Fig 1.
The four basic designs of Lenz lenses.
They are either made from solid metal (subfigures (a) and (b)) or wire material (sub-figures (c) and (d)), arranged symmetrically ((b) and (d)) or non-symmetrically ((a) and (c)). The slit(s) guide induced current I′ from the outer edge to the inner edge, while reversing the flow direction, as further depicted in (e), where two lenses are arranged in parallel in a Helmholtz pair like configuration, denoted as a double Lenz lens configuration.
Fig 2.
Simulated distribution of the z-component, Bz, of the B1 magnetic flux density for different geometrical arrangements and optimisation of the magnetic field’s homogeneity.
Note that the B0-field is oriented parallel to the planes of the coil pair and the lenses (e.g. along the x or y-axis). (a) The Bz-field induced by a Helmholtz pair and a variety of different lenses: i.e. none, one or two lenses of different inner loop size and/or axial position. The colour contour plots are all plotted on the yz-plane as depicted in the illustrative example at the upper right of the figure. (b) Three optimised systems consisting of a Helmholtz pair and either one, two or four lenses. The size and position of the lens elements have been optimised to maximise the amplification within a cylindrical volume, depicted in the yz-plane by the blue dashed rectangle, whilst constraining the average field error to be 1% within this region of interest. The example with four lenses exhibits a threefold amplification of field sensitivity.
Table 1.
Overview of the four different double Lenz lens variants manufactured.
Fig 3.
Obtained SNR line profiles from the different designs and at different excitation powers.
(a) Extracted SNR line profiles of LL1-LL4 and of the reference scan along the y-axis, as exemplified by the broken line in the reference image. All scans were acquired at a global flip angle of 90°. The mean noise was calculated from a 12 × 12 pixel matrix in the upper right corner of the same scan, as depicted. Statistics were derived from the regions illustrated by filled symbols. The powers for LL1 to LL4 and the reference scan were 0.18 W, 0.25 W, 0.18 W, 0.32 W and 1 W. (b) SNR profiles of LL4 at global flip angles of 90°, 106°, 119° and 126° and corresponding pulse powers of 0.32 W, 0.45 W, 0.56 W and 0.63 W. Statistics were derived from the regions illustrated by filled symbols.
Table 2.
Calculated mean, maximum, and standard deviation (STD) of the SNR values from Fig 3a and 3b as well as derived figures of merit.
Fig 4.
SNR line profiles to compare the measurements and the model developed above as well as to verify the influence of design parameters.
(a) Comparison of the measured SNR profile for LL4 and the simulated SNR profiles for two differently defined 90°-pulses: at the highest signal intensity in accordance with the experiment; at the centre-point of the arrangement. (b) Measured and simulated SNR profiles for LL3 at the 90°-pulse power. Simulated profiles were calculated for two different lens spacings (90 μm and 100 μm), while in both cases, the 90°-pulse was defined at the centre-point.
Fig 5.
Fabrication steps of the double Lenz lens chips.
(a) Au-electroplating of lenses on two glass substrates. (b) Lamination and structuring of dry film photoresist on first wafer. (c) UV-laser drilling of microfluidic ports into second wafer. (d) Adhesive full-wafer bonding of both substrates. (e) Dicing of individual chips.