Mug Shot Delay For Lost Star Matthew Fox

TMZ has learned ... Fox returned to the Deschutes County Adult Jail in Bend, Oregon on June 29th to finally take the mug shot from his May 4th arrest ... and TMZ has the pic.

So why did it take so long for cops to get the shot? Turns out, the camera at the jail was BROKEN on the night Fox was arrested ... so the judge made the former "Lost" star come back for a makeup photo.

As we previously reported, Fox struck a plea deal with prosecutors so he wouldn't have to serve any time in jail -- and in exchange he pled no contest to one count of DUI.

As part of the deal, Fox can't drink alcohol for one year and is required to complete a drug and alcohol treatment program.