Federated learning (FL) is a machine learning framework that allows remote clients to collaboratively learn a global model while keeping their training data localized. It has emerged as an effective tool to solve the problem of data privacy protection. In particular, in the medical field, it is gaining relevance for achieving collaborative learning while protecting sensitive data. In this work, we demonstrate the feasibility of FL in the development of a deep learning model for screening diabetic retinopathy (DR) in fundus photographs. To this end, we conduct a simulated FL framework using nearly 700,000 fundus photographs collected from OPHDIAT, a French multi-center screening network for detecting DR. We develop two FL algorithms: 1) a cross-center FL algorithm using data distributed across the OPHDIAT centers and 2) a cross-grader FL algorithm using data distributed across the OPHDIAT graders. We explore and assess different FL strategies and compare them to a conventional learning algorithm, namely centralized learning (CL), where all the data is stored in a centralized repository. For the task of referable DR detection, our simulated FL algorithms achieved similar performance to CL, in terms of area under the ROC curve (AUC): AUC =0.9482 for CL, AUC = 0.9317 for cross-center FL and AUC = 0.9522 for cross-grader FL. Our work indicates that the FL algorithm is a viable and reliable framework that can be applied in a screening network.Clinical relevance- Given that data sharing is regarded as an essential component of modern medical research, achieving collaborative learning while protecting sensitive data is key.