Signal-to-noise ratio and aberration statistics in ocular aberrometry

We define a signal-to-noise ratio (SNR) for eye aberrometry in terms of the sensor geometry, measurement noise, and population statistics. The overall estimation error is composed of three main contributions: the bias in the estimated modes, the truncation error, and the error due to the noise propagation. This last term can be easily parametrized by the proposed SNR. We compute the overall error as well as the magnitude of its three components for a typical sensor configuration, population statistics, and different SNR. We show that there are an optimum number of Zernike aberration modes to be retrieved in each case.     

Amending the Anisotropy Barrier and Luminescence Behavior of Heterometallic Trinuclear Linear [MIILnIIIMII] (LnIII=Gd,Tb, Dy; MII=Mg/Zn) Complexes by Change from Divalent Paramagnetic to Diamagnetic Metal Ions

The sequential reaction of a multisite coordinating compartmental ligand [2‐(2‐hydroxy‐3‐(hydroxymethyl)‐5‐methylbenzylideneamino)‐2‐methylpropane‐1,3‐diol] (LH₄) with appropriate lanthanide salts followed by the addition of [Mg(NO₃)₂] ? 6 H₂O or [Zn(NO₃)₂] ? 6 H₂O in a 4:1:2 stoichiometric ratio in the presence of triethylamine affords a series of isostructural heterometallic trinuclear complexes containing [Mg₂Ln]³⁺ (Ln=Dy, Gd, and Tb) and [Zn₂Ln]³⁺ (Ln=Dy, Gd, and Tb) cores. The formation of these complexes is demonstrated by X‐ray crystallography as well as ESI‐MS spectra. All complexes are isostructural possessing a linear trimetallic core with a central lanthanide ion. The comprehensive studies discussed involve the synthesis, structure, magnetism, and photophysical properties on this family of trinuclear [Mg₂Ln]³⁺ and [Zn₂Ln]³⁺ heterometallic complexes. [Mg₂Dy]³⁺ and [Zn₂Dy]³⁺ show slow relaxation of the magnetization below 12 K under zero applied direct current (dc) field, but without reaching a neat maximum, which is due to the overlapping with a faster quantum tunneling relaxation mediated through dipole–dipole and hyperfine interactions. Under a small applied dc field of 1000 Oe, the quantum tunneling is almost suppressed and temperature and frequency dependent peaks are observed, thus confirming the single‐molecule magnet behavior of complexes [Mg₂Dy]³⁺ and [Zn₂Dy]³⁺.