Optimization of femtosecond laser spot coverage: analytical modeling of spatial frequencies, anisotropy, and saturation boundaries
Year: 2026
Type: article
Abstract: Keratorefractive lenticule extraction (KLEx) relies on dense, spatially uniform femtosecond laser photodisruption to create intrastromal cleavage planes that permit controlled mechanical separation of corneal tissue. While scanning trajectories vary between discrete meander scans and continuous Archimedean spirals, the geometric limits governing coverage efficiency remain unified under local planarity. In this work, we present a mathematical framework describing the asymptotic fill fraction achieved by circular laser spots. By modeling the fundamental 3-bubble dynamics via Boolean triangle tessellation, we derive exact closed-form equations for aligned and staggered spot arrangements. We determine the dependence of the row-to-row phase shift (δ) in the global average fill fraction. We establish analytical boundaries for full coverage (saturation) based on circumradius limits and introduce an invertible master equation to directly calculate required pulse densities for any target fill fraction. This comprehensive model confirms that hexagonal packing is the unique asymptotic optimum and geometrically supports physiological advantages of high-anisotropy scanning strategies.
Source: Biomedical Optics Express
DOI: 10.1364/boe.596245
Author: Samuel Arba Mosquera
Institution: SCHWIND eye-tech-solutions (Germany)
Language: English
Subfield: Radiology, Nuclear Medicine and Imaging
Field: Medicine
Domain: Health Sciences
Open Access status: gold
Estimated APC paid: $1,913
OpenAlex ID: W7155239995