I figured out a way of doing it but it involves potatochop as well as Illustrator.
Step 1: Create a Greyscale document, relatively large (say around 25cm, 300dpi)
Step 2: Make a circular fill gradient fill (black to white).
Step 3: Using the Levels controls, bring the dark up high to boost the contrast and move the midtone slightly towards the white to retain a small amount of gradient.
Step 4: Convert to a bitmap, using 300 dpi output and Halftone Screen Pattern... with an angle of 45 degrees and a frequency of about 5 lines/inch
Step 5: Convert back to greyscale.
Step 6: Select a section of black using the wand and then Select Similar.
Step 7: Go to the Paths panel and, using the little black arrow, choose Make Workpath... with a tolerance of 0.5 pixels.
Step 8: File > Export > Paths to Illustrator, save this somewhere you can find it again in a second.
Step 9: Open the exported file in Illustrator.
Step 10: Select all, make the fill colour whatever colour you want your halftone pattern to be (eg black).
Step 11: Go back to the photoshop document and delete the work path.
Step 12: Using the wand selector again, choose one of the white dots that appears inside the large black blob (where it transitions from black circles to white circles).
Step 13: Again using the colour wand, DESELECT the background outside the black blob (hold down alt and click outside the black blob).
Step 14: Make an workpath from this selection as before.
Step 15: Export this workpath, being sure to name it differently fromt he first one.
Step 16: Open the new workpath in illustrator.
Step 17: Select all and change the fill to your background colour (eg, white).
Step 18: Copy this selection to the other file and position it appropriately on top of the black pattern.
Yeah, one of the examples he linked is from istock. I'm assuming that he doesn't want to do a circle specifically though otherwise he could just register with istock and get one with the free credits. Besides, it's handy to know how to do this stuff anyway.
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Step 1: Create a Greyscale document, relatively large (say around 25cm, 300dpi)
Step 2: Make a circular fill gradient fill (black to white).
Step 3: Using the Levels controls, bring the dark up high to boost the contrast and move the midtone slightly towards the white to retain a small amount of gradient.
Step 4: Convert to a bitmap, using 300 dpi output and Halftone Screen Pattern... with an angle of 45 degrees and a frequency of about 5 lines/inch
Step 5: Convert back to greyscale.
Step 6: Select a section of black using the wand and then Select Similar.
Step 7: Go to the Paths panel and, using the little black arrow, choose Make Workpath... with a tolerance of 0.5 pixels.
Step 8: File > Export > Paths to Illustrator, save this somewhere you can find it again in a second.
Step 9: Open the exported file in Illustrator.
Step 10: Select all, make the fill colour whatever colour you want your halftone pattern to be (eg black).
Step 11: Go back to the photoshop document and delete the work path.
Step 12: Using the wand selector again, choose one of the white dots that appears inside the large black blob (where it transitions from black circles to white circles).
Step 13: Again using the colour wand, DESELECT the background outside the black blob (hold down alt and click outside the black blob).
Step 14: Make an workpath from this selection as before.
Step 15: Export this workpath, being sure to name it differently fromt he first one.
Step 16: Open the new workpath in illustrator.
Step 17: Select all and change the fill to your background colour (eg, white).
Step 18: Copy this selection to the other file and position it appropriately on top of the black pattern.
The halftone filter blows goats.