The golf analogy

Much understanding of the Alpins astigmatism-analysis method can be gained by considering a golf putt, performed on a perfectly flat plane under ideal conditions (no wind or other external forces).

The vector mapping of a putt, shown above, is superimposed over an X-Y axis. Three important concepts of the Alpins method -- target induced astigmatism (TIA), surgical induced astigmatism (SIA) and difference vector (DV) -- are adequately represented in this scenario.

The vector map of the golf putt can be superimposed over a double-angle vector diagram (DAVD) of refractive surgery. The target induced astigmatism (TIA) is calculated to be the vector defined by 1, the patient's preoperative astigmatism, and 2, the target astigmatism the surgeon plans to achieve. A nonzero target such as shown here is unavoidable when a discrepancy exists between refractive and corneal astigmatism. For example, in this patient, the surgeon may have a zero target for refractive astigmatism, and this graph may represent what's happening to the corneal astigmatism. The discrepancy relates to what Alpins calls ocular residual astigmatism, which is discussed later in the article (to jump ahead to the graphics depicting ORA and surgical planning, go here).

It is worth noting that astigmatism can be measured, but vectors can only be calculated. The vector representing the TIA above has a length (magnitude) and a direction (axis), which correspond to actual laser settings (a conversion is made from the DAVD and the mathematics is described in Alpins papers). The TIA is the effect the surgeon wishes to induce. In the above example, the surgeon missed. The actual measured astigmatism after surgery is depicted as rule 3. The surgical induced astigmatism (SIA), then, is the vector defined by 1, the patient's preoperative astigmatism, and 3, the actual surgical result. The SIA is the effect the surgeon actually induced with the operation.

The difference vector (DV) is the vector defined by the actual result of the surgery (3) versus the intended result (2). The DV, representing the "second putt" needed to hit the cup after missing the first time, has a length (magnitude) and direction (axis) that correspond to actual laser settings that could be used to hit the original target in a second operation.

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