Some Considerations on the Statistical Error Analysis in Holographic Interferometry with Application to an Optimized Interferometer

In-plane and out-of-plane motions of the human tympanic membrane

Computer-controlled digital holographic techniques are developed and used to measure shape and four-dimensional nano-scale displacements of the surface of the tympanic membrane (TM) in cadaveric human ears in response to tonal sounds. The combination of these measurements (shape and sound-induced motions) allows the calculation of the out-of-plane (perpendicular to the surface) and in-plane (tangential) motion components at over 1,000,000 points on the TM surface with a high-degree of accuracy and sensitivity. A general conclusion is that the in-plane motion components are 10-20 dB smaller than the out-of-plane motions. These conditions are most often compromised with higher-frequency sound stimuli where the overall displacements are smaller, or the spatial density of holographic fringes is higher, both of which increase the uncertainty of the measurements. The results are consistent with the TM acting as a Kirchhoff-Love's thin shell dominated by out-of-plane motion with little in-plane motion, at least with stimulus frequencies up to 8 kHz.

Three-dimensional vibrometry of the human eardrum with stroboscopic lensless digital holography

The eardrum or tympanic membrane (TM) transforms acoustic energy at the ear canal into mechanical motions of the ossicles. The acousto-mechanical transformer behavior of the TM is determined by its shape, three-dimensional (3-D) motion, and mechanical properties. We have developed an optoelectronic holographic system to measure the shape and 3-D sound-induced displacements of the TM. The shape of the TM is measured with dual-wavelength holographic contouring using a tunable near IR laser source with a central wavelength of 780 nm. 3-D components of sound-induced displacements of the TM are measured with the method of multiple sensitivity vectors using stroboscopic holographic interferometry. To accurately obtain sensitivity vectors, a new technique is developed and used in which the sensitivity vectors are obtained from the images of a specular sphere that is being illuminated from different directions. Shape and 3-D acoustically induced displacement components of cadaveric human TMs at several excitation frequencies are measured at more than one million points on its surface. A numerical rotation matrix is used to rotate the original Euclidean coordinate of the measuring system in order to obtain in-plane and out-of-plane motion components. Results show that in-plane components of motion are much smaller (<20%) than the out-of-plane motions’ components.

Measurement of three-dimensional deformation vectors with digital holography and stereophotogrammetry

We present a method to determine the three-dimensional (3D) deformation vectors of an arbitrary stressed object by combining stereophotogrammetry and digital holography in a setup with four cameras. The resulting data consists of a dense 3D point cloud, where every point is associated with a deformation vector. Our method is able to calculate the deformation without prior knowledge of the sensitivity vectors or the object surface. In the experimental setup only the base distance of the cameras needs to be known.

Miniaturized digital holography sensor for distal three-dimensional endoscopy

A miniaturized sensor head for endoscopic measurements based on digital holography is described. The system was developed to measure the shape and the three-dimensional deformation of objects located at places to which there is no access by common measurement systems. A miniaturized optical sensor, including a complete digital holographic interferometer with a CCD camera, is placed at the end of a flexible endoscope. The diameter of the head is smaller than 10 mm. The system enables interferometric measurements to be made at speeds of as many as five reconstructions per second, and it can be used outside the laboratory under normal environmental conditions. Shape measurements are performed with two wavelengths for contouring, and the deformation is measured by digital holographic interferometry. To obtain full three-dimensional data in displacement measurements we illuminate the object sequentially from three different illumination directions. To increase the lateral resolution we use temporal phase shifting.