Lateral resolution enhanced interference microscopy using virtual annular apertures

Abstract

The lateral resolution in microscopic imaging generally depends on both, the wavelength of light and the numerical aperture of the microscope objective lens. To quantify the lateral resolution Ernst Abbe considered an optical grating illuminated by plane waves. In contrast, the Rayleigh criterion holds for two point sources or point scatterers separated by a lateral distance, which are supposed to emit spherical waves. A portion of each spherical wave is collected by the objective lens and results in an Airy disc corresponding to a diffraction limited intensity point spread function (PSF). If incoherent illumination is employed the intensity PSFs related to different scatterers on an object are added resulting in the well-known Rayleigh resolution criterion. In interference microscopy instead of the intensity the electric field scattered or diffracted by an object will be affected by the transfer function of the optical imaging system. For a reflective object the lateral resolution of an interference microscope can be again characterized by the Abbe limit if the object under investigation is a grating. However, if two irregularities on a flat surface are being imaged the resolution no longer obeys the Rayleigh criterion. Instead, it corresponds to an optical system with an annular aperture and thus surpasses the prediction given by the Rayleigh criterion. This holds true for both, amplitude as well as phase objects, as it will be elucidated in this study by theoretical considerations, simulation results and an experimental proof of principle.

Comparison of approximate methods for modelling coherence scanning interferometry

“…Using FDA-phase, the height value is calculated by interpolating the linear fit at the spatial frequency for which the Fourier magnitude is greatest. In the context of the UFO model, it has been shown that the lateral resolution for interference microscopy can be enhanced by selecting specific Fourier components, rather than using linear phase fitting 32 . However, in this paper, the primary goal is the comparison of different scattering and imaging models, rather than the comparison of reconstruction algorithms.…”

Simulative investigation of microcylinder-assisted microscopy in reflection and transmission mode

“…This result is in good agreement to the results obtained for interference microscopy 26 and can be explained with a local enhancement of the NA combined with a limited field of view through the cylinder. For an explanation of the effect of an improved resolution if only a few periods of the grating are in the field of view we refer to Lehmann et al 36 Generally, the std values obtained for an infinitely extended grating and a grating of finite extent differ. Hence, internal reflections at the grating seem to affect the results.…”

Universal Fourier optics model for virtual coherence scanning interferometers

“…However, for piecewise continuous diffracting or tilted specular surfaces the intensity distribution in the exit pupil plane is no longer uniform and thus a slightly different 3D transfer function occurs. 18,19 H(q ρ , q z , k 0 ) = q z 2k 0 for q ∈ area 1 ,…”

“…the minimum value of q z,eval , where the 3D TF is different from zero. 19 The 3D TF introduced so far describes the transfer characteristics of interference microscopes under monochromatic illumination given by the wavenumber k 0 = 2π/λ 0 and the central wavelength λ 0 . However, CSI instruments commonly use broadband light sources such as light emitting diodes (LEDs).…”

“…The UFO model is based on previous investigations published in recent years. [16][17][18][19] In addition to a fast computation of simulated CSI measurement results, analysing the 3D TF and the interference signals in the spatial frequency domain gives insight into the signal formation process and helps choosing most appropriate parameters for signal analysis. This is especially important when phase analysis is performed since this can be done for different frequency components of the interference signal.…”