## 6 Summary and Conclusions  
This paper set out to evaluate OAM transmitted turbulent, free-space and attenuated, underwater images. The specific purpose is to identify, which, if any, of the state-of-the-art CNN architectures performs best in the two environments. Steps were taken, using a parameter search, to identify the best performing optimizer and near-ideal learning rates for training the architectures. Four underwater and three free-space data sets were then used to train each architecture. With the trained architectures, test sets were presented from each data set to evaluate their classification accuracy. For the baseline testing (no out of set images), architectures with the underwater set appeared to perform at a level comparable to each other. The lone outlier was SqueezeNet. The turbulent free-space images, however, presented a challenge sufficient to start separating out varying levels of performance. DenseNet was the best performer from this set of tests. Advancing to the inter-set testing, additional performance differences emerged. These tests took architectures trained with a data set, such as AL0, and then that trained architecture was presented holdout data from more attenuated data sets. This was repeated with the turbulent, free-space data as well. In the end, it was found that DenseNet consistently performed the best, or as a close second, all the time. This finding is interesting considering its parameter count is at least a factor of three less than the other architectures that performed well. This result implies that DenseNet generalizes well during training. For systems that are more resource constrained, three architectures with lower parameter count were tested: ShuffleNet, SqueezeNet, and MobileNet. In evaluating the results, ShuffleNet consistently performed better than or was close to the performance of the other two. It is also has considerably fewer parameters than the others. For a resource constrained system, ShuffleNet would be the clear choice due to its low parameter count and competitive accuracy. For the turbulent, free-space data sets DenseNet was trained for 5 epochs with the learning rate set to \(4.2\times 10^{-5}\), while ShuffleNet was trained for 21 epochs with the learning rate set to \(3.1.\times 10^{-4}\). Their respective batch sizes were 32 and 128. Nadam was used as the optimizer used in training all architectures. For the attenuated underwater data sets, DenseNet was trained for 5 epochs with a learning rate of \(4.2\times 10^{-5}\) and a batch size of 32. ShuffleNet was trained for 21 epochs with the learning rate set to \(4.2\times 10^{-4}\) with batch size of 128. This work provides an in-depth comparison of state-of-the-art, deep convolutional neural networks in turbulent free-space and attenuated underwater environments. It shows which architectures provide the most robust performance for degraded conditions outside of the training set. For low memory systems, ShuffleNet performed the best. For higher capacity systems, DenseNet consistently performed the best. Training parameters for both architectures are provided. Future work includes evaluating architectures in environments that include both attenuation and turbulence. Also, it may be that a better architecture, with fewer parameters still exists that is best suited for OAM images. A network architecture search could be used to identify a better architecture for classifying OAM images. Contributions by the authors include the following breakout conceptualization, P.L.N. and A.T.W. ; Methodology, N.S.F. ; Software, P.L.N. ; Validation, P.L.N. and N.S.F. ; Formal analysis, P.L.N. ; Investigation, P.L.N. ; Resources, A.T.W. ; Data curation, J.R.L. ; Writing--original draft preparation, P.L.N. ; Writing--review and editing, A.T.W. ; Supervision, K.P.J. ; Project administration, K.P.J. ; Funding acquisition, K.P.J. All authors have read and agreed to the published version of the manuscript.