Generalized metric spaces for correlation fringes and applications

A novel conception and its applications, the generalized metric for correlation fringes, are presented, which can be used to develop and analyze the relevant algorithms. The relationship between the metric and the correlation fringes representation is examined and the generalized metric is defined. The theoretical analysis of traditional algorithms for correlation fringes indicates that all of them can be regarded as the generalized metrics. In addition, the generalized metric for correlation fringes is applied in developing a new algorithm. A novel generalized metric for correlation fringes based on cross entropy is presented and is proved by theoretical derivation and experimental verification. All the investigations show that it is reasonable and valid to define the generalized metric for correlation fringes in digital speckle pattern interferometry (DSPI). The fringes obtained by cross-entropy metric can be used to represent the same desired information by subtracting. There are different vector function structures among the generalized metrics, which directly influence the quality of fringes and the difficulty in post-processing.