# A Parallel-Phase Demodulation-Based Distance-Measurement Method Using Dual-Frequency Modulation
## 1 Introduction  
3D depth maps contain position and orientation information of objects unavailable in color images. Such 3D spatial information can be utilized in various types of engineering applications, such as unmanned vehicles, robots, human-recognition systems, medical applications, and even personal IT devices [1; 2; 3; 4; 5; 6; 7]. Specifically, in the field of machine vision, 3D depth maps are widely used for many purposes, including human motion capturing [5; 6] and object recognition [7]. There are several ways to obtain a 3D depth map, such as stereoscopy [8; 9], the structured light method [10; 11], and the Time-of-flight (ToF) measurement method [12; 13; 14; 15; 16]. However, the stereoscopy and structured light methods require many cameras and incur excessive computational loads [13]. In addition, these methods can achieve high depth resolutions only when a relatively large triangulation base is obtained, meaning that the systems are often bulky [13]. Consequently, the ToF measurement method has been widely adopted as an alternative for 3D depth sensing due to its compactness and low calculation loads [12; 13; 14; 15; 16]. During ToF measurements [12; 13; 14; 15; 16; 17], a pulsed or continuous optical signal is emitted to the object and the traveling time of the reflected light signal is measured. The traveling time, i.e., the ToF, is then converted into the distance. The direct ToF measurement method [13; 15; 17], which uses a pulsed optical signal for emission, is one way to measure the ToF. After the emitted light is reflected from the object, the time-to-digital converter (TDC) returns the ToF of the reflected light. Although the direct ToF measurement methodis logically simple, a high-precision and expensive TDC capable of nanosecond-timed resolutions is required. Moreover, a relatively high-powered laser source is required for pulse modulation. To cope with this drawback, the use of the AMCW method is growing. In the AMCW method, continuously periodic (a single sine waveform) light is generated by modulating an illumination source, such as laser diode [12; 13; 14]. After this modulated light is emitted onto the object, the reflected light is received by the detector, such as an avalanche photodiode [13]. In the AMCW method, the time delay between the emitted and reflected light signals is determined by corresponding phase delay, which is calculated from the cross correlation [12] between the reflected light signal and external demodulation signal. This indirect ToF method can achieve adequate accuracy and provides the compactness of the sensor system [12]. Many types of AMCW-based cameras have been developed and analyzed [13; 16]. Among them, Mesa Imaging developed the SR4000/4500 cameras [13] which provide 3D depth maps at a resolution of \(176\times 144\). In addition to the SR series, many other companies and research teams have developed promising sensor devices for obtaining 3D depth information [13; 16]. Performance improvements of ToF cameras have been pursued by enhancing the accuracy of distance measurement. [PERSON] et al. [18] reduced the degree of nonlinearity in phase measurements using a phase-encoding approach, which improved the accuracy of distance measurements. [PERSON] [19] solved the problem of motion blur stemming from rapid motions of objects using an altered form of the conventional four-bucket method. The use of multiple frequency components in the modulation and demodulation process to improve the performance has been studied. [PERSON] et al. [20] and [PERSON] [21] tried the various combinations of multiple frequency components. In these works, optimal waveforms of modulation and demodulation signals were determined to improve distance accuracy. [PERSON] et al. [22] and [PERSON] et al. [23] adopted a dual-frequency modulation scheme to increase maximum range limited by the \(2\pi\) ambiguity problem. The above mentioned AMCW ToF method utilizes sequential phase demodulation implemented in hardware.