The three-point criterion for sparks in focus. (A) The spatial (z) profile of fluorescence of a spark, represented as a Gaussian function, of σ = 1.4 µm, centered at ζ = 0 (black), 0.825 (red), or 1.65 (green). Segments a1–a3, b1–b3, and c1–c3 join the intersections of these curves with the lines at z1 (−1 µm) and z3 (+1 µm). The difference between the ordinates at these intersections increases as the central abscissa ζ moves away from z = 0. (B) δ, absolute value of the difference between fluorescence at z = z1 and z = z3, normalized by the value at z = z2 (according to Eq. A1), and plotted versus ζ, the central position (z value) of the Gaussian spark. Note that sparks of σ = 1.4 µm will have δ < 0.2 (or 20%) when their central z value satisfies the inequalities, −0.37 ≤ ζ ≤ 0.37, in other words, when the origin of release is within a spatial slice of height 2 × 0.37 (or 2D). (C) Generalization of the calculation in B to include σ as a variable. δ, calculated by Eq. A1, is plotted versus ζ and FWHM = (2 × ln2)1/2σ. This function works as a threshold criterion (hence it is labeled C3) as follows: given a set thickness 2D of the slice of space deemed to be in focus, an experimentally recorded spark will be in focus if its calculated δ is ≤C3 at the set value of D and the FWHM measured for the individual spark. In the graph, the line plots are intersections of the C3 (D, FWHM) surface by planes of constant C3 (black), D (red), or FWHM (green).
