No one in astronomy uses TIFFs. Most scientific images are stored in FITS format, either in integer form for some raw data or in floating-point form.
I used to work on on of the larger imaging tools, supporting over 150 scientific file formats. The vast majority, over 80%, were using TIFF as a container. The next most popular was HDF5. FITS was not something I saw commonly, and we were getting images from researchers all over the world.