Using Vector Analysis to Calculate Surgically Induced Astigmatism and Refractive Change

  • Eric J. Kim
  • Mitchell P. WeikertEmail author


  1. 1.

    Calculation of surgically induced astigmatism (SIA) is based on the summation of two obliquely crossed spherocylindrical lenses.

  2. 2.

    Astigmatism is a vector quantity, and SIA can be calculated if the pre- and postoperative astigmatism values are known.

  3. 3.

    Fourier analysis can be applied to represent spherocylinders as power vectors for the analysis of surgically induced refractive change (SIRC).

  4. 4.

    The SIRC can be calculated if the pre- and postoperative keratometric K readings are known.

  5. 5.

    With-the-wound and against-the-wound astigmatic change can be calculated by using the meridian of the incision as the reference meridian.



Surgically Induced Astigmatism (SIA) Astigmatic Changes Reference Meridian Flat Meridian Jackson Cross Cylinder (JCC) 
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Supplementary material

Video 2.1

Toric over rotation (WMV 21005 kb)

Video 2.2

ToricBackCalculation (MP4 12382 kb)


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of OphthalmologyBaylor College of MedicineHoustonUSA

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