We describe the concept of Doppler asymmetric spatial heterodyne spectroscopy (DASH) and present a laboratory Doppler-shift measurement using an infrared laser line. DASH is a modification of spatial heterodyne spectroscopy optimized for high precision, high accuracy Doppler-shift measurements of atmospheric emission lines either from the ground or a satellite. We discuss DASH design considerations, field widening, thermal stability and tracking, noise propagation, advantages, and trade-offs. DASH interferometers do not require moving optical parts and can be built in rugged, compact packages, making them suitable for space flight and mobile ground instrumentation.