A th eory is d eveloped for di electric multilay cr coati ngs in which t he layers d epart from calculated thickncss. The t heory is a ppli ed t o alternating syst ems of quarter wa ve layer of ZnS a nd MgF2• The cffects of thickness errors arc : (1) A s hift of the wavelength at which maximum reflectance occur; and (2) a change in pha e shift upon refle ction. The m agn itud e of t hese effects, and also their dependence on various param eters, a re d et ermined. Statistical t ole ra nces for layer thickn esses a re computed for g iven tolerances on t he multilayer performancc. The accuracy required for p roducing di electric interference fi lters is u p to about '10 t imes h igher tha n t he a ccma cy s ufficient for the production of dielectri c mirrors and beam splitters. Various t echniqu es of experim e ntally controlli ng film thicknesses, and t heir acc uraci es, a rc discus cd . Th e production of mirrors a nd beam spli tters d eviatin g fr om t heoretical maximum refiecta nce by only 1 percent see ms to be possible with Dufour 's simple sin gle photocell method of monitoring film t hi ckn esses. \-Vith more precise me t hod s, suc h as those d evelop d by Giacomo a nd J acqu in ot, or T raub, t he p roduction of interference fi lters appears to be poss ible to wi thin plus or minu s one half their half widths.