The Cepheid Period-Luminosity Relation at Mid-Infrared Wavelengths: II.   Second-Epoch LMC Data
  We present revised and improved mid-infrared Period-Luminosity (PL) relations for Large Magellanic Cloud (LMC) Cepheids based on double-epoch data of 70 Cepheids observed by Spitzer at 3.6, 4.5, 5.8 and 8.0um. The observed scatter at all wavelengths is found to decrease from +/-0.17 mag to +/-0.14 mag, which is fully consistent with the prediction that the total scatter is made up of roughly equal contributions from random sampling of the light curve and nearly-uniform samplings of stars across the instability strip. It is calculated that the Cepheids in this sample have a full amplitude of about 0.4 mag and that their fully-sampled, time-averaged magnitudes should eventually reveal mid-infrared PL relations that each have intrinsic scatter at most at the +/-0.12 mag level, and as low as +/-0.08 mag after correcting for the tilt of the LMC. 
Barry F. Madore, Wendy L. Freedman, Jane Rigby, S.E. Persson, Laura   Sturch and Violet Major