# Lightning Interferometry with the Long Wavelength Array
## 4 Summary and Discussion  
In this study, we have presented a foundation for the use of measurements from the LWA to detect and locate lightning VHF sources. The resulting maps of lightning are possibly the most sensitive radio measurements of lightning to date. Sources can and are located with received power well below the galactic VHF background. It would be impossible to identify these VHF sources by examining the VHF signals received at only one antenna. For the LWA, the ability to identify pulses in the time series is further hampered because the noise level of the time series is actually significantly higher when lightning is present than when it is not. This happens because, when the complex visibilities are compressed to 8 bits (split equally between real and imaginary components), the observation can and frequently does clip at \(\pm\)7 counts. This clipping in the frequency domain causes additional noise for the entire 40 \(\upmu\)s observation window for this antenna. Remarkably, simulations indicate that this clipping does not adversely affect source location retrieval. The locations of VHF sources were achieved using a projection imaging routine that is fully equivalent to aperture synthesis imaging. The method is not the most computationally efficient way to image a source and is particularly inefficient when the number of baselines is large, as in this study. The current implementation takes several seconds to image a single integration period with all 256 antennas; imaging all integration periods in a flash requires a significant amount of time (days to months on a single computer). The primary motivation for using projection imaging versus any other imaging method was simply because we were familiar with it and so it could be implemented fairly quickly. Nevertheless, there are benefits to projection imaging. The largest of these is that Equation (5) can be trivially extended to other coordinate systems. This allows imaging to be achieved in any coordinate system for which \(\tau\) can be uniquely calculated for each baseline. For example, the image can be easily computed in the azimuth-elevation projection, as seen in [PERSON] et al. [44] and [PERSON] et al. [11]. If the baselines are long enough, the image can also be projected onto three spatial dimensions. This was achieved using VHF signals in [PERSON] et al. [39] and with electric field change records in [PERSON] et al. [45]. While not used in the present study, it should be similarly possible to make near-field corrections for sources observed with the LWA. For the flash examined in this study, the LWA was able to locate at least one VHF source in virtually every integration period, independent of the integration period used and with very low false alarm rates. In comparison, other lightning interferometer studies that mapped a significant portion of a lightning flash were able to locate \(\sim\)2-14% of their observing windows [8; 39; 46]. Until now, lightning interferometer studies have universally assumed that if the integration period is small enough, lightning can be modeled as a single point radiator. A major advantage of using so many antennas to image lightning is that multiple VHF lightning sources can be identified in each integration window. In the flash in this study, around 51% of the integration windows examined had more than one VHF source, and this fraction was relatively independent of integration period. This estimate is almost certainly a lower bound as the deconvolution method employed in this study, which enabled multiple sources to be identified, was effective but crude. Much more sophisticated deconvolution algorithms exist and should allow sources to be identified even farther into the background noise. The fact that lightning emits VHF radiation from multiple locations at once should be no surprise; high-speed video observations of lightning routinely show multiple simultaneously active branches [47; 48; 49; 50; 51].