It has been shown that conclusions about the human mental state can be drawn from eye gaze behavior by several previous studies. For this reason, eye tracking recordings are suitable as input data for attentional state classifiers. In current state-of-the-art studies, the extracted eye tracking feature set usually consists of descriptive statistics about specific eye movement characteristics (i.e., fixations, saccades, blinks, vergence, and pupil dilation). We suggest an Imaging Time Series approach for eye tracking data followed by classification using a convolutional neural net to improve the classification accuracy. We compared multiple algorithms that used the one-dimensional statistical summary feature set as input with two different implementations of the newly suggested method for three different data sets that target different aspects of attention. The results show that our two-dimensional image features with the convolutional neural net outperform the classical classifiers for most analyses, especially regarding generalization over participants and tasks. We conclude that current attentional state classifiers that are based on eye tracking can be optimized by adjusting the feature set while requiring less feature engineering and our future work will focus on a more detailed and suited investigation of this approach for other scenarios and data sets.