  Many areas of optical science require an accurate measurement of optical
spectra. Devices based on laser speckle promise compact wavelength measurement,
with attometer-level sensitivity demonstrated for single wavelength laser
fields. The measurement of multimode spectra using this approach would be
attractive, yet this is currently limited to picometer resolution. Here, we
present a method to improve the resolution and precision of speckle-based
multi-wavelength measurements. We measure multiple wavelengths simultaneously,
in a device comprising a single 1 m-long step-index multimode fiber and a fast
camera. Independent wavelengths separated by as little as 1 fm are retrieved
with 0.2 fm precision using Principal Component Analysis. The method offers a
viable way to measure sparse spectra containing multiple individual lines and
is likely to find application in the tracking of multiple lasers in fields such
as portable quantum technologies and optical telecommunications.
