Predictability of the spherical equivalent or the astigmatism correction
Updated on version: 1.0.3


Computes de standard plot for the Journal of Refractive Surgery in order to report the Accuracy or Predictability of a Laser Refractive Surgery Procedure by means of ploting the attempted versus the achieved refraction


Predictability of the spherical equivalent or the astigmatism correction


Scattergram of the attempted refractive change vs. the achieved refractive change for each eye to represent the accuracy of a procedure. The plot can be used either for representing the spherical equivalent or astigmatism correction even though for the latter we recommend the double angle plot. 

This function calculates the standardized graph from a matrix of data of two columns:

  1. In Spherical Equivalent [Attempted, Achieved] 
  2. In Cylinder [Target, Induced] in positive notation

This is a good plot for spherical equivalent but could lead to a missinterpertation in astigmatism analysis representing Target Induced Astigmatism [TIA] versus Surgically Induced Astigmatism [SIA], this is due to the plot does not considers the angles for the SIA and TIA.5


  1. Koch DD, Kohnen T, Obstbaum SA, Rosen ES. Format for reporting refractive surgical data. J Cataract Refract Surg. 1998; 24: 285–7. 
  2. Waring 3rd GO. Standard graphs for reporting refractive surgery. J Refract Surg. 2000; 16: 757–8. 
  3. Reinstein DZ, Waring GO. Graphic reporting of outcomes of refractive surgery. J Refract Surg. 2009; 25: 975–8. 
  4. Reinstein DZ, Archer TJ, Randleman JB. JRS Standard for Reporting Astigmatism Outcomes of Refractive Surgery. J Refract Surg. 2014; 30: 654–9. 
  5. Koch DD, Wang L, Abulafia A, Holladay JT, Hill W. Rethinking the optimal methods for vector analysis of astigmatism. J Cataract Refract Surg. 2021; 47: 100–5.

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How to obtain the Toolbox?

The Refractive Analysis is an Open Source Toolbox for Matlab developed by Rodríguez-Vallejo M for the Analysis of Vision Science Results. It is freely available for the students of our online course but you need the Matlab software to use it. Matlab software is not provided with the course.

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