determine the Fresnel limit of the telescope. At a distance of $\gtrsim 10^{4}$ km, the S/Ns of the modeled pulse in FB 212 and FB 213, match that of the observations with non-detections in the other fan-beams.[]{data-label="fig:fresnel"}](Fig5.pdf){width="3.5"}

![image](Fig6){width="6.0"}

Two of the three FRBs have been discovered relatively close to the Galactic plane, with the locations marked as stars in Figure \[fig:skydist\]. All three have DMs significantly in excess of the Galactic contribution, suggesting an extragalactic or cosmological origin. Under this assumption, the contribution from the IGM to the DM can be used to infer a redshift, using the scaling relation in [@Ioka] and [@Inoue]. This places FRBs 160317, 160410 and 160608 at a redshift upper limit of 0.7, 0.2 and 0.4 respectively, assuming zero contribution from any potential host galaxy. Any contribution from a host galaxy or the immediate vicinity of an associated source, could be a significant fraction of the total DM depending on its orientation and location. The average DM for elliptical galaxies is 37 pc cm$^{-3}$ and for spiral galaxies is 45 pc cm$^{-3}$ based on the probability distribution of DMs computed for a range of host galaxies [@Xu]. For spirals, the weighted average over a range 