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# Optonet Vision Unit Documentation

Please note that this User Guide is being currently updated; new sections will be added shortly.

### 4.2.Logarithmic Notation#

The logarithmic acuity values are obtained by calculating the logarithm of the minimum angle of resolution (MAR). For example, a VA of 1.0 Dec (Snellen equivalent of 6/6 or 20/20) corresponds to a MAR of 1 minute of arc. Since the logarithm of 1 is 0, the logarithmic value corresponding to this VA (6/6 or 20/20) will thus be 0.

In a logMAR chart, the optotypes (letters or symbols) change in size from one line to another in geometric progression, multiplying by a factor of 1.26.  With this progression, the letter size is doubled every 3 rows, and increased 10 times per every 10 rows. If we take the log of the visual angle for each letter size, we convert the geometric sequence into a linear sequence, in which each row changes 0.1 log units.

In the logarithmic scale the acuity values vary with the letter size, such that the smaller the letters the patient sees, the smaller the log acuity value will be. Each row is 0.1 logarithmic units less than the previous one and since every line contains 5 letters, so we can assign to each letter the value of -0.02 log units (subtract 0.02 log units for each letter the patient identifies). Thus, the logMAR acuity value tells how many letters the patient identified correctly, simplifying numerical notations, increasing the accuracy of the VA measurement, and allowing more standardized measurements. The logMAR notation is always used in clinical research due to these advantages.

In the following example we have crossed out the letters that the patient correctly identified: The patient saw all the letters in the line 0.6 log and three letters in the next row (K, H and D). Therefore, at the value of 0.6 we will subtract 0.02 for each successful letter of the next row (0.5) and thus we conclude that the acuity is: 0.6 – 0.06 = 0.54 log units.

In this other example: The patient saw all lines on the line 0.6 plus 4 letters on the 0.5 and 2 on the 0.4. The acuity will therefore be 0.6 – 0.08 – 0.04 = 0.48 log units.

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