## 1 Introduction  
Microdevices comprising of film layers have been used in a wide range of fields, such as semiconductors, solar photovoltaic industries, and material sciences [1, 2, 3]. The film structure metrology is an essential area, since the qualitative and quantitative analysis of film structures provides insight into the influence of manufacturing processes on functional characteristics [4, 5]. In past decades, optical techniques have drawn much attention in the characterization of thin material layers due to their ability to provide nondestructive measures. The most well-established of these are ellipsometers, reflectometers, and white-light interferometry (WL) [6, 7, 8]. Ellipsometers and reflectometers are used in many cases, since they can measure the layer thickness and refractive index of thin films [9, 10]. However, to provide a full-field thickness profile as well as the topography of the corresponding surfaces, these two approaches both require a time-consuming process or complicated system configuration. Another method, WLI, fulfills the requirements of high efficiency for the 3D inspection of the internal structure of a film. Although WLI allows the simultaneous measurement of a film surface and substrate surface with a high precision [11, 12, 13], the interference originating at each surface imposes strict demands on the reconstruction algorithm and library of theoretical signals. Recently, [PERSON] et al. introduced structured illumination microscopy (SIM) into the field of film measurement because the SIM-based method has a high axial resolution and efficiency in 3D measuring [14; 15; 16; 17; 18; 19]. In SIM, several sinusoidal patterns with predefined phases are projected on the sample surface. The modulation distribution of the captured images reflected from the surface can be determined by the phase-shifting technique [20]. The modulation depth response (MDR) curve of each pixel, which indicates the modulation distribution on the point changing with the scanning distance, can be achieved by vertically scanning the sample around the focal plane. Therefore, detecting the peak of the MDR curves makes it easy to reconstruct the three-dimensional surface topography. When SIM is applied in the film structure measurement, the MDR involves several peaks as the projected sinusoidal pattern reflects on the corresponding surfaces. As a result, the surface profiles and film thickness can be obtained by identifying the peaks. However, when the thickness between adjoining layers is thinner, the peaks of the MDR start to overlap to create distorted peaks. As the extent of the peak overlap increases, the change in the peak shape is enlarged, amplifying the location extraction error and decreasing the accuracy in conventional SIM. Further, if the overlapped peaks are bent into one, the traditional methods become failed because they find the only maximum point. Consequently, the maximum-point-based approach has a circumscribed thickness resolution, which limits the application for SIM in the field of film structure measurement. To develop the measurement threshold of thickness in SIM, we developed a new method iterative peak separation structured illumination microscopy (IPS-SIM). Since the incoherent light reflected from the sample is the combination of reflections from the surface of the interior layers, the MDR curve can be considered as a Gaussian model. For a single-film-layer sample, the MDR curve is a sum of two Gaussian functions. To optimize the location of each peak of the MDR, the IPS-SIM utilizes the iterative optimization algorithm of which the model function is the sum of Gauss. Compared with the traditional SIM, the proposed method provides accurate peak detection even when the peaks of the MDR are highly overlapping. Then, the precise location of peaks is used to determine the height of the layers. Hence, the IPS-SIM provides a lower detection threshold for thickness than the existing SIM method for film thickness profile measurement.