In the following discussion, the term antioxidant refers mainly to non-nutrient compounds in foods, such as polyphenols, which have antioxidant capacity in vitro and so provide an artificial index of antioxidant strength – the ORAC measurement.ypical cooked vegetables rich in antioxidants are artichokes, cabbage, broccoli, asparagus, avocados, beetroot and spinach. Nuts are a moderate source of polyphenol antioxidants. Typical nuts are pecans, walnuts, hazelnuts, pistachio, almonds, cashew nuts, macadamia nuts and peanut butter.