Due to physical and chemical effects in industrial production, various deformations can occurs on the surface of optical products such as glass fiber and quartz fiber. Although it is micro-nano-scale deformation, the properties of materials and related products can be seriously affected. Therefore, enterprise spends a lot of time and money every year to monitor these deformations. Since the microscope is the most common and practical detection device, microscopic detection technology is always the focus of research. At present, the three-dimensional deformation measurement methods used in microscopic system mainly include white light micro-interferometry, micro-fringe projection, digital holographic microscopy, three-dimensional digital image correlation. Although the optical arrangements of white light micro-interferometry is simple, this method needs multiple images to complete the test, which takes a long time and can not realize rapid industrial detection. The measuring devices of micro-fringe projection method and digital holographic microscopy method are usually complex, and the methods above need phase unwrapping operation, which can undoubtedly increase the calculation difficulty and measurement error. Conventional digital image correlation method is a high-precision and stable in-plane displacement measurement technique. With the development of research, scientists have proposed a variety of three-dimensional digital image correlation methods in recent years and have been widely used in real-time dynamic measurement field. However, three-dimensional digital image correlation methods usually require two industrial cameras or a 3CCD camera to complete the test. The inevitable oscillation and disturbance in industrial production can increase the detection error of such binocular or beam splitting techniques. Considering the detection practicability and cost, enterprises and the researchers in production line look forward to the three-dimensional deformation measurement method based on the microscopy with single camera. In 2019, the research group has successfully explained the image rotation phenomenon of micro channel plate by using image spherizing algorithm. Since the algorithm can simulate the reflection image of deformed object, it provides a new idea for three-dimensional micro-deformation measurement. Differential theory shows the fact that all curves can be considered as the integral of infinite small line segments. Therefore, it is easy to figure out that the spherical or hemispherical deformation can be treated as the integral of infinite small slopes and all the deformation observed under microscope is slope-shaped. On this basis, a general slope model, which relates the in-plane displacement and out-of-plane displacement is proposed, then the three-dimensional deformation measurement can be realized. Firstly, two images of the object before and after deformation are taken by the monocular microscopic imaging system. Secondly, the in-plane displacement field between the images is calculated. Finally, the out of plane displacement is extracted from the in-plane displacement field according to the image spherical model, thereby the measurement of three-dimensional deformation is realized. Because the out-of-plane displacement is estimated by the in-plane displacement, the measurement accuracy of in-plane displacement has a significant influence on the measurement results of out-of-plane displacement. In this paper, digital image correlation method and optical flow method are chosen as in-plane displacement estimation techniques to ensure the measurement accuracy. The test object in the application experiment is an optical fiber inverter with a diameter of 20 mm. In order to minimize the error caused by environmental oscillation during measurement, all experimental devices are placed on the air suspension damping platform, and the amplitude of the damping platform is less than 1 μm. The experimental pictures before and after deformation are captured by an industrial camera(Andor, ZYLA 4.2 Plus) which fixed on the microscope with a magnification of 50X. All the pictures are filtered by homomorphic and wiener filter to prove the image quality. The absolute errors and relative errors of all the out-of-plane displacement measurement results are less than 0.2 μm and 5% respectively, which verifies the effectiveness of the presented method. Note that the accuracy of out-of-plane displacement measurement can also prove the accuracy of in-plane displacement measurement. This method only needs two images captured by a microscope with single industrial camera to complete the measurement, and the measuring time is less than 30 s. The measurement theory shows that the new method makes full use of the out-of-plane displacement information carried by the in-plane displacement field, and it does not need frequency conversion or phase unwrapping operation, which provides a new way for the dynamic measurement of micro-nano-scale deformation.