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.
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