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2.11.3 Internal Calibration

The ASAR instrument incorporates a very comprehensive system for internal calibration. There is an individual calibration path for each of the 320 transmit/receive modules (T/R modules).

T/R Module
Figure 2.68 T/R Module

Internal calibration will be carried out on a row by row basis for each of the 32 rows. The calibration pulses are included in the instruments timeline during imaging and consist of the following:

Transmit Calibration Pulses P1 (representative of T/R module load)

Since T/R modules of the four adjacent rows share the same power supply, the ten modules of the 'wanted' row are set to their nominal phase and amplitude settings whilst the phase of the modules of the three 'unwanted' rows are set so that their combined contribution out of the calibration network is nominally zero. Thereby minimising their interference to the measurement of the 'wanted' row. The equation for this is given below:

$a_{1,n}(t) = e^{j\phi_{1,n}(t)}$
eq 2.16

Transmit Calibration Pulse P1A

A second type of transmit pulse is added in order to characterise the residual parasitic contribution of the three unwanted rows during P1. During P1A, the three unwanted rows are set as for P1 and the previously wanted row is now switched off. Even though the load conditions on the power supplies are not exactly representative, the small error introduced into the estimation of P1A is negligible. The equation for this is given below:

eq 2.17
$a_{1A,n} (t) e^{j\phi_{1A,n}(t)}$

Receive Calibration Pulse P2

The receive path of the instrument is also characterised, but since no variation is expected from power supply load variations it is possible to characterise on a row-by-row basis. The equation follows:

eq 2.18
$a_{2,n}(t) = e^{j\phi_{2,n}(t)}$

Central Electronics Calibration Pulse P3

The auxiliary receive and transmit path of the central electronics are included in the P1/P1a and P2 characterisations, respectively. This part of the central electronics is therefore characterised independently by means of P3. The equation is as follows:

eq 2.19
$a_{3,n}(t) e^{j\phi_{3,n}(t)}$

Except for WV mode, the individual, mode and beam dependent chirps are used as calibration pulses, i.e. they have the same characteristics as the transmit chirps. WV mode calibration pulses are not chirped (cw-signal).

These calibration pulses are being used to monitor any transmit/receive gain variations and to reconstruct the chirp replica for range compression.

Calibration pulse measurements are being performed at the beginning of an acquisition (so-called initial cal sequence) and also during the acquisition with a mode-dependent repeat cycle of 5 - 35 seconds (periodic cal sequence). The processor is only using the periodic cal sequences.


2.11.3.1 Elevation Gain Monitoring

Using the amplitude and phase of the calibration pulses (P1/P1a, P2 and P3) for each row it is first necessary to calculate the amplitude and phase of P2 relative to P3 and to subtract P1a vectorially from P1. From these values for each of the 32 rows and together with the external characterisation factor, it is possible to calculate the elevation beam pattern. This is then used to detect any deviation to the reference instrument gain pattern as characterised on ground. The typical update rate for this calculation is 5 to 35 seconds (mode dependent).

The first step in the elevation gain monitoring is the calculation of amplitude and phase of the individual calibration pulses. Amplitudes are derived by averaging the pulse ( see note 1 below ), phase is derived after pulse compression from the peak response (in WV mode by multiplication with a reference cw-signal). Nominal or replica pulses can be used for calibration pulse compression. P1 pulses are then corrected for the P1A contribution and formalised to the nominal P1 pulse value (amplitude only) for beam IS0:

eq 2.20
$a_{t,n} e^{j\phi_{t,n}} = ( a_{1,n} e^{j\phi_{1,n}} - a_{1A,n} e^{j\phi_{1A,n}}) / a^0_{1,nom,n}$

If necessary, normalisation by the nominal pulses P1 for IS0 can be easily reverted by setting the values in the ASA_INS_AX file to 1.

