getoptimalnewcameramatrix function for omndirectional camera?

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I am working on stereo rectification of wide FOV fisheye lens. I want to do stereo rectification in latitude and longitude space so stretching at the edges can be avoided. Hence I am using opencv omndir package with RECTIFY_LONGLATI flag for stereo rectification. I am getting good results but the most of the portion of image is cropped. I want to scale the camera matrix such that no region is cropped while stereo rectification. I don't know how to scale the camera matrix keeping epipolar constraint for stereo rectification. I have found functions for estimating new camera matrix in calibration and fisheye module but not in omnidir module.

I tried to scale (double) the focal length in order to check can i get whole image without cropping. I am getting both left and right image without cropping but stereo rectification is disturbed. I know just scaling the focal length will disturb the rectification. Principal point also need to scaled considering distortions coefficients. I don't know how to do this, hence I was searching for function similar to getoptimalnewcameramatrix in omndir package. I will be helpful If anyone can help me with the maths behind scaling camera matrix and keeping epipolar constraint in stereo rectification.

I am attaching small portion of my code, camera calibration output file and results below.

raw left image

raw right image

rectified image without scaling camera matrix

non rectified image with focal length scaling

output calibration file

code snippet.

Mat left_img = imread("../data/left42.png");
Mat right_img = imread("../data/right42.png");
Mat left_img_undistorted, right_img_undistorted;

Mat R1, R2;
cv::omnidir::stereoRectify(rvec, tvec, R1, R2);
int flags_ = cv::omnidir::RECTIFY_LONGLATI;
cv::Size imgSize = left_img.size();

// K1 and K2 are estimated camera matrix from calibration. 
// D1 and D2 are estimated distortion coefficients from calibration
// xi11 and xi2 are estimated Mei's coefficients from calibration

Mat K1_ = K1.clone();
Mat K2_ = K2.clone();

// scaling focal length
K1_.at<double>(0,0) = K1_.at<double>(0,0)*2;
K1_.at<double>(1,1) = K1_.at<double>(1,1)*2;

cv::Matx33d Knew(imgSize.width / (3.1415), 0, 0, 0, imgSize.height /(3.1415), 0, 0, 0, 1);

cv::omnidir::undistortImage(left_img, left_img_undistorted, K1_, D1, xi1, flags_, Knew, imgSize, R1);
cv::omnidir::undistortImage(right_img, right_img_undistorted, K2_, D2, xi2, flags_, Knew, imgSize, R2);
Mat final;
hconcat(left_img_undistorted, right_img_undistorted, final);
for( int j = 0; j < final.rows; j += 40 )
    line(final, Point(0, j), Point(final.cols, j), Scalar(0, 255, 0), 1, 8);

imwrite("../out/rectified.png", final);