Three-dimensional measurement of the droplets out of focus in shadowgraphy systems via deep learning-based image-processing method

For the shadowgraphy techniques with a single camera, it is difficult to accurately obtain the shape, size, and depth location of the droplets out of focus due to the defocus blur. This paper proposed a deep learning-based method to recover the sharp images and infer the depth information from the defocused blur droplets images. The proposed model comprising of a defocus map estimation subnetwork and a defocus deblur subnetwork is optimized with a two-stage strategy. To train the networks, the synthetic blur data generated by the Gauss kernel method are utilized as the input data, which mimic the defocused images of droplets. The proposed approach has been assessed based on synthetic images and real sphere blur images. The results demonstrate that our method has satisfactory performance both in terms of depth location estimation and droplet size measurement, e.g., the diameter relative error is less than 5% and the location error is less than 1 mm for the sphere with a diameter of more than 1 mm. Moreover, the present model also exhibits considerable generalization and robustness against the transparent ellipsoid and the random background noise. A further application of the present model to the measurement of transparent water droplets generated by an injector is also explored and illustrates the practicability of the present model in real experiments. The present study indicates that the proposed learning-based method is promising for the three-dimensional (3D) measurement of spray droplets via a combination of shadowgraphy techniques using a single camera, which will greatly reduce experimental costs and complexity.