Why does apple stereo cameras depth map have a constant error

According to WWDC event 2017 (19 min), apple stereo camera can only output relative depth map due to the constant changing baseline (the lens of iPhones are moving to offset shaky hands). It also mentioned that our depth map would have a constant amount of error throughout the entire picture. I just can't figure out why it is true.


According to the formula in the earlier slides (12 min), the inverse of depth = disparity /(focal length * baseline)

1/z = d/(fl * b)


The focal length (fl) and the inaccurate baseline (b) are constant in one picture.

1/z = (inaccurate constant) * disparity.


How come this would result in a constant amount of error in the depth map for the whole picture? Shouldn't it differ in proportion to disparity changes?


# disparity in point a is d, disparity in point b is d+deltaD
1/za = (inaccurate constant) * d
1/zb = (inaccurate constatn) * (d+deltaD)
changeInNormalizedDisparity = 1/zb - 1/za = (inaccurate constant) * deltaD
# inverse of depth is porportional to deltaD, but apple says it is constant, something I got wrong?


link for WWDC2017 https://developer.apple.com/videos/play/wwdc2017/507