Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates

Ritter, André

doi:10.1364/oe.22.026265

Cited by 16 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ritter [19] developed an AS method for off-axis field calculations with a reduced sampling frequency that is restricted to band-limited fields propagating in off-axis direction. Hillenbrand et al [20] proposed a tile summation for AS for focused field calculations with reduced sample size.…”

mentioning

confidence: 99%

“…Shimobaba and co-workers [16,17] developed scaled AS employing a nonuniform Fourier Transform, and Yu et al [18] proposed an approach based on the chirped z-transform. Ritter [19] developed an AS method for off-axis field calculations with a reduced sampling frequency that is restricted to band-limited fields propagating in off-axis direction. Hillenbrand et al [20] proposed a tile summation for AS for focused field calculations with reduced sample size.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Kozacki

Falaggis

2015

Opt. Lett.

View full text Add to dashboard Cite

Rigorous propagation methods enable diffraction calculations at high NA. However, for the case of large propagation distances and full NA calculations of a signal, common solutions require zero padding or upsampling. This Letter overcomes these problems by introducing a sampling scheme based on compact space bandwidth product representation, which adjusts the sampling frequency of input and propagated field according to the evolution of the generalized space bandwidth product. This sampling concept allows proposing a novel AS method enabling high efficiency, high accuracy, and high-NA diffraction computations at larger propagation distances without need of zero padding or upsampling. The method has several advantages: (1) high accuracy for larger propagation distances; (2) reduced sampling with minimal computation effort; (3) zooming capability; and (4) both focusing and defocusing propagations possible.

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Kozacki

Falaggis

2015

Opt. Lett.

View full text Add to dashboard Cite

show abstract

“…Hence, (14) can be equivalently expressed as a 2D aperiodic convolution of the complex amplitude a with the kernel p x3 ( · )e −j( · ) Tkin , followed by a modulation in the space domain. This approach is called tilt transfer because the shift of y in in the Fourier domain is transferred to the propagation kernel [37,38]. The advantage of this formulation is that, by contrast to y in , the complex amplitude a is not far from a constant signal, up to some noise and optical aberrations.…”

Section: Computation Of the 3d Incident Field: U Inmentioning

confidence: 99%

Three-Dimensional Optical Diffraction Tomography With Lippmann-Schwinger Model

Pham

Soubies

Ayoub

et al. 2020

IEEE Trans. Comput. Imaging

View full text Add to dashboard Cite

A broad class of imaging modalities involve the resolution of an inverse-scattering problem. Among them, three-dimensional optical diffraction tomography (ODT) comes with its own challenges. These include a limited range of views, a large size of the sample with respect to the illumination wavelength, and optical aberrations that are inherent to the system itself. In this work, we present an accurate and efficient implementation of the forward model. It relies on the exact (nonlinear) Lippmann-Schwinger equation. We address several crucial issues such as the discretization of the Green function, the computation of the far field, and the estimation of the incident field. We then deploy this model in a regularized variational-reconstruction framework and show on both simulated and real data that it leads to substantially better reconstructions than the approximate models that are traditionally used in ODT. IntroductionOptical diffraction tomography (ODT) is a noninvasive quantitative imaging modality [1,2]. This label-free technique allows one to determine a three-dimensional map of the refractive index (RI) of samples, which is of particular interest for applications that range from biology [3] to nanotechnologies [4]. The acquisition setup sequentially illuminates the sample from different angles. For each illumination, the outgoing complex wave field (i.e., the scattered field) is recorded by a digital-holography microscope [5,6]. Then, from this set of measurements, the RI of the sample can be reconstructed by solving an inverse-scattering problem. However, its resolution is very challenging due to the nonlinear nature of the interaction between the light and the sample. Related WorksTo simplify the reconstruction problem, pioneering works focused on linearized models. These include Born [1] and Rytov [7] approximations, which are valid for weakly scattering samples [8]. Although originally used to deploy direct inversion methods, these linearized models have been later combined with iterative regularization techniques to improve their robustness to noise and to alleviate the missing-cone problem [9,10].Nonlinear models that adhere more closely to the physic of the acquisition are needed to recover samples with higher variations of their refractive index. For instance, beam-propagation methods (BPM) [11][12][13][14] rely on a slice-by-slice propagation model that accounts for multiple scatterings within the direction of propagation (no reflection). Other nonlinear models include the contrast source-inversion method [15] or the recursive Born approximation [16]. Although more accurate, all these models come at the price of a large computational cost.The theory of scalar diffraction recognizes the Lippmann-Schwinger (LS) model to be the most faithful. It accounts for multiple scatterings, both in transmission and reflection. Iterative forward models that solve the LS equation have

show abstract

“…The structure of a mini-camera is such that the beam propagation is divided into three general processes based on their different propagation models. We derived the light-field distribution of the reflection on the screen through a detailed analysis of the model as well as a calculation using the angular spectrum method (ASM) [6] and the combined aperture method [4]. Based on the theoretical model, we found that the experimental results were in agreement with the corresponding simulation results with little error.…”

Section: Introductionmentioning

confidence: 98%

Analysis of Mini-Camera's Cat-Eye Retro-Reflection for Characterization of Diffraction Rings and Arrayed Spots

et al. 2019

View full text Add to dashboard Cite

Mini-cameras are one of several emerging types of cat-eye devices using small lenses with insufficient retro-reflection for traditional detection systems to identify. Based on a structural analysis of these devices, this paper provides an accurate theoretical description of the received beam profile. The simulated and experimental results have good similarity in terms of profile shapes and trends with different incident angles and defocus distances. An analysis of the detection conditions and the reflection image features described in this article can thus be applied to hidden camera detection. Mini-cameras can be detected according to these features of the received beam profiles.

show abstract

Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates

Cited by 16 publications

References 18 publications

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

Three-Dimensional Optical Diffraction Tomography With Lippmann-Schwinger Model

Analysis of Mini-Camera's Cat-Eye Retro-Reflection for Characterization of Diffraction Rings and Arrayed Spots

Contact Info

Product

Resources

About