Coherence scanning and phase imaging optical interference microscopy at the lateral resolution limit

Abstract

To get physical insight into the 3D transfer characteristics of interference microscopy at high numerical apertures we study reflecting rectangular grating structures. In general, the height obtained from phase information seems to be reduced, whereas height values resulting from coherence scanning sometimes seem to be systematically overestimated. Increasing the numerical aperture of an interference microscope broadens the spectra of the resulting interference signals, thus offering a broad variety of wavelength contributions to be analyzed. If phase analysis of a measured far-field interference wavefront is performed at very short wavelengths the periodical profiles obtained from coherence scanning and phase shifting analysis differ only by the measured amplitude. However, at longer wavelength there is a 180° phase shift of the measured profiles obtained from phase analysis compared to coherence peak analysis. Increasing the evaluation wavelength improves the lateral resolution since the long wavelength contributions are related to electromagnetic waves of high angles of incidence. This behavior is to the best of our knowledge not documented in literature so far. It was first observed experimentally and could be confirmed by simulation results obtained from either Kirchhoff diffraction theory or an extended Richards-Wolf model developed in our group. Compared to original input profiles used for the simulation the profiles obtained from phase evaluation correspond quite well at longer wavelength, whereas the results obtained from coherence peak analysis are typically inverted with respect to height.

Three‐dimensional transfer function of optical microscopes in reflection mode

“…24 Furthermore, modelling based on the 3D spatial frequency representation explains that the axial spatial frequency, at which CSI signals are analysed, affects the lateral resolution achieved in CSI measurements. 20,25,26 In this context, it should be noticed that the 3D intensity TF cannot be observed directly as a bandwidth limitation in a conventional microscope. This is a consequence of the fact that microscopic imaging is based on intensities, whereas the transfer characteristics are determined through amplitude and phase modulated signals, which only appear in interferometric systems such as CSI or holographic microscopy.…”

Spectral composition of low-coherence interferograms at high numerical apertures

“…2 the absolute value of the Fourier transform of such signals shows that additional low frequency (long wavelength) contributions occur at high NA. These are attributed to oblique angles of incidence and appear even if a narrow band light source is used [15,16]. For this reason the corresponding effect in the spatial domain is related to the longitudinal spatial coherence [16].…”

“…In an earlier paper we documented the dependence of the lateral resolution of a phase measuring interference microscope on the so-called evaluation wavelength λ eval , which is the wavelength that is used for phase analysis [15].…”

Modeling of interference microscopy beyond the linear regime

“…Under elementary Fourier optics, it is assumed that the measured field's phase is a linear function of surface height for surfaces close to a plane, beyond which the relationship no longer exactly holds. 14 Nonetheless, CSI models based on this simple assumption can still predict the main features of an interference signal, 15,16 and reconstruction methods that assume this are effective. 12 In particular, a CSI model based on this assumption has been used to simulate batwing effects, accounting for diffraction effects by convolution of the theoretical twodimensional (2-D) point spread function of the imaging system.…”