Spatial transcriptomics techniques such as STARmap  enable the subcellular detection of RNA transcripts within complex tissue sections. The data from these techniques are impacted by optical microscopy limitations, such as shading or vignetting effects from uneven illumination during image capture. Downstream analysis of these sparse spatially resolved transcripts is dependent upon the correction of these artefacts. This paper introduces a novel non-parametric vignetting correction tool for spatial transcriptomic images, which estimates the illumination field and background using an efficient iterative sliced histogram normalization routine. We show that our method outperforms the state-of-the-art shading correction techniques both in terms of illumination and background field estimation and requires fewer input images to perform the estimation adequately. We further demonstrate an important downstream application of our technique, showing that spatial transcriptomic volumes corrected by our method yield a higher and more uniform gene expression spot-calling in the rodent hippocampus. Python code and a demo file to reproduce our results are provided in the supplementary material and at this github page: https://github.com/BoveyRao/Non-parametric-vc-for-sparse-st.