional total power channel calibration.

A Total power channel calibration
Identification of the gain and offset of the total power channels in (14) allow an antenna temperature estimate to be made. The output of the total power channel is related to the antenna temperature estimate by: where the left hand side is the linearized digital variance, 9,_ is the radiometer system gain in K -x, and the receiver temperature TREC,,_ is the system offset.
This system is easily solved for _ and Tn_c,o: cl, c3, and c_ are given by (20), and 7r6 is the offset product (36). The fifth-order term csp_ can be ignored if p0 < 0.1, which is usually the case when Tu = 0.
The two calibration targets provide unpolarized emission at two different radiation intensities. Sequential views of the hot and cold targets provide the digital correlation measurements r_b°t and _ta for the hot and cold looks, respectively.
Using these two measurements a system of equations can be formed: The coefficients _ot and c_,'ad are computed by using the relative threshold values O_ t and O_ a, respectively.
Using only a third-order expansion in/90 allows the above system to be solved ana- lytically. An estimate of the threshold-offset product can be found by: and an estimate of the correlation bias is a root of the following cubic: The solution of a cubic equation is given in [21, (3.8.2)]. For this particular cubic there is typically one real root and a pair of complex conjugate roots. The real root is the desired solution for P0 and where q and r are defined as aircraft-based studies of land and ocean emission (Figure 9). The radiometer operated successfully in a conical scanning configuration to measure the first three Stokes parameters over the wind-driven ocean at 10.7 GHz (X-band) and 37.0 GHz (Ka-band) [3]. In-situ calibration was accomplished using unpolarized hot and ambient temperature blackbody calibration targets and verified using a ground-based polarimetric calibration target [8].

A Hardware
The 10.7 GHz radiometer was a superheterodyne single-sideband (SSB) system with a low noise Estimates of second-order digital signal statistics were made by squaring and cross-multiplying the A/D converter outputs, then accumulating using digital counters. The total power, or variance, of an individual channel was measured by counting the number of times the input signal exceeded either the positive or negative threshold levels as in (9). The correlation coefficient was similarly determined by separately counting the number of positive and negative correlation counts. A total of eight AND/NAND gates composed the entire three-level multiplier circuit. The outputs of the digital multiplier were accumulated in four 24-bit counters providing 16.8 ms of integration time.
The initial 1-Gbit multiplier outputs were prescaled using high-speed 8-bit ECL ripple counters.
The system clock was distributed differentially to the counters using 50 f_ odd-mode coupled microstrip lines. The high-speed ECL signals exhibit transition times shorter than 250 ps; therefore, the digital signals have spectral content >4 GHz. On-chip and interconnect propagation delays within the multiplier circuit were compensated with clock delays generated by programmable delay chips. To save power, the output from these counters were carried to 16-bit TTL counters. The most-significant 16 bits were buffered and read by computer. The circuit was fabricated on sixlayer G 10 fiberglass circuit board. Microstrip interconnects were placed on the outer two layers of 1/2-oz copper and power was distributed via the internal layers of 2-oz copper.
Redundant analogtotal-power channels wereimplemented in parallelwith thedigital radiometers. ThesameIF signalsfedto thedigitalcorrelators werecoupledto square-law detectors at ,-_-23 dBm power level. Video amplifiers following the square-law detectors used integration times of 8 msec. The video amplifier output ranged from 0-10 V and was sampled by a 12-bit A/D converter. An analog offset was added to the video amplifier output to maintain the signal level within the operating voltage range of the A/D.

B Calibration
The unpolarized hot and ambient method of Section IV was used to identify the correlation offset and the threshold-offset product system parameters. Microwave foam absorber in ambient and liquid nitrogen conditions provided unpolarized radiation fields.   Figure 11. By visual inspection, T, and Th mixing into :_tr appears to be nonexistent, but the correlator output is attenuated N25% at 37 GHz and ,-_70% at 10.7 GHz compared to Tu.
Using these data, the gains and offsets for the 10.7 and 37.0 GHz Tu channels were calculated according to the methods in [8] and presented in The calibration exercise also yielded analog and digital total-power measurements that were compared for consistency.
One hundred twenty-five samples with TB = 80 to 290 K were compared. The mean and standard deviation of the analog-digital measurement differences are tabulated in Table 3 In all, the digital total-power radiometer tracks the analog system quite well.

