Recent updates: https://www.notion.so/astrosujin/8e42181dd8ee4a779bc4169a45477d32?v=4742be7ceb844bf1b1e2909fc5a3912b&pvs=25#aa8ad99433e44647af1d7788efe537e5

Sun imaging
1.1 Single frequency, single baseline
1.2 All frequency channels
1.2.1 Single baseline
1.2.1 All baselines
Cyg A imaging
2.1 Single frequency, single baseline
2.2 All frequency channels
2.2.1 Single baseline
2.2.1 All baselines

analysis

# Load visibility data
vis_data.shape = (n_times, n_channels, n_baselines)

u_grid = np.linspace(-35, 35, 701)
v_grid = np.linspace(-35, 35, 701)
uv_data = np.zeros((len(u_grid), len(v_grid), nBl), dtype=np.complex128)

for bl_index in range(nBl):
    for t in range(nWin):
        # Calculate baseline vector
        B = calculate_baseline_vector(t*1.024, bl_meters[bl_index])
        
        # auto-correlation of two antennas
        auto_a = vars()[ant_comb[bl_index][0]]
        auto_b = vars()[ant_comb[bl_index][1]]
        
        for freq_index in range(nChan):
            # Calculate U, V
            frequency = freqs[freq_index] * 1e6
            u = B[0] / (c / frequency)
            v = B[1] / (c / frequency)

            # Find the closest indices in the UV grid
            u_index = np.argmin(np.abs(u_grid - u))
            v_index = np.argmin(np.abs(v_grid - v))

            # Bin visibility data onto UV grid for each frequency
            uv_data[u_index, v_index, bl_index] += (vis_data[t, freq_index, bl_index] / np.sqrt(auto_a[t, freq_index]**2 + auto_b[t,freq_index]**2) / (c/frequency)**2)

            # Find the closest indices in the UV grid for (-u, -v)
            u_index_neg = np.argmin(np.abs(u_grid + u))
            v_index_neg = np.argmin(np.abs(v_grid + v))

            # Bin visibility data onto UV grid at (-u, -v) and take complex conjugate
            uv_data[u_index_neg, v_index_neg, bl_index] += (np.conj(vis_data[t, freq_index, bl_index]) / np.sqrt(auto_a[t, freq_index]**2 + auto_b[t,freq_index]**2) / (c/frequency)**2)


# Fourier Transform to obtain image in (l, m) space
tmp = np.sum(uv_data, axis=2) # V(u, v) for all baselines
lm_data = np.fft.fftshift(np.fft.ifft2(np.fft.ifftshift(tmp)))

u_min = (u_grid[1]-u_grid[0]).round(3) # 0.2
l_max = 1/(2*u_min) # 2.5
l_grid = np.linspace(-l_max, l_max, len(u_grid))
m_grid = l_grid.copy()

plt.pcolormesh(l_grid, m_grid, lm_data.T, shading='nearest')

Sun on 2023 June 20

* Observation: June 20th, 2023, from 9 am to 12 pm (3 hours)
* Sun transit at 11:55:09
* (RA, Dec) of the Sun ~ (88 $\degree$, 23 $\degree$)
* Visibility recording for 4 antennas (IDs: 2, 6, 10, 14)

UV plane fringes of the Sun

Sun fringes in UV plane for 3 hours and 1024 frequency channels from 400 to 800 MHz)
Reference: Figure 3 of Peterson, Pen, & Wu (2004) (link)

Sun image at a single frequency channel

click to see details

Sun image for 450 MHz

Sun image in (l, m) space at 450 MHz with the baseline lengths of 4m (left) and 12m (right). The image center is set to be the North Celestial Pole. The grid size in (l, m) space corresponds to ~ 8.5 arcmin.

With the UV grid of (-200, 200, 2000), the max($l$) are max($m$) are 2.5. To see more of the dirty beam structure, the plots below are presented up to the max($l$) = 2.5, max($m$) = 2.5.

baseline = 4m

Sun image for 610 MHz

Sun image in (l, m) space at 610 MHz with the baseline lengths of 4m (left) and 12m (right). The image center is set to be the North Celestial Pole.

baseline = 4m

Sun image for all frequency channels

Sun image for 4-m baseline

$V(u, \ m)$

After simple gain calibration

np.fft.fftshift( $V(u, \ m)$ )

After simple gain calibration

$I(l, , m)$ = np.fft.fftshift(np.fft.ifft2(np.fft.fftshift( $V(u, \ m)$ )))

Before gain calibration

zoom-in

After gain calibration

zoom-in

Sun image for all baselines

1. UV plane fringes for all frequency channels at different baselines.

UV image for each baseline. Antennas IDs are noted on the top of each panel.

UV image for all baselines. Same as the first figure on this page.

2. after simply adding all frequency channels

The sky images for 1024 frequency channels are added. Since low-frequency components are dominated (see also upper images), bandpass calibration is required.

3. Visibilities divided by the squared root of auto-correlations

3.1. visibility vs FFT-shifted visibility

(left) Visibility after the gain calibration. (right) FFT-shifted visibility.

3.2. sky image

Sun_step3-2 _lm_data_acal_all

zoom-in

Sun_step3-2 _lm_data_acal_all_zoom

4. Simple gain correction: dividing by $\lambda^2$

4.1. visibility vs FFT-shifted visibility

(left) Visibility after the gain calibration. (right) FFT-shifted visibility.

4.2. Sky image

Sun_step3-2 _lm_data_gcal_all

zoom-in

Sun_step3-2 _lm_data_gcal_all_zoom

Cyg A on 2023 June 26

* Observation: June 26th, 2023, from 1 am to 4 pm Taiwan Time (3 hours)
* Cyg A transit at 01:39:33
* (RA, Dec) of the Cyg A = (300 $\degree$, 41 $\degree$)
* Visibility recording for 4 antennas (IDs: 2, 6, 10, 14)

Note. At 400 MHz, Sun flux ~ 4.6e5 Jy, Cyg A flux ~ 3500 Jy