Hypnopompic

hypnopompic \ˌhip-nə-ˈpäm-pik\ adjective: of, relating to, or occurring in the period of drowsy semiconsciousness immediately preceding waking

Etymology: Greek hypn- sleep + pompē act of sending

Wikipedia’s article on hypnagogia states that some people in the scientific community question the need for separate terms to distinguish between “the state from waking to sleeping” and “the state from sleeping to waking” since the same experiences occur in both states and because drifting in and out of sleep produces transitional states that are simultaneously post-sleep and pre-sleep. With that in mind, hypnagogia is used by some to cover both situations. Others employ a different term altogether: wakefulness-sleep transition state.