Abstract-In this paper, a new direction of arrival (DOA) estimation approach is addressed for the case of more sources than physical receiving antennas by considering a novel nonuniform array design. The new design utilizes the concept of minimum sparse rulers which are rulers having incomplete marks. The differences between marks in a sparse ruler cover all lags of the autocorrelation. In array processing, this set of differences can be used as a basis to construct a virtual uniform linear array having a higher number of antennas than the actual linear array. In order to attain the required rank condition of the observation matrix, the most recent spatial smoothing method is used. The MUSIC algorithm can then be applied leading to the desired high resolution result. It is also possible to compromise the resolution for a lower complexity level by exploiting the least-squares approach to generate the angular spectrum.Index Terms-direction of arrival (DOA) estimation, nonuniform array, sparse rulers, MUSIC algorithm, spatial smoothing

Whole Slide Imaging (WSI) systems are high-throughput automated microscopes for digital pathology applications. We present a method for testing and monitoring the optical quality of WSI-systems using a measurement of the through-focus Optical Transfer Function (OTF) obtained from the edge response of a custom made resolution target, composed of sagittal and tangential edges. This enables quantitative analysis of a number of primary aberrations. The curvature of the best focus as a function of spatial frequency is indicative for spherical aberration, the argument of the OTF quantifies for coma, and the best focus as a function of field position for sagittal and tangential edges allows assessment of astigmatism and field curvature. The statistical error in the determined aberrations is typically below 20 mλ. We use the method to compare different tube lens designs and to study the effect of objective lens aging. The results are in good agreement with direct measurement of aberrations based on Shack-Hartmann wavefront sensing with a typical error ranging from 10 mλ to 40 mλ.

We present an investigation of the impact of partial coherence on optical imaging systems with the focus on whole slide imaging (WSI) systems for digital pathology. The investigation is based on the analysis of the edge response of the optical system, which gives rise to an apparent optical transfer function (OTF) that can be linked to two elementary complex functions Q and U. The function Q is directly related to the transmission cross coefficient (TCC) and can be identified with the performance function first introduced by Kintner and Sillitto. The function U depends on the TCC in a more involved way. When there are no aberrations the Q-function corresponds to the real part of the apparent OTF and the U function to the imaginary part of the apparent OTF. Close to the incoherent limit the effect of the U function is a mere shift of the edge compared to the fully incoherent case. We propose a new expression for the dependence of the depth of focus (DOF) on spatial frequency and on the partial coherence factor σ, and validate it by simulation. Partial coherence effects are investigated experimentally on a WSI system with a compact LED-based Köhler illumination unit with variable condenser NA. This unit incorporates a top hat diffuser for providing a reasonably uniform illumination field, with variations below 10% across the imaged field of view. The measurements of the apparent through-focus OTF derived from edges on a custom resolution chart for different σ were substantially in agreement with the simulations. Finding an optimal value for σ is not straightforward as lateral resolution and the level of edge ringing improve with increasing σ, whereas edge contrast and DOF improve with decreasing σ. We assess that the trade-off for the particular application of WSI systems for digital pathology is optimized for a σ value in the range of 0.55-0.75.

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Whole Slide Imaging (WSI) systems are used in the emerging field of digital pathology for capturing high-resolution images of tissue slides at high throughput. We present a technique to measure the optical aberrations of WSI systems using a Shack-Hartmann wavefront sensor as a function of field position. The resulting full-field aberration maps for the lowest order astigmatism and coma are analyzed using nodal aberration theory. According to this theory two coefficients describe the astigmatism and coma inherent to the optical design and another six coefficients are needed to describe the cumulative effects of all possible misalignments on astigmatism and coma. The nodal aberration theory appears to fit well to the experimental data. We have measured and analyzed the full-field aberration maps for two different objective lens-tube lens assemblies and found that only the optical design related astigmatism coefficient differed substantially between the two cases, but in agreement with expectations. We have also studied full-field aberration maps for intentional decenter and tilt and found that these affect the misalignment coefficient for constant coma (decenter) and the misalignment coefficient for linear astigmatism (tilt), while keeping all other nodal aberration theory coefficients constant.