Digital in-line holography (DIH) has been proven to provide 3-dimensional droplet position, size, and velocity distributions with a single-camera. This data is crucial for understanding multi-phase flows. However, the limits of usability and accuracy of DIH for dilute fields of very small particles, such as sprays, have yet to be studied in detail. In this work, we examine the performance of this diagnostic in the limit of very small particles, on the order of a pixel in diameter and smaller, and propose a post-processing method to improve them: Lanczos interpolation. The Lanczos interpolation kernel is the digital implementation of the Whittaker sinc filter, and strikes a compromise between maintaining the spatial frequency ceiling of the original digital image and computational cost of the interpolation. Without Lanczos interpolation, or super-sampling, the ultimate detectable particle size floor is on the order of 4 pixel widths. We show in this work that this limit can be reduced by 50% or more with super-sampling, depending upon the desired diameter accuracy, and examine the effect of super-sampling on the resulting accuracy of the extracted size and position of spherical particles. Extending this resolution limit increases the overall detection efficiency of the diagnostic. It also allows a larger field-of-view to be captured with any expected particle size floor.