Numerical characterization of an ultra-high NA coherent fiber bundle part II: point spread function analysis.

Straightforward numerical integration of the Rayleigh-Sommerfeld diffraction integral (R-SDI) remains computationally challenging, even with today's computational resources. As such, approximating the R-SDI to decrease the computation time while maintaining a good accuracy is still a topic of interest. In this paper, we apply an approximation for the R-SDI that is to be used to propagate the field exiting a Coherent Fiber Bundle (CFB) with ultra-high numerical aperture (0.928) of which we presented the design and modal properties in previous work. Since our CFB has single-mode cores with a diameter (550 nm) smaller than the wavelength (850 nm) for which the CFB was designed, we approximate the highly divergent fundamental modes of the cores with real Dirac delta functions. We find that with this approximation we can strongly reduce the computation time of the R-SDI while maintaining a good agreement with the results of the full R-SDI. Using this approximation, we first determine the Point Spread Function (PSF) for an 'ideal' output field exiting the CFB (identical amplitudes for cores on a perfect hexagonal lattice with the phase of each core determined by the appropriate spherical and tilted plane wave front). Next, we analyze the PSF when amplitude or phase noise is superposed onto this 'ideal' field. We find that even in the presence of these types of noise, the effect on the central peak of PSF is limited. From these types of noise, phase noise is found to have the biggest impact on the PSF.

Numerical characterization of an ultra-high NA coherent fiber bundle part I: modal analysis.

Advances in fiber optics and CCD technology in the last decades have allowed for a large reduction in outer diameter (from centimeters to submillimeter) of endoscopes. Attempts to reduce the outer diameter even further, however, have been hindered by the trade-off, inherent to conventional endoscopes, between outer diameter, resolution and field of view. Several groups have shown the feasibility of further miniaturization towards so called micro-endoscopes, albeit at the cost of a very reduced field of view. In previous work we presented the design of an ultra-high NA (0.928) Coherent FiberBundle (CFB) that, in combination with proximal wave front shaping, could be used to circumvent this trade-off thus paving the way for even smaller endoscopes. In this paper we analyze how the modal properties of such an ultra-high NA CFB determine the required input field to achieve any desired output field. We use the periodicity of the hexagonal lattice which characterizes a CFB, to define a unit cell of which we analyze the eigen-modes. During the modal analysis, we also take into account realistic variations in lattice constant, core size and core shape due to the limitations of the fabrication technology. Realistic values for these types of fabrication-induced irregularities were obtained via SEM images of a CFB fabricated according to the aforementioned design. The presence of these irregularities results, for a desired output, in the required input to be different from the required input for a defect-free CFB. We find that of the different types of fabrication-induced irregularities present in the CFB, variations in core ellipticity have the biggest impact on the required input for a given desired output.