The paper presents optimal strategies for precise measurement of diffusion in anisotropic systems using magnetic resonance imaging (MRI). The authors describe an algorithm that minimizes bias in measurements by spreading them out in 3-dimensional gradient vector space. They also optimize the set of \( b \)-matrices and echo times to estimate the diffusion tensor and its scalar invariants. The optimized scheme reduces the standard deviation in the tensor trace estimate by more than 40% and artefactual anisotropy by more than 60% compared to conventional schemes. The optimized schemes are shown to improve scan times, precision, and resolution in diffusion tensor images. The theory behind the optimization is detailed, including the estimation of the diffusion tensor and its trace, and the effects of transverse relaxation on optimal parameters. Experimental results in a water phantom and human brain demonstrate the advantages of the optimized schemes, including higher signal-to-noise ratios and improved contrast between white matter structures. The optimal strategies can be applied to any diffusion-weighted sequence if all timings are known.The paper presents optimal strategies for precise measurement of diffusion in anisotropic systems using magnetic resonance imaging (MRI). The authors describe an algorithm that minimizes bias in measurements by spreading them out in 3-dimensional gradient vector space. They also optimize the set of \( b \)-matrices and echo times to estimate the diffusion tensor and its scalar invariants. The optimized scheme reduces the standard deviation in the tensor trace estimate by more than 40% and artefactual anisotropy by more than 60% compared to conventional schemes. The optimized schemes are shown to improve scan times, precision, and resolution in diffusion tensor images. The theory behind the optimization is detailed, including the estimation of the diffusion tensor and its trace, and the effects of transverse relaxation on optimal parameters. Experimental results in a water phantom and human brain demonstrate the advantages of the optimized schemes, including higher signal-to-noise ratios and improved contrast between white matter structures. The optimal strategies can be applied to any diffusion-weighted sequence if all timings are known.