VI Discussion
The design techniques and radiometer hardware described here demonstrate the utility and technological feasibility of the digital polarimetric radiometer for earth remote sensing applications.
Other polarimeter topologies such as the analog correlating polarimeter or the analog adding polarimeter are possibilities. Such systems, however, can exhibit polarization cross-coupling beyond that caused by the antenna system that is not easily identifiable without sophisticated calibration techniques.
On the contrary, the digital polarimeter, if built to the proper design specifications, has the distinct advantage of negligible Stokes parameter cross-coupling and affords in-flight periodic calibration of all polarimetric channel parameters. Further, use of a three-level digital correlator provides a simple means of calibrating both correlation offsets as well as total power measurements.
To reiterate, the following design rules developed in Section III for the A/D converter parameters required to limit offset and gain perturbations are: 1. v_ < 0.01av_ to minimize correlator offsets rab[p:0 and _rab 2. minimize hysteresis, timing skew, and phase differences to maximize 9trtr Adherence to these rules is highly desirable in order that the radiometer can be used to make accurate measurements of the third and fourth Stokes parameters. However, if these design specifications cannot be met, the radiometer may still be used pending regular calibration using a polarimetric calibration standard or a similar method such as correlated noise injection to compensate for gainandoffsetvariations.
ThePSR/Dhardware demonstration confirmstheability to fabricate, operate, and calibrate a digital polarimetric radiometer in the field and exemplifies its utility in earth remote sensing, particularly in the observation of ocean surface winds. As a follow-on to the PSR/D demonstration, an implementation suitable for satellite deployment using lower-power space-qualified CMOS logic at comparable sample rates is feasible and is currently under development [30]. An incidental consequence of this work also exists in the application of digital correlators for synthetic aperture interferometric radiometry (e.g., [31]). Such systems will be susceptible to the same effects of nonlinearity, threshold asymmetry, timing skew, A/D converter hysteresis, and phase errors, all of which have been discussed here.

ACKNOWLEDGMENTS
The authors extend their appreciation to W.

A Correlation Coefficient Inversion
The digital correlation coefficient can be computed by the following: Rewriting the expression for r_b using the bivariate normal pdfyields: The task at hand is to expand the integrand in a Taylor series and then integrate. The integrand of the above is This can be expanded in a Taylor series in terms ofp':

I(P')=I(O)+I(1)(O)P'+_I(2)(O)P'2+II(a)(O)P'3+_. I(4)(O)p
The algebra involving the derivatives is quite cumbersome and the computer algebra package MapleV was used to evaluate the derivatives. The derivatives ofp(0a, --Ob, p) are easily found by substituting --Oh for Ob in the above. Because the first and third derivatives are odd functions of 0_ and 0b, it is immediately seen that the Taylor series terms with odd powers of p will cancel leaving only the even powers of p. Adding the appropriate derivatives yields the following for the integrand: Finally, integrating the above yields: This appendix contains a derivation of the sensitivities of both the cross-and autocorrelating channels of the digital polarimeter. These sensitivities are assumed to be optimized with respect to the A/D converter threshold level.

A Cross-correlator Sensitivity
The sensitivity of the third Stokes parameter cross-correlating channel is Using the chain rule, the derivative in the denominator is expanded: The derivative Or_b/Op evaluated for small p can be computed using (15) and ( The above expression can be written in terms of 0 by substituting in (7) and (11) B

Total-power Sensitivity
The sensitivity of the total-power channel is found similarly: Once again, the denominator is expanded using the chain rule: The firsttermin theproductis thedifferentialrelationship between theinputvoltagevarianceand the outputof thetotal-power channel of thedigitalcorrelator. From (11) = _ y_ <h2(vn(nT))) + -N_Z Z (h2(vn(nr))) <h_(v'_(mT))) Thus, the variance of _ is Forming the quotient (97)   The Taylor series of this product is (2)  Substituting these results into (115), the first term of the integrand is O-_p(--Oa +6a,Ob +6b, P) p:o+ _P(--Oa +6a,--Ob +6b, P) o:ol P' The first partial derivative with respect to p, evaluated at zero, of the bivariate normal pdf is Finally,substituting theaboveseriesintothea and b terms of (122) yields the following: The third term in the series expansion of I (p') contains Consider the following expression by expanding Z in a power series: Table1: Digital correlating polarimeter system parameters foundusinghot andambientunpolarizedcalibrationtargets. Table 2: Gain and offset terms for the 10.7 and 37.0 GHz digital polarimeters as measured using the polarized calibration standard. Table 3: Comparison of digital and analog total-power radiometer measurements. Figure 1: Block diagram of a typical digital polarimetric radiometer. This direct correlating polarimeter, utilizes a dual polarized antenna, dual channel superheterodyne receiver, and a 3-level digital correlator.
The IF signals are also coupled to traditional square law detectors and video amplifiers.