The goal of this thesis research was to investigate the possibilities and limitations of the Fluid Jet Polishing (FJP) technique. FJP is a new optical fabrication technique that is capable of making shape corrections and reducing the surface roughness of glass and other materials. The principle of operation is that a mixture of water and abrasives (the slurry) is sprayed on the surface at a low pressure. The experimental setup has been described in detail in this thesis. The advantage of FJP over existing techniques is the fact that it can both grind and polish and that areas can be reached that are not accessible with existing techniques. Measuring techniques are important in order to judge the effect of a shaping or polishing technique. Therefore, special attention has been given to in-process measurement techniques. One of the described techniques is iTIRM (intensity-detecting Total Internal Reflection Microscopy). iTIRM can be used for in-process monitoring of the total surface quality, which includes the surface roughness, sub-surface damage, and scratches in the surface. The iTIRM technique can measure the surface quality of both very rough and very smooth surfaces (total range from some m to 0.8 nm). Surface roughness improvements of 0.1 nm rms can be detected with this technique. The surface shape can also be measured in-process. A measurement technique is shown that is based on the interference of an object and a reference beam that both reflect from the inside of the surface to be measured at the total internal reflection condition. The information on the surface shape is obtained from the reflected beams via a temporal phase unwrapping method. Unwrapping problems are avoided by comparing successive images instead of comparing any image to the first image. In order to gain a better understanding of the FJP technique several models have been described. Some have been found in literature, others have been developed especially for FJP. The formation of cracks has been described with Lawn's model [law75]. The theoretical pressure distribution in the slurry has been described by the numerical calculation developed by Rehbinder [reh76] and Leach and Walker [lea66]. Based on the pressure distribution as developed by Rehbinder, a prediction of the stationary footprint that occurs in the case of a cylindrical nozzle has been computed for the FJP case. Based on a general description of flows by Milne-Thomson [mil77] the velocity of the flow in the case of FJP has been computed, the trajectory of the particles in the flow has been derived, and the position and velocity at the moment of impact with the surface has been determined. The interaction between the abrasive particle and the surface of impact has been considered at the microscopic level by a description of three different analysis: first of all, the finite element approach as developed by Woytowitz and co-workers [woy99], secondly, a very simple estimation derived in this thesis, based on the material removal as observed with a SEM, and finally, Finnie's estimation [fin58] which describes the material removal of a single impacting particle in air as a function of the angle of impact. Since the material removal should be known over an area larger than the footprint of the nozzle an analysis has been described that explains the material removal in the case of scanning or rotation of the work piece with respect to the nozzle. The shape inaccuracies that can occur in the center of a work piece have been described as well. In order to get a better understanding of the resulting surface roughness a model has been developed that predicts the roughness as a function of the initial surface and some process parameters. This model is based on the random impacts of particles on a surface. The effect of various process parameters on the material removal and the surface roughness has been investigated experimentally as well. These parameters include the slurry parameters such as the number of particles, the type and size of the particles, the particle velocity, and several process parameters such as the processing time, the processed material, the impact angle and the nozzle type. We also report on some relevant experiments that we carried out with the FJP setup, like the reproducibility of the process, the homogeneity of a translating spot, the degradation of the slurry over time, the formation and removal of mid-spatial frequencies, and the detection whether the FJP process is ductile or brittle. The shaping capabilities have been shown, by prescribing a surface and attempting to produce this surface shape. Some roughness experiments have been described, showing a.o. the roughness as a function of time, the effect of the initial roughness on the final roughness, the roughness as a function of the pressure, and the lowest roughness that could be obtained. Conclusions are drawn and two alternative setups are suggested. The conclusions concerning the shaping accuracy and the roughness reduction are that shape corrections are limited to an accuracy of 4% in depth in the setup that is used at this moment. The material removal is accurate to 1% when the effects of the pressure fluctuation and of the abrasive particle diameter average out by processing the surface several times. A roughness reduction on BK7 can be obtained in a one-step process (one slurry, one fixed pressure during the entire process) from a fine-ground surface (average roughness R a = 300 nm) to R a = 3.6 nm. The first suggestion for comparable techniques that has been described is chemically assisted FJP, the second alternative is a close contact version of FJP. Some initial experiments that have been conducted with this second alternative have been described as well. Fluid Jet Polishing is a new technique that is well suited for making shape alterations to glass surfaces, and for reducing the surface roughness of glasses to a few nanometers. Especially harder to reach areas can ideally be treated with FJP.