Beyond the lateral resolution limit by phase imaging

We present a theory stating how to overcome the classical Rayleigh-resolution limit. It is based upon a new resolution criterion in phase of coherent imaging process and its spatial resolution is thought to be only SNR limited. Recently, the experimental observation of systematically occurring phase singularities in coherent imaging of sub-Rayleigh distanced objects has been reported.1 The phase resolution criterion relies on the unique occurrence of phase singularities. A priori, coherent imaging system's resolution can be extended to Abbe's limit.2 However, by introducing a known phase difference, the lateral as well as the longitudinal resolution can be tremendously enlarged. The experimental setup is based on Digital Holographic Microscopy (DHM), an interferometric method providing access to the complex wave front. In off-axis transmission configuration, sub-wavelength nano-metric holes on a metallic film acts as the customized high-resolution test target. The nano-metric apertures are drilled with focused ion beam (FIB) and controlled by scanning electron microscopy (SEM). In this manner, Rayleighs classical two-point resolution condition can be rebuilt by interfering complex fields emanated from multiple single circular apertures on an opaque metallic film. By introducing different offset phases, enhanced resolution is demonstrated. Furthermore, the measurements can be exploited analytically or within the post processing of sampling a synthetic complex transfer function (CTF).

Compact lensless digital holography

Manon Rostykus

Microscopy is of high interest for biology since it allows imaging features that are too small to be seen with naked eyes. However, cells are mostly transparent to visible and infrared light which makes it difficult to see with a traditional microscope. To do so, phase imaging was invented by F. Zernike, who received the Nobel prize in 1953 for this invention. It provides intensity contrast to visualize transparent samples such as those found in biology without any staining. Among the different implementations of phase imaging, digital holographic microscopy (DHM) is a well-known phase method which provides a quantitative value of the phase generated by the sample under test. Implementations of DHMs without the help of any lens element (so called lensless) offer the added advantage to provide large field of views (severalmm2 compared to several hundred ¹m2) and more compact setups than traditional DHMs which have high quality microscope objectives. The lateral resolution is limited by the pixel size of the camera. However, several techniques have been developed to obtain subpixel resolution with lensless setups, hence giving a resolution smaller than the pixel size. In this thesis, two lensless transmission DHMs are presented using a side illumination technique in order to further reduce the device size and keep a visual access to the sample. The first one operates in an in-line configuration: the most compact but using time-consuming image post-processing. The second one is also lensless and uses an off-axis configuration allowing quasi-real time imaging but less compact. Their practical use is described and images of transparent (phase only) samples are shown. Super-resolution (subpixel) using several subpixel shifted holograms was then investigated for the in-line configuration and demonstrated on absorptive samples. Since those microscopes are compact and made out of off-the-shelf low priced elements, they could be broadly spread in schools for educational purposes. They could also be implemented in cells incubators, allowing visualization inside processes at low cost and multiplication of the number of measurements made at the same time.

EPFL2018

Beyond the lateral resolution limit by phase imaging

Yann Jérôme Michel Pascal Cotte, Christian Depeursinge, Muhammed Fatih Toy

We present a theory to extend the classical Abbe resolution limit by introducing a spatially varying phase into the illumination beam of a phase imaging system. It allows measuring lateral and axial distance differences between point sources to a higher accuracy than intensity imaging alone. Various proposals for experimental realization are debated. Concretely, the phase of point scatterers’ interference is experimentally visualized by high numerical aperture (NA = 0.93) digital holographic microscopy combined with angular scanning. Proof-of-principle measurements are presented by using sub-wavelength nanometric holes on an opaque metallic film. In this manner, Rayleighs classical two-point resolution condition can be rebuilt. With different illumination phases, enhanced bandpass information content is demonstrated, and its spatial resolution is theoretically shown to be potentially signal-to-noise ratio limited.

2011

Resolution and Complex Deconvolution in Holographic Microscopy

Yann Jérôme Michel Pascal Cotte

Interest in high resolution imaging techniques has recently multiplied due to their importance in bio-medical research. Quantitative phase measurements by holographic microscopy is an extraordinary tool to gain new understanding of transparent biological samples. The extremely high demand on resolution well beyond the diffraction limit, however, sets new benchmarks for imaging techniques. Digital Holographic Microscopy is an interferometric method providing access to the complex wave front. Its capacity to image amplitude and quantitative phase simultaneously makes it an attractive research tool in many fields of biological research. It is on the verge of becoming an appealing alternative to classical fluorescence microscopy. For intensity-based microscopy, however, super-resolution methods are well established. In this thesis, approaches to unleash resolution for phase imaging techniques are explored. Based on truncated inverse filtering, a theory for deconvolution of complex fields is developed. It is a post-processing method that does not require any additional optics in the holographic microscopy setup. Gain in resolution arises by accessing the object's complex field – containing the information encoded in the phase – and deconvolving it with the characteristic coherent transfer function (CTF). By efficient harvest of a diffraction limited bandpass, complex deconvolution is demonstrated to exceed the coherent resolution limit. A novel method, called a complex point source, serves to characterize the holographic microscopy system. It consists of a coherently illuminated nano-metric hole, located on a conventional microscope slide, most common in bio-microscopy. A thin opaque film is directly evaporated on the slide and the circular sub-wavelength structures are drilled with a focused ion beam. Theoretical as well as practical work on transmission properties of apertures confirms the advantageous signal-to-noise yield of proposed method. More abstractly, the thus gained experimental amplitude point spread function is demonstrated to be suitable for experimental CTF reconstruction. Herefrom, experimental parameters are extracted and introduced into scalar and vectorial Debye theory, called synthetic CTF, adaptable to realistic imaging conditions. Also, it allows to study the role of noise in the context of complex field deconvolution. The resolution power of holographic microscopy systems is systematically examined with pairs of nano-metric apertures separated by sub-resolution pitches. Theory of information content is elaborated depending on different experimental configurations. Resolution extends beyond classical Abbe's limit by introducing spatially a varying phase into the illumination beam of a phase imaging system. In a last step, the novel deconvolution method is generalized to three-dimensional image processing of complex fields. By combining scattering theory and signal processing, the method is demonstrated to yield the reconstruction of the scattering object field under non-design microscope objective imaging conditions. The suggested technique is best suited for an implementation in high-resolution diffraction tomography based on sample and/or illumination rotation.