When will new Lytro LightField camera orders ship?

It seems like production of Lytro’s LightField camera is catching up: While pre-orders from October 2011 took as long as February 2012 to ship, orders made last November shipped in April.
According to Lytro, new orders are currently placed in the “May/June” timeframe, so if you order now, you could enjoy your brand new Lytro camera within two weeks – that is, if everything goes super-fast (which it might not).