Theoretical Analysis and Experimental Validation of Sampling Volume in Tilted Imaging System

A method for accurately calculating the sampling volume in a tilted imaging system is proposed. Two types of tilted imaging systems are investigated, i.e., Type I (only the object plane is inclined to the optical axis) and Type II (both the object plane and the image plane are inclined to the optical axis). Based on geometrical optics, the sampling volumes of these two types of tilted imaging systems have been simulated. Compared with the central magnification of an imaging system and the focal length and F-number of the imaging lens, the effect of the tilted angle of the object plane on the sampling volume is determined to be more important. A tilted imaging experimental setup has been established, calibration plate images at various tilted angles and positions have been acquired, and the sampling volume has been obtained by image processing. The experimental results are in very good agreement with the theoretical predictions. As the tilted angle increases, for the Type-I system, the sampling volume increases, whereas for the Type-II system, the sampling volume decreases. In addition, the sampling volume of the Type-II system is larger than that of the Type-I system. Knowledge of the sampling volume is necessary in many quantitative applications of tilted imaging systems.