250
J. Eur. Opt. Society-Rapid Publ. 22, 24( 2026)
Fig. 4. Feasible solution space defined by inequalities( Eqs.( 16) and( 18)). The rectangle represents the bounded domain of dose( F1 F2) and asymmetry( F2 / F1). The four corner points correspond to extreme combinations. The most favorable setting is found at minimum dose and maximum asymmetry( Indicated with a Green star), while the least desirable of the optimum conditions is at maximum dose and minimum asymmetry( indicated with a Red star). The vertical and horizontal lines illustrate intermediate tradeoffs across dose and asymmetry, from which a proper optimum is derived( blue marker), located near Solution 4.
Table 2. Values of F1 and F2 corresponding to the four corner solutions defined by the inequalities( Eqs.( 16) and( 18)), together with the additional case F1 = 1.
F1 F2 |
F2 / F1 |
F1 |
F2 |
1.27 |
3.46 |
0.61 |
2.10 |
2.00 |
3.46 |
0.76 |
2.63 |
1.27 |
1.15 |
1.05 |
1.21 |
2.00 |
1.15 |
1.32 |
1.52 |
1.27 |
1.27 |
1.00 |
1.27 |
2.00 |
2.00 |
1.00 |
2.00 |
In Table 5, three different LIOB threshold energies( Eth = 35 nJ, 50 nJ, and 70 nJ) were analyzed, which loosely represent the range of commercial femtosecond laser systems currently applied for ultrashort-pulse corneal tissue cutting. For each threshold energy, three different singlepulse energies( E p) wereevaluated. TheselectionofEth values follows the rationale established in our previous work [ 9 ].
The first E p for each Eth was set at approximately 1.4 Eth, corresponding to the minimum optimum predicted by the PlasmaCRT model( exp( 1 / 3) Eth). The second E p was set at approximately 2 Eth, representing the maximum optimum from the PlasmaCRT model( exp( 2 / 3) Eth), while also coinciding with the proper optimum predicted by the Photodisruption model. The third E p was set at approximately 3 Eth, nearly aligning with the maximum optima from both the Photodisruption and PlasmaSQRT models( exp( 1) Eth). This design also allows direct cross-comparison of specific E p values across
Table 3. Calculated maximum and minimum ranges for F1 andF2.
|
F1 |
F2 |
Min |
0.61 |
1.21 |
Max |
1.32 |
2.63 |
categories: for example, 70 nJ and 100 nJ were tested at both Eth = 35nJandEth = 50nJ, while100nJand 145 nJ were tested at both Eth = 50nJandEth = 70nJ. In addition, E p = 100 nJ was included in all three categories to explicitly demonstrate the effect of varying threshold energy on outcomes at a constant single-pulse energy.
4 Discussion
The bubble overlap plays a pivotal role in determining cutting smoothness and efficiency. There is no strict requirement for spot spacing to be smaller than the cavitation bubble diameter because effective tissue dissection in femtosecond laser procedures depends not solely on overlap along the scanning path( governed by spot spacing), but on the overall spatial and temporal interaction of cavitation bubbles, which is jointly determined by spot and track spacing. In this work, we defined universal ranges for F1 andF2 in relation to spot and track distances, where F represents the scaling factor relative to bubble size. As demonstrated in Tables 2 – 5, F1( the scaling factor for spot distance) is consistently below unity under most conditions, indicating little to no overlap along the spot pathway. In contrast,