  We present the design and test results of a compact optical fiber
double-scrambler for high-resolution Doppler radial velocity instruments. This
device consists of a single optic: a high-index $n$$\sim$2 ball lens that
exchanges the near and far fields between two fibers. When used in conjunction
with octagonal fibers, this device yields very high scrambling gains and
greatly desensitizes the fiber output from any input illumination variations,
thereby stabilizing the instrument profile of the spectrograph and improving
the Doppler measurement precision. The system is also highly insensitive to
input pupil variations, isolating the spectrograph from telescope illumination
variations and seeing changes. By selecting the appropriate glass and lens
diameter the highest efficiency is achieved when the fibers are practically in
contact with the lens surface, greatly simplifying the alignment process when
compared to classical double-scrambler systems. This prototype double-scrambler
has demonstrated significant performance gains over previous systems, achieving
scrambling gains in excess of 10,000 with a throughput of $\sim$87% using
uncoated Polymicro octagonal fibers. Adding a circular fiber to the fiber train
further increases the scrambling gain to $>$20,000, limited by laboratory
measurement error. While this fiber system is designed for the Habitable-zone
Planet Finder spectrograph, it is more generally applicable to other
instruments in the visible and near-infrared. Given the simplicity and low
cost, this fiber scrambler could also easily be multiplexed for large
multi-object instruments.

Instrumentation and Methods for Astrophysics;Earth and Planetary Astrophysics