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A 2-D tetralateral position-sensitive detector (PSD) is able to provide continuous position measurements with high position resolution, fast response, and low cost. However, it suffers from the nonlinearity problem, which leads to inaccurate measurements. In this paper, two linearity indices are proposed as measures of linearity for its position measurement. Then, a systematic procedure is developed to design new formulas to achieve any degree of linearity through the use of the linearity indices. As an example, a simple estimation formula for the 2-D tetralateral PSD has been derived based on the procedure. Compared to the conventional formula, the linearity of the measurement is greatly improved when the new formula is used. To verify its effectiveness, the new formula is implemented in analog circuits and tested in our experiment. Similar linearity improvement for other 2-D PSDs can also be achieved by following the same design procedure.