Contribution of the phase transfer function of extended measurement cavities to mid spatial frequencies and the overall error budget

Abstract

A challenge of coaxial - measurement cavity based - interferometer is to realize an interference contrast in the vicinity of one and to realize a complete elimination of the parasitic reflections. Another challenge, which also exists in non-coaxial setups, is the phase transfer function of extended measurement cavities. Ideally, the surface under test (SUT) and the reference surface (REF) are both exactly imaged onto the detector plane. In practice, SUT and REF have to be placed within the depth of field (DOF), which refers to the object space. The term depth of focus refers to the image space. To avoid confusion, the depth of field might be referred to as DOOF (depth of object field) and the depth of focus might be referred to as DOIF (depth of image field). However, in many measurement situations, the REF is not placed within the DOOF, which is the small z-range, which is imaged onto the detector plane. Furthermore, the phase transfer function (PTF) of the REF and the image distortion of the REF are both dependent on the focal plane used to image the SUT onto the detector plane. Effects as phase deformation, image distortion and image blurring have to be taken into account when using extended measurement cavities. This can be done by using a look up table (LUT), which contains simulated and/or calibrated data. Thus, the related system error can be subtracted. A remaining challenge is an unknown object under test (OUT), which is measured by using a double path arrangement. The measured wave front depends on the two surfaces of the OUT and the position of the return mirror. For simplicity, a homogeneous substrate and a perfect return mirror might be presumed. The simulation of waves propagating within extended measurement cavities, as well as measurement results, will be discussed. In addition, the influence on the power spectral density (PSD) will be described. This is important for high end correction techniques as e.g. magneto rheological figuring (MRF) and ion beam figuring (IBF).