For a single image like the one above of M-51, the separation has to be fabricated.  A simple rotate to move a part of the image below the plane can be done this way:

1. With the image in PhotoShop, select all and copy to clipboard.
2. Run the action (F-11 as downloaded but can be changed) which will create a separation image perfectly aligned (will look the same as before the action was run).
3. Select the top layer, and do "edit / transform / distort".
4. Drag the upper left and lower right corners slightly away from the image horizontally (Shift-drag) while observing with 3D glasses.  The upper left should appear to tilt back below the page and the lower right should be slightly above the page.
5. Flatten and crop then increase saturation as needed.

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The image of M-51 above was done in two steps (M-51 and stars separated). 

1. The star field (less M-51) was selected using the magic wand at 99 on a star and then deleting the nebula from the selection (ALT-lasso).  This star field selection was expanded (select / modify / expand - I used 2 pixels here) and copied to a new image.
2. The background of this star field image was filled with black and the image flattened.
3. To make this star field 3D, select the black area and invert to get the stars, expand selection slightly and then copy to the clipboard.
4. Run the action.
5. With the upper (red) layer selected, do "edit / transform / distort" and drag the lower right and upper left corners inward horizontally (Shift-drag).  The stars in the lower right should now appear below the page when viewed with red-blue glasses.   The upper left stars will appear slightly above the page.  Do not distort too much; the red and blue stars should almost touch.
6. For additional effect, move individual stars in or out of the screen plane by selecting them individually (top, red layer) and moving this red star image horizontally to the opposite side of the lower, cyan layer.  This was done on several stars in the M-51 image.
7. Flatten this star image - do not crop at this time.
8. On the original image (M-51), the stars should still be selected (and expanded).   Fill this selection with black (or a sample of your image background) to eliminate the stars and then use the clone to eliminate any ghosts left over (add a temporary levels layer to brighten the space to help, then remove this levels layer).
9. Select all and copy to clipboard, then run the action.
10. Select the top layer, and "edit / transform / distort", then drag the upper left and lower right corners horizontally (Shift-drag) away from the image.  M-51 will tilt backward at the upper left and up at the lower right.
11. Flatten this image.
12. On the star image, use the magic wand at 10 to select the black, then invert the selection and expand by about 1-2 pixels.  Copy this to the clipboard.
13. Go back to the M-51 image, and paste the stars over M-51 and align as needed.   Flatten and clean up any red only or blue only stars.
14. Increase the saturation slightly and you are done.  The stars should be below the page on the lower right and M-51 should tilt down on the upper left.

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To use the action with a stereo pair (not Astrophotography):

Stereo pairs can be taken hand-held by taking two shots with the camera moved slightly (eye spacing).  I pick a distant point and keep it in the center of the image.  The image layers can be aligned by rotating one layer, but try to keep the camera level.

1. Load both images into PhotoShop.
2. On the left image, "select all" and copy to clipboard.  This image may now be closed.
3. With the right image selected, run the action.
4. Move the top (red) layer to align the layers so that the red and blue layers are side by side. If necessary, rotate the top layer so that there is no vertical offset throughout the image.  An easy way to do this is to use the measure tool and drag between two points on the lower layer (top turned off).  Record the angle (in info bar at top), and then repeat the operation on the same points on the top layer (bottom off).  Rotate the top layer as needed to give the same value as the bottom layer (edit-transform-rotate, observe rotate angle in top info area).
5. Align (red directly over blue) someplace near the part of the image closest to the camera.  Confirm that all other parts of the image have the layers offset to the side only, not vertically.
6. Check with glasses, then flatten and crop.
7. Increase saturation some to make up for lost saturation in the process.