Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition

Şahin, Erdem; Onural, Levent

doi:10.1364/josaa.29.001459

Cited by 9 publications

(17 citation statements)

References 20 publications

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“…Note that Eq. (10) is not an exact diffraction formula for curved surface, but only an approximation [10,15,18] which can be justified in our experimental condition where the maximum radial distance of the object point from the coordinate origin 1.8 × 10 −1 cm is much smaller than the radius of the synthesized hologram 9.57 cm. We used Eq.…”

Section: Methodsmentioning

confidence: 86%

Synthesis of computer-generated spherical hologram of real object with 360° field of view using a depth camera

Phan

Kim

et al. 2013

Appl. Opt.

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A method for synthesizing a 360° computer-generated spherical hologram of real-existing objects is proposed. The whole three-dimensional (3-D) information of a real object is extracted by using a depth camera to capture multiple sides of the object. The point cloud sets which are obtained from corresponding sides of the object surface are brought into a common coordinate system by point cloud registration process. The modeled 3-D point cloud is then processed by hidden point removal method in order to identify visible point set for each spherical hologram point. The hologram on the spherical surface is finally synthesized by accumulating spherical waves from visible object points. By reconstructing partial region of the calculated spherical hologram, the corresponding view of the 3-D real object is obtained. The principle is verified via optical capturing using a depth camera and numerical reconstructions.

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Section: Methodsmentioning

confidence: 86%

Synthesis of computer-generated spherical hologram of real object with 360° field of view using a depth camera

Phan

Kim

et al. 2013

Appl. Opt.

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“…Recently, using a Gaussian decomposition method, electric fields propagating off curved surfaces have been calculated in Refs. [16][17][18]. We present another semi-analytical approach and summarize a method given in the literature for the more simple case of a spherical source.…”

Section: From the Curved Surface To The Plane: Working In Curved Smentioning

confidence: 99%

Generalized propagation of light through optical systems I Mathematical basics

Tessmer

Groß

2015

J. Opt. Soc. Am. A

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The propagation of an input field through tilted and curved surfaces is presented and applied for a field tracing routine. This routine employs a ray tracing method for optimal coordinate customization, which is done due to the strong linear phase terms that arise because of tilted coordinates on one hand and the possibility of an application of fast numerical routines on the other. Several methods are proposed on how to optimize the field sampling during the propagation process, as for the astigmatic phase front problem and the curvature of the surface itself. Two solution methods are given to propagate from the curved surface through the homogeneous space to another two-dimensional submanifold. The approach is fully vectorial, Maxwell exact excluding only surface curvature terms for the Fresnel coefficients. A simple numerical propagation example is given.

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“…The reason is that they ignore the mutual couplings between the field samples on the given curved surface. As a result, the subsequently reconstructed field on the same curved surface is found to be inconsistent with the original one [8,9].…”

Section: Introductionmentioning

confidence: 96%

“…The local Gaussian beam decomposition proposed in [8] reduces the mutual coupling effects with respect to point source models [1][2][3][4][5][6][7]. In that work of Şahin and Onural [8], the signal given on the curved surface is decomposed into a sum of modulated Gaussian window functions.…”

Section: Introductionmentioning

confidence: 99%

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Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams

Şahin

Onural

2013

J. Opt. Soc. Am. A

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We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a two-dimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.

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Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition

Cited by 9 publications

References 20 publications

Synthesis of computer-generated spherical hologram of real object with 360° field of view using a depth camera

Synthesis of computer-generated spherical hologram of real object with 360° field of view using a depth camera

Generalized propagation of light through optical systems I Mathematical basics

Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams

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