In this paper we characterise 3D optical imaging techniques as 3D linear shift invariant filtering operations. From the Helmholtz equation that is the basis of scalar diffraction theory we show that the scattered field, or indeed a holographic reconstruction of this field, can be considered to be the result of a linear filtering operation applied to a source distribution. We note that if the scattering is weak, the source distribution is independent of the scattered field and a holographic reconstruction (or in fact any far-field optical imaging system) behaves as a 3D linear shift invariant filter applied to the refractive index contrast (which effectively defines the object). We go on to consider tomographic techniques that synthesise images from recordings of the scattered field using different illumination conditions. In our analysis we compare the 3D response of monochromatic optical tomography with the 3D imagery offered by confocal microscopy and scanning white light interferometry (using with quassi-monochromatic illumination) and explain the circumstances in which these approaches are equivalent. Finally, we consider the 3D response of polychromatic optical tomography and in particular the response of spectral optical coherence tomography and scanning white light interferometry.

This paper presents the first application of digital speckle pattern interferometry (DSPI) to detect inhomogeneous heat generation on a superconducting ceramic at cryogenic temperatures. The light scattered by the object is recorded with a CCD camera at the same time as a smooth reference beam. Comparison of two non-simultaneous frames provides information about the out-of-plane deformation field. Spatial phase shifting is used in order to get a good quality fringe pattern. The technique has been applied as a non-destructive evaluation of the performance of ceramic high temperature superconducting materials. DSPI allows the determination of the point where a hot spot will be generated with heating levels that do not deteriorate the sample properties. An excellent agreement between DSPI hot spot location and the position of the melting point that appeared in a destructive experiment has been obtained.

Holographic Particle Image Velocimetry (HPIV) has been used successfully to make threedimensional, three-component flow measurements from holographic recordings of seeded fluid. It is clear that measurements can only be made in regions that contain particles, but simply adding more seeding results in poor quality images that suffer from the effects of multiple scattering. Optical Diffraction Tomography provides a means to reconstruct a 3D map of refractive index from coherent recordings of scattered fields with different illumination conditions. Although the Born Approximation limits the applicability of the technique to weakscattering problems, this approach has been used to create three-dimensional images using a Digital Holographic Microscope (DHM). A non-linear optimization technique, the Conjugated Gradient optimisation Method (CGM) has been previously proposed in microwave imaging for strong scattering problems. In this paper we propose a modification of the CGM which uses apriori information to reduce the number of unknown variables that characterize the object to the position of the seeders. Some 2D numerical experiments have been computed, showing promising results and the value of these is fluid velocimetry is discussed.

Scanning white light interferometry (SWLI) is an increasingly popular method to measure the surface profile of miniature components. Although it is tolerant to step changes in profile, its capability to measure the large surface gradients that are characteristic of high‐aspect‐ratio surfaces is limited. This is in part due to the numerical aperture of the objective lens which restricts the spatial frequency content of both the illumination and recorded fields. More fundamentally, though, SWLI instrumentation neglects the effects of multiple scattering and assumes that the field which illuminates the object is that which would be present if the object were absent. Although this is a reasonable approximation for slowly varying surfaces, it is generally not true for those with steep gradients. In this paper the 3D theory of SWLI is presented and the approximations made by current instrumentation are discussed in this context. Using finite element methods (FEM), SWLI interferograms are calculated, for the cases of 2D Silicon V‐grooves and step artefacts, and the effects of multiple scattering are illustrated. Methods to improve the capability of SWLI to measure large surface gradients, first by tilting the sample and subsequently by using an iterative FEM model to provide improved estimates of the illuminating conditions are introduced.

In this paper digital speckle pattern interferometry (DSPI) as a digital image plane holography (DIPH) technique is presented and its potential for fluid velocimetry are discussed. The recording is carried out with a spatial phase shifting (SPS) DSPI set-up, which can also be viewed as an off-axis DIPH set-up. A theoretical study of both SPS-DSPI analysis using a Fourier transform method and DIPH analysis is presented for a set-up with only one illuminated plane. From the DIPH analysis, a way to extend the SPS-DSPI set-up to simultaneously record but independently reconstruct several fluid planes is inferred. Some preliminary results from a convective flow illustrate the feasibility of the quasi 3D recording.