Proposition for the analysis of background toner distribution to sequence ink lines and printing with a statistical method.

Determining the sequence of handwriting and laser-printed text on documents that do not intersect is a recurring challenge in forensic document examination. This study proposes using background toner particle distribution analysis combined with kernel density estimation and likelihood ratio calculation to evaluate printing-writing sequence. Toner particle density was measured by manual counting under near-infrared microscopic imaging at 200× magnification across controlled conditions using three black-toner laser printers. Toner particle density within pen strokes differed significantly by sequence, while intra-page location, distance from pen strokes, and writing orientation showed no significant effect. Pages containing printed text exhibited significantly higher background toner density in unprinted regions than blank pages. A diminishing depletion effect was observed across successive paper layers in stacked printing. The proposed framework provides a quantitative and transparent approach to sequence determination, with a Student's t-test alternative when reference materials are unavailable.