"Time-averaged holography" and "holographic interferometry" enable recording of the complete vibration pattern of a surface within several seconds. The results appear in the form of fringes. Vibration amplitudes smaller than 100 nm are not readily measurable by these techniques, because such small amplitudes produce variations in gray level, but not fringes. In practice, to obtain clear fringes in these measurements, stimulus sound pressures higher than 100 dB SPL must be used. The phase of motion is also not obtainable from such fringe techniques. In this study, a sinusoidal phase modulation technique is described, which allows detection of both small amplitudes of motion and their phase from time-averaged speckle pattern interferometry. In this technique, the laser injection current is modulated and digital image processing is used to analyze the measured patterns. When the sound-pressure level of stimuli is between 70 and 85 dB SPL, this system is applied to measure the vibratory response of the tympanic membrane (TM) of guinea pig temporal bones at frequencies up to 4 kHz where complicated vibration modes are observed. The effect of the bulla on TM displacements is also quantified. Results indicate that this system is capable of measuring the nanometer displacements of the TM, produced by stimuli of 70 dB SPL.

An improved illumination system is proposed for creating a temporally coherent and spatially incoherent extended source to be used for spatial coherence control and reconstruction of a coherent hologram. Taking into account the fact that a rotating ground glass does not behave as an ideal Lambertian diffuser, the new illumination system tailors the directivity of the scattered lights to direct the lights efficiently into an interferometer so that a spatial coherence function can be better controlled and detected with higher fidelity. Experimental results are presented that demonstrate improved performance of the proposed system.

We propose a model-based fringe analysis technique that enables the Fourier transform method to analyze dense fringe patterns with large phase variations. The conventional Fourier-transform method has a limited dynamic range of measurable phase because the Fourier spectra broadened by large phase variations cannot be separated by the spatial carrier frequency. Our model-based iterative technique effectively narrows the broad spectrum and reduces phase errors. Results of simulations and experiments are presented that demonstrate the validity of the proposed spectrum-narrowing technique for high-density fringe patterns.

We propose a general approach to eliminating some error source effects in phase-calculation algorithms for phase-shifting interferometry. We express the actual phase shift in a convenient form that takes the errors into account and develop in series the detected phase from a generic algorithm. Setting to zero the terms of the series that involve unwanted errors leads to a set of linear equations for the algorithm coefficients, which can thus be found. By using this approach, one could develop an algorithm series for an individual interferometer based on relevant concerns about the main error sources in it and eliminate the error source effects to any desired order. Two examples of algorithm series, to eliminate distorted phase shifts caused by the geometric effect in an interferometer with a spherical Fizeau cavity and to eliminate vibration effects, are discussed.

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