  We describe operation of the CESR-TA vertical beam size monitor (xBSM) with
$e^\pm$ beams with $E_{\rm b}$=4 GeV. The xBSM measures vertical beam size by
imaging synchrotron radiation x-rays through an optical element onto a detector
array of 32 InGaAs photodiodes with 50 $\mu$m pitch. The device has previously
been successfully used to measure vertical beam sizes of 10-100 $\mu$m on a
bunch-by-bunch, turn-by-turn basis at $e^\pm$ beam energies of $\sim$2 GeV and
source magnetic fields below 2.8 kG, for which the detector required
calibration for incident x-rays of 1-5 keV. At $E_{\rm b}=4.0$ GeV and $B$=4.5
kG, however, the incident synchrotron radiation spectrum extends to $\sim$20
keV, requiring calibration of detector response in that regime. Such a
calibration is described and then used to analyze data taken with several
different thicknesses of filters in front of the detector. We obtain a relative
precision of better than 4% on beam size measurement from 15-100 $\mu$m over
several different ranges of x-ray energy, including both 1-12 keV and 6-17 keV.
The response of an identical detector, but tilted vertically by 60$^\circ$ in
order to increase magnfication without a longer beamline, is measured and shown
to improve x-ray detection above 4 keV without compromising sensitivity to beam
size. We also investigate operation of a coded aperture using gold masking
backed by synthetic diamond.
