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Fresnel beamforming is a beamforming method that has a delay profile with a shape similar to a physical Fresnel lens. With 4-8 transmit channels, 2 receive channels and a network of single-pole/single-throw switches, Fresnel beamforming can reduce the size, cost and complexity of a beamformer. The performance of Fresnel beamforming is highly dependent on focal errors due to phase wraparound and quantization of its delay profile. Compared to linear arrays, curvilinear arrays have larger path length differences among elements, which result in larger focal errors. In this paper, we present the concept and performance evaluation of Fresnel beamforming combined with a novel clutter suppression method, dual apodization with cross-correlation (DAX), for curvilinear arrays. The spatial resolution and contrast-to-noise ratios (CNR) obtained from simulation and experiment show that Fresnel beamforming followed by DAX has higher CNR and comparable spatial resolution compared to delay-and-sum (DAS) beamforming. We also evaluate the performance of Fresnel beamforming in the presence of phase aberration and sound speed error.