Basic Principles and Methodology 201 $10,000 steps, which is more than adequate for a smooth profile. These para- meters are discussed in Section 5.3. This technique has been applied to the fabrication of apodized chirped grat- ings as well. In this case, not only does the mark­space ratio have to be changed but also the period. 5.2.5 Position-Weighted Fabrication of Top-Hat Reflection Gratings The MPF method is suited to writing gratings with a "top-hat" (TH) reflec- tion spectrum, shown in Fig. 5.8, along with the spatial profile of the refractive index modulation of the grating required for these characteristics (Fig. 5.9). For a perfect TH, an infinite number of cycles of a rect or sinc function are needed. This is not possible for practical gratings, since the continuous sinc function can only be approximated in a discrete number of steps. This task is demanding in any case, but a good approximation is possible with a few cycles. In order to invert the phase between the sections, additional UV exposure is given to induce a l/2 phase shift. The MPF scheme caters for both the changes in the amplitude of the refractive index modulation and the phase change. For the former, overlaid subgratings with