Digital holographic microscopy plays an important role in the surface topography measurement of micro-optical elements. It is based on the interference superposition of waves, and realizes the measurement of three-dimensional information of objects through digital recording and diffraction reproduction. However, due to the interference of background information in the process of microscopic imaging, there are some problems such as poor focusing effect and unsatisfactory image quality. For the wave-front phase detection of micro-optical elements with different structures, the traditional digital holographic 3D field reconstruction method cannot effectively reconstruct part of the angular spectrum components of object light wave, resulting in low accuracy of the wave-front phase measurement of micro-optical elements. Therefore, this paper proposes a phase reconstruction method of compressed sensing based on sparse sampling in the frequency domain. In combination with the characteristic that most phase information is contained in the frequency domain, the sparse characteristics of compressed sensing theory are utilized to conduct random sparse sampling of the spectrum information of holograms during the reconstruction process of the traditional digital holographic reconstruction algorithm. The effective spectral information of the reconstructed object is recovered in the domain of wavelet transform, and then the frequency domain is transformed into the spatial domain by Fourier inverse transform, and the complex amplitude distribution of the reconstructed object is obtained. Finally, experimental research is carried out for continuous and discontinuous phase objects, and the phase reconstruction results of higher quality than the traditional method are obtained by analyzing the quality of phase image reconstruction and the accuracy of 3D reconstruction, respectively, and the accurate measurement of the phase information of the object is realized. After spectral filtering in the frequency domain is carried out by the traditional method, it is easy to lose high-frequency information after conversion from the frequency domain to the spatial domain. However, based on the compressed sensing theory, the proposed method takes advantage of the sparse characteristics of the image to sparsely sample the spectral signals in the frequency domain and sparsely expand them in the wavelet base domain. This means that even if the expansion term has only a few effective terms, the effective spectrum of light wave of sparsely recovered object can still be guaranteed. Experimental results show that the wave-front phase reconstructed by this method is more stable and has higher contrast. Compared with the phase reconstruction results of traditional digital holography, the peak to Valley Value (PV) and Root Mean Square Value (RMS) of residual errors are reduced by 26.97% and 15.04%, respectively, the method based on compressed sensing theory with the compression of imaging mechanism, can be obtained through the low resolution of sampling high-resolution reconstruction of wave-front phase object under test, for surface topography measurement of micro-optics element provides effective information acquisition, improve the reconstruction quality of micro-optics element wave-front phase and 3D measurement accuracy, in discontinuous object wave-front phase measuring has potential advantages.