The P2 pulses are then divided by P3 to correct for contributions from the AUX transmit and receive units, which only affect the cal pulses but not the signal.

eq 2.21
$a_{n,n} e^{j\phi_{n,n}} = \frac{a_{2,n} e^{j\phi_{2,n}}}{a_{3,n} e^{j\phi_{3,n}}}$

The antenna gain for an array antenna is given as the weighted coherent sum of the subarray radiation patterns (in our case the so-called embedded row patterns image ). The weights (taper) are given by the calibration pulse measurements. As the calibration pulses do not cover the passive part of the antenna (radiating elements) but are influenced by differences in the calibration network, we have to include the factors image , which are determined in the external characterisation. Calibration pulses, image and image are polarisation dependent.

The transmit/receive gain variation is then calculated at the reference elevation angles:

image eq 2.22

The two-way gain variations are then given by:

eq 2.23
$G_2(\theta_0) = G_t(\theta_0) G_r(\theta_0)$

In the current implementation in PF-ASAR we repeat this calculation for a set of nominal pulses for this beam to generate image and finally derive the elevation gain change with respect to this nominal gain:

eq 2.24
$G'_2(\theta_0) = G_2 (\theta_0) / G_{2,nom}(\theta_0)$

If we add a flag in PF-ASAR to set image to 1 we can revert this normalisation step. Together with the nominal pulses for IS0 set to 1, we obtain elevation gain factors that reflect the full change in antenna gain from beam to beam with any time/temperature dependent instrument gain variation on top.

2.11.3.2 Chirp Replica Construction

A replica of the chirped pulse is calculated from a complete calibration row cycle using the P1/P1a, P2 and P3 measurements, the ground characterised row patterns and the external characterisation data. This is also typically updated every 5 to 35 seconds.

The chirp replica, including the full transmit and receive path of the ASAR instrument, is also reconstructed from the calibration pulses. The chirp replica reconstruction uses the time-dependent signals instead of single pulse amplitude and phase values, but otherwise performs similar operations as in the elevation gain monitoring. The replica is given as the convolution of the P1A-corrected P1 pulse with the P2 pulse. The correction for the AUX transmit and receive units (pulse P3), which only affect the cal pulses but not the signal, is performed by a de-convolution. All these operations are performed in the frequency domain, where convolutions/de-convolutions simplified to multiplications/divisions. The required processing steps are:

eq 2.25
image

where the < > operator denotes an average over n. The replica energy is then calculated in PF-ASAR in the frequency domain (assuming a well-normalised FFT-operation):

eq 2.26
image

No normalisation of the transmit pulses for IS0 nominal pulses P1 and no normalisation like image are being performed. If we switch off these two steps in the elevation gain monitoring, we should end up with comparable results, i.e. the elevation gain factor multiplied by the chirp duration should be equivalent to the replica energy.

Despite the comprehensive nature of the internal calibration system, it is not possible to use it to calibrate the passive part of the antenna, which falls outside of the calibration loop. This is achieved through external characterisation by using the ground transponders.

2.11.3.3 PF-ASAR Normalisation

PF-ASAR calculates the replica and the elevation gain factor from the calibration pulses in one calibration cycle. Only one calibration cycle is considered in scene products. In stripline, where multiple cycles are available, the replica and the elevation gain are updated for every calibration cycle.

PF-ASAR uses two different processing algorithms (Range Doppler and the SPECAN), which follow different normalisation implementations. For both algorithms three different cases are considered which are already implemented in the processor:

1. The chirp replica can be reconstructed from the internal calibration pulses contained in the Level 0 and it is used during range compression.

2. The chirp replica cannot be reconstructed from the internal calibration pulses (replica quality measurements fall below the thresholds) and the processor automatically uses the nominal chirp during range compression.

3. The chirp replica can be reconstructed from the internal calibration pulses but the processor is forced to use the nominal chirp reconstructed from the coefficients.


2.11.3.4 Module Stepping

ASAR has a dedicated Module Stepping Mode, which is used to gather data from all 320 transmit/receive modules automatically. The entire procedure takes less than one second. The data are downloaded to the ground for processing. After processing, the results are compared with the reference data from on-ground tests in order to determine any T/R Module (TRM) module gain or phase drifts, temperature behaviour and any eventual module failures. Using this information it is possible to implement any necessary correction to the TRM coefficients and eventually re-synthesise the antenna beam patterns if required.