Loudness equalization coefficient of lateral sound source at various distances in near-field

In free field, we can perceive the sound source distance depending on the loudness and near-field binaural cues. Binaural cues mainly include the interaural level difference (ILD) and interaural time difference (ITD), which can be calculated by using near-field head-related transfer function (HRTF). In order to focus on the influence of near-field binaural cues in experiment of sound source distance localization, the loudness decay related to the sound source distance can be removed or compensated by using loudness equalization coefficients, so that the loudness of sound sources at different distances are nearly constant. According to traditional operation method, the loudness equalization coefficient can be calculated using the distance factor r/r0 (r is the target distance, r0 is the reference distance). However, in near-field, the binaural loudness will be influenced by head-and-torso reflection and shadow effect and also the auditory difference among listeners. Therefore, we proposed the equalization coefficient consist of three parts, namely the distance factor r/r0, the near-field factor resulting from head-and-torso reflection and shadow effect, and the psychoacoustic scale of subjects' auditory loudness. The near-field factor can be obtained via aligning the impulse of HRTF, and the psychoacoustic scale can be obtained through distance localization experiment. In current work, we measured 8 subjects' loudness equalization coefficients of lateral sound sources from 0.2 m to 1.0 m. Results show that the loudness equalization coefficients decrease from 0.98 to 0.63 as the sound source distance increases. In addition, the coefficient is individualized, and also changes in different frequency bands, which is significant to the investigation of the sound source distance localization.