Combined plane wave — Point source near-field far-field transformation for short measurement distances

Abstract We investigate the far-field pattern generation for a micro-lens array (MLA) illuminated under different conditions. Plane wave and Gaussian beam illumination are considered for an MLA with a small diameter of 27 microns and 30 microns period. At these dimensions, the optical effects are governed by diffraction and refraction and sometimes the regime is called the refraction limit. For Gaussian beam illumination, a high contrast dot pattern can be obtained in the far field according to the self-imaging theory for point source illumination and it is investigated in the simulation part. Also, we designed an interference microscopy setup to record both the phase and intensity in near field behind the MLA and also in the far field. The new instrument allows us to change illumination conditions from plane wave to point source. We then experimentally compare the near-field phase modulation and resulting far-field intensity for different conditions. For plane wave illumination, a high contrast pattern is observed in the far field. For the Gaussian beam illumination, the contrast of the far-field pattern depends on the distance of the source and MLA resulting in high contrast and a larger field of view only for particular distances depending on the interference of the Gaussian beam curved phase front and the MLA.

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Near-field far-field transformation exploiting the benefits of plane wave expansion and diagonal translation operators

2007 European Microwave Conference ◽

10.1109/eumc.2007.4405254 ◽

2007 ◽

Cited By ~ 1

Author(s):

Carsten H. Schmidt ◽

Martin M. Leibfritz ◽

Thomas F. Eibert

Keyword(s):

Plane Wave ◽

Near Field ◽

Far Field ◽

Plane Wave Expansion ◽

Wave Expansion ◽

Field Transformation ◽

Translation Operators

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Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

Computation ◽

10.3390/computation9110120 ◽

2021 ◽

Vol 9 (11) ◽

pp. 120

Author(s):

Isaac Harris

Keyword(s):

Point Source ◽

Scattered Field ◽

Sampling Methods ◽

Near Field ◽

Curve Surface ◽

Cauchy Data ◽

Far Field ◽

Direct Sampling ◽

Field Transformation ◽

Resolution Analysis

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data, which allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer with full and partial aperture data.

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