## 1 Introduction  
The direct machining of microstructures by pulsed excimer lasers has attracted significant interest over the past 30 years or so [1; 2; 3]. Figure 1 presents a schematic illustration of a typical excimer laser micromachining system based on a mask projection approach [4; 5]. As shown, the system consists of an excimer laser source, a laser beam homogenizer, a photo-mask, an optical image projection system, and a multi-axis translation stage. Typically, the laser source is provided by ArF (193 nm), KrF (248 nm), or XeF (308 nm) pulsed lasers, which emit a continuous train of short pulses with a high energy. The laser beam homogenizer re-shapes the laser beam profile such that a uniform laser intensity distribution is obtained on the photo-mask surface. The light passing through the mask is projected by an optical imaging system onto the surface of the sample, which is mounted on a servo-controlled multi-axis translation stage. The whole system is operated under the control of a personal computer, which synchronizes the laser firing sequence and the sample movement during the machining process in such a way as to achieve the required micromachined features on the substrate surface. Femtosecond lasers are also used in micro-machining based on cold ablation. When materials are radiated by laser pulses with ultrashort pulse duration (a few hundred or tens of femtoseconds), the heat-affected zone (HAZ) is negligible, so cold laser ablation is achieved [6]. However, in some cases the femtosecond lasers operate with a higher pulse repetition rate (up to 100 kHz or less) to increase the machining rate, and the heat effect becomes significant. In other words, it is a trade-off between machining quality and machining time. Furthermore, most femtosecond lasers are still used for 2D machining or direct patterning while in this work we are focused on machining 3D-microstructures based on optical diffraction modulation. The mask projection system shown in Figure 1 was intended originally for two-dimensional (2D) micromachining. In such a system, the machined area on the sample surface has the same dimensions as those of the photo-mask pattern other than for the de-magnification effect of the optical imaging system. Since the wavelength of excimer lasers is typically in the deep ultraviolet (UV) region, the photon energy can be high (5 eV for KrF-248 nm, for example), so certain covalent bonds in polymer substrates (polycarbonate, polyimide, etc.) are broken directly when subjected to laser irradiation. This phenomenon is known as photochemical laser ablation and is favorable in laser machining due to the minimal thermal damage and burning which it causes. When applying pulsed excimer lasers to certain polymer materials, the photochemical etching effect dominates the laser ablation process and results in the formation of smooth and clearly defined micro-features. Since the laser fluence projected onto the sample surface is uniform, each laser pulse removes a constant depth of material over the projected image area. In practice, the laser machining rate depends on both the projected laser fluence and the material properties of the sample. By firing a continuous train of laser pulses, material removal is carried out layer by layer and the machining depth accumulates proportionally. The final laser-machined 2D microstructures have a surface pattern defined by the photo-mask design and a machining depth (or structure height) determined by the number of laser pulses received at each particular point on the substrate surface and the laser machining rate. The literature contains various proposals for 3D micromachining systems based on the configuration shown in Figure 1. Broadly speaking, these systems fall into two main categories depending on the characteristics of the photo-mask used in the ablation process, namely binary or grey-scale.