A method for measuring the focal length of the lens and the radius of curvature of the spherical surface using wavefront difference method is proposed. Based on Fizeau interferometer, an experimental system for focal length measurements is set up to verify the principle. Based on the point diffraction interferometer, an experimental system for radius of curvature measurements is proposed to verify the proposed method. With the focal length testing system, both the positive and negative lens experimental results indicate that the measurement accuracy is less than 0.16%under normal experimental environment. With the radius of curvature testing system, the radius of curvature of spherical mirrors and the surface figure can be measured in a higher precision simultaneously. The experimental results indicate that the measurement accuracy is in the order of 10<sup>-4</sup> .
Multi-beam interference will exist in the cavity of Fizeau interferometer due to the high reflectivity of test optics. The random phase shift error will be generated by some factors such as the environmental vibration, air turbulence, etc. Both these will cause phase retrieving error. We proposed a non-iterative approach called Carrier Squeezing Multi-beam Interferometry (CSMI) algorithm, which is based on the Carrier squeezing interferometry (CSI) technique to retrieve the phase distribution from multiple-beam interferograms with random phase shift errors. The intensity of multiple-beam interference was decomposed into fundamental wave and high-order harmonics, by using the Fourier series expansion. Multi-beam phase shifting interferograms with linear carrier were rearranged by row or column, to fuse one frame of spatial-temporal fringes. The lobe of the fundamental component related to the phase and the lobes of high-order harmonics and phase shift errors were separated in the frequency domain, so the correct phase was extracted by filtering out the fundamental component. Suppression of the influence from high-order harmonic components, as well as random phase shift error is validated by numerical simulations. Experiments were also executed by using the proposed CSMI algorithm for mirror with high reflection coefficient, showing its advantage comparing with normal phase retrieving algorithms.
A white-light microscopy interferometer was developed for measurement of the 3D profile and roughness.10X, 20X and 50X Mirau interference microscope objectives with the numerical aperture of 0.3, 0.4 and 0.55 were designed, manufactured and then provided as the accessories. Thickness deviation between beam splitter plate and reference mirror plate as well as the numerical aperture will both affect the contrast of interference fringe, according to optical modeling and image evaluation. The former would generate dispersion and then decrease the fringe contrast, while the latter would not produce dispersion separately but impact the amount of dispersion when thickness deviation exists, and their influence on fringe contrast was based on the expression of white-light interference intensity. Simulations for interference fringes from Mirau interference microscope objectives with different NA and thickness deviation were implemented, demonstrated that the fringe contrast will be falling with NA and thickness deviation increasing. A standard step with the nominal step value of 110 nm was used to calibrate the white-light microscopy interferometer, showing that less than1nm deviation can be reached.