3 The scheme

The present scheme is described with reference to the array configuration of the GRH which has 16 antenna groups along a E-W arm and another 16 along a South arm. The redundant shortest baseline in the E-W arm is used along with those formed by the multiplications between the antenna groups in the E-W and South arm. Consider the multiplications between the groups G₁, G₂,  G₃ . . . G₁₆ in the E-W arm and G₁₇ in the South arm. The possible closure equations are,

$$\theta_{1,2,17}=\phi_{1,2}^{\rm obs}+\phi_{2,17}^{\rm obs}-\phi_{1,17}^{\rm obs}$$ (1)

$$\theta_{2,3,17}=\phi_{2,3}^{\rm obs}+\phi_{3,17}^{\rm obs}-\phi_{2,17}^{\rm obs}$$ (2)

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$$\theta_{15,16,17}=\phi_{15,16}^{\rm obs}+\phi_{16,17}^{\rm obs}- \phi_{15,17}^{\rm obs}.$$ (15)

These 15 equations can be solved for the 16 unknowns using the standard singular value decomposition technique [9, (Press et al. 1992).] The method gives the best possible solution in the least squares sense. It can be shown that the error due to the number of equations being one less than the number of unknowns is only 6% [11, (Ramesh 1999).] The above process is repeated 16 times corresponding to each one of the 16 groups in the South arm. In each step, a set of 16 phases are determined and thus at the end of $16^{\rm th}$step, we have all the 256 true visibility phases that correspond to the E-W $\times$ S multiplications. It is to be noted that in the above set of equations, the visibility phases ($\phi_{1,2}^{\rm obs}, \phi_{2,3}^{\rm obs}~.~.~.~\phi_{15,16}^{\rm obs}$)corresponding to the redundant shortest baseline in the E-W arm is assumed to be zero, since the baseline length is small to resolve a source like Sun in our frequency range (40-150 MHz) of observation.

Figure 1 shows the radio map of the solar corona at 75 MHz obtained with the GRH on April 20, 1997 using the above method. The map made using the external calibration method i.e., by correcting for the instrumental errors using the observations of radio source Virgo A (which is a point source for the GRH and happens to be close to the Sun's declination during the month of April) is shown in Fig. 2. The similarity between the two maps is good.

  

Figure 2: Radio map of the Sun obtained on the same day as in Fig. 1 but using the external calibration method with the radio source Virgo A as the calibrator

  

Figure 3: Radio map of the Sun at 75 MHz made using self-calibration technique in AIPS with the map in Fig. 1 as the starting model. The peak brightness in the map is $\sim 1.6 \ 10^{6}$ K and the rms noise is $\sim 10^{4}$ K

A map obtained using the self-calibration technique with the map in Fig. 1 as the starting model, is shown in Fig. 3. One can notice that the features in the self-calibrated map are seen more clearly with improvement in the signal to noise ratio. We also found that our method is quite successful in extracting weak and diffuse features particularly during times when Sun is active and is dominated by emission from strong and localised radio emitting discrete source(s). Figure 4 shows one such map obtained on September 28, 1997. Although the map is dominated by the strong source close to the limb in the S-W quadrant, the presence of weak, diffuse features close to the east limb can be seen clearly. A comparison of the GRH maps shown above with those obtained with the Nancay radioheliograph at 164 MHz indicates that our method works reasonably well.

  

Figure 4: Radio map of the Sun at 109 MHz obtained using our method. The brightness temperature of the bright source close to the limb in the S-W quadrant is $\sim 8 \ 10^{7}$ K and that of the source close to the east limb is $\sim 10^{6}$ K