## 2 The Excimer Laser Micromachining System and the Optical Diffraction Effect
In preparing the hole-array patterns, three different element sizes (d) were used, i.e., 10, 15, and 20 \(\upmu\)m. Moreover, for each element size, masks were patterned with several different hole-radii, thereby resulting in different hole-area opening ratios. Through varying the element size (d) and hole-radius (r) in this way, it was possible not only to vary the average transmission coefficients of the photomasks but also to vary the degree of optical diffraction. For a given element size, the feasible hole-radius range was limited by the production capability for the Cr/glass photo-mask. In this study, the photo-masks were fabricated using a laser writing system (Alta 3000, Etec Systems Inc., Hayward, CA, USA) with a smallest attainable line-width of 2 \(\upmu\)m.  
Using the Cr/glass photo-masks described above, excimer laser machining tests were carried out using 500-\(\upmu\)m-thick polycarbonate (PC) substrates (CT301310, Goodfellow Cambridge Ltd., Huntingdon, UK). (Note that PC was specifically chosen as the substrate material due to its excellent machined surface roughness which was less 10 nm [11].) The experiments commenced by determining the basic laser machining rate, i.e., the machining rate in the absence of optical diffraction. The machining trial was thus performed using a simple 1 \(\times\) 1 mm\({}^{2}\) opened square window with no mask pattern. Given a fluence setting of 600 mJ/cm\({}^{2}\), 100 laser pulses were applied to the PC substrate, and the machined profile was then measured using a 3D topography laser scanning confocal microscope (VK-9700, Keyence Ltd., Osaka, Japan). The machined depth was found to be 26.5 \(\upmu\)m. Thus, the basic laser machining rate was determined to be 0.265 \(\upmu\)m/pulse. To investigate the effect of the feature size on the optical diffraction phenomenon, mask patterns were designed with three different element sizes (d = 10, 15, and 20 \(\upmu\)m) and different values of the hole-radius (r). Each mask pattern had dimensions of 500 \(\times\) 500 \(\upmu\)m\({}^{2}\), so the projected machining area on the PC substrate had a size of 50 \(\times\) 50 \(\upmu\)m\({}^{2}\) due to the 10\(\times\) de-magnification factor of the image projection system. Figure 3a-c shows the machined cross-sectional profiles obtained on the PC substrate using mask patterns with element sizes of 10, 15, and 20 \(\upmu\)m, respectively, and a constant hole-area opening ratio of 0.65. It is seen that the optical diffraction effect becomes more significant as the feature size of the mask pattern reduces. For example, given an element size of 10 \(\upmu\)m, the machined surface profile approaches a flat surface in which the individual features of the arrayed holes can be barely discerned (see Figure 3a). However, for larger element sizes of 15 and 20 \(\upmu\)m, periodic machined profiles with periods of 1.5 and 2.0 \(\upmu\)m, respectively, are vaguely visible (see Figure 3b,c). In general, the results presented in Figure 3a-c show that the average machined depth decreases as the feature size of the mask pattern reduces even though the hole-area opening ratio remains constant (i.e., 0.65). In other words, it is inferred that the amount of energy rejected by the pupil of the optical imaging system increases with a reducing feature size due to the greater diffraction effect. Figure 2: (**a**) Mask pattern design using arrayed square elements with hole-opened apertures. Possible cross-section profiles of machined microstructures at the corresponding position of line (A-A) marked in the mask pattern with (**b**) negligible, (**c**) intermediate, and (**d**) heavy optical diffraction effect during excimer laser machining. Figure 4 shows the variation of the machining rate with the hole-area opening ratio as a function of the element size. Note that the machining rate is normalized with respect to the basic machining rate obtained in the absence of optical diffraction (i.e., 0.265 \(\upmu\)m/pulse).