Convert tiff (I;16) to JPG with PIL/pillow

I have a problem converting a tiff image from a microscope to a jpeg, which should be shown within a web application. I tried the following:

image = Image.open(file_name)
image.convert(mode="RGB")
image.save('my.jpeg')

>>IOError: cannot write mode I;16 as JPEG

Anybody has some experience in converting 16-bit TIFF files to jpegs... I have linked such a file below. Thanks for your help!