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Direct -imaging and plane -projection instruments are mainstays for definitive calibrationquality measurements of small dimensions for industrial and clinical applications.Lightand electron -optical techniques span six orders of sizes, from millimeters through micrometers down to nanometers.A common assumption is that, above the resolution limit of a device, accurate measurements can be made based on the geometric optic relation of image size xi to object size xo: x = Mxo, where M is the scalar magnification of the device. However, in measurements of lengths, widths or diameters, the relation fails long before the resolution limit of the device is approached. As a result, substantial systematic errors in dimensional measurements occur in industrial applications from particle sizing to photomask metrology.