Abstract
We explore possible advantages of cyclic spectroscopy for observations of
pulsars in instances where full cyclic deconvolution is not feasible. We
compute cyclic merits and full-deconvolution regime boundaries for pulsars
observed by NANOGrav and discuss which sources stand to benefit the most from
using cyclic spectroscopy when observed with the Green Bank Telescope and
DSA-2000 in a given frequency range. We compare data products, namely the
wavefield, in both full-deconvolution and partial-deconvolution regimes to
demonstrate what can be accomplished with incomplete phase retrieval.
Additionally, we show how some phase retrieval can still be achieved in the
partial-deconvolution regime and how this allows for additional information in
scintillation-based data products, like the dynamic wavefield power, compared
to what can be found in traditional dynamic spectra. An examination of dynamic
wavefield phase as a function of observing frequency reveals more complete
phase retrieval is achieved the closer one gets to the full deconvolution
regime, agreeing with the expectations of cyclic merit. While we demonstrate
that fragmentary recovery of the secondary wavefield can be accomplished in the
partial-deconvolution regime, we advocate for a synergistic approach with phase
retrieval methods like the $\theta-\theta$ transform, although we also provide
discussion about shortcomings of this strategy. Finally, we use the combination
of modest cyclic merit and lack of discernible results for PSR J1903$+$0327 to
motivate the creation of an updated "cyclic merit 2.0", which relies on
scintillation bandwidth instead of observing bandwidth.