Traditional optical imaging systems project images of a scene at different distances onto a two-dimensional image, which results in the loss of distance information of targets in the scene. This limitation makes it difficult to meet the requirements of many fields, such as autonomous driving, biological imaging, and deep space exploration. Compared to active ranging methods, passive ranging methods have become a research hotspot in recent years due to their simplicity, low power consumption, and rich texture structure. Furthermore, they do not require additional active light sources for illumination. Currently, passive ranging methods mainly include multi-view stereo vision, monocular defocus, and monocular computational reconstruction via wavefront coding. Due to their simplicity, lower cost, and better application prospects, passive ranging systems based on monocular defocus have recently gained widespread attention. However, this method has limitations in measurement accuracy and non-unique distance decoupling. In this paper, we propose a high-precision passive ranging and refocusing method based on traditional optical imaging systems and two-frame detection signals. The proposed method can not only restore the target’s focused image when it is defocused but also solve the problem of non-unique decoupling of distance information, which is present in traditional monocular defocus ranging methods and achieve higher ranging accuracy. This work is useful for the accurate recognition of airborne targets and three-dimensional (3D) microscopic imaging.

By combining the compressive sensing image reconstruction algorithm with the gradient difference image quality evaluation function, we propose a high-precision passive ranging and refocusing method based on a traditional optical imaging system and two-frame detection signals (Fig. 2). Firstly, the point spread function (PSF) measurement matrix library is pre-calibrated/pre-computed in combination with the optical imaging system. Secondly, two frames of images of the scene target are recorded by the CCD. Thirdly, two sets of image sequences are reconstructed based on the theory and reconstruction algorithm of compressive sensing, and the image quality evaluation function (IQEF) is used to evaluate the image reconstruction results. Using the value of IQEF, the optimized image of the target can be achieved, and preliminary distance information of the target is obtained through the distance decoupling method (Fig. 3). Finally, highly accurate target distance information can be obtained by using the compressive sensing image reconstruction algorithm with an orthogonal constraint and an evaluation function based on the slice image information ratio.

To demonstrate the validity of the proposed passive ranging and refocusing method, we build an optical imaging experimental system based on Fig. 2(a) for verification. In this case, the system’s depth of field is set as $\mathrm{\Delta }L=$1.43 mm. According to Eq. (4), the reconstruction results and normalized IQEF curves are shown in Figs. 4?6 based on two-frame detection signals and different PSF measurement matrices. Similar to the monocular defocus ranging method, the IQEF curve for each detection signal shows a structure of two peaks due to the symmetrical decoupling problem (Fig. 6). By combining the peak position of the IQEF curve, the coarse ranging architecture in Fig. 3, and Eq. (8), the problem of symmetrical decoupling is effectively solved in monocular defocus ranging, and it can be determined that the distance of the target is approximately 254.5 mm. Furthermore, by analyzing the influence of the searching step and the axial distance deviation ($\mathrm{\Delta }z$) of two-frame detection signals on the accuracy of coarse ranging, the experimental results show that when the axial distance deviation $\mathrm{\Delta }z$ is greater than $\mathrm{\Delta }L/\mathrm{2}$, the accuracy of coarse ranging method can reach $\mathrm{\Delta }L/\mathrm{2}$ (Figs. 7 and 8). On the basis of the coarse ranging method, when the proposed TVAL3+OC reconstruction algorithm and the evaluation function of slice image information ratio are adopted, the target’s distance is confirmed near 252.8 mm and its ranging accuracy can reach $\mathrm{\Delta }L/\mathrm{16}$ (Fig. 10), which is one order of magnitude higher than the existing monocular defocus ranging method.

Faced with the low ranging accuracy and non-unique decoupling of distance information in the monocular defocus ranging method using a traditional optical imaging system, we propose a passive ranging and refocusing method based on two-frame detection signals. By combining the compressed sensing image reconstruction theory and two-frame detection signals, a clear target image can still be obtained even if the target is defocused and the accuracy of coarse ranging can reach half of the system depth of field ($\mathrm{\Delta }L/\mathrm{2}$) when the axial distance deviation of two-frame detection signals is not smaller than $\mathrm{\Delta }L/\mathrm{2}$. Based on the results of coarse ranging, the ranging accuracy of the target can reach $\mathrm{\Delta }L/\mathrm{16}$ when the proposed precision ranging algorithm with orthogonal constraint is used. This work not only solves the problem of non-uniqueness in distance information acquisition that exists in the traditional monocular defocus ranging method, but also achieves higher-precision ranging. The proposed method has important application prospects in scenarios such as passive detection and ranging of aerial targets at medium and long distances, and three-dimensional microscopic imaging. When deep learning technology is introduced into the reconstruction process of coarse and precision ranging, the speed of target image reconstruction and distance information extraction is expected to improve dramatically. Moreover, high-precision ranging of small targets under conditions of low detection signal-to-noise ratio is an issue that needs further investigation in future work.