Coherent transfer functions and extended depth of field

To preserve the speed advantage of Fourier Domain detection in Optical Coherence Microscopy (OCM), extended depth of field is needed. With a narrow probing volume that extends over a long axial range, tissue could be measured in vivo and at cellular resolution. To assess and improve the DOF and the lateral resolution, we analyzed the coherent transfer function (CTF) of OCM. Both the illumination and detection optics contribute equally to the overall imaging performance. In the Fourier domain detection, each pixel of the spectrometer has its specific CTF, sampling a different region of the object’s spatial frequency spectrum. For classical optics and increasing numerical apertures these regions start to overlap and bend, which limits the depth of field. Annular apertures, created with Bessel-like beams produced by axicon lenses or phase filters, circumvent these detrimental effects, but introduce strong side lobes. Decoupling the detection and the illumination apertures is needed to provide the flexibility in engineering a CTF that optimizes the lateral resolution and the DOF at the same time all while reducing these side lobes. We evaluated different combinations of Gaussian and Bessel-like illumination and detection optics, both theoretically and experimentally. Using Bessel-like beams as well in the illumination as in the detection paths, but with annular apertures of different lobe radii, we obtained a lateral resolution of 1.3 μm and an extended depth of field of more than 300 μm, which was completely decoupled from the numerical aperture and scalable to high lateral resolution.

Measurement of the coherent transfer function

Theo Lasser, Christophe Pache, Martin Villiger

It is important to characterize and quantify the imaging performance of optical coherence tomography (OCT) and especially optical coherence microscopy (OCM) systems for validation and calibration of the setup. We suggest using a simple rubber surface, presented to the setup at different focal positions, to measure the system’s lateral resolution and depth of field. Rubber is a nearly perfect scatterer and produces a fully developed speckle pattern. The speckle size and shape are directly defined by the optical system and its illumination and detection apertures. Analysis of the speckle pattern reveals the system’s coherent transfer function (CTF) and hence the point spread function (PSF) in a straightforward computation.

2010

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

Multiple scattering in wide-field optical coherence tomography

Boris Karamata

Optical Coherence Tomography (OCT), a well-established imaging method based on low-coherence interferometry, provides cross-sectional images of the internal structure of biological samples with a resolution in the micrometer range. OCT was successfully applied on various tissues such as for instance the retina, the skin or a tooth. In highly scattering tissues like the skin, probing depth is limited to approximately 2mm, mainly due to insufficient rejection of multiply scattered light. Presently, the contribution of multiple scattering in OCT is not fully understood. Therefore, there is a strong and urgent need to develop models allowing a reliable evaluation of the system's limitations as well as the improvement of the imaging capabilities. It is generally believed that a relevant model should account for loss of correlation between the reference and the sample field due to multiple scattering. We developed a new comprehensive model of OCT. Our preliminary study revealed that the reference and sample fields are actually fully correlated. This important result allowed us to model the OCT signal as a sum of stationary random phasors and treated it as a statistical signal. The mean of this signal can be calculated thanks to classical results of statistical optics and to a Monte Carlo simulation. Unlike other existing models, our model accounts for the source autocorrelation function. The model proved to be in excellent agreement with a whole range of experimental data gathered in a comprehensive study of cross-talk in wide-field OCT. Moreover, our results put in question the applicability of widely used models of OCT based on the "extended Huygens-Fresnel principle", which assume a partial correlation between interfering fields due to multiple scattering. The construction of conventional OCT images is based on lateral scanning of a beam focused within the sample. To increase image acquisition speed and eliminate the need for lateral scanning, wide-field OCT was recently developed. Our experimental and theoretical investigations of the potential and limitations of wide-field OCT revealed the crucial role played by the spatial coherence of the light source. Spatially coherent illumination generates considerable coherent optical cross-talk, which prevents shot-noise-limited detection and diffraction-limited imaging in scattering samples. The dependence on several parameters of the optical system and of the sample properties was investigated in a comprehensive study. Cross-talk increases with the wide-field diameter, numerical aperture, source coherence length, and sample optical density; and strongly depends on sample anisotropy. We showed that spatially incoherent illumination realized with a thermal light source permits cross-talk suppression in wide-field OCT, i.e. rejection of multiply scattered light to a level comparable to that of point scanning OCT. We performed a theoretical study which revealed that the power per spatial mode radiated by thermal light sources is too low to permit a high signal-to-noise ratio while maintaining a fast acquisition speed. Therefore, wide-field OCT realized with either spatially coherent or spatially incoherent illumination suffers from inherent fundamental limitation. This led us to investigate the possibility of exploiting a spatially incoherent light source brighter than a thermal light source. We came to the conclusion that such a "pseudothermal" light source can potentially lead to wide-field OCT systems devoid of cross-talk and an image acquisition speed higher than that of a point scanning OCT system. However, the attractive properties of pseudothermal light sources could be gained at the expense of the simplicity and the economical advantages offered by thermal light sources. Furthermore, fast acquisition speed also relies on a performing "smart pixel detector array". Presently, such detectors do not have sufficient sensitivity and their frequency readout is too low as shown in our feasibility study. We performed a theoretical investigation of the potential of thermal light sources in terms of axial resolution and power per mode. The former revealed that the maximum power per mode is radiated at a wavelength higher than the spectral peak of a blackbody radiator. This led to the important practical conclusion that, at 6000 K, the maximum power is collected in the therapeutic spectral window in OCT (600 - 1300 nm), while at 3000 K this peak is shifted out of the therapeutic window leading to significant power losses. More generally, our work provides a design tool for choosing the optimal thermal light source for a given therapeutic window in terms of signal-to-noise ratio. Currently available sources at 6000 K consist of high pressure gas arc lamps providing a spectrum endowed with spectral lines deleterious for OCT. By suppressing a portion of the spectrum devoid of spectral lines of a mercury arc lamp, we obtained amongst the highest axial resolution so far reported in OCT. Furthermore, the importance of the speckle statistics in OCT incited us to clarify the origin of a difference between two theoretical results reported in the literature. Indeed, two calculations of the amplitude distribution of speckles in OCT, each of them based on a different mathematical formulation, yield different results. We showed that a modification of an initial assumption in one of the formulation leads to equivalent results. In conclusion, this thesis provides a deeper understanding of the potential and limitations of widefield OCT, leading to important design rules. Moreover, it presents a new comprehensive model of OCT putting in question other widely used models.

EPFL2004

Multiple scattering in wide-field optical coherence tomography

Boris Karamata

EPFL2004