  The detection and characterization of Earth-like exoplanets is one of the
major science drivers for the next generation of telescopes. Current direct
imaging instruments are limited by evolving non-common path aberrations
(NCPAs). The NCPAs must be compensated for by using the science focal-plane
image. A promising sensor is the self-coherent camera (SCC). An SCC modifies
the Lyot stop in the coronagraph to introduce a probe electric field. However,
the SCC has a weak probe electric field due to the requirements on the pinhole
separation. A spectrally modulated self-coherent camera (SM-SCC) is proposed as
a solution to the throughput problem. The SM-SCC uses a pinhole with a spectral
filter and a dichroic beam splitter, which creates images with and without the
probe electric field. This allows the pinhole to be placed closer to the pupil
edge and increases the throughput. Combining the SM-SCC with an integral field
unit (IFU) can be used to apply more complex modulation patterns to the pinhole
and the Lyot stop. A modulation scheme with at least three spectral channels
(e.g. IFU) can be used to change the pinhole to an arbitrary aperture with
higher throughput. Numerical simulations show that the SM-SCC increases the
pinhole throughput by a factor of 32, which increases the wavefront sensor
sensitivity by a factor of 5.7. The SM-SCC reaches a contrast of
$1\cdot10^{-9}$ for bright targets in closed-loop control with the presence of
photon noise, phase errors, and amplitude errors. The contrast floor on fainter
targets is photon-noise-limited and reaches $1\cdot10^{-7}$. For bright
targets, the SM-SCC-IFU reaches a contrast of $3\cdot10^{-9}$ in closed-loop
control with photon noise, amplitude errors, and phase errors. The SM-SCC is a
promising focal-plane wavefront sensor for systems that use multiband
observations, either through integral field spectroscopy or dual-band imaging.
