A method to measure the temperature of a metal plate is presented using a Riesz transform method and the monogenic signal to extract the optical phase distribution from a fringe pattern from which one can get the unknown temperature. The performance of this method is evaluated by the RFSIM metric obtained from the 2nd-order Riesz transform. A phase distribution with a good accuracy is provided. 1. Introduction The measurement of temperature field is of great significance to scientific research and national economic development. This is because the measurement of thermal physical quantities is widely used in the implementation and control of industrial processes such as power, aerospace, chemical industry, and oil refining, among others [1]. Temperatures are usually measured by inserting thermocouples into tested fields and entire temperature fields are reconstructed using readings from the thermocouples. However, this method has drawbacks. Temperatures at different points are not obtained simultaneously and tested fields are disturbed by the thermocouples themselves. In addition, obtained readings need to be compensated against the effect brought about by radiation. Various optical methods that are full-field, sensitive, and noncontact include holographic interferometry [1, 2], speckle shearing interferometry [3], Moiré deflectometry [4], effect mirage [5], and digital speckle pattern interferometry (DSPI) [6], which have been used to measure the temperature. Digital speckle pattern interferometry is a whole field optical method for noncontact and nondestructive surface analysis. It is now considered as a powerful tool for industrial measurements. It enables full-field measurement of optical phase changes via the acquisition of speckle patterns [7–9]. After acquisition, a simple subtraction is usually performed to obtain a correlation fringe pattern. The greatest challenges in speckle interferometry focus on relating fringe patterns to phase mapping, permitting the direct determination of surface displacement. However, as DSPI fringes are characterized by a strong speckle noise background, a denoising method [10–12] must be used before the phase evaluation. The removal of speckle noise in DSPI is a complex problem which has generated an active area of research. The aim of this study is the application of the Riesz transform and the monogenic signal to extract the optical phase distribution from a single fringe pattern without the step of speckle denoising from which one can get the unknown temperature. Felsberg and Sommer [13] proposed two-dimensional
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