A Cherenkov detector based on an array of five lead fluoride ($beta$-PbF$_2$) crystals of size 30 mm$times$30 mm$times$160 mm read out by reverse-type avalanche photodiodes (APDs) of active area 10 mm$times$10 mm was used to measure the flux of secondary particles emerging from the annihilation of pulsed beams of antiprotons at the Antiproton Decelerator of CERN. We compared the relative photon yields of radiators made of $beta$-PbF$_2$, fused silica, UV-transparent acrylic, lead glass, and a lead-free, high-refractive-index glass. Some {it p-i-n} photodiodes were also used for the readout, but the output signals were dominated by the nuclear counter effect (NCE) of secondary particles traversing the 300 $mu{rm m}$ thick depletion regions of the photodiodes. Smaller NCE were observed with the APDs, as the maximum electronic gain in them occurred predominately for electron-ion pairs that were generated in the thin ${it p}$-type semiconductor layer that proceeded the {it p-n} junction of high electric field where amplification took place.
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