  We consider the problem of conjugate phase retrieval in Paley-Wiener space
$PW_{\pi}$. The goal of conjugate phase retrieval is to recover a signal $f$
from the magnitudes of linear measurements up to unknown phase factor and
unknown conjugate, meaning $f(t)$ and $\overline{f(t)}$ are not necessarily
distinguishable from the available data. We show that conjugate phase retrieval
can be accomplished in $PW_{\pi}$ by sampling only on the real line by using
structured convolutions. We also show that conjugate phase retrieval can be
accomplished in $PW_{\pi}$ by sampling both $f$ and $f^{\prime}$ only on the
real line. Moreover, we demonstrate experimentally that the Gerchberg-Saxton
method of alternating projections can accomplish the reconstruction from
vectors that do conjugate phase retrieval in finite dimensional spaces.
Finally, we show that generically, conjugate phase retrieval can be
accomplished by sampling at three times the Nyquist rate, whereas phase
retrieval requires sampling at four times the Nyquist rate.
