Fat rays revisited: a synthesis of physical and geometrical optics with Gauβlets

Greynolds, Alan W.

doi:10.1117/12.2073087

Cited by 6 publications

(4 citation statements)

References 8 publications

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“…However, secondary beamlets can be traced from these intermediate structures to aid in the accuracy of the simulation. 52 At the focal plane of a diffraction-limited system, the rays are highly concentrated while the diffracted field spreads out considerably (e.g., the Airy disk). Because of GBD's reliance on ray tracing, it cannot represent diffraction from structure in the focal plane well without redecomposing the field.…”

Section: Hybrid Propagation Physicsmentioning

confidence: 99%

Hybrid propagation physics for the design and modeling of astronomical observatories: a coronagraphic example

Ashcraft,

Douglas,

Kim

et al. 2023

J. Astron. Telesc. Instrum. Syst.

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.For diffraction-limited optical systems, an accurate physical optics model is necessary to properly evaluate instrument performance. Astronomical observatories outfitted with coronagraphs for direct exoplanet imaging require physical optics models to simulate the effects of misalignment and diffraction. Accurate knowledge of the observatory’s point-spread function (PSF) is integral for the design of high-contrast imaging instruments and simulation of astrophysical observations. The state of the art is to model the misalignment, ray aberration, and diffraction across multiple software packages, which complicates the design process. Gaussian beamlet decomposition (GBD) is a ray-based method of diffraction calculation that has been widely implemented in commercial optical design software. By performing the coherent calculation with data from the ray model of the observatory, the ray aberration errors can be fed directly into the physical optics model of the coronagraph, enabling a more integrated model of the observatory. We develop a formal algorithm for the transfer-matrix method of GBD and evaluate it against analytical results and a traditional physical optics model to assess the suitability of GBD for high-contrast imaging simulations. Our GBD simulations of the observatory PSF, when compared to the analytical Airy function, have a sum-normalized RMS difference of ≈10 − 6. These fields are then propagated through a Fraunhofer model of an exoplanet imaging coronagraph where the mean residual numerical contrast is 4 × 10 − 11, with a maximum near the inner working angle at 5 × 10 − 9. These results show considerable promise for the future development of GBD as a viable propagation technique in high-contrast imaging. We developed this algorithm in an open-source software package and outlined a path for its continued development to increase the accuracy and flexibility of diffraction simulations using GBD.

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Section: Hybrid Propagation Physicsmentioning

confidence: 99%

Hybrid propagation physics for the design and modeling of astronomical observatories: a coronagraphic example

Ashcraft,

Douglas,

Kim

et al. 2023

J. Astron. Telesc. Instrum. Syst.

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“…For the MEM, the decomposition time is the time spent on the integration to calculate the coefficients of the higher-order modes. For the GBD, it is the time needed for the QR decomposition to solve Equation (27). Therefore, the decomposition time depends not only on the mode order and grid size but also on the properties of the input field.…”

Section: Criteria For a Fair Comparisonmentioning

confidence: 99%

“…Another decomposition method, which involves the concept of decomposing an arbitrary wavefield into Gaussian beams, was proposed by Popov in 1982 for acoustics [26]. A similar idea was conceived by Graynolds in 1981 [27], when he began developing a ray-tracing code that eventually became the commercial software ASAP (version number 1.0) and published his paper on the subject in 1985 [27,28]. In the original description, the fundamental Gaussians were all parallel, all had the same waist size, and the waist was positioned in the decomposition plane.…”

Section: Introductionmentioning

confidence: 99%

“…Regarding the GBD, the publication status seems fairly sparse. About 30 years after the proposal of the basic concept of decomposing arbitrary electric fields into fundamental Gaussian beams, in Graynolds' overview article [27], he revisited the GBD, described the method's history and development over time, and provided detailed implementation steps for the field decomposition, tracing, and computation of the resulting field in the target plane. In [42], various examples of modeling complex optical phenomena using the GBD were demonstrated, including interference and diffraction.…”

Section: Introductionmentioning

confidence: 99%

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Method Comparison for Simulating Non-Gaussian Beams and Diffraction for Precision Interferometry

Zhao,

Tao,

Weber

et al. 2023

Sensors

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In the context of simulating precision laser interferometers, we use several examples to compare two wavefront decomposition methods—the Mode Expansion Method (MEM) and the Gaussian Beam Decomposition (GBD) method—for their precision and applicability. To assess the performance of these methods, we define different types of errors and study their properties. We specify how the two methods can be fairly compared and based on that, compare the quality of the MEM and GBD through several examples. Here, we test cases for which analytic results are available, i.e., non-clipped circular and general astigmatic Gaussian beams, as well as clipped circular Gaussian beams, in the near, far, and extremely far fields of millions of kilometers occurring in space-gravitational wave detectors. Additionally, we compare the methods for aberrated wavefronts and their interaction with optical components by testing reflections from differently curved mirrors. We find that both methods can generally be used for decomposing non-Gaussian beams. However, which method is more accurate depends on the optical system and simulation settings. In the given examples, the MEM more accurately describes non-clipped Gaussian beams, whereas for clipped Gaussian beams and the interaction with surfaces, the GBD is more precise.

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An open-source gaussian beamlet decomposition tool for modeling astronomical telescopes

Ashcraft¹,

Douglas

2020

Modeling, Systems Engineering, and Project Management for Astronomy IX

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In the pursuit of directly imaging exoplanets, the high-contrast imaging community has developed a multitude of tools to simulate the performance of coronagraphs on segmented-aperture telescopes. As the scale of the telescope increases and science cases move toward shorter wavelengths, the required physical optics propagation to optimize high-contrast imaging instruments becomes computationally prohibitive. Gaussian Beamlet Decomposition (GBD) is an alternative method of physical optics propagation that decomposes an arbitrary wavefront into paraxial rays. These rays can be propagated expeditiously using ABCD matrices, and converted into their corresponding Gaussian beamlets to accurately model physical optics phenomena without the need of diffraction integrals. The GBD technique has seen recent development and implementation in commercial software (e.g. FRED, CODE V, ASAP) 1-3 but appears to lack an open-source platform. We present a new GBD tool developed in Python to model physical optics phenomena, with the goal of alleviating the computational burden for modeling complex apertures, many-element systems, and introducing the capacity to model misalignment errors. This study demonstrates the synergy of the geometrical and physical regimes of optics utilized by the GBD technique, and is motivated by the need for advancing open-source physical optics propagators for segmentedaperture telescope coronagraph design and analysis. This work illustrates GBD with Poisson's spot calculations and show significant runtime advantage of GBD over Fresnel propagators for many-element systems.

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Fat rays revisited: a synthesis of physical and geometrical optics with Gauβlets

Cited by 6 publications

References 8 publications

Hybrid propagation physics for the design and modeling of astronomical observatories: a coronagraphic example

Hybrid propagation physics for the design and modeling of astronomical observatories: a coronagraphic example

Method Comparison for Simulating Non-Gaussian Beams and Diffraction for Precision Interferometry

An open-source gaussian beamlet decomposition tool for modeling astronomical telescopes

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