Application of radial basis functions to shape description in a dual‐element off‐axis eyewear display: Field‐of‐view limit

Cakmakci, Ozan; Vo, Sophie; Thompson, Kevin P.; Rolland, Jannick P.

doi:10.1889/jsid16.11.1089

Cited by 11 publications

(3 citation statements)

References 19 publications

(25 reference statements)

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“…Guided by this result, we applied RBFs in a dual-element catadioptric magnifier system where the mirror was freeform. We have been able to extend the field of view from 20 degrees full-field to 25 degrees full-field replacing the x-y polynomial terms of the mirror with RBFs [4]. We also extended the pupil size from 8 mm to 12 mm in the dual-element catadioptric magnifier by using an RBF description on the freeform mirror [5].…”

Section: Application Of Radial Basis Functions To Represent Optical Fmentioning

confidence: 99%

Application of radial basis functions to represent optical freeform surfaces

et al. 2010

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Section: Application Of Radial Basis Functions To Represent Optical Fmentioning

confidence: 99%

Application of radial basis functions to represent optical freeform surfaces

et al. 2010

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“…In this section, guided by the results given in Table 2, we apply the radial basis function framework to the description of optical mirror shapes in a dual-element magnifier and study field of view 26 and pupil size 27 limits in this section.…”

Section: Dual-element Design Revisited: Pupil Size and Field Of Viementioning

confidence: 99%

Meshfree approximation methods for free-form surface representation in optical design with applications to head-worn displays

et al. 2008

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In this paper, we summarize our initial experiences in designing head-worn displays with free-form optical surfaces. Typical optical surfaces implemented in raytrace codes today are functions mapping two dimensional vectors to real numbers. The majority of optical designs to date have relied on conic sections and polynomials as the functions of choice. The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries. The choice of polynomials from the point of view of surface description can be challenged. The advantage of using polynomials is that the wavefront aberration function is typically expanded in polynomials. Therefore, a polynomial surface description may link a designer's understanding of wavefront aberrations and the surface description. The limitations of using multivariate polynomials are described by a theorem due to Mairhuber and Curtis from approximation theory. In our recent work, we proposed and applied radial basis functions to represent optical surfaces as an alternative to multivariate polynomials. We compare the polynomial descriptions to radial basis functions using the MTF criteria. The benefits of using radial basis functions for surface description are summarized in the context of specific magnifier systems, i.e., head-worn displays. They include, for example, the performance increase measured by the MTF, or the ability to increase the field of view or pupil size. Full-field displays are used for node placement within the field of view for the dual-element head-worn display.

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“…With the emergence of slow servo diamond turning, freeform optical elements are beginning to appear in rotationally nonsymmetric precision optics, e.g. head worn displays [1], IR-seekers [2], and illumination systems [3]. Freeform surfaces may be described by full aperture polynomials, as for example Zernike polynomials [4], or other descriptions such as splines [5], and radial basis functions (RBFs) [6,7].…”

Section: Introductionmentioning

confidence: 99%

Comparative assessment of freeform polynomials as optical surface descriptions

Kaya¹,

Thompson²,

Rolland³

2012

Opt. Express

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Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enables the fabrication of freeform optics, or more specifically, optical surfaces for imaging applications that are not rotationally symmetric. Various forms of polynomials for describing freeform optical surfaces exist in optical design and to support fabrication. A popular method is to add orthogonal polynomials onto a conic section. In this paper, recently introduced gradient-orthogonal polynomials are investigated in a comparative manner with the widely known Zernike polynomials. In order to achieve numerical robustness when higher-order polynomials are required to describe freeform surfaces, recurrence relations are a key enabler. Results in this paper establish the equivalence of both polynomial sets in accurately describing freeform surfaces under stringent conditions. Quantifying the accuracy of these two freeform surface descriptions is a critical step in the future application of these tools in both advanced optical system design and optical fabrication.

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Application of radial basis functions to shape description in a dual‐element off‐axis eyewear display: Field‐of‐view limit

Cited by 11 publications

References 19 publications

Application of radial basis functions to represent optical freeform surfaces

Application of radial basis functions to represent optical freeform surfaces

Meshfree approximation methods for free-form surface representation in optical design with applications to head-worn displays

Comparative assessment of freeform polynomials as optical surface descriptions

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