  The design of a complex phase mask (CPM) for inscribing aperiodic filters in
fibers is presented. The complex structure of the mask surface relief consists
of discrete aperiodic phase-steps at periodic intervals. We show that the
diffraction of the inscribing laser beam from the phase-step locations of the
CPM produces periodically located half phase-steps along the fiber. The
accumulated phase, along with controlled index modulation, generates the
desired aperiodic reflection spectrum. Compared to a complex 'running-light'
interferometry based inscription method, CPM offers the well known convenience
and reproducibility of the standard phase mask inscription technique. The
complexity of an aperiodic grating is encoded into the structure of the CPM.
Complex filters fabricated with CPM can be used for suppressing the near
infrared (NIR) OH- emission lines generated in the upper atmosphere, improving
the performance of ground based telescopes.
