Rasterizing "linked document" removes sharpness

[photoshop1.0]

I have an image in AP which the layers panel describes as a "Linked document" (it was cut and pasted from Publisher). If I right click the layer and choose "rasterize", the image then loses its sharpness (the loss is very noticeable). The same loss of sharpness occurs if one exports the linked image (thus rasterizing it) as a high res JPG or PNG, etc.

This loss of sharpness does not occur in Photoshop when rasterizing a Smart Object (which is more or less the equivalent of a "linked document").

[walt.farrell]

I'm not sure how you would "export the linked image". (And, it may be important whether you're truly meaning a linked image or a linked document. The kind of document/image is important in some cases, and you've used both in your post. I do not know if it is important in this case.)

I suspect you mean that you exported the entire document, and the linked layer became blurry.

Please check this: With the Linked document/image layer selected, and the Move Tool selected, look at the Transform studio panel. What are the X and Y coordinates, in px? If they are not integer values, then rasterizing may have the effect you noted. (You may need to open the Photo Preferences, User Interface section, and increase the number of displayed decimal units for px measurements to 3 or more to be sure where the layer is positioned.)