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J. Eur. Opt. Society-Rapid Publ. 22, 46( 2026)
To determine the laser-induced damage threshold( LIDT) of the DMD, Liu’ s method was employed [ 35 ], which measures the radius of damage on the material’ ssur- face as a function of the Gaussianr laser beam’ s fluence. In this method, a beam with a Gaussian profile is considered. Then, the spatial irradiation distribution of a Gaussian beam can be expressed as U( r):
UðÞ¼U r th exp
� 2r2 q 2
: ð1Þ
Subsequently, assuming the centre of the laser beam coincides with the centre of the damage area A i, the damage threshold fluence U th can be expressed as
Ar ð i Þ ¼ 2pr 2 i ¼ q 2 In U
: ð2Þ
U th
By adjusting the experimental damage area as a function of fluenceusingasemilogfit, the threshold fluence can be determinedaccordingtoequation( 2).
This experiment was conducted using an ultrafast Ti: sapphire laser( PRO-Compact Femtolaser). The amplifier produces pulses with a duration of around 32 fs at the transform Fourier limit, a central wavelength around of 800 nm, a spectral bandwidth near 30 nm, and operates at a repetition rate of 1 kHz. The DMD used in this study( DMD, DLP7000, Texas Instruments) comprises a 756 1024 square micromirror, each with a width of 13.6 um. For the experimental setup, the device was maintained in the off state throughout the measurement of threshold fluences. The experimental arrangement is shown in Figure 2. Before the focussing lens, a pair of concatenated linear polarisers was used to control the energy level, and a motorised shutter was employed to regulate the exposure time. The mean energy was measured for each pair of polariser angles to obtain the testing points. The shutter exposure time was set to 1 s, corresponding to approximately 1000 pulses per irradiation, according to the laser repetition rate. A convergent lens with a focal length of 550 mm was used to focus the laser beam into the DMD micromirrors surface. The DMD was mounted on a motorised translation stage, allowing precise control of the incident beam position along the X, Y, andZ axes. The motorised XY stage allowed precise lateral positioning of the sample, while the Z axis was used to place the DMD at the focal plane.
The incident beam at the focal spot area was meticulously measured, using a commercial beam profiler( WinCam D, Data Array Inc, minimum pixel size 6.45 lm). In our case, the Gaussian beam showed small ellipticity thus, the effective area is obtained instead using the equation as A eff = pq 1 q 2. Along the horizontal axis, the measured FWHM was 64 ± 6 lm and the diameter( 1 / e 2) wasq 1 = 103 ± 6lm. While for the vertical axis, the FWHM was 73 ± 6 lm and the diameter( 1 / e 2) was 2q 2 = 123 ± 6lm. Additionally, the focal spot used to irradiate all points on the sample has a value of 9.01 10 �4 ± 0.01 10 �4 cm 2 in air, for the specific focallength used in the experiment. The pulse energy used ranged from 1.4 lJ to18lJ. Using a confocal microscope( Sensofar PLu
2300), different planes in the DMD were identified along the optical path. Then, the distance between the external surface of the protective window and the micromirror plane was corroborated to be 2.5 mm, while the glass was confirmed to be 2 mm thick [ 36 ]. Thus, in this experiment, the change in the focal spot area due to the window was assumed to be negligible.
Each fluence level was tested at three different positions on the DMD to obtain an average damage-spot size for each fluence value. Three measurements were performed for each fluence, and the average damage area was reported. To measure the damage area, a confocal microscope was used to obtain an image of the irradiated regions, on the DMD’ s surface. For an accurate evaluation of the induced damage, initially, greyscale and depth-resolved images( Z-stack) of the DMD’ s micromirrors were obtained. The addition of Z-stack images provides a higher resolution in identifying damaged micromirrors either by a deviation of their relative planes with neighbouring micromirrors or by a discrepancy in texture or colour.
In Figure 3 at a fluence of 0.11 J / cm 2, five damaged micromirrors are observed. One missing micromirror is located at the centre of the beam, while the remaining four are at different positions and can be identified as damaged because they lie in a different plane( yellow) from the undamaged micromirrors( orange). Afterward, any deviation from the initial position could affect micromirror functionality, and only the missing micromirrors, as well as darkened micromirrors, were included in the evaluation of the total damaged area shown in Figure 3. Based on the analysis of the acquired images, no visible damage was observed at fluences below 0.07 J / cm 2. The onset of damage was identified at 0.09 J / cm 2, asshowninFigure 3, where the first affected micromirror appeared slightly displaced from its plane. At this fluence, a minor deformation type was identified, corresponding to micromirrors that show small displacements while remaining in their original positions within the DMD array, as seen in the greyscale image. The first instance of a completely missing micromirror was observed at 0.10 J / cm 2, this result is consistent with the recommendation given in the technical notes in reference [ 37 ], while symmetrical central damage became evident at fluences exceeding 0.15 J / cm 2.
According to Lui’ s method, the experimental damage area is adjusted as a function of fluence using equation( 2). Under our specific laserconditions, thefluence threshold was identified as 0.12 ± 0.02 J cm 2, considering the equation Ar ð i Þ ¼ 1:66 10 �4 lnðUÞþ3:54 10 �4. Figure 3a presents the experimental data of damage area as a function of fluence. The point where the damage begins to appear and the corresponding fluence threshold can be appreciated. In Figure 3a, the graph was obtained from 18 different fluence levels, each measured three times. The scatter bars represent the dispersion in the measured damage areas. The damage was characterised using two types of images: z-stacks of 40 confocal microscope images with 1-lm axial steps( b), and bright-field microscope images( c). The measurements were categorized into three zones, separated by dashed lines: Zone I, Zone II( green line), and Zone III( red line). In Zone I, no damage was observed