Rapid shape measurement based on the measurement of the mutual coherence function using a shear interferometer (Gamma-Profilometry)
Final Report Abstract
Within the frame of project Gamma-Profilometry, a new approach for optical shape measure-ment has been developed and investigated. The technique is based on spatio-temporal sam-pling of the coherence function of partially coherent light reflected or scattered by a specimen under test. A reference wave is not required, which makes the method insensitive towards mechanical vibrations. Similar to white light interferometry, it enables measurements over ex-tended axial ranges with measurement uncertainties well in the sub-micrometer range, be-cause of the limited temporal coherence of the light. The following results have been achieved: • A model, which relates the height differences across the specimen under test to temporal shifts within the coherence function of the reflected light. • An extension of the model towards rough surfaces by simply scaling with the speckle am-plitude, as long as the surface roughness Ra does not significantly exceed 2 μm. • An experimental arrangement which allows for the spatio-temporal sampling of the coher-ence function. The arrangement consists of a shear interferometer, that not only allows lateral shifting of the images, but additionally also enables temporal detuning of the optical paths. Adjustment of the optical paths is realized by a Soleil-Babinet-Compensator (SBC). The light source is a light emitting diode (LED) with a coherence length of approx. 20 μm. • A numerical integration procedure, which allows to calculate a shape profile from the measured height differences. • A first experimental validation of the method using a reflective step object. A measure-ment uncertainty of σ = +/-84 nm has been achieved over an axial range of 60 μm. • The experimental validation of the method using a step object with rough surface Ra=0.25 μm. The measurement uncertainty was in the range of the surface roughness.
Publications
- Quantitative phase contrast im-aging using a Nomarski microscope with variable shear distance, Proc. SPIE, 9718, 97182I-1-7 (2016)
Falldorf, C; Agour, M; Kötter, J; Bergmann, R B
(See online at https://doi.org/10.1117/12.2212757) - Coherent imaging using the mutual intensity function, SPIE-Proc. Face2Phase 2017, 32 (2017)
Falldorf, C; Agour, M; Bergmann, R B
(See online at https://doi.org/10.1109/isbi.2017.7950510) - Spatio-temporal sampling of the coherence function for step height measurements, Proc. SPIE, 10749, 107490Y-1-8 (2018)
Falldorf, C; Hyra, A; Simic, A; Bergmann, R B
(See online at https://doi.org/10.1117/12.2321145) - Γ-profilometry: A new paradigm for precise optical metrology, Opt. Exp. 29 (22), 36100-36110, (2021)
Falldorf, C.; Agour, M.; Bergmann, R. B.: Γ-profilometry
(See online at https://doi.org/10.1364/oe.434510)
