Cullen M. Crain, 77, an electrical engineer and Rand Corp. researcher who developed an improved hot line between Washington and Moscow. Educated at the University of Texas, Crain invented an instrument called the microwave atmospheric refractometer that helped explain how radio signals are transmitted in the atmosphere. He moved to Rand in Santa Monica in 1957 and worked there for 40 years. He was among the first to investigate the effects of electromagnetic pulses resulting from high-altitude nuclear explosions. Crain later developed improvements in radar tracking, nuclear test detection and communications satellite technologies. He was an advisor to the White House Office of Telecommunications Policy and served on several defense science boards. On Feb. 15 in Santa Monica.