Particle shape is an important parameter in irregular particle measurement, which has scientific and practical significance for studying environmental climate changes and ensuring engineering production safety. The interferometric particle imaging (IPI) technique has been widely employed in recent years to measure the sizes and shapes of irregular particles. Irregular particles form complex speckle patterns at defocused planes, which have been utilized to retrieve size and shape features such as 2D auto-correlation estimation and particle orientation. However, there are still two main problems during processing defocused speckles detected in IPI measurement. On one hand, the existing methods in IPI have slower processing time and thus incur significant time costs when processing large amounts of speckle data. On the other hand, a large amount of speckle data also brings enormous pressure to the storage and transmission of detected datasets. Therefore, we propose a method for rapid shape analysis of a large number of defocused speckles to reduce the memory cost brought by the dataset through data compression.

We apply a deep learning method to rapidly analyze large amounts of defocused speckle data of ice crystal particles collected by the IPI system. The proposed method includes two steps of data collection and network training. In data collection, we build an experimental particle IPI system to obtain a sufficient number of defocused speckles of ice crystal particles and provide different particle shapes in the dataset with unique speckle fields through the diffuser update strategy. In network training, we adopt the DenseNet network structure to classify the shapes corresponding to the speckle patterns, input the speckle data of the training set into the untrained DenseNet, and output the prediction category. After completing the training step, trained DenseNet is leveraged to classify the shape of the test set speckle data to test the ability to distinguish particle speckle patterns of different shape categories. Furthermore, we utilize bit-depth compression to compress the speckle dataset to eliminate information redundancy in DenseNet classification. Meanwhile, the original speckle dataset is segmented by a grayscale threshold strategy to generate a low bit-depth speckle dataset, and DenseNet is trained for shape classification and feasibility verification.

By comparing three different network structures (Fig. 10 and Table 1), we choose the DenseNet structure for speckle classification. Firstly, we compare the classification accuracy of DenseNet under defocused speckle dataset from different defocused distances. The experimental results (Fig. 11) show that the classification accuracy exceeds 90% at all four different defocused distances, with the highest accuracy up to 92.7%. Our experimental results on low bit-depth speckle datasets (Fig. 13) show that the classification accuracy of DenseNet decreases with the reducing speckle data bit-depth, while the lowest classification accuracy still exceeds 85% when the information compression ratio reaches 12.5%. For the 1 bit-depth speckle data with the lowest information compression ratio, the classification results of the dataset (Fig. 14) indicate that the threshold near the average grayscale threshold could achieve the highest classification accuracy. Moreover, the speckle sparsity increases with the rising binarization threshold. Finally, the size analysis of the defocused speckle (Fig. 15) indicates that the size of the defocused speckle pattern cannot be too small to ensure that the neural network can recognize the hidden particle shape features in the speckle pattern.

The proposed deep learning-based method can rapidly analyze the shape information of a large number of defocused speckle patterns detected in IPI measurement. The experimental results show that compared with traditional methods, our method has an average processing time of only 0.06 s for each defocused speckle pattern to greatly reduce the time cost of speckle processing. Meanwhile, the trained DenseNet network has high classification accuracy on the collected ice crystal particle speckle dataset with a maximum of 92.7%. Furthermore, DenseNet trained on low bit-depth speckle datasets still maintains classification accuracy of over 85% with a minimum information compression ratio of 12.5%, significantly reducing the data storage and transmission pressure. Thus, this method is of significance for rapidly analyzing a large amount of speckle data in IPI measurement and could facilitate low-cost storage and efficient transmission of speckle data.