For the past thirty years, microchips have doubled in complexity every two years. This increasing complexity required that the size of the structures written on silicon halve at the same rate. A fundamentally limiting factor to the size of microchip structures is the wavelength of the lithographic projection processes used in their manufacture. Consequently, the wavelengths used to produce microchips have shrunk from 436nm, at the boundary of the visible spectrum, to 193nm, in the ultraviolet, between 1975 and 2002. A next generation process aims to use light with a wavelength of 13nm, in what is called extreme ultraviolet lithography (EUVL). Unlike previous processes, which could use lens systems to project the required patterns onto the microchips, EUVL requires the use of mirror projection systems. The mirrors used are highly aspheric and must be manufactured with unprecedented accuracies, of the order of 0.1nm. There are currently no affordable and easy to use systems to measure such mirrors with the required accuracy in optical workshops during manufacture. While the primary push for the development of such a measurement tool has come from the semiconductor industry, there are a number of other technology branches which could benefit from increased reflector accuracies. These include astronomy at ultra-short wavelengths, plasma physics, and biological microscopy. This thesis describes the construction and use of a novel interferometer to accurately measure the shape of such EUVL mirror substrates. Since tools to measure the surface roughness of these mirrors are readily available, we are concentrating on the measurement of spatial frequencies below 1mm-1 for the entire mirror surface. The main advantages of our interferometer over competing instruments are its independence from reference optics, which could introduce significant errors in other types of interferometers, its ability to measure the whole surface of most EUVL optics in one go and the possibility of using a more accurate type of interferometry - heterodyne interferometry - instead of the usual phase stepping. In contrast with a number of methods already available, this instrument is suitable for use in optical workshops, both in terms of cost and ease of use. Although the accuracy of 4nm reported here for our preliminary measurements falls short of the desired accuracy of 0.1nm, several improvements not yet implemented are likely to improve the accuracy of the instrument to desired levels. The most significant source of error at this time is believed to be the sensor. A sensor designed specifically to meet the requirements of our interferometer was still under development at the time of writing. In constructing the interferometer presented here, advances have been made in a number of fields: The novel nature of the interferometer required the development of a unique mathematical tool - an inverse propagation algorithm - to retrieve the shape of the surface under test from the measurement data. This has been achieved using a combination of analytic raytracing and numerical diffraction methods based on the idea of boundary diffracted waves, to obtain a good balance between computational speed and accuracy. A rigorous method for diffraction calculations was also developed and used to confirm the accuracy of the fast hybrid method finally used in the inverse propagation algorithm. The light source constructed is capable of providing a stable set of wavelengths which can be used to perform full-field multiple wavelength heterodyne interferometry at three wavelengths simultaneously. In the absence of a suitable sensor, the light source can also be used to perform sequential multiple wavelength interferometry using phase shifting methods. To ensure a minimum susceptibility to drift and vibrations, several optical mounting structures were re-designed from scratch. The custom designed mounts have been shown to outperform commercially available mounts. Two different types of sensors were tested and compared. A commercially available CCD sensor already allowed us to make measurements coming close to the desired accuracy by using calibration techniques to reduce the influence of a number of systematic error sources. A recently developed sensor, with phase-measuring active pixels, was used to demonstrate new approaches to interferometry: full-field heterodyne interferometry, as well as the beat frequency de-multiplexing of multiple wavelengths, allowing interferometry at several wavelengths simultaneously. An interferometer frame, which allows the stable placement of the mirror and various other components, has been designed and constructed entirely from invar to ensure optimum immunity against temperature fluctuations. Theoretical models were used to show that substrates with numerical apertures as large as 0.26 may be measured with the desired accuracy, limited only by the optical fibers used. Measurements carried out on the optical fibers showed that the sphericity of the wave fronts produced was in agreement with our theoretical models. By tapering and polishing the fiber ends, it may be possible to measure optics with even larger numerical apertures. Preliminary measurements of a test substrate, performed using phase shifting techniques and a standard CCD, yielded promising results. The measurement resulted in a retrieved mirror shape within 4.2nm rms of the nominal mirror shape, and an even smaller deviation from the mirror shape as measured by conventional interferometry techniques. The three main factors thought to limit the instrument's accuracy are the non-uniformity of the features on the CCD, the presence of a cover-glass on the sensor and insufficient a-priori knowledge of the relative positions of the interferometer components. All of these factors can be overcome or reduced, leading to measurements with the required accuracy in the foreseeable future. The result will be an ultra-precise metrology instrument suitable for use in optical workshops.