Shan Shan Kou

Transport-of-intensity approach to differential interference contrast (TI-DIC) microscopy for quantitative phase imaging

Differential interference contrast (DIC) microscopy is an inherently qualitative phase-imaging technique. What is obtained is an image with mixed phase-gradient and amplitude information rather than a true linear mapping of actual optical path length (OPL) differences. Here we investigate an approach that combines the transport-of-intensity equation (TIE) with DIC microscopy, thus improving direct visual observation. There is little hardware modification and the computation is noniterative. Numerically solving for the propagation of light in a series of through-focus DIC images allows linear phase information in a single slice to be completely determined and restored from DIC intensity values.

Phase from chromatic aberrations

We show that phase objects may be computed accurately from a single color image in a brightfield microscope, with no hardware modification. Our technique uses the chromatic aberration that is inherent to every lens-based imaging system as a phase contrast mechanism. This leads to a simple and inexpensive way of achieving single-shot quantitative phase recovery by a modified Transport of Intensity Equation (TIE) solution, allowing real-time phase imaging in a traditional microscope.

Imaging in digital holographic microscopy.

We present a theoretical formalism for three dimensional (3D) imaging properties of digital holographic microscopy (DHM). Through frequency analysis and visualization of its 3D optical transfer function, an assessment of the imaging behavior of DHM is given. The results are compared with those from other types of interference microscopy. Digital holographic microscopy does not result in true 3D imaging. The main advantage of holographicmicroscopy lies in its quick acquisition of a single 2D image. Full 3D imaging can be obtained with DHM using a broad-band source or tomographic reconstruction.

Image formation in holographic tomography

Tomography has been applied to holographic imaging systems recently to improve the 3D imaging performance. However, there are two distinct ways to achieve this: either by rotation of the object or by rotation of the illumination beam. We provide a transfer function analysis to distinguish between these two techniques and to predict the 3D imaging performance in holographic tomography when diffraction effects are considered. The results show that the configuration of rotating the illumination beam in one direction while fixing the sample leads to different 3D imaging performance as compared to the configuration of rotating the sample. The spatial frequency cutoff is nonisotropic in the case of rotating the illumination, and a curved line of singularity is observed. Rotating of the sample, on the contrary, has more symmetry in spatial frequency coverage but has a single point of singularity. The 3D transfer function derived can be used for 3D image reconstruction.

On-chip photonic Fourier transform with surface plasmon polaritons

The Fourier transform (FT), a cornerstone of optical processing, enables rapid evaluation of fundamental mathematical operations, such as derivatives and integrals. Conventionally, a converging lens performs an optical FT in free space when light passes through it. The speed of the transformation is limited by the thickness and the focal length of the lens. By using the wave nature of surface plasmon polaritons (SPPs), here we demonstrate that the FT can be implemented in a planar configuration with a minimal propagation distance of around 10 μm, resulting in an increase of speed by four to five orders of magnitude. The photonic FT was tested by synthesizing intricate SPP waves with their Fourier components. The reduced dimensionality in the minuscule device allows the future development of an ultrafast on-chip photonic information processing platform for large-scale optical computing.

Image formation in holographic tomography: high-aperture imaging conditions

Three-dimensional (3D) imaging by holographic tomography can be performed for a fixed detector through rotation of either the object or the illumination beam. We have previously presented a paraxial treatment to distinguish between these two approaches using transfer function analysis. In particular, the cutoff of the transfer function when rotating the illumination about one axis was calculated analytically using one-dimensional Fourier integration of the defocused transfer function. However, high numerical aperture objectives are usually used in experimental arrangements, and the previous paraxial model is not accurate in this case. Hence, in this analysis, we utilize 3D analytical geometry to derive the imaging behavior for holographic tomography under high-aperture conditions. As expected, the cutoff of the new transfer function leads to a similar peanut shape, but we found that there was no line singularity as was previously observed in the paraxial case. We also present the theory of coherent transfer function for holographic tomography under object rotation while the detector is kept stationary. The derived coherent transfer functions offer quantitative insights into the image formation of a diffractive tomography system.

Quantitative phase restoration by direct inversion using the optical transfer function

Quantitative phase recovery of phase objects is achieved by a direct inversion using the defocused weak object transfer function. The presented method is noniterative and is based on partially coherent principles. It also takes into account the optical properties of the system and gives the phase of the object directly. The proposed method is especially suitable for application to weak phase objects, such as live and unstained biological samples but, surprisingly, has also been shown to work with comparatively strong phase objects.

Direct calculation of a three-dimensional diffracted field

We present an approach to calculating the complex amplitude of a three-dimensional (3D) diffracted light field in the paraxial approximation based on a 3D Fourier transform. Starting from the Huygens-Fresnel principle, the method is first developed for the computation of the light distribution around the focus of an apertured spherical wave. The method, with modification, is then extended to treat the 3D diffraction of an aperture with an arbitrary transmittance function.

Realistic 3D coherent transfer function inverse filtering of complex fields

We present a novel technique for three-dimensional (3D) image processing of complex fields. It consists in inverting the coherent image formation by filtering the complex spectrum with a realistic 3D coherent transfer function (CTF) of a high-NA digital holographic microscope. By combining scattering theory and signal processing, the method is demonstrated to yield the reconstruction of a scattering object field. Experimental reconstructions in phase and amplitude are presented under non-design imaging conditions. The suggested technique is best suited for an implementation in high-resolution diffraction tomography based on sample or illumination rotation.

Mode-matching metasurfaces: coherent reconstruction and multiplexing of surface waves

Metasurfaces are promising two-dimensional metamaterials that are engineered to provide unique properties or functionalities absent in naturally occurring homogeneous surfaces. Here, we report a type of metasurface for tailored reconstruction of surface plasmon waves from light. The design is based on an array of slit antennas arranged in a way that it matches the complex field distribution of the desired surface plasmon wave. The approach is generic so that one can readily create more intricate designs that selectively generate different surface plasmon waves through simple variation of the wavelength or the polarization state of incident light. The ultra-thin metasurface demonstrated in this paper provides a versatile interface between the conventional free-space optics and a two-dimensional platform such as surface plasmonics.