The influence of random phase errors on the angular resolution of a focused synthetic aperture radar system is treated. The principal measure of performance has been taken as the mean envelope power at the system output. This system output power is evaluated exactly, although not in closed form, based on the following reasonable assumptions: (1) the real beam pattern is Gaussian; (Z) the random phase error is essentially a geometry independent ergodic process with a Gaussian amplitude distribution and zero mean; and (3) the random phase error has a Gaussian co.rrelation function.The curves presented in this report can be used to estimate expected system power response, expected system resolution, and effective aperture length beyond which, inthe presence of phase error, little gain in resolution is expected.It was found that multiple sources of error with different correlation intervals make explicit solution of the integral equation for system power response practicallyimpossible. Inthis situation, a reasonable approach is to evaluate the system power response separately for 'ach error. If one of the errors is clearly dominant, it maybe regarded as bounding achievable performance.
One of the most significant developments in life sciences—the discovery of bacteria and protists—was accomplished by Antoni van Leeuwenhoek in the 17th century using a single ball lens microscope. It is shown that the full potential of single lens designs can be realized in a contact mode of imaging by ball lenses with a refractive index of n ≈ 2, suitable for developing compact cellphone‐based microscopes. The quality of imaging is comparable to basic compound microscopes, but with a narrower field‐of‐view, and is demonstrated for various biomedical samples. The maximal magnification (M > 50) with the highest resolution (≈0.66 µm at λ = 589 nm) is achieved for imaging of nanoplasmonic structures by ball lenses made from LASFN35 glass, the index of which is tuned near n = 2 using chromatic dispersion. Due to limitations of geometrical optics, the imaging theory is developed based on an exact numerical solution of the Maxwell equations, including spherical aberration and the nearfield coupling of a point source. The modeling is performed using multiscale analysis: from the field propagation inside ball lenses with diameters 30 < D/λ < 4000 to the formation of the diffracted field at distances of ≈105 λ. It is shown that such imaging enables the transition from pixel‐ to diffraction‐limited resolution in cellphone microscopy.
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