This work describes the problem of retrieval of temperature profiles from Nimbus 4 Selective Chopper Radiometer (SCR) measurements of emission from the 15µm CO₂ absorption band. Vertical resolution diagnostics are discussed for : (a) an optimum retrieval estimator which uses a priori statistical information (the maximum likelihood or maximum a posteriori estimator), and (b) a Backus Gilbert estimator which uses essentially no a priori information. Confidence regions are calculated for the optimum retrieval estimator. At stratospheric heights, and for Nimbus 4 SCR data, the resolving power of the optimum estimator is poorer than that of the satellite observations and is sensitive to the size of the measurement noise, and the choice of first guess profile. The retrieval from the optimum estimator is unstable when detecting vertical wave-like disturbances on temperature profiles. It is suggested that retrieval estimators using a priori statistical information should not be used when trying to detect vertical wave-like structure in the atmosphere.