  It is generally thought that correcting chromatic aberrations in imaging
requires multiple surfaces. Here, we show that by allowing the phase in the
image plane of a flat lens to be a free parameter, it is possible to correct
chromatic aberrations over an almost unlimited bandwidth with a single
diffractive surface. Specifically, we designed, fabricated and characterized a
flat multi-level diffractive lens (MDL) that images at the wavelengths from
450nm to 850nm. We experimentally characterized the focusing efficiency,
modulation-transfer function, wavefront aberrations, vignetting, distortion and
signal-to-noise ratio performance of a camera comprised of this MDL and a
conventional image sensor. Further, we designed two MDLs with operating
wavelengths from 500nm to 15{\mu}m, and from 2{\mu}m to 150{\mu}m,
respectively. With no apparent limitation in the operating bandwidth, such flat
lenses could replace multiple refractive surfaces that are traditionally
required for chromatic corrections, leading to thinner, lighter and simpler
imaging systems with bandwidth limited primarily by the quantum efficiency of
the sensor.
