# Headphone-To-Ear Transfer Function Estimation Using Measured Acoustic Parameters
## 1 Introduction  
The headphone-to-ear transfer function (HpTF) is defined as the electroacoustic transfer function from the input of a headphone to the sound pressure at the eardrum [1]. In general, HpTFs can be measured by using standard ear simulators on dummy heads. However, current standard ear simulators with fixed acoustic structures cannot simulate the average human ears above 10 kHz and individual differences in ear canal geometry and eardrum impedance [2]. Thus, HpTFs measured by standard ear simulators may not be satisfactory if individual HpTFs over the audible frequency range are needed. It is shown that HpTFs vary considerably with headphones and listeners [3; 4]. In the time domain, the impulse response of the HpTF involves the reflections between the inner surface of the headphone and the eardrum. If binaural signals are reproduced through headphones, these reflections interfere with the sound localization cues formed by direction-dependent pinna reflections in the binaural signals, and may cause the front-back confusion in sound localization [5; 6]. In the frequency domain, HpTFs introduce timbre distortions [7; 8]. Therefore, to faithfully reproduce binaural signals to different listeners through headphones, HpTFs need to be characterized and compensated.  
Theoretically, HpTFs should be measured at a point in the ear canal where the binaural signal is recorded [9]. However, direct measurements of individual HpTFs inside human ear canals are difficult and risky. Recently, a method of estimating the HpTF given the headphone acoustic reflectance and equivalent sound source to the ear canal, the ear canal area function and the eardrum impedance has been developed [10]. This means that HpTFs for different headphones and listeners can be estimated through computations based on the parameters of headphones and external ears. In previous studies, there have been some results of the eardrum impedance and reflectance [11] and the ear canal cross-sectional area functions [12; 13] measured on human ears. Furthermore, a method for estimatingeardrum reflectance and ear canal cross-sectional area functions from ear canal input impedance has also been presented [14]. Thus, in order to estimate the HpTFs for different headphones, the headphone acoustic reflectance and equivalent sound source to the ear canal need to be measured.  
The acoustic reflectance of a headphone to the ear canal can be measured by using a single microphone at five measurement positions in an impedance tube sequentially [10]. However, it may be time-consuming to perform sequential measurements if a large number of headphones need to be measured, especially for a wide frequency range with a linear frequency step. To solve this problem, five microphones are simultaneously used to measure the sound pressure signals in the impedance tube [15]. With respect to the determination of the headphone equivalent sound source to the ear canal, some researchers utilize known acoustic impedance as reference loads [16; 17]. However, acoustic loads made of long tubes may result in some operation difficulties in the experiments, and the measurement accuracy may be degraded by using the probe microphones as well.  
In this paper, an optimal five-microphone array method for measuring the headphone acoustic reflectance and equivalent sound sources needed in the estimation of HpTFs is presented. In contrast to the previous work [15], a compensation function is introduced to compensate the mismatch between microphone sensitivities, and the measurement accuracy of the proposed measurement method is further improved by using a two-stage searching algorithm. The performance of the measurement method is theoretically evaluated and experimentally investigated. With the measured headphone acoustic reflectance and equivalent sound sources, HpTFs for different headphones and ear canal area functions are then estimated through computations based on an acoustic model.