David P. Towers

Optimum frequency selection in multifrequency interferometry

We describe a novel technique for measurement of absolute order of interference in multifrequency interferometry. An optimization criterion is introduced that leads to frequency selection formulations that are optimized with respect to the minimum number of frequencies required for achieving the maximum target dynamic range. The method is generalized to N frequencies and gives a definition of measurement reliability. We demonstrate the technique by means of coherent fringe projection for nonintrusive, full-field profilometry. Experimental data for three frequencies are presented.

Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multi-wavelength interferometry.

We present a computationally efficient method for solving the method of excess fractions used in multi-frequency interferometry for absolute phase measurement. The Chinese remainder theorem, an algorithm from number theory is used to provide a unique solution for absolute distance via a set of congruences based on modulo arithmetic. We describe a modified version of this theorem to overcome its sensitivity to phase measurement noise. A comparison with the method of excess fractions has been performed to assess the performance of the algorithm and processing speed achieved. Experimental data has been obtained via a full-field fringe projection system for three projected fringe frequencies and processed using the modified Chinese remainder theorem algorithm.

Generalized frequency selection in multifrequency interferometry

We present a generalized frequency selection method for N-frequency interferometry to form an optimum geometric series at synthetic wavelengths. The absolute range that is measurable is bounded by the number of beat frequency operations, phase noise, and the number of wavelengths used to form the geometric series of synthetic wavelengths. Theoretical predictions are compared with experimental results from a full-field fringe projector. A comparison of this technique with the method of excess fractions shows orders-of-magnitude faster processing with similar measurement reliability.

Fiber interferometer for simultaneous multiwavelength phase measurement with a broadband femtosecond laser

We present a fiber interferometer for the simultaneous measurement of phase at multiple wavelengths from a single broadband femtosecond laser. Narrow-bandwidth fiber Bragg gratings isolate a particular frequency from the broad-bandwidth laser pulse produced. The multiwavelength phase data permit the unambiguous measurement range to be significantly increased compared with the wavelengths used in the interferometer. Preliminary experimental results are presented for a two-frequency sensor with an absolute range of 0.13 mm and associated dynamic range of 43,000:1.

Multipoint laser vibrometer for modal analysis

Experimental modal analysis of multifrequency vibration requires a measurement system with appropriate temporal and spatial resolution to recover the mode shapes. To fully understand the vibration it is necessary to be able to measure not only the vibration amplitude but also the vibration phase. We describe a multipoint laser vibrometer that is capable of high spatial and temporal resolution with simultaneous measurement of 256 points along a line at up to 80 kHz. The multipoint vibrometer is demonstrated by recovering modal vibration data from a simple test object subject to transient excitation. A practical application is presented in which the vibrometer is used to measure vibration on a squealing rotating disk brake.

Lasers measure up for the car industry

This paper details the use of laser interferometry techniques in automotive engineering. Optical (laser) instruments can provide measurements over extended areas, yielding simultaneous sub-micron scale information about the shape, vibration and deformation of components, including complete car bodies. Laser measurement techniques can be non-contacting and non-destructive and data are captured as an image of the object. This article concentrates on electronic speckle pattern interferometry (ESPI) and related developments in structured-light techniques. The theory of interferometry and the techniques used are described. Some applications include stress analysis of engineered components, used in engine development work: the ESPI system produced for this purpose is detailed. Structured light techniques are used to investigate wind-induced distortion of a convertible soft-top sports car. Further uses include vibration analysis. Potential future developments of the laser measurement systems are considered.

Fiber-optic delivery of high-peak-power Q-switched laser pulses for in-cylinder flow measurement

A bundle of optical fibers was constructed to deliver Q-switched frequency-doubled Nd:YAG laser pulses for the purpose of particle image velocimetry. Data loss that is due to fiber speckle was reduced by ensuring that each fiber was different in length by more than the coherence length of the laser being delivered. Hence, their speckle patterns will overlap but not interfere, producing more even illumination that is shown to reduce data loss. A custom-made diffractive optical element and careful endface preparation help to reduce damage to the fibers by the required high peak powers. With this method, pulse energies in excess of 25 mJ were delivered for a series of experimental trials within the cylinder head of an optically accessed internal combustion engine. Results from these trials are presented along with a comparison of measurements generated by conventionally delivered beams.

Hollow-core waveguides for particle image velocimetry

The use of a hollow-core fibre waveguide to deliver a light sheet for particle image velocimetry (PIV) inside an optically accessed internal combustion engine is presented. Fibre delivery applied to such small scale, high-speed fluid flow applications gives the potential to minimize the optical access required to an enclosed measurement volume. A 0.54 mm internal diameter hollow fibre was used to deliver 13 mJ, 8 ns pulses from a frequency-doubled (532 nm) Nd:YAG laser. The output from the fibre was focused into a thin light sheet and used to take PIV measurements as the test engine was cycled. Comparative measurements were also taken using a conventionally (bulk optic) delivered light sheet with closely similar properties. The PIV data taken using the two techniques are compared to demonstrate that the use of a hollow-core fibre generates similar data quality to conventional measurement techniques and is a viable alternative when complex access is required.

Generalized multifrequency selection for full-field interferometric shape measurement

We present two novel multi-frequency techniques for absolute range measurement in interferometry. A comparison of these techniques with the method of excess fractions has been performed by computer simulation and experimental data is presented.

Multi-wavelength phase unwrapping: a versatile tool for extending the measurement range, breaking the Nyquist limit, and encrypting optical communications

Multi-wavelength phase unwrapping techniques have traditionally been used to unwrap the phase at the shortest measurement wavelength, where numerous techniques have been developed with distinct advantages for a given application. Nevertheless, multi-wavelength techniques are more than phase unwrapping approaches: super-sensitive multiwavelength interferometers have a lower uncertainty than conventional interferometers, multi-wavelength techniques can break the Nyquist limit and thereby relax the requirements on the measurement system, and multi-wavelength techniques have also unconventional applications as e.g. optical encryption. This work discusses different multi-wavelength techniques, derives new noise criteria with no approximations, and outlines important, but still little researched areas of multi-wavelength phase unwrapping techniques.