The point spread function (PSF) effect is ubiquitous in remote sensing images and imposes a fundamental uncertainty on subpixel mapping (SPM). The crucial PSF effect has been neglected in existing SPM methods. This paper proposes a general model to reduce the PSF effect in SPM. The model is applicable to any SPM methods treating spectral unmixing as pre-processing. To demonstrate the advantages of the new technique it was necessary to develop a new approach for accuracy assessment of SPM. To-date, accuracy assessment for SPM has been limited to subpixel classification accuracy, ignoring the performance of reproducing spatial structure in downscaling. In this paper, a new accuracy index is proposed which considers SPM performances in classification and restoration of spatial structure simultaneously. Experimental results show that by considering the PSF effect, more accurate SPM results were produced and small-sized patches and elongated features were restored more satisfactorily. Moreover, using the novel accuracy index, the quantitative evaluation was found to be more consistent with visual evaluation. This paper, thus, addresses directly two of the longest standing challenges in SPM (i.e., the limitations of the PSF effect and accuracy assessment undertaken only on a subpixel-by-subpixel basis). © 2020 Elsevier Inc.