## 1 Introduction
For photo mechanics methods, which include fringe analysis methods, such as electronic speckle pattern interferometry [17; 18] and Moire interferometry [17; 19], as well as image analysis methods, such as DIC [17; 20; 21] and the marker method [17; 22] images are the basic data. Therefore, the previously mentioned image errors will inevitably result in significant measurement errors in all photo mechanics methods. To improve the measurement accuracy of photo mechanics methods, investigation of temperature compensation methods is imperative. Currently, there are some studies aimed at compensating the thermal-induced measurement error and enhancing the accuracy of measurement results to a certain degree under specific application conditions. [PERSON] et al. [8] reported that imaging parameters change due to temperature variation, which directly influences the camera accuracy. Furthermore, [PERSON] et al. [9] systematically performed calibration experiments on imaging parameters during camera temperature variations and found that the focal length and position of the principal point changed. Based on these findings [8; 9], the imaging parameters can be recalibrated to eliminate thermal-induced measurement errors, which has significantly complicated the experimental process. [PERSON] et al. [10] proposed a method to eliminate thermal-induced measurement errors using a compensation specimen. The principle of this method is to place an undeformed compensation specimen around the tested specimen and subtract the photo mechanics measurement result of the compensation specimen from that of the tested specimen to eliminate the measurement error. This method requires the preparation of compensation specimens before measurement, and it also significantly decreases the effective measurement resolution of the image. According to our investigation, the compensation method has strict requirements for image error forms. Another effective method to compensate for the errors in photo mechanics measurements is to establish quantitative relationships between the temperature and measurement error. [PERSON] [11] deduced and established a mathematical model to characterise the relationship between temperature, the change in imaging parameters, and the thermal-induced pixel drift and further corrected the measurement result. In this investigation, however, the underlying physical mechanism in the variation of imaging parameters induced by temperature variation was not addressed. Therefore, this model could not be applied in cases involving complex temperature changes. What is noteworthy is that the variation in imaging parameters is due to thermal deformation responses of mechanical camera components to temperature variations [3; 12; 13; 14]. [PERSON] [3; 12] regarded the displacement of the focal plane caused by thermal deformation of its mechanical fixed component as the cause of the variation in the imaging parameters, which, thereby, resulted in pixel drifts. Based on this finding, [PERSON] presented a pixel drift model to compensate the thermal-induced error during the temperature variation period of a camera. Based on the analysis of digital camera structures and the experimental measurement of thermal deformation along the optical axis of mechanical camera components, including the camera case, mount, and lens, [PERSON] et al. [13; 14] proposed a physical model to elucidate the formation mechanism of image distortion errors. Furthermore, it determines the temperature compensation for strain errors. However, these thermal deformations considered in the above investigations [3; 12; 13; 14] are only part of the thermal responses of mechanical camera components for temperature variations. Therefore, the image error models may not be applicable in situations involving the use of cameras that are sensitive to thermal responses.