Considering that you are using OpenCV, the best way to convert between data types is to use normalize function.
img_n = cv2.normalize(src=img, dst=None, alpha=0, beta=255, norm_type=cv2.NORM_MINMAX, dtype=cv2.CV_8U)
However, if you don't want to use OpenCV, you can do this in numpy
def convert(img, target_type_min, target_type_max, target_type):
imin = img.min()
imax = img.max()
a = (target_type_max - target_type_min) / (imax - imin)
b = target_type_max - a * imax
new_img = (a * img + b).astype(target_type)
return new_img
And then use it like this
imgu8 = convert(img16u, 0, 255, np.uint8)
This is based on the answer that I found on crossvalidated board in comments under this solution https://stats.stackexchange.com/a/70808/277040