多频外差法（三频四步相移）

四步相移法求主值

计算相位函数：

 代码：

void MultifrequencyHeterodyeMethod::fourStepPhaseShifting(cv::Mat grating_img[])//四步相移法
{
	cv::Mat PhasePrincipalValuePicture_temp[3] =
	{
		cv::Mat::zeros(grating_rows, grating_cols, CV_8UC1),
		cv::Mat::zeros(grating_rows, grating_cols, CV_8UC1),
		cv::Mat::zeros(grating_rows, grating_cols, CV_8UC1)
	};

	uchar* p[12] = { NULL };

	for (int y = 0; y < grating_rows; ++y)//图像行遍历
	{
		for (int img_num = 0; img_num < 12; ++img_num)
		{

			p[img_num] = grating_img[img_num].ptr(y);

		}//遍历12幅图

		for (int x = 0; x < grating_cols; ++x)//图像列遍历
		{
			double phaseValue1_temp = atan2((double)(p[3][x] - p[1][x]), (double)(p[0][x] - p[2][x]));//3-1 0-2
			if (phaseValue1_temp >= 0)
				PhasePrincipalValuePicture[0].at(y, x) = phaseValue1_temp;
			else
				PhasePrincipalValuePicture[0].at(y, x) = phaseValue1_temp + CV_PI * 2;

			double phaseValue2_temp = atan2((double)(p[7][x] - p[5][x]), (double)(p[4][x] - p[6][x]));//7-5 4-6
			if (phaseValue2_temp >= 0)
				PhasePrincipalValuePicture[1].at(y, x) = phaseValue2_temp;
			else
				PhasePrincipalValuePicture[1].at(y, x) = phaseValue2_temp + CV_PI * 2;

			double phaseValue3_temp = atan2((double)(p[11][x] - p[9][x]), (double)(p[8][x] - p[10][x]));//11-0 8-10
			if (phaseValue3_temp >= 0)
				PhasePrincipalValuePicture[2].at(y, x) = phaseValue3_temp;
			else
				PhasePrincipalValuePicture[2].at(y, x) = phaseValue3_temp + CV_PI * 2;

			PhasePrincipalValuePicture_temp[0].at(y, x) = PhasePrincipalValuePicture[0].at(y, x) / (2 * CV_PI) * 255;
			PhasePrincipalValuePicture_temp[1].at(y, x) = PhasePrincipalValuePicture[1].at(y, x) / (2 * CV_PI) * 255;
			PhasePrincipalValuePicture_temp[2].at(y, x) = PhasePrincipalValuePicture[2].at(y, x) / (2 * CV_PI) * 255;
		}
	}

	//三张不同频率的主值图
	cv::namedWindow("PhasePrincipalValuePicture[0]", 0);
	cv::resizeWindow("PhasePrincipalValuePicture[0]", cv::Size(800, 600));
	cv::imshow("PhasePrincipalValuePicture[0]", PhasePrincipalValuePicture_temp[0]);


	cv::namedWindow("PhasePrincipalValuePicture[1]", 0);
	cv::resizeWindow("PhasePrincipalValuePicture[1]", cv::Size(800, 600));
	cv::imshow("PhasePrincipalValuePicture[1]", PhasePrincipalValuePicture_temp[1]);

	cv::namedWindow("PhasePrincipalValuePicture[2]", 0);
	cv::resizeWindow("PhasePrincipalValuePicture[2]", cv::Size(800, 600));
	cv::imshow("PhasePrincipalValuePicture[2]", PhasePrincipalValuePicture_temp[2]);

	cv::waitKey(500);
}

atan2的含义：
C 语言里 double atan2(double y,double x) 返回的是原点至点(x,y)的方位角，即与 x 轴的夹角。返回值的单位为弧度，取值范围为（-π, π]。结果为正表示从 X 轴逆时针旋转的角度，结果为负表示从 X 轴顺时针旋转的角度。若要用度表示反正切值，请将结果再乘以 180/π。另外要注意的是， 函数atan2(y,x)中参数的顺序是倒置的，atan2(y,x)计算的值相当于点(x,y)的角度值。

运行结果：

频率1主值图：

频率2主值图：

频率3主值图：

 参考博客：

三维重建之条纹投影结构光（二）——四步相移+三频外差法_beyond951的博客-CSDN博客_三频外差

atan2相关知识汇总_sxl545的博客-CSDN博客_atan2