k-Microscopy: resolution beyond the diffraction limit

We present a novel Fourier domain method for microscopic imaging - so- called k-microscopy - with lateral resolution independent of the detection numerical aperture. The concept is based on sample illumination by a lateral fringe- pattern of varying spatial frequency, which probes the lateral spatial frequency or k- spectrum of the sample structure. The illumination pattern is realized by interference of two collimated coherent beams. Wavelength tuning is employed for modulation of the fringe spacing. The uniqueness of the proposed system is that a single point detector is sufficient to collect the total light corresponding to a particular position in the sample k- space. By shifting the phase of the interference pattern, we get full access to the complex frequencies. An inverse Fourier transformation of the acquired band in the frequency- or k-space will reconstruct the sample. The resulting lateral resolution will be defined by the temporal coherence length associated with the detected light source spectrum as well as by the illumination angle. The feasibility of the concept has been demonstrated in 1D.

Diffractionless Fourier Domain Microscopy

Cédric Blatter, Theo Lasser, Rainer Leitgeb, Tilman Schmoll

Several methods have been proposed and realized to increase the lateral resolution in microscopy and ultimately to beat the actual diffraction limit as stated by Abbe. Structured illumination for example enhances the lateral resolution by virtually extending the spatial frequency support of the system transfer function. Higher spatial frequencies are in fact mapped into the range covered by the detection transfer function. The set of spatial frequencies can be further enhanced by decoupling illumination and detection and by employing concepts similar to synthetic apertures. We present a novel method for diffractionless microscopic imaging – Fourier Domain or k-Microscopy[1] (FDM). Again we decouple illumination from detection to achieve a lateral resolution that is independent of the detection numerical aperture. Similar to structured illumination we produce a set of fringes covering a band of spatial frequencies on the sample. However, instead of detecting with an area sensor we use a simple PIN detector: By tuning the spatial frequency of the illumination we obtain the Fourier coefficient from the measured total backscattered or transmitted intensity for the particular spatial frequency in the sample dimension normal to the fringe orientation. The fringe pattern is obtained from two collimated coherent beams that are superimposed. The spatial frequency of the pattern is controlled via tuning the wavelength. In order to obtain an unambiguous Fourier representation of the one dimensional sample structure it is necessary to record at least two π/2 phase shifted copies of the frequency response signal. The lateral resolution is then determined by the tuning bandwidth of the laser as well as the subtended angle and the central wavelength of the laser. This relation is in fact very similar to the concept of Fourier Domain Optical Coherence tomography, only that it acts on the transverse instead of the longitudinal resolution. We give first experimental proof of the concept in one dimension using a slowly tuning broad- bandwidth Ti:Sapph laser. We resolve the defined structure of a resolution test target. A particular feature of the method is that the reconstructed sample will appear spatially band-pass filtered due to the finite spectral support given by the tuned fringe frequencies. Hence only the edges of the test target lines are visible. We believe that the concept of FDM will greatly benefit from new developments in rapidly- wavelength tuning source technology that recently entered the field of OCT. 1. M. Geissbuehler, T. Lasser, and R. A. Leitgeb, "K- Microscopy - resolution beyond the diffraction limit," in Progress in Biomedical Optics and Imaging - Proceedings of SPIE(2008).

2011

k-Microscopy: resolution beyond the diffraction limit

Theo Lasser, Rainer Leitgeb

We introduce a novel microscopy method of probing the spatial frequencies of a two dimensional sample with a single point detector allowing for sub- micron resolution with low NA lenses as well as for lateral phase resolution in the nanometer range. We synthesize the spatial frequency coordinate space by illuminating a sample with a TIR configuration and lateral interference fringes generated by a wavelength tunable light source. Similar to OCT the temporal coherence defines the resolution up to the illumination angle but now laterally. The structure is finally reconstructed via inverse Fourier transform of the synthesized k-space.

2008

Endoscopic low coherence interferometry applied to tri-dimensional contouring of upper airways

Yves Delacrétaz

This thesis presents a novel approach for optical tri-dimensional contouring, requiring only one acquisition to extract a contour depth. It is based on an interferometric setup, using a reduced coherence light source, and is fully adaptable to endoscopic procedure commonly in used in ear-nose-throat (ENT) medicine. It has been demonstrated that the method can be successfully applied to imaging of porcine upper airways. Although this method uses interferometry to obtain depth range measurement, the phase signal is not directly evaluated, rather the location of the coherent superposition of two waves is extracted, and thus provides a robust technique even in harsh environment. The key feature is to extract the coherent area on the image by locating intentionally induced fringes created by off-axis superposition of a smooth reference wave and an object wave coming from a rough or diffusing sample through an optical system with limited aperture. A model for the propagation of the light through the optical system has been developed. It takes into account the broadened emission spectrum of the light source, as well as the statistical speckle effect induced by the illumination of a rough surface with partially coherent light. Simulated results have been carefully compared with measurements, both in the spatial domain and in the Fourier domain (spatial frequencies response), which has permitted to better understand the processes involved in the creation of the interference fringes, and improve the design of the device. Different filters have been investigated in order to extract the depth information from acquired interferograms. By using Gabor filterbanks, which do not need any a priori knowledge of the signal, selectivity of the extracted signal has been enhanced by a factor of 1.3 compared to a simple local Fourier spectrum evaluation, and time of the extraction procedure divided by 6, even when compared to fast iterative calculation in the Fourier spectrum. Moreover, by imposing the frequency and/or orientation of the signal to detect, which can be known by a simple calibration procedure, it has been proved that the selectivity can be further enhanced by a factor of 2.5, keeping the calculation time as short or even shorter. A compact prototype has been designed and built, with a specific multiple fibers arrangement for illumination. The system is separated in two parts: the first one is directly attached to the rigid endoscope, and contains imaging as well as recombining object/reference wave optics, and the detector. It fits into a box with overall dimensions of 115 × 83 × 94 mm. The second part contains the laser source, the scanning arm and the injection optics for the fibered system. It is designed to be left on a small cart. This device can potentially be brought to the bedside, and used during routine endoscopic check-up. Associated with the device, a complete framework has been elaborated in order to simplify the acquisition procedure as well as the signal processing. This results in a fully automated environment taking in charge hardware control, data storage and signal processing, up to the tri-dimensional scene rendering.