Diffractionless Fourier Domain Microscopy

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).

k-Microscopy: resolution beyond the diffraction limit

Theo Lasser, Rainer Leitgeb

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.

SPIE2008

Enhancement of extended depth of field by digital focusing

Cédric Blatter, Theo Lasser, Rainer Leitgeb, Martin Villiger

With the use of a Bessel-like illumination beam produced by an axicon lens an extended depth of field can be achieved. The resulting illumination pattern exhibits a strong central lobe extending over 300um along the optical axis without diffraction. Here we present a fast digital focusing algorithm to correct for remaining out of focus artifacts, manifest in sidelobes for out of focus scatterers, due to the decoupled Gaussian detection. The waist of the detection in the focal plane is 2.1um, with a Rayleigh-range of ~35um. The FDOCT data is Fourier transformed in the lateral spatial directions. Passing from the spectral (K) to the spatial (Z) domain, the correction term is implemented in a chirped z- transform algorithm, performing a resampling in the K domain. Finally the data is transformed back in the lateral direction to spatial coordinates. The illumination scheme provides a tightly focused spot over the whole axial extent of the illumination needle, providing the high signal to noise ratio necessary to correct for the diffraction effects of the detection. Signals from scatterers multiple Rayleigh distances away from the focal plane are recovered with minimal loss in resolution. With this digital focusing algorithm the performance of the physically extended depth of field is further enhanced, presenting a uniform high lateral resolution of 1.3um, corresponding to an effective numerical aperture of NA=0.24, over more than 300um in the axial direction.

2008

Extended focus Fourier domain optical coherence microscopy assists developmental biology

Cathrin Brisken, Theo Lasser, Rainer Leitgeb

We present a novel detection scheme for Fourier domain optical coherence microscopy (FDOCM). A Bessel-like interference pattern with a strong central lobe was created with an axicon lens. This pattern was then imaged by a telescopic system into the sample space to obtain a laterally highly confined illumination needle, extending over a long axial range. For increased efficiency, the detection occurs decoupled from the illumination, avoiding a double pass through the axicon. Nearly constant transverse resolution of ~1.5µm along a focal range of 200µm with a maximum sensitivity of 105dB was obtained. A broad bandwidth Ti:Sapphire laser allowed for an axial resolution of 3µm in air, providing the nearly isotropic resolution necessary to access the microstructure of biological tissues. Together with the speed- and sensitivity-advantage of FDOCT, this system can perform in vivo measurements in a minimally invasive way. Tomograms of the mouse mammary gland and the mouse follicle, recorded in vitro, revealed biologically relevant structural details. Images acquired with classical microscopy techniques, involving stained and fluorescent samples, validate these structures and emphasize the high contrast of the tomograms. It is comparable to the contrast achieved with classical techniques, but employing neither staining, labeling nor slicing of the samples, stressing the high potential of FDOCM for minimally invasive in vivo small animal imaging.

SPIE2007