It sounds as though the goal is to produce a map of the height of the printbed, rather than assuming it's flat and simply measuring its tilt. If that's the case, wouldn't it be necessary to print the pattern directly on the surface of the bed? It strikes me that almost any material you might print on would be insufficiently flexible to conform to a warped surface just by being laid on top of it.
If the bed were close-but-not-quite flat and you already knew its overall tilt, it might suffice to have the printer lay down a pattern (Hilbert curve?) of single-width lines, and let the camera measure their width to map the surface, but the departure from perfect flatness would have to be smaller than the nozzle diameter. Or perhaps you could use a force-sensitive resistor and drag a probe across the surface? That would handle a larger range of irregularities, though I imagine the data would be rather noisy.
If the bed were close-but-not-quite flat and you already knew its overall tilt, it might suffice to have the printer lay down a pattern (Hilbert curve?) of single-width lines, and let the camera measure their width to map the surface, but the departure from perfect flatness would have to be smaller than the nozzle diameter. Or perhaps you could use a force-sensitive resistor and drag a probe across the surface? That would handle a larger range of irregularities, though I imagine the data would be rather noisy.