Ultra precision micro nano devices are the core devices in the manufacturing field. With the rapid development of ultra-precision machining technology, the corresponding micro nano detection technology is required to be higher and higher. Micro nano measurement technology is an important means to ensure the accuracy and stability of ultra-precision machining technology and is the premise for further development. The surface profile detection methods for micro/nanodevices can be divided into optical and non-optical types according to whether optical principles are used. Non-optical detection usually adopts point scanning and contact detection, which is inefficient and easy to damages the surface morphology of the device to be tested. Optical detection methods are mostly surface scanning, and non-contact measurement, which will not scratch the device to be tested, and the detection efficiency is high. In optical detection, white light interferometry has been widely concerned by researchers at home and abroad because of its short coherence length, which can achieve high-precision measurement of three-dimensional morphology of micro-nano devices. In white light interference detection technology, the signal demodulation algorithm is very important to the entire detection system. Traditional white light interference signal demodulation algorithm only uses part of the information of the interference signal, which has low demodulation accuracy. However, high-precision phase shift demodulation algorithm depends on the accuracy of rough positioning, which cannot directly achieve the high-precision three-dimensional shape recovery. In order to solve the above problems, this paper proposes a signal demodulation algorithm based on the correlation. This algorithm calculates the correlation through a three-level sliding window and uses all the white light interference signal information. Without rough positioning, it can directly determine the three-dimensional surface topography information of the object to be measured. In order to verify the performance of the algorithm, this paper has carried out simulation and experimental verification. The simulation results show that the method is feasible and can accurately restore the 3D structure morphology to be measured. The setting of a three-stage sliding window can effectively improve the calculation efficiency. At the same time, the white light interference vertical scanning experimental system is built, and the grating structure and microlens structure are measured. The experimental results are compared with the traditional gravity center and phase shift methods. The experimental results show that this method can accurately restore the three-dimensional topography of different objects, and its accuracy and robustness are better than the improved barycenter method, which is close to the phase-shifting method. The grating height recovery results show that the error between this and phase-shifting methods is less than 0.5 nm. The simulation and experimental results show that the white light interference signal demodulation method based on the correlation proposed in this paper is feasible. It can achieve high-precision recovery of the three-dimensional surface topography of the object to be measured without rough positioning and has the characteristics of high precision and high robustness.