In order to recover the phase map φ(x, y) from sinusoidally phase-shifted interferograms obtained with the integrating-bucket method, two images Ψ_s and Ψ_c should be calculated first which are proportional to sin(φ) and cos(φ) respectively, and one of them needs to be scaled by a scale factor before they are used to solve the phase with the arctangent function. Because parameters deciding the scale factor such as the sinusoidal phase modulation amplitude and initial phase are difficult to be set accurately, miscalibration of it can always happen and result in significant error in the phase demodulation. Therefore, in this paper we propose a simple scale factor calibration method which performs the calibration directly with the phase-shifted interferograms and avoids the need for accurate parameter setting. First, we introduce high-density fringes to the interferograms; then, we construct a new image variable Γ with the squares of Ψ_s and Ψ_c; last, we find the value of the scale factor by minimizing the second harmonic amplitude in Γ’s spatial spectrum. Simulation results show that the proposed method is robust against noise and fringe distortion, and it was tested in a fiber-optic fringe projection profilometer.

为了恢复相位图φ（X，Y）从与积分桶法得到的正弦相移干涉，两个图像Ψ_小号和Ψ _Ç应当首先计算它们与sin（φ）和cos（φ），并且其中之一需要先使用比例因子进行缩放，然后才能使用反正切函数求解相位。由于决定比例因子的参数（例如正弦波相位调制幅度和初始相位）很难准确设置，因此始终会发生校准错误，并且会在相位解调中造成重大误差。因此，在本文中，我们提出了一种简单的比例因子校准方法，该方法可以直接使用相移干涉图执行校准，并且无需进行精确的参数设置。首先，我们在干涉图中引入了高密度条纹。然后，我们构建了一个新的图像变量Γ与Ψ的平方_小号和Ψ _Ç; 最后，我们通过最小化Γ空间频谱中的二次谐波幅度来找到比例因子的值。仿真结果表明，该方法具有良好的抗噪声和条纹畸变的能力，并在光纤条纹投影轮廓仪上进行了测试。