Various attempts to measure precisely impulse response waveforms and frequency transfer functions of a plastic optical fiber (POF) of 1mm in diameter and 0.5 in N.A. are reported in this paper. The waveforms showed a remarkable difference when the POF end surface was placed at the glass window position of the hermetic container of the photodiode (PD) on one hand, and in contact with the semiconductor surface after breaking the glass on the other. An optical oscilloscope (OOS) was tested. Output waveforms measured with the OOS showed insignificant differences from those measured with the PD with the POF end surface placed at the glass window position. The waveforms measured with the PD changed their profiles as the POF length was varied: The peak of the pulse moved from the pulse rear to the front with increasing length. Waveforms theoretically calculated by using measured far-field patterns (FFPs) and non-scattering approximation could clearly explain the features of the measured waveforms. Measurements of frequency transfer functions were carried out by using a newly designed 1:1 relay lens placed in front of the PD. The measured transfer function was characterized by well-known large attenuation at the frequency equal to the reciprocal of the waveform width. The frequency transfer function measured with and without the relay lens especially showed a difference at the frequency mentioned above.