Sayyiduna al-Hajjaj bin Ghaziyyah (may Allah be pleased with him), who was a Companion of the Prophet (peace and blessings be upon him), says: You people think that when someone keeps offering voluntary prayers at night and prays continuously until morning, he has offered tahajjud. Rather, the one who offers tahajjud is the one who prays after sleeping for a while, and then prays again after sleeping for a while. This is how the prayer of the Prophet (peace and blessings be upon him) used to be.
Al-Tabarani recorded it in al-Mu'jam al-Kabir. It is reported with a sahih (authentic) chain, and its narrators are the narrators of the "Sahih".