The analog holographic wavefront sensor (AHWFS) is a simple and robust solution to wavefront sensing in turbulent environments. Here, the ability of a photopolymer based AHWFS to detect refractively generated spherical aberration is modelled and verified

Branigan, Emma

Martin, Suzanne

Murphy, Kevin

Sheehan, Matthew

English

Arrow@TUDublin

Technological University Dublin ARROW@TU Dublin Conference Papers Centre for Industrial and Engineering Optics 2022-7 Modelling spherical aberration detection in an analog holographic wavefront sensor Emma Branigan Technological University Dublin, emma.branigan@tudublin.ie Suzanne Martin Technological University Dublin, suzanne.martin@tudublin.ie Matthew Sheehan Technological University Dublin, matthew.sheehan@tudublin.ie See next page for additional authors Follow this and additional works at: https://arrow.tudublin.ie/cieocon2  Part of the Numerical Analysis and Computation Commons, and the Optics Commons Recommended Citation E. Branigan, S. Martin, M. Sheehan, and K. Murphy, "Modelling spherical aberration detection in an analog holographic wavefront sensor," in Imaging and Applied Optics Congress 2022 (3D, AOA, COSI, ISA, pcAOP), Technical Digest Series (Optica Publishing Group, 2022), paper OF2B.4. DOI: 10.1364/AOA.2022.OF2B.4 This Conference Paper is brought to you for free and open access by the Centre for Industrial and Engineering Optics at ARROW@TU Dublin. It has been accepted for inclusion in Conference Papers by an authorized administrator of ARROW@TU Dublin. For more information, please contact arrow.admin@tudublin.ie, aisling.coyne@tudublin.ie, gerard.connolly@tudublin.ie. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License Funder: Science Foundation Ireland Authors Emma Branigan, Suzanne Martin, Matthew Sheehan, and Kevin Murphy This conference paper is available at ARROW@TU Dublin: https://arrow.tudublin.ie/cieocon2/43 Modelling spherical aberration detection in ananalog holographic wavefront sensorEmma Branigan1, Suzanne Martin1, Matthew Sheehan2, Kevin Murphy1,∗1. Centre for Industrial and Engineering Optics, School of Physics & Clinical & Optometric Sciences, TU Dublin2. School of Physics & Clinical & Optometric Sciences, TU Dublin*kevin.p.murphy@tudublin.ieAbstract: The analog holographic wavefront sensor (AHWFS) is a simple and robust so-lution to wavefront sensing in turbulent environments. Here, the ability of a photopolymer-based AHWFS to detect refractively generated spherical aberration is modelled and veri-fied. 1. Introduction1.1. Wavefront sensingReal-time compensation for both low and high order aberrations (e.g. defocus and spherical aberration) can beapplied through adaptive optics systems, typically comprised of corrective optics and a wavefront sensor (WFS).The role of the WFS is to detect the magnitude and type of the aberrations present in an incident wavefrontand, for many years, has been used as an assistive technology for corrective procedures such as laser refractivesurgery [1] and high-resolution imaging in astronomy [2].When a wavefront containing arbitrary aberration modes is incident on the AHWFS it is optically decomposedinto a set of paired diffracted beams [3–5] associated with each mode and are detected by a photodiode array. Asimple ratio of intensities, given by Eq. 1 [6], determines the type and magnitude of the aberration. This elegantalgorithm for wavefront fitting offers a significant reduction in computational overhead compared to other WFSand its speed is limited only by the chosen photodiode. It also ensures insensitivity to scintillation and obscuration.WB =g−(a)−g+(a)g−(a)+g+(a)(1)1.2. A third-order approximation of spherical aberrationWavefront aberrations can be considered in terms of geometrical ray intercept errors at the image plane [7], oras optical path length differences. Here, we employ the former technique in order to quantify the magnitude ofspherical aberration introduced by a series of refractive elements. This treatment of the geometrical aberrationswas first published by Ludwig von Seidel and includes all of the third order terms in a centered system of sphericalsurfaces [8]. Longitudinal spherical aberration (LSA) can be defined as the difference between the paraxial andthe marginal foci. LSA can be related to the Seidel aberration coefficient by Eq. 2, where A is the Seidel aberrationcoefficient, ∆z is the magnitude of LSA, R is the reference sphere radius and y is the ray height.A =∆z3R2y2(2)2. Materials and methodsThe reproducibility and chemical post-processing and developing of materials such as silver halide and DCG aresome of the major material challenges that can be avoided through recording