Fizeau Mask Interferometry of Solar Features Using the Multi-application Solar Telescope at the Udaipur Solar Observatory

Abstract

Efforts are made to demonstrate high-resolution observations of the solar atmosphere using spatial interferometry. Covering the telescope pupil with a Fizeau mask consisting of two small circular apertures separated by a vector distance known as the baseline is the first step towards interferometric imaging. A mask with two circular holes of diameter 7 cm each and separated by a distance of 19 cm is placed in the pupil plane of the Multi-application solar telescope at Udaipur solar observatory. The fringe pattern observed in the image plane signifies the presence of solar structures with sizes smaller than the fringe period. The study is extended with baselines of 29 cm and 38 cm. It is observed that an increase in the baseline causes a reduction in the fringe period and the fringe contrast. Observations are carried out in two spectral lines/bands, centered at 656.3 nm and 861.0 nm using filters of bandwidth 1 nm and 330 nm, respectively. The effect of bandwidth on the fringe visibility is also discussed based on the bandwidth decorrelation function.

Appendix: Bandwidth Decorrelation Function for Filters Used in This Work

In stellar interferometry and imaging, the bandwidth decorrelation function $G(x)$ is defined as the absolute value of the Fourier transform of the function representing the spectral transmission function $T(k)$ expressed in wavenumber ($k= 1/\lambda$) space. Figure 6 shows the near-infrared spectral transmission function of the spectral filter used for NIR observations. The central or mean wavelength of this filter is estimated using:

$$ \bar{\lambda} = \frac{\int^{1200}_{690} \lambda F(\lambda) T(\lambda) \,\textrm{d}\lambda}{\int^{1200}_{690}F(\lambda) T(\lambda)\, \textrm{d}\lambda}, $$

(6)

where $F(\lambda)$ and $T(\lambda)$ are the solar terrestrial spectral irradiance, and the spectral transmission in wavelength space, respectively. The limits of integrations indicate wavelength in nm. From this the mean wavelength is estimated as 860.9 nm. The full width at half maximum of this filter measured based on the definition is ${\approx}\,330$ nm.

Figure 6

Spectral transmission function of NIR filter used for the observations. The transmission function is shown in wavenumber space. The mean wavelength is estimated as 861 nm. The full width at half maximum of this filter is measured as ${\approx}\,330$ nm.

Figure 7 shows the bandwidth decorrelation function $G(x)$, estimated as the absolute value of the discrete Fourier transform of $T(k)$. We note that the first minimum of the bandwidth decorrelation function is around 2250 nm which is close to the coherence length $\Lambda= {\lambda}^{2}/\Delta\lambda$ ($= 861\times861/330 = 2246$ nm). In practice, the squared visibility is multiplied by the square of the bandwidth decorrelation function. The value of the bandwidth decorrelation function could be deduced from the two plots shown in Figure 7. The theoretical value of the rms OPD for a given baseline is given by $0.417\lambda(L/r_{0})^{5/6}$. This is shown in the left panel of Figure 7. The attenuation corresponding to that OPD is then extracted from the right panel of Figure 7. The estimated squared visibilities is divided by the bandwidth decorrelation function to remove the finite bandwidth effect.

Figure 7

Left: OPD for a given baseline, estimated theoretically. Right: Bandwidth decorrelation function estimated from the filter transmission function. The attenuation of the power spectra due to finite bandwidth could be determined from these two plots. Baseline ⟶ OPD ⟶ bandwidth decorrelation function.