Most current arbitrary-scale image super-resolution (SR) methods has commonly relied on simulated data generated by simple synthetic degradation models (e.g., bicubic downsampling) at continuous various scales, thereby falling short in capturing the complex degradation of real-world images. This limitation hinders the visual quality of these methods when applied to real-world images. To address this issue, we propose the Continuous Optical Zooming dataset (COZ), by constructing an automatic imaging system to collect images at fine-grained various focal lengths within a specific range and providing strict image pair alignment. The COZ dataset serves as a benchmark to provide real-world data for training and testing arbitrary-scale SR models. To enhance the model's robustness against real-world image degradation, we propose a Local Mix Implicit network (LMI) based on the MLP-mixer architecture and meta-learning, which directly learns the local texture information by simultaneously mixing features and coordinates of multiple independent points. The extensive experiments demonstrate the superior performance of the arbitrary-scale SR models trained on the COZ dataset compared to models trained on simulated data. Our LMI model exhibits the superior effectiveness compared to other models. This study is of great significance in developing more efficient algorithms and improving the performance of arbitrary-scale image SR methods in practical applications. Our dataset and code will be publicly available.