## 2 Materials and Methods
### Principle of High-Speed Holographic for Shape and Displacement Measurements
#### 2.1.2 High-Speed Digital Holographic (HDH) Method for Displacement Measurement  
We have previously developed and implemented the HDH method based on correlation interferometry that could \"instantaneously\" measure the full-field-of-view (\(>\)200,000 points at 67,200 camera frame rate) transient displacements of the TM in response to impulsive acoustical and mechanical excitations [24; 28; 30]. As described in [31], the HDH uses [PERSON]'s correlation to locate two reference frames \(I_{ref}\) and \(I_{ref+\pi/2}\) with 0 and \(\pi\)/2 prior to the sample's excitation based on Equation (3). The zero-order terms of all correlated kernels are removed by summation of reference frames that are within one period of optical phase shifts. The interference phase \(\Delta\theta\) as a result of the sample's motion of a small window centered at (\(x\), \(y\)) is  
\[\Delta\theta(t)=arctan  
fresh non-fixed human postmortem temporal bones were used for the measurements. The cartilaginous and bony parts of the ear canal were removed to provide optical access to the TM. The middle-ear cavity was opened to check the health of the middle-ear ossicles, and then it was sealed using the sealing cement. A small metal tube was installed through the eustachian tube for injecting fluid into the middle-ear cavity. The TM surface was sprayed with a thin layer of HOLBEIN water soluble oil color (commercial trade name: TITANIUM WHITE) using a commercially available airbrush (MASTER(r) Model S68).  
Primary experiments measured the transient TM responses to a short acoustic click (i.e., a 50 us square pulse) generated by a speaker, as shown in Figure 1, and the TM shape information to calculate the true out-of-plane motion of the entire TM [4]. We also acquired the acoustic excitation profile using a high-frequency microphone situated close to the TM, as shown in Figure 1. After the control measurement on the normal ear (closed middle-ear cavity), the sample was subjected to a series of manipulations that simulated different middle-ear conditions and pathologies. The manipulations included: (i) open middle-ear cavity, (ii) closed middle-ear cavity, (iii) injecting saline into the middle-ear cavity to the level of half TM in contact with fluid, as shown in Figure 2b, (iv) injecting saline until the full TM was in contact with fluid, (v) removing the injected fluid, (vi) immobilizing the footplate of the stapes with super glue, and (vii) interrupting the incudo-stapedial (IS) joint, as shown in Figure 2c. The shape and transient acoustic-induced displacements were measured at each manipulation (experimental setup is shown in Figure 2a). The human temporal bone study was approved by the Institutional Review Board of the Massachusetts Eye and Ear Infirmary. The use of de-identified human cadaveric tissue (only age and gender information are available) does not require a human subject study protocol.  
Figure 1: Schematic of high-speed digital holographic (HDH) system [4]. The 532 nm laser is used for displacement measurements, and the 770–780 nm tunable laser is used for shape measurements. The two lasers are coupled into the same optical path to ensure the shape and displacement measurements are in the same coordinate system avoiding the need for image registration.