I. Introduction
Measurement of wide-range linear displacement with nanometer resolution and micrometer accuracy is vital for various fields, such as precision manufacturing, aerospace industry, and military application [1], [2], [3], [4]. Unlike incremental sensors, absolute sensors can measure the absolute position of a target without calibration and more than 60% of linear displacement sensors currently belong to the absolute types [5], [6], [7], [8]. The main evaluation performance criteria of displacement sensors used are: non-linearity, resolution, sensitivity, compactness, long-term stability, and so on [2], and [9].