multiplexed holographic opticalelements (HOE) in photopolymers. Here we use a self-developing acrylamide-based photopolymer which is massproducible [9, 10] and has good reproducibility, from one volume hologram to the next, without post-processing.We have previously shown that various powers of the defocus aberration, within a range of +/-15.0D, can bedetected by a photopolymer-based AHWFS [11]. A biconvex refractive lens was recorded holographically toproduce two extremes of a sensing range. The result was the separate recording of a holographic converging lensand a holographic diverging lens. Here, in addition to improved results for defocus detection, we seek to extendthe sensing capability of the AHWFS to include spherical aberration. First a theoretical model was developed toOF2B.4 Imaging and Applied Optics Congress 2022 (3D, AOA, COSI, ISA, pcAOP) @ Optica Publishing Group 2022investigate the angular selectivity of the recording medium at various layer thicknesses to establish the capabilityof the device. By changing both the thickness and the central recording spatial frequency, it was possible to tunethe sensitivity of the device. A Zemax model of the optical system gave a magnitude of the Seidel aberrationcoefficient for spherical aberration, from which the LSA was calculated by Eq. 2. Trigonometry was then used topredict the angular shift of the fringes inside the recording medium.3. ResultsTwo biconvex lenses arranged in a 4f imaging system, with focal lengths of 50mm and 35mm respectively, weremodelled with Zemax optical design software at λ = 532nm. The magnitude of spherical aberration generated bythe lens combination was 0.67λ or 2.85µm, given in Seidel aberration coefficients (Fig. 1). The LSA was modelledacross an entrance beam of 5.7mm in diameter. At the marginal rays, ±2.85mm in height, the magnitude of ∆zwas greatest and caused a 1.69◦ shift off the Bragg reconstruction angle. However, as ∆z ∝ y2 this shift is notablysmaller with a reduction in ray height.Fig. 1: Output of Zemax model of the recording system,showing 0.67λ (2.85µm) of spherical aberration.50 60 70 80 90 100 110 120 130 140 150Grating thickness ( m)00.511.522.53Full Width Half Maximum (degrees)497 lines/mm816 lines/mm1050 lines/mm1250 lines/mmFig. 2: Modelled grating angular selectivity, describedby the Bragg diffraction efficiency curve FWHM, atvarious spatial frequencies & layer thickness.The angular selectivity of gratings produced at central spatial frequencies of 497, 816, 1050, and 1250 lines/mmwas examined at layer thicknesses from 50µm to 150µm (Fig. 2). As the spatial frequency and layer thicknesswere increased, it was possible to significantly increase the sensitivity of the grating to enable the detection ofthe small angular shift caused by the introduction of the spherical aberration. An AHWFS consisting of a HOEmultiplexed with a collimated beam, 0µm, and +2.85µm of spherical aberration was produced experimentally.4. ConclusionSpherical aberration induced by solely refractive elements and the angular selectivity of a holographic grating inan acrylamide-based photopolymer have been modelled. By predicting the recording conditions and grating be-haviour necessary to introduce and detect a spherical aberration, we can extend the sensing capability of the AH-WFS through experimental work. This has been shown for an AHWFS with a sensing range of 0µm to +2.85µmof spherical aberration. Multiplexing a HOE with both defocus, as shown previously, and spherical aberration willallow for the simultaneous detection of both aberration modes by a single sensor.References1. J. Schwiegerling, Proc. SPIE, 9186, 91860U (2014).2. S. Esposito et al., Proc. SPIE, 814902, 8149 (2011).3. F. Kong and A. Lambert, Appl. Opt., 55, (2016).4. G. P. Andersen et al., Optical Engineering, 48, 8, (2009).5. A. Zepp, S. Gladysz, and K. Stein, Advanced Optical Technologies, 2, (2013).6. M. J. Booth, Proc. SPIE, 5162, (2003).7. M. J. Kidger ”Aberrations”, in Fundamental Optical Design, SPIE Press, (2001).8. M. Born and E. Wolf, ”Geometrical theory of aberrations”, in Principles of Optics, Cambridge University Press, (2003).9. D. Vather et al., Appl. Opt., 57, 22 (2018).10. B. Rogers, S. Martin and I. Naydenova, Polymers, 12, 4, 743, (2020).11. E. Branigan et al., Proc. SPIE, 11860, 118600H, (2021).OF2B.4 Imaging and Applied Optics Congress 2022 (3D, AOA, COSI, ISA, pcAOP) @ Optica Publishing Group 2022

Modelling spherical aberration detection in an analog holographic wavefront sensor

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Modelling spherical aberration detection in an analog holographic wavefront sensor

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