Homogeneous deformations: determination by fringe vectors in hologram interferometry

Measurements of three-dimensional shape and sound-induced motion of the chinchilla tympanic membrane

Opto-electronic computer holographic measurements were made of the tympanic membrane (TM) in cadaveric chinchillas. Measurements with two laser wavelengths were used to compute the 3D-shape of the TM. Single laser wavelength measurements locked to eight distinct phases of a tonal stimulus were used to determine the magnitude and the relative phase of the surface displacements. These measurements were made at over 250,000 points on the TM surface. The measured motions contained spatial phase variations consistent with relatively low-order (large spatial frequency) modal motions and smaller magnitude higher-order (smaller spatial frequency) motions that appear to travel, but may also be explained by losses within the membrane. The measurement of shape and thin shell theory allowed us to separate the measured motions into those components orthogonal to the plane of the tympanic ring, and those components within the plane of the tympanic ring based on the 3D-shape. The predicted in-plane motion components are generally smaller than the out-of-plane perpendicular component of motion. Since the derivation of in-plane and out-of plane depended primarily on the membrane shape, the relative sizes of the predicted motion components did not vary with frequency.

SUMMARY

A new method for simultaneously measuring the shape and sound-induced motion of the tympanic membrane is utilized to estimate the 3D motion on the membrane surface. This article is part of a special issue entitled "MEMRO 2012".

Holographic contour and deformation measurement using a 1.4 million element detector array

Holographic interferometry enables the measurement of object deformations due to stress induced by pressure, heat, or applied force and the measurement of surface shape. Real-time double-exposure holographic interferometry and phase-measurement interferometry have been combined to measure both static changes in objects and their shape. However, the number of detector points available has limited the number of fringes which can be measured. This paper shows results of measurements using a Videk Megaplus camera with 1320 x 1035 detector elements to enable measurements with high fringe densities. Results of measurement of object deformation and object shape show wavefronts with fringe densities up to 500 fringes per diameter can be measured with an rms repeatability of lambda/50.

The initial reaction of a macerated human skull caused by orthodontic cervical traction determined by laser metrology

Tensile forces were applied to the maxilla of a macerated human skull in a backward direction 10 degrees below the occlusal plane. The skull was fixed to a heavy metal support at the occipital and parietal bones. These forces were applied near the first permanent molars via a rigid stainless steel bar, which was fitted to a cast-metal splint attached to the palatal surface and buccal region of the maxillary arch. Forces were increased step by step from 2.0 N (1N = 100 grams) to 7.25 N per side. Using a holographic configuration with two 5 mW HeNe lasers, double-exposure holograms were made from the frontal and from the left lateral sides. Fringe shifts in different points of the hologram were measured and the x, y, and z components of the displacement were calculated for eight points located on various bones of the skull. Viewed from the frontal, force application to the maxilla resulted in a downward and backward rotation. The zygomatic bone was also rotated downward and backward with a small rotation in a transverse direction. Other craniofacial structures were also affected. With a force of 7.25 N per side, a deformation of the temporal bones and zygomatic arches occurred.

Determination of sensitivity vectors in hologram interferometry from two known rotations of the object

The fringes generated in holographic interferograms by independent rotations of an object are used to determine the sensitivity vectors of a hologram recording setup. This is done by identifying the fringes observed on the surface of a 3-D object with a fringe vector, which, in turn, equals the vector product of the sensitivity vector with object rotation. These vector relationships are formulated in terms of the projection matrices, and a least square error solution is derived that extracts the sensitivity vectors from the fringe data from two or more known rotations.

Holographic determination of rigid-body motions, and application of the method to orthodontics

A method for holographic determination of rigid-body motions is presented. In the calculations, parameters characterizing three or more arbitrarily chosen points on the object are used to evaluate translations and rotations, which, in turn, are entered in subsequent analysis of relative motions of deformed points on the object. This method finds particular applications in studies of orthodontic tooth movement.

Holographic strain analysis: an experimental implementation of the fringe-vector theory

The fringe-vector theory of holographic strain analysis was applied experimentally to determine strain and rotation tensors of rotated and deformed objects. One object was supported in a specially designed positioner, and the other was heated internally with a temperature controlled device. The rigid body motions and deformations were determined directly from the fringes that were observed on the surface of the object. This was done by taking photographs of the virtual image of the object from several different directions through the same hologram; the photographs were digitized manually, and the parameters obtained were, in turn, analyzed using a computer. The strains and rotations determined experimentally from holograms compared satisfactorily with the theoretical ones.

Implementation of hologram interferometry with a continuously scanning reconstruction beam

A system for fringe evaluation in hologram interferometry is studied in which a conjugate reconstruction beam scans the hologram, and the resulting fringe motion is observed in the real image of the object. The principle is suitable for semiautomatic evaluation. An earlier article presented a detailed theoretical analysis of the measuring principle, and the present paper deals with the practical aspects. It is shown that the system is capable of interpolating fringes to 1/100 of a fringe, which is experimentally verified by the determination of 3-D displacement components with an accuracy of about 40 nm and of strain with an accuracy of about 10 microstrain over an observation length of 1 cm. An analysis of the different error sources shows that the mechanical measures of the recording and evaluation setup have to be known to a small fraction of a millimeter.

Holographic strain analysis: extension of fringe-vector method to include perspective

A method has been published recently that permits determination of complete strain and rotation tensors of homogeneously deformed objects directly from fringes that are observed on their surfaces. However, the illumination and observation directions had to be considered constant over the regions of interest to apply the technique. This paper presents an extension of that theory to include both observation and illumination perspectives. It is shown that bulk translations of an object combine with linear variations in the directions of observation and illumination to generate fringe vectors that add directly to those generated by the object's homogeneous transformations. These linear variations are calculable from illumination and observation geometry.