Large displacement visual sensing method using absolute compound sinusoidal fringe pattern grating

Vision-based displacement sensing enables non-contact measurement and flexible spatial sampling in precision linear metrology. However, incremental vision-based methods reconstruct displacement from inter-frame changes, so errors propagate across sampling intervals and can compromise long-range measurements. Here, we present a large-range absolute visual displacement sensing method based on an absolute compound sinusoidal fringe-pattern grating (ACSFPG). The ACSFPG co-encodes a pseudorandom m-sequence and two-dimensional (2D) sinusoidal fringes. We recover the wrapped phase by calculating the Pearson correlation coefficient (PCC) between each image column and sinusoidal and cosine reference signals. The m-sequence independently identifies absolute fringe-period indices, while a spatial-consistency constraint reconstructs missing or unreliable indices across consecutive periods. Because both quantities are recovered from a single frame, each position is estimated independently without propagating inter-frame errors. The displayed ACSFPG encoded a range of 520 mm. Across an independently evaluated 400 mm interval, the mean of five estimates yielded a maximum absolute error of 0.932 μm, a mean absolute error of 0.139 μm, and a root-mean-square error of 0.183 μm. In a separate bidirectional test over a 300 mm reciprocating stroke, the maximum forward–reverse deviation at the same position across four reference positions was 1.02 μm. These results demonstrate single-frame absolute displacement sensing with micrometre-level accuracy over a long range under controlled laboratory conditions.