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J. Eur. Opt. Society-Rapid Publ. 22, 46( 2026)
Figure 3. Damage area as a function of fluence.( a) Experimental measurements taken at 18 fluence levels, each repeated three times; scatter bars indicate variability in the damage area. Three regions are separated by dashed lines: Zone I, where no damage is observed( example at 0.07 J / cm 2); Zone II, where apparent coating damage occurs but is not counted( example at 0.09 J / cm 2); and Zone III, where missing micromirrors define the quantified damage area( examples at 0.11, 0.12, and 0.18 J / cm 2). Damage characterisation uses( b) confocal z-stacks of 40 images with 1-lm steps and( c) bright-field microscopy.
U out ðx; xÞ ¼ rffiffiffiffiffiffiffiffiffiffiffiffi x exp i xL Z 1 2pcLi c �1
exp �i x
Lc x 0 x � 2pcmL px
dx 0:
U in ðx; xÞ ð3Þ
In equation( 3), L denotes the on-axis propagation distance between the input and output planes, and c is the speed of light. After solving the previous integral, and reordering terms, if we omit the square root that represents the intensity factor, we obtain the following,
U out ðx; xÞ exp i xL
exp �x 2 r 2 t c 2
x � 2pcmL 2
3 px exp 6�
7 4
5; ð4Þ
4r 2 xx
where r xx ¼ cL = 2 xr x. To simplify the analytical derivation, the first order approximation is applied around x 0, the central angular frequency of the pulse. This assumption