## 1 Introduction  
Digital holography (DH) is utilized for recording and reconstructing the intensity and phase of microstructures with high efficiency and precision, due to recent advances in charge-coupled devices (CCDs) and computers [1; 2]. Indeed, digital holography has been widely employed in the applications of surface topography measurement, particle field analysis, and medical diagnosis during the past decades [3; 4; 5; 6]. Zeroth-order beam and the twin image noise are the most important factors affecting the quality of the reconstructed object wavefront in DH. In optical holography, the off-axis geometry is an effective configuration for separating the zeroth-order beam and the twin image [7]. However, it is difficult to record a high-quality off-axis hologram in digital holography. When on-axis geometry is employed, we can eliminate the zeroth-order beam and twin-image noise with phase-shifting holography (PSH) [8; 9]. Among the various techniques in PSH, two-step quadrature phase-shifting holography is one of the most widely used techniques by virtue of fewer recordings and easy operations as compared to other PSH techniques [10].  
In order to eliminate the zeroth-order beam and twin-image noise, two phase-shifted holograms and one or two intensity images (namely, intensity images of both the object and the reference or one of them) are collected in two-step quadrature phase-shifting holography (QPSH). [PERSON] et al. [11] have proposed an algorithm called two-step generalized phase-shifting interferometry, which still needs two intensity images. [PERSON] et al. [12] have researched an algorithm using only two holograms and one intensity image, but the original complex object wave also needs to be recorded. [PERSON] and [PERSON] have studied a method called two-step-only quadrature phase-shifting holography (TSO-QPSH) [13], which estimates the reference intensity by iterative computations instead of an actual recording of the intensity map. Other researchers have optimized [PERSON] and [PERSON]'s algorithm to decrease the computational speed [14; 15], but their proposed estimation methods are still relatively complex and computationally intensive.  
Recently, we have proposed a very simple setup to calculate a complex hologram by using only two holograms with quadrature phase-shifting [16; 17]. The constructed complex hologram contains the original information or its conjugate of the test object, which means the hologram can be reconstructed without the twin-image noise. However, the reconstructed image is not of good quality because the zeroth-order beam still exists on the reconstruction plane. Besides, all the investigations given above discuss the intensity reconstruction rather than the phase reconstruction of the object. The phase distribution of the test sample could not be retrieved precisely since there exists a complex zeroth-order term in the constructed complex hologram, giving rise to a zeroth-order beam upon reconstruction. In this contribution, we have focused on two-step phase shifting digital holography and proposed a fast method to recover the reference-wave intensity from the complex hologram without using either iteration procedure or physical measurement for exact phase retrieval. In the following sections, we describe our proposed method. Computer simulation and experimental results are then performed to verify the effectiveness and feasibility of our proposed idea.