An optical system containing multi- faceted holographic optical elements (HOEs) was constructed to correctfor aberrations introduced by a non -flat window in NASA Laser Doppler Velocimetry (LDV) experiments in aninternal combustion engine. For this experiment, two green beams separated by 82 mm in a vertical plane, andtwo blue beams separated by 82 mm in a horizontal plane, are brought into coincident focus inside a thickwalled sapphire cylinder. The focal power to bring these beams to a common focus and the aberrationcorrection required by the presence of the cylinder were built into the holographic elements.A modular optical breadboard system was configured to fabricate, test, and use the custom made HOE's.Additional HOE's were also fabricated to provide aberration correction and color separation for themultispectral output waves emerging from the focal volume. Compensation for the birefringence of a thicksapphire cylindrical window in the experiments is also accomplished.A general system such as we have built is useful wherever high efficiency, localized optical correction ofwavefront errors is needed in LDV or other optical experiments.IntroductionLaser Doppler velocimetry (LDV) has become an important tool to researchers interested in makingnon -invasive flow measurements for a wide class of engineering problems. Figure 1(a) shows a normal 4 -beamLDV setup where 2 pairs of parallel input beams are brought to focus at a common intersection position.Because the beams arrive from different angles at the focal volume, two sets of linear, equally spaced,orthogonal interference fringes exist within the intersection zone. Particles moving through this measurementvolume will scatter light, with the fluctuation rate of the scattered light being directly proportional to thevelocity of the particles. The use of two wavelengths allows the simultaneous measurement of two orthogonalvelocity components.A major impediment to the use of LDV is gaining optical access to the system of interest. This problem isparticularly difficult if nonflat windows are a part of the system under consideration. Experimenters haverecognized the problems associated with making laser velocimetry measurements through windows whgsq surfacesare not normal to the incident wave fronts and have reported on various aspects of this problem. '0 Ofparticular interest in this paper is the measurement of flows within a cylinder. More specifically, aninternal combustion engine has been built in which the engine cylinder is fabricated from a single crystal