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calculate disparity value for distance

Hi everyone, I want to reverse the whole procsess of projecting a disparity value to 3D word space in order to get the exact disparity value belonging to a specific distance.

This is the code I use to calculate a 3d-coordinate:

cv::Mat_<float> coordinate(1,4);
dValue /= 16.0;

if(dValue > 0) {
  coordinate(0)=x;
  coordinate(1)=y;
  coordinate(2)=dValue;
  coordinate(3)=1;

  coordinate = cv::Mat(coordinate);

  coordinate = Q * coordinate.t();
  coordinate /= coordinate(3);
  return coordinate;

} else {
  coordinate(0) = 0;
  coordinate(1) = 0;
  coordinate(2) = 1000000;
  coordinate(3) = 0;
  return coordinate;
}

Now I thought about writing the inverse calculation in Order to get the disparity value for a specific distance:

// coordinate in the world origin with a distance of 1.0 meter.
cv::Mat_<float> coordinate(1,4);
coordinate(0) = 0.0f;
coordinate(1) = 0.0f;
coordinate(2) = 1.0f;
coordinate(3) = 1.0f;

cv::Mat Q_inv = Q.inv(cv::DECOMP_SVD);
Q_inv.convertTo(Q_inv, CV_32FC1);

cv::Mat_<float> back = Q_inv * coordinate.t();
// just makes the value bigger and does not result in a correct value
// back(2) */ 16;

To my mind the calculation is mathematically correct. But the returned values do not match anything related to the disparity values:

disparityValue: 688  distance: 0.901838
calculated coordinate:
[1.5896965;
 1.3923311;
 119.25928;
 0.0015376776]

Does somebody know where the problem could be?