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Table 2

Interpolation algorithms (IA) or subpixel minimum finding algorithms.

Acronym Name Location of minimum

2LS 2D Least squares (x2,y2) where 
2QI 2D Quadratic interpolation (x2,y2) where 
1LS 1D Least squares (x1,y1) using a2,a3,a4,a5 from 2LS above
1QI 1D Quadratic interpolation (x1,y1) using a2,a3,a4,a5 from 2QI above

Notes. Notation in the table refers to the elements, si,j, of the submatrix s of the correlation matrix centered on its sample minimum, (imin,jmin), the expression for a second order polynomial of two variables, f(x,y) = a1 + a2x + a3x2 + a4y + a5y2 + a6xy, and the location of its 1D minimum, x1 = imin − a2 / 2a3; y1 = jmin − a4 / 2a5 and its 2D minimum, ; . The notation  ⟨ · ⟩ i denotes averaging over index i ∈  {− 1,0,1} .

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