254
J. Eur. Opt. Society-Rapid Publ. 22, 24( 2026)
Fig. 6. Visual representation of asymmetric pulse spacing on an Archimedean spiral for a constant dose( F1 F2 = 1.41) with two asymmetry configurations: F2 / F1 = 1.73( left) and F2 / F1 = 0.58( right). Here, the parameters“ F1” and“ F2” are scaling factors for spot and track distance respectively. The grey contour marks the cavitation bubble boundary, and the orange fill indicates the bubble interior.
The equation( 10) in our results represents the minimum dose one can apply while safely using laser energy with the highest efficiency, while equation( 14) represents the maximum Dose for coalescence of cavitation bubbles leaving no tissue bridges. Any dose applied beyond these limits does not contribute to the physical process and is therefore redundant. The current development trend is toward lower threshold energies for cavitation bubble generation, with ~ 40 nJ as a representative value. Applying our method to this threshold energy allows identification of the proper optimum dose ranges. Considering minimum and maximum doses( F1 F2 = 4 / p and F1 F2 = 2, respectively), and applying the Photodisruption model assuming the value of K( i. e., the coefficient of the irradiated tissue) equal to 1.42 [ 26 ], and a single pulse energy of 75 nJ( corresponding to the Proper Optimum of the Photodisruption model), yields an optimum dose range from 441 nJ to 695 nJ. Using proper optimum asymmetry( F2 / F1 = 2.62), this leads to ideal spot and track spacings of 6.7 lm and2.5lm vs. 5.3lm and2.0lm, for min and max doses, respectively. For the same Eth but for a single pulse energy E p = 55nJ( correspondingtothelowestOptimum of the Plasma CRT model), yields a higher optimum dose range from 570 nJ to 897 nJ. Using the same proper optimum asymmetry( F2 / F1 = 2.62), this leads to slightly tighter spot and track spacings of 5.0 lm and1.9lm vs. 4.0 lm and 1.5 lm, for min and max doses, respectively.
The precise mechanism underlying the observed reduction in surface roughness with increasing F2 / F1 ratio( asymmetry) remains unclear. Nevertheless, previous studies consistently support this relationship from a geometrical and clinical perspective.
An optimization problem as this one provides for a better treatment of the localized spacing of pulses in the used lattice pattern. The findings build upon the necessary spacing to ensure pulses effectively align to a hexagonal packed array( as determined for excimer lasers [ 33 ], and leading to the asymmetry range of 1.15 – 3.46 [ 24 ]). This gives the absolute minimum number of pulses to cover a specified area for near-constant overlap. We acknowledge that this may be difficult to do practically because of the laser properties: repetition rate most notably.
For a constant pulse energy, increasing the track distance reduces overlap between adjacent spot pathways, leaving residual ridge patterns. Conversely, larger spot distances produce a stepwise response, as the number of pulses contributing to a single corneal location decreases; while greater overlap lowers surface roughness, it simultaneously increases the local dose. This oscillatory behavior is analogous to Gauss’ s circle problem in lattice geometry, as previously described for excimer ablations [ 33 ], where the number of overlapping pulses depends on the spacing of lattice nodes relative to the spot boundary. The underlying principle remains consistent across ablation modalities. The theoretical predictions discussed here align with observed clinical transitions in commercial femtosecond systems, where spot and track spacings are being decoupled to achieve superior ablation outcomes. Furthermore, the theoretical foundations are strongly supported by clinical evidence from recent studies [ 28 ], directly mirroring the model’ s [ 24, 25 ] recommendation for maintaining a constant energy-per-area product.
Bohac et al. [ 34 ] analyzed longitudinal epithelial changes after the treatment of myopia with KLEx and the zonal change in epithelial thickness up to 12 months after SmartSight for myopic astigmatism with the SCHWIND ATOS femtosecond laser. They reported clinical outcomes in 80 eyes treated with Pulse energies ranging from 80 to 105 nJ, with a total energy dose between 440 and 583 mJ / cm 2. Their outcomes led to the conclusion that changes in epithelial thickness after KLEx for moderate myopia with SmartSight were minimal, indicating a low level of epithelial hyperplasia without resembling a regression-inducing lentoid. Besides these results, Spot and track settings such as 5.9 2.9 lm, 6.0 2.1 lm, 6.0 4.4 lm, or 7.6 2.3 lm have been shown to deliver optimal stromal dissection with pulse energies as low as 75 – 80 nJ, corresponding to total fluences between 440 and 595 mJ / cm 2. These parameters yielding low total doses without compromising tissue separation are not only