Holographic particle image velocimetry: analysis using a conjugate reconstruction geometry

Holographic recording techniques have recently been studied as a means to extend two-component, planar particle image velocimetry (PIV) techniques for three-component, whole-field velocity measurements. In a similar manner to two-component PIV, three-component, holographic PIV (HPIV) uses correlation-based techniques to extract particle displacement fields from double-exposure holograms. Since a holographic image contains information concerning both the phase and the amplitude of the scattered field it is possible to correlate either the intensity or the complex amplitude. In previous work we have shown that optical methods to compute the autocorrelation of the complex amplitude are inherently more tolerant to aberrations introduced in the reconstruction process, Coupland, Halliwell, Proc. Roy. Soc. 453 (1960) (1997) 1066. In this paper we introduce a new method of holographic recording and reconstruction that allows a constant image shift to be introduced to the particle image displacement. The technique, which we call conjugate reconstruction, resolves directional ambiguity and extends the dynamic range of HPIV. The theory of this method is examined in detail and a relationship between the image and object displacement is derived. Experimental verification of the theory is presented.