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Rob: I presently have all my images stored on an external drive, with my Catalog on my hard drive. What I would like to do is copy all my “master” TIFF and PSD files, with their edited detail, to a different backup disk. But I can’t simply copy the files across as they will all be the unedited basic files. So how do I achieve that? Seems like quite a mission, and then something that would have to be done manually going forward to keep everything updated.
Andrew: There are three options. The first two will work, and the third is the one I recommend (and the way I do it).
Option 1: Save Metadata to file then export
The first one works with TIFF files but not PSD files.
Go to All Photographs in the Catalog panel, click on Metadata in the Filter bar, set the filter to File Type and then TIFF. This brings up all the TIFF files in your Catalog.

Select All then go to Metadata > Save Metadata to File. This updates the files with any changes you’ve made in Lightroom Classic. You can then copy them to another hard drive.
Note that Save Metadata to File will be grayed out if Lightroom Classic doesn’t know where one or more of the selected files is saved.
Option 2: Export files
The second option is to select the TIFF files you want to copy in Lightroom Classic (you can use the search method above or even add them to a new Collection or use a Smart Collection) and then go to File > Export. Select TIFF under File Settings and make sure you don’t change the file size, name, apply sharpening or add a watermark. Then you can export them to your back up hard drive.

You can repeat with PSD files, setting File Type to PSD.
The disadvantage of this method is that it doesn’t retain your original folder structure. You’ll have copies, but they won’t be much use to Lightroom Classic if they’re not in the right folder.
Option 3: Put a good, automated backup system in place so you don’t have to do it manually (my recommendation)
The third method (and the one I use) is to save all your photos that you’ve imported into Lightroom Classic on an external hard drive. Then you can simply copy all those photos to another hard drive to back them up. I use a date based folder structure as that makes backing up easier.
For this to work you need to make sure that your Lightroom Classic Catalog is backed up regularly. I set it to back up to the hard drive that I keep my photos on.
I also use BackBlaze to give me an off-site backup of both photos and Catalog. As long as your Catalog is backed up you don’t have to worry about whether your master PSD and TIFF files are up to date or not.
You can learn more about backing up your photos in my article A Secure Photo Backup Strategy for Photographers