The detectors in positron emission tomography (PET) can be based on detection of Cherenkov light instead of the traditional approach of using scintillation light. This enables excellent time resolution that can be used in time-of-flight (TOF) PET, but it proved difficult to achieve efficiency in detection of annihilation gammas comparable to traditional methods. The Cherenkov method however has another advantage - low cost of the most suitable conversion material (lead fluoride) compared to the most commonly used scintillators. Especially when incorporating silicon photomultiplier (SiPM) photodetectors, such PET detectors could be realized at a very competitive price. In this work the performance of such PET module is presented, with an emphasis on the efficiency of detection. Two modules consisting of 4x4 lead fluoride Cherenkov radiator arrays coupled to Hamamatsu 4x4 SiPM arrays were assembled and their performance was tested using annihilation gammas from a sodium source.