  A double planet system or planet binary undergoes eclipses that modify the
reflective light curve. In the time domain, the eclipse events are fast and
weak. This would make their signal difficult to find and recognize in the phase
light curve, even for small inclinations when eclipses happen frequently.
However, due to the quasiperiodic nature of the phenomenon, the Fourier
transform of the direct reflection signal consists of a double sum of sharp
peaks. These peaks can be resolved for large close binaries and sufficiently
long observation times with a star coronagraph. Eclipses modulate the phase
curve, having an orbital period $2\pi/\omega$, with a contribution from the
relative motion in the binary plane of a period $2\pi/\Omega$. This leads to a
spectral structure with basis frequencies $\omega$ and $\Omega$. We aim to
characterize these spectra. We studied the regime of short eclipses that occur
when the planet radii are small compared to the planet separation. We derived
formulas for the peak amplitudes applicable to homogeneous (Lambertian) planet
binaries in circular orbit with small inclination. The effects of an eclipse
and of double reflection appear as first- and second-order contributions (in
planet radius over separation) in the reflection signal respectively. Small
peaks appear as observable side bands in the spectrum. Identical structures
around $m\Omega$ are characteristic of short-duration eclipses. Deceasing side
bands could indicate double reflection between companions. Fourier analysis of
the light curve of non-transiting planets can be used to find planets and their
moons. Difficulties in interpreting the structures arise for small planet
separation and when there are several moons in mean-motion resonance.
