Freeform surface descriptions. Part I: Mathematical representations

Broemel, Anika; Lippmann, Uwe; Groß, Herbert

doi:10.1515/aot-2017-0030

Cited by 19 publications

(11 citation statements)

References 14 publications

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“…However, in real systems with a large field of view and prominent pupil aberrations, the real chief rays intersect the optical axis often in a considerable distance from the common pupil plane. Thus, in order to provide lens designer with point-imaging properties of the system, the real chief ray is selected as a reference ray and the individual locations of the exit pupil reference spheres are assigned to each field point; see Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) requires subtraction of two terms, each with the order of magnitude similar to the length of the optical system (typically hundreds of mm), to obtain the wavefront error, which is measured with the multiple of the wavelength. Thus, in the past formulas reducing the demand on the numerical precision were developed [3].…”

Section: The Optical Path Difference (Opd) Formulamentioning

confidence: 99%

“…a sphere, a conic, or a biconic. The freeform sag contribution is added to characterize the deviation from the basic shape and is the part allowing for the direct correction of higher order aberrations [18].…”

Section: Freeform Opticsmentioning

confidence: 99%

“…properties [17][18][19] were developed. After the design stage, it is necessary to assess the performance of the "as-built" freeform system.…”

Section: Chapter Introductionmentioning

confidence: 99%

“…The geometry for deriving the OPD resulting from refraction on the surface of an ideal incoming wavefront.Thus, OPD accumulated along the real ray (RR) as a result of refraction is obtained as the deviation from the spherical wavefront:=´̅ ̅̅̅̅ −´̅ ̅̅̅̅ = ´̅ ̅̅̅̅ − ̅̅̅̅ (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). …”

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confidence: 99%

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Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

Oleszko

Groß

2018

Appl. Opt.

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The application of freeform elements in optical systems increases the number of variables available for correction. This creates the potential to design compact systems with excellent imaging performance. However, it is non-trivial to determine which configuration of the system to choose and where to place the freeform element to obtain the best design. The knowledge of aberration distribution in the system is very helpful in answering these questions. In the following paper, we analyze Zernike surface contributions to the total wave aberration in non-symmetric freeform mirror systems using the method introduced in [J. Opt. Soc. Am. A34, 1856 (2017)JOAOD60740-323210.1364/JOSAA.34.001856]. We demonstrate the benefits of the proposed method in determining effective location of the freeform element and in finding critical differences between possible configurations. By analyzing surface contributions to the total wave aberration characterized by Zernike fringe coefficients, it is possible to find solutions corrected for aberrations of orders higher than the order of coefficients used for freeform sag contribution described with the same Zernike polynomial set.

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Section: The Optical Path Difference (Opd) Formulamentioning

confidence: 99%

Section: Freeform Opticsmentioning

confidence: 99%

“…properties [17][18][19] were developed. After the design stage, it is necessary to assess the performance of the "as-built" freeform system.…”

Section: Chapter Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

Oleszko

Groß

2018

Appl. Opt.

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“…The advantages of freeform are weight and space reduction, image enhancement, and aberrations' reduction. A freeform surface mathematical representation has also been recently proposed [8]. Nevertheless, manufacture methods and processes evolve to obtain symmetrical and asymmetrical freeform surfaces [7,9,10].…”

Section: Introductionmentioning

confidence: 99%

Freeform geometrical optics II: from parametric representation to CAD/CAM

et al. 2019

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Freeform optical surfaces are of great importance because of two main properties. The first is their ability to enhance the image quality of image-forming optical systems while the second is their inherent reduction in the number of surfaces in image and non-image forming optical systems. However, the main characteristic of freeform surfaces is that they lack symmetry about any spatial axis. This attribute allows describing freeform surfaces with a mathematical parametric representation. Unfortunately, parametric representation can be extremely extended. On the other hand, when describing freeform surfaces, the explicit representation is commonly preferred because of its compactness and CAD-format exportable easiness. Parametrically represented freeform surfaces can be nonetheless exported to a CAD format with no significant departure of surface shape, as shown here. The vector method presented here guarantee that the surface's sampling density be proportional to the irradiance on the surface.

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Optical design of a freeform, gradient-index, head-mounted display

Boyd

2023

Opt. Eng.

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.I present the results of an optical design study into the performance benefits of non-rotationally symmetric “freeform” gradient-index (GRIN) media on a pupil-relay head-mounted display. A range of design variants are presented based on freeform-GRIN lenses consisting of ternary base-material combinations that are enabled by recent developments in additive manufacture. The optical performance of these designs is compared to homogeneous solutions comprising combinations of spherical, aspheric, toric, and freeform surfaces. I show that freeform-GRIN media represent powerful degrees of freedom for aberration correction in tilted and off-axis optical systems, performing comparably to homogeneous freeform optics while illustrating significant potential reductions in lens count and mass.

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Freeform surface descriptions. Part I: Mathematical representations

Cited by 19 publications

References 14 publications

Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

Freeform geometrical optics II: from parametric representation to CAD/CAM

Optical design of a freeform, gradient-index, head-mounted display

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