Interstellar Interferometry: Precise Curvature Measurement from Pulsar Secondary Spectra

The parabolic structure of the secondary or conjugate spectra of pulsars is often the result of isolated one-dimensional (or at least highly anisotropic) lenses in the ISM. The curvature of these features contains information about the velocities of the Earth, ISM, and pulsar along the primary axis of the lens. As a result, measuring variations in the curvature over the course of a year, or the orbital period for pulsars in binaries, can constrain properties of the screen and pulsar. In particular the pulsar distance and orbital inclination for binary systems can be found for multiple screens or systems with prior information on $\sin(i)$. By mapping the conjugate spectra into a space where the main arc and inverted arclets are straight lines, we are able to make use of the full information content from the inverted arclet curvatures, amplitudes, and phases using eigenvectors to uniquely and optimally retrieve phase information. This allows for a higher precision measurement than the standard Hough transform for systems where these features are available. Our technique also directly yields the best fit 1D impulse response function for the interstellar lens given in terms of the Doppler shift, time delay, and magnification of images on the sky as seen from a single observatory. This can be extended for use in holographic imaging of the lens by combining multiple telescopes. We present examples of this new method for both simulated data and actual observations of PSR B0834+06.