## 1 Introduction  
Optical 3D measurement plays a pivotal role in all aspects of our lives, such as industrial production, biological medicine, and consumer entertainment [1; 2; 3; 4; 5]. Many optical technologies including structured light, stereo vision, and digital fringe projection (DFP) have been exploited to achieve high-density and full-field 3D measurement [6]. Among those technologies, DFP has become the most popular one because of its speed, accuracy, and flexibility [7]. Fourier transform and phase-shift are two main methods applied in the DFP system [8]. The former method only uses one pattern for computing phase map, but the measured surfaces must be rather simple to avoid a spectral overlapping problem. On the other hand, the phase-shift method exploits at least three patterns to compute the phase map pixel-by-pixel, which can achieve higher accuracy and stronger robustness, especially for complex surfaces. However, those two methods can only work out wrapped phases which need to be unwrapped for absolute phase maps. Ideally, when referring to the neighboring pixels, the wrapped phase can be unwrapped by adding integral multiple of \(2\pi\) at each pixel. In reality, however, local shadows, random noises, and isolated objects are very usual occurrences that make the unwrapping phase difficult [9]. Thus, many absolute phase retrieval algorithms have been proposed, which can be divided into two major classes: spatial algorithms and temporal algorithms [7]. The spatial algorithms are generally used for smooth surfaces, while the temporal algorithms are more suitable for complex surfaces and attract more attention [10]. Research conducted in this field brings forth several typical examples. [PERSON] et al. [11; 12] first proposed two-wavelength phase-shift interferometry, and then developed multi-wavelength phase-shift interferometry to enhance the measurement capability. [PERSON] et al. [13] combined phase-shift and gray-code into the 3D vision system, which greatly improved the measurement performance. [PERSON] et al. [14] put forward an effective and robust phase-coding method. [PERSON] et al. [15] improved the phase-coding method for a large number of code words. [PERSON] et al. [16; 17] successively developed a quantized phase-coding method and a modified gray-level coding method, which achieved good results when measuring isolated objects. Nevertheless, all the aforementioned methods require three or more extra patterns, which will limit the speed of measurement. To reduce the number of patterns, some researchers have utilized color patterns for 3D measurement [18; 19; 20]. However, these methods have always failed for colorful objects. Other researchers have employed more cameras to capture the patterns from different perspectives, such that the multi-view geometric constraints can be used for absolute phase calculation [21; 22; 23]. However, the measurement field reduces because of the multiple perspectives, and the cost and complexity of the system increase due to additional cameras [24]. To realize high-speed measurement, [PERSON] et al. [25] recently proposed a pixel-wise phase unwrapping method with no additional pattern. Based on the geometric constraints of fringe projection system, an artificial phase map \(\Phi_{min}\) at the closest depth plane \(z_{min}\) is generated, and then the phase unwrapping can be executed by referring to \(\Phi_{min}\). Subsequently, a number of algorithms were developed for phase unwrapping based on [PERSON]'s method [26; 27; 28; 29]. However, the maximum depth range this method can handle is within \(2\pi\) in phase domain. When the object points far away from depth plane \(z_{min}\) brings more than \(2\pi\) changes, this method is no longer applicable. Inspired by [PERSON]'s method, this paper presents an absolute phase retrieval method using only one additional coded pattern to improve the measurement depth range. Firstly, the wrapped phase is calculated from three phase-shift patterns, and the code word is extracted from the coded pattern.