Diabetic retinopathy is a serious ocular complication that poses a significant threat to patients' vision and overall health. Early detection and accurate grading are essential to prevent vision loss. Current automatic grading methods rely heavily on deep learning applied to retinal fundus images, but the complex, irregular patterns of lesions in these images, which vary in shape and distribution, make it difficult to capture the subtle changes. This study introduces RadFuse, a multi-representation deep learning framework that integrates non-linear RadEx-transformed sinogram images with traditional fundus images to enhance diabetic retinopathy detection and grading. Our RadEx transformation, an optimized non-linear extension of the Radon transform, generates sinogram representations to capture complex retinal lesion patterns. By leveraging both spatial and transformed domain information, RadFuse enriches the feature set available to deep learning models, improving the differentiation of severity levels. We conducted extensive experiments on two benchmark datasets, APTOS-2019 and DDR, using three convolutional neural networks (CNNs): ResNeXt-50, MobileNetV2, and VGG19. RadFuse showed significant improvements over fundus-image-only models across all three CNN architectures and outperformed state-of-the-art methods on both datasets. For severity grading across five stages, RadFuse achieved a quadratic weighted kappa of 93.24%, an accuracy of 87.07%, and an F1-score of 87.17%. In binary classification between healthy and diabetic retinopathy cases, the method reached an accuracy of 99.09%, precision of 98.58%, and recall of 99.64%, surpassing previously established models. These results demonstrate RadFuse's capacity to capture complex non-linear features, advancing diabetic retinopathy classification and promoting the integration of advanced mathematical transforms in medical image analysis. The source code will be available at https://github.com/Farida-Ali/RadEx-Transform/tree/main .