The key to making this work is to modify the XMP Metadata so that the viewer software understands that the view is limited. Here are some of the more important metadata for a photosphere (source here):
Here is one way to do a 180-degree photosphere that can be viewed on Facebook as a partial photosphere:
1. Take a normal 360 photo.
2. For a 180 photosphere, crop the equirectangular photo's width by 50%. The resulting image will have an aspect ratio that is 1:1 (square).
3. Edit the metadata using exiftool or other similar apps. In my case, I used exiftoolgui. Change the following parameters:
- CroppedAreaImageWidthPixels: this should be the width of the new cropped image. If you cropped half for a 180-view, change it to half of the original number.
- CroppedAreaImageHeightPixels: this should be the height of the new cropped image. If you cropped half for a 180-view, you don't need to change it.
- CroppedAreaLeftPixels: this should be the imaginary distance (in pixels) from the left edge of the 360 panorama to the left edge of the partial panorama. For a 180-degree view, this should be 1/4th of the original length.
- CroppedAreaTopPixels: this should be the imaginary distance (in pixels) from the top edge of the 360 panorama to the top edge of the partial panorama. For a 180-degree view, you don't need to change it.
4. Post the image. Some viewers such as Facebook will automatically limit the view to the cropped area. Other viewers such as Google Photos will put the partial panorama in a black background.