# Headphone-To-Ear Transfer Function Estimation Using Measured Acoustic Parameters
## 3 Experiments  
### Measurements of Headphone Acoustic Reflectance  
The proposed five-microphone array method is used here to measure the acoustic reflectance for different headphones in a customized impedance tube, which is made of stainless steel with an inner diameter of 8 mm, an outer diameter of 20 mm, and a total length of 380 mm. One end of this tube is connected to a standard small right pinna simulator DB 61 removed from the KEMAR dummy head, and the other end is connected to a sound source (headphone). At the measurement positions, five miniature microphones (Sonion 8002, Suzhou, China) are flush mounted on the tube.  
To compensate the microphone mismatch, the frequency responses of all microphones are sequentially measured at position \(x_{1}\) in the impedance tube. The B&K PULSE 3560C  
Figure 2: (Color online) Comparisons of singularity factors determined by the uniform microphone array (blue), the previous five non-uniform microphone array [15] and the optimal microphone array (green).  
(Naerum, Denmark) drives the sound source to produce a linear sweep signal from 20 Hz to 20 kHz. Then the compensation functions in terms of Equation (3) can be determined as  
\[J_{n}(f)=\frac{M_{n}(f)}{M_{1}(f)}=\frac{U_{n}(f)}{U_{1}(f)},\quad n=1,2,\ldots,5, \tag{15}\]  
where \(U_{n}(f)\) denotes the frequency response of the \(n\)th microphone measured at position \(x_{1}\). The compensation functions obtained by Equation (15) are shown in Figure 3. After compensation, the five microphones are mounted at the positions \(x_{1}\) to \(x_{N}\), and the sound source plays the same sweep signal. With the measured compensation functions and sound pressure signals, the headphone acoustic reflectance \(r_{0}(f)\) can be determined by the Equations (7) and (8).  
In the experiments, three different types of (insert, semi-open, closed-back) headphones are measured. As shown in Figure 4, the headphone chosen as a representative of each of the headphone type is Huawei AM12 (insert), Beyerdynamic DT880 (semi-open circumaural) and AKG K550 (closed-back circumaural). Figure 5a,b show the magnitude and phase responses of the acoustic reflectance for the above three different types of headphones measured using the proposed five-microphone array method. To validate the proposed method, the magnitude and phase responses of the headphone acoustic reflectance obtained with the single microphone method, which is sequentially measured at each measurement position, are also presented (blue lines) in Figure 5a,b. It can be seen that the results measured by the proposed method are in good agreement with those measured by using the single microphone method, suggesting that the proposed method for accurate measurements of the headphone acoustic reflectance over a wide frequency range is reliable. It should be mentioned that, the measurement results without the compensation function are close to those obtained with the compensation function. This is because the magnitudes of the compensation functions are less than 3 dB, which shows good consistency for all microphones.  
Figure 4: (Color online) The insert, semi-open and closed-back headphones used in the experiments.  
Figure 3: (Color online) The measured \(J_{1}\) to \(J_{5}\) used for compensating the microphone mismatch in the proposed five-microphone array.