Radio Correlators

Radio astronomy is moving towards arrays with thousands, or even tens of thousands, of small antennas. A traditional correlator cross multiplies the voltage signals from each pair of antennas, forming the fundamental measurement of an interferometer, the visibility. This operation scales as the number of antennas squared, and will soon reach the peta-FLOP regime, making the correlator the dominant cost of future instruments.

I am working to develop an alternative correlator architecture called the Modular Optimal Fast Fourier (MOFF) correlator, which grids the voltages from the antennas and performs a fast Fourier transform (FFT) to directly form images. This operation scales as a more gentle N log(N), potentially saving orders of magnitude in computational complexity in future arrays. In a way, the MOFF is an example of the more broad category of direct imaging correlators. But the MOFF does not constrain antennas to be identical, or on a regular grid. In that way the MOFF is more general than most direct imaging methods like the Omniscope.

At ASU I am working with Nithya Thyagarajan to implement the MOFF in software, which we have called the E-field Parallel Imaging Correlator (EPIC). We recently received funding from the NSF to deploy this implementation onto the Long Wavelength Array station in Sevilleta, NM (LWA-SV). This will give us the opportunity to demonstrate the practicality of both EPIC and direct imagers in general, taking a crucial step towards realizing the many-thousand element arrays of the future.

I am specifically interested in the challenge of calibrating direct imaging arrays. Because they never forms visibilities, we cannot use traditional calibration methods, which rely on visibilities. Instead I developed an algorithm which correlates a pixel of the output image with the input antenna voltage to solve for direction dependent complex gains. This method requires only N correlations, so retains the computational benefit of the MOFF, and estimates gains which are nearly statistically equivalent to those formed from visibilities.

EPICal
The EPICal algorithm is able to calibrate the LWA without ever forming visibilities.

While direct imaging telescopes were originally motivated to enable very large arrays designed to detect faint wide-field signals, we realized that they offer an unanticipated advantage for transient searches – built-in access high time resolution, wide-field sky images, with far lower output bandwidth than visibilities. This means that real-time transient detection modules can be attached to the backend of a direct imaging correlator, potentially resulting in some of the most thorough surveys ever conducted on the time-dependent radio sky. I am exploring the technical challenges of implementing these transient buffers and looking to exploit algorithmic improvements which will enable faster searches.