Optical diffraction tomography in fluid velocimetry: the use of a priori information

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

Holography, tomography and 3D microscopy as linear filtering operations

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