Melt ponds occupy a large fraction of the Arctic sea ice surface during spring and summer. The fraction and distribution of melt ponds have considerable impacts on Arctic climate and ecosystem by reducing the albedo. There is an urgency to obtain improved accuracy and a wider coverage of melt pond fraction (MPF) data for studying these processes. MPF information has generally been acquired from optical imagery. Conventional MPF algorithms based on high-resolution optical sensors have treated melt ponds as features with constant reflectance; however, the spectral reflectance of ponds can vary greatly, even at a local scale. Here we use Sentinel-2 imagery to demonstrate those previous algorithms assuming fixed melt pond-reflectance greatly underestimate MPF. We propose a new algorithm ("LinearPolar") based on the polar coordinate transformation that treats melt ponds as variable-reflectance features and calculates MPF across the vector between melt pond and bare ice axes. The angular coordinate θ of the polar coordinate system, which is only associated with pond fraction rather than reflectance, is used to determinate MPF. By comparing the new algorithm and previous methods with IceBridge optical imagery data, across a variety of Sentinel-2 images with melt ponds at various stages of development, we show that the RMSE value of the LinearPolar algorithm is about 30% lower than for the previous algorithms. Moreover, based on a sensitivity test, the new algorithm is also less sensitive to the subjective threshold for melt pond reflectance than previous algorithms. Plain Language Summary Melt ponds are pools of open water that form on the sea ice surface in the Arctic in summer months. Sea ice covered by melt ponds absorbs more solar heat than solid ice which speeds up the rate of sea ice melt. To study this process, we need melt pond coverage data that are generally obtained from satellite observations. There are several methods to calculate the melt pond fraction from high-resolution optical satellite imagery but these methods assume that melt ponds have constant optical properties, which is not true. In this study, we show that these existing methods significantly underestimate melt pond fraction. To address this problem, we present a new method that treats melt ponds as features having variable optical properties. Images of sea ice from aircraft are used to assess the new algorithm and two previous methods, demonstrating that the new algorithm has higher accuracy and precision.