Shape from focus is a passive three-dimensional reconstruction technology that restores three-dimensional topography from multi-focused image sequences of target objects. To improve the reconstruction accuracy of this technology in practical applications, the existing methods mostly remove image jitter noise, improve focus measure operator and evaluation window, and optimize data interpolation or fitting algorithms. Although these methods can improve the accuracy of shape from focus, the influence of imaging parameters on reconstruction accuracy is not considered, and the accuracy of shape from focus should be further improved. We explore the influence of imaging parameters on the accuracy of shape from focus of large-depth objects and then clarify the improvement measures of the imaging system when the reconstructive accuracy of shape from focus does not meet the requirements in practical applications. Finally, our study helps select imaging parameters in the application of shape from focus technology to obtain better reconstruction accuracy.

Based on constructing the evaluation index of 3D reconstruction accuracy of shape from focus, we firstly analyze the influence degree of focal length, F-number, pixel size, and other parameters in the imaging system on the accuracy of shape from focus by the equal-level orthogonal experiment of a single index. Meanwhile, the primary and secondary orders of the influence of these imaging parameters on the accuracy of shape from focus are determined. Then, the influence of main and sub-main imaging parameters on the 3D reconstruction accuracy is analyzed emphatically by experiments, and the relationship between the optimal imaging parameters and the sampling interval of multi-focus images is revealed. Finally, considering that the change of imaging parameters affects the restoration accuracy of shape from focus by changing the depth of field of the system, it is necessary to explore the influence of imaging parameters on the restoration accuracy of shape from focus of large-depth objects via the depth of field. The experiments help establish the empirical formula between the sampling interval of multi-focus images and the optimal depth of field, providing a theoretical basis for setting imaging parameters of the system.

According to the orthogonal experiment results (Table 3), focal length and F-number are the main and sub-main parameters affecting the accuracy of shape from focus, the influence of pixel size is less than focal length and F-number, and the influence of blank column is the least, which means that there are no important parameters that have not been analyzed. In practical applications, adjusting the focal length and F-number can be realized by adjusting the zoom lens with variable apertures, and meanwhile adjusting the pixel size usually requires replacing the camera, which is costly and usually not considered. Thus, the pixel size is regarded as a non-main influencing parameter. Analyzing the influence of main and sub-main parameters on the accuracy of shape from focus shows that there is the best focal length (Table 4) and the best F-number (Table 5) for the highest reconstruction accuracy under a given multi-focus image sampling interval, and with the decreasing sampling interval, the best focal length increases (Fig. 3) and the best F-number reduces (Fig. 4). Considering that the change of imaging parameters affects the accuracy of shape from focus by changing the depth of field of the system, we establish an empirical formula between the sampling interval of multi-focus images and the optimal depth of field. The fitting accuracy of the empirical formula is 97.28% (Table 6), and the verification accuracy is 94.76% (Table 7), which can be adopted to calculate the optimal depth of field. The optimal depth of field can significantly improve the accuracy of shape from focus (Table 9), which provides a new way for improving the accuracy of shape from focus of large-depth objects.

The primary and secondary orders of the influence of imaging parameters on the accuracy of shape from the focus of large-depth objects are discovered, including focal length, F-number, and pixel size. The influence of main and sub-main imaging parameters, focal length, and F-number is analyzed emphatically. It is known that the root mean square error of object reconstruction results decreases first and then increases with the rising focal length or F-number in a given multi-focus image sampling interval, and there is an optimal focal length and F-number that leads to the highest reconstruction accuracy. With the decreasing sampling interval, the optimal focal length increases and the optimal F-number reduces. We consider that the change of imaging parameters affects the accuracy of shape from focus by changing the depth of field of the system. The experiments indicate that the empirical formula between the optimal depth of field and the sampling interval of multi-focused images is obtained. The accuracy of the empirical formula obtained by the verified data is 94.76%, which can be employed to calculate the optimal depth of field. Our experiments show that adjusting the focal length and F-number of the imaging system according to the optimal depth of field can significantly improve the 3D reconstruction accuracy of large-depth objects.