Digital in-line Holography applied to fluid mechanics measurements

Holography is a process for recording the phase and amplitude of a light wave diffracted by an object in the form of an interference pattern. In the online version, the wave used to illuminate objects also serves as a reference wave. This is known as "Gábor holography", in reference to the physicist Dénes Gábor (Denis Gabor), who expounded its principle in 1948. Historically, holograms were recorded on high-resolution photographic plates. Digital holography arose from the replacement of these plates by digital matrix sensors (CCD, CMOS) from the 2000s onwards, following the idea first proposed in 1967 by J. W Goodman and R. W Laurence. Very early on, the technique was applied to experimental fluid mechanics studies, enabling the size, position and velocity of moving particles in a flow to be measured with a simple experimental set-up. In the 2000s, its 3D character positioned it as a promising alternative to tomographic methods of particle image velocimetry, which in their stereoscopic version can measure all three components of velocity fields, but are limited to one section of the flow. Today, despite the rapid development of three-dimensional particle tracking techniques using four (or more) cameras, holography still has many advantages. It can be adapted to complex experimental configurations where optical access is limited, and goes beyond the simple positioning of particles to simultaneously measure all their characteristics, from their size to information on their composition via their refractive index. However, holography comes up against a number of limitations. Measurement accuracy along the optical axis is often low with lensless in-line setups, due to the small numerical aperture. The density of particles that can be measured in a single acquisition is limited, which, like many other imaging methods, restricts it to dilute flows. Finally, in its simplest version, without additional image transfer optics, the measurement volume remains limited by the small size of the sensors. For these reasons, on-line digital holography remains essentially a laboratory technique. Nevertheless, it has strong development potential and is increasingly used by researchers and engineers, taking advantage of constant technological advances in sensors, in terms of size, resolution (ever-smaller pixels, down to 1 μm), dynamics (up to 16 real bits) and acquisition frequencies (several tens of kilohertz for images of several megapixels). This article describes on-line digital holography and its application to experimental fluid mechanics. The diffraction and light propagation phenomena on which the technique is based are reviewed in the first section within the framework of scalar optics. In the second part of the article, the most common optical set-ups and the various numerical reconstruction methods are described. The third...