The title says it all. I have a document with embedded pictures at various resolutions (300dpi, 220dpi, ...) and I'd like to export them to their original size (in pixels).
A simple copy-and-paste into photoshop doesn't work... what to do?
This is a kind of last resort, when you're really stuck. Realize that no matter what the original size and resolution of the image were, AI considers "full size" (100%) to be the physical dimensions of the image at 72 ppi -- a legacy of the original Mac screen resolution that has somehow got itself stuck, regardless of the fact that it's been obsolete for more than 20 years. (InDesign shares this gritty dedication to 72 ppi.)
Select your embedded image and note the PPI that AI reports. Shift-drag to scale the image until the reported ppi is 72, then copy and paste for Photoshop. For an alternative approach to setting the ppi, select the image on the artboard, then look for the blue 'Image' link on the left side of the options bar. Click that link and you get a flyout. In the flyout, use the little top-right menu icon to select "Link File Info...". In the pop-up that follows, expand the topmost Schema item, which reveals the original file's pixel dimensions. Width is PixelXDimension and height is PixelYDimension. Type one of the dimensions, say width, into the W (width) field of the options bar while constraining the aspect ratio, and voila,72 ppi. Make sure to append 'px' (e.g. 3405px not 3405) if you're working in something other than pixels by default. Then copy into Photoshop as with the dragging method.
The new Photoshop document will open at the original pixel dimensions, but will report 72 ppi. You can assign a different resolution in Image > Size (just be sure to uncheck "Resample" so you don't change the image itself).
This isn't a perfect process. There are subtle pixel-shifts, but in a pinch this is a way to recover a full-size version of an embedded image.
AFAIK there isn't any way to do this natively in Illustrator. There is a plugin for Illustrator that claims to do this, preserving the original image:
It's paid, but there's a 30-day free trial, so if it's a one time thing, you could just use the trial. If you need to use it past the 30 days, it's $30. Not bad at all.
Illustrator lets you edit LINKED files only, so I try not to embed anything into it.
The workflow I got into is to create all the pieces of a layout in Illustrator, Photoshop or whatever program necessary, and then put everything together in InDesign, which CAN do what you're describing: save out an embedded file in its original form. Just something to consider.