4.1.- The double angle plot and ellipses

In the BigSIA, astigmatism (positive cylinder) is considered with-the-rule from 60º to 120º and against-the-rule between 30º and 150º in the double angle plot. Remaining meridians are considered oblique. Therefore, if the mean (square black point) is located at the left side of the plot you are inducing WTR astigmatism, on the other hand, at the right side you are inducing against the rule astigmatism and in top and bottom locations of the plot, oblique astigmatism. 

Two ellipses are included in the plot:

  • Red ellipse: 95% confidence ellipse of the centroid. If the center of the coordinates from the graph is within this ellipse, the magnitude of the mean astigmatism may be due to chance, so it should not be considered.
  • Blue ellipse: 95% limits of agreement of the centroid. Estimates the variability in the sample in such a way that 95% of the sample is inside the blue ellipse. It is an indicator of the bias of your astigmatism results, the smaller the size of the ellipse, the lower is the variability
SIA calculator


The incision that is required for IOL implantation during cataract surgery induces astigmatism —this is referred to as surgically induced astigmatism (SIA)— so the total amount of astigmatism to be corrected with the toric IOL must consider the flattening (FE) or steepening (SE) effect on the meridian of the preoperative corneal astigmatism on which the IOL is going to be aligned. The SIA will depend on several factors, including incision type, location and size, and its design or architecture. 

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