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Despite its high prevalence, anemia is often undetected due to the invasiveness and cost of screening and diagnostic tests. Though some non-invasive approaches have been developed, they are less accurate than invasive methods, resulting in an unmet need for more accurate non-invasive methods. Here, we show that deep learning-based algorithms can detect anemia and quantify several related blood measurements using retinal fundus images both in isolation and in combination with basic metadata such as patient demographics. On a validation dataset of 11,388 patients from the UK Biobank, our algorithms achieved a mean absolute error of 0.63 g/dL (95% confidence interval (CI) 0.62-0.64) in quantifying hemoglobin concentration and an area under receiver operating characteristic curve (AUC) of 0.88 (95% CI 0.86-0.89) in detecting anemia. This work shows the potential of automated non-invasive anemia screening based on fundus images, particularly in diabetic patients, who may have regular retinal imaging and are at increased risk of further morbidity and mortality from anemia.