Extended algebraic reconstruction technique (ART) for density-gradient projections: Laser speckle photographic tomography

An extended algebraic reconstruction technique (ART) is presented for tomographic image reconstruction from the density-gradient projections, such as laser speckle photography. The essence of the extended ART is that the density-gradient projection data of speckle photography are first numerically integrated to the algebraic representation of interferometric fringe number data, which ART can readily reconstruct into the cross-sectional field. The extended ART is numerically examined by using two computer synthesized phantom fields, and experimentally by using asymmetric single and double helium jets in air. The experimentally reconstructed images were also compared with the direct measurements of helium concentration using an oxygen analyzing probe. The extended ART method shows an improved accuracy and is proposed to use to tomographically reconstruct the density-gradient projections over the previous Fourier convolution (FC) method.