2023
Yesiltepe, M.; Bauer, A.; Karci, O.; Rolland, J. P.
Sigma vector calculations in nodal aberration theory and experimental validation using a Cassegrain telescope Journal Article
In: Optics Express, vol. 31, iss. 25, pp. 42373-42387, 2023.
Abstract | Links | BibTeX | Tags: CeFO related, design
@article{Yesiltepe2023,
title = {Sigma vector calculations in nodal aberration theory and experimental validation using a Cassegrain telescope},
author = {M. Yesiltepe and A. Bauer and O. Karci and J. P. Rolland},
doi = {https://doi.org/10.1364/OE.502744},
year = {2023},
date = {2023-12-01},
urldate = {2023-12-01},
journal = {Optics Express},
volume = {31},
issue = {25},
pages = {42373-42387},
abstract = {Nodal Aberration Theory (NAT) was developed to explain the field dependency of aberration field centers in the image plane of nominally rotationally symmetric optical systems that have lost their symmetry through misalignments. A new insight into the theory led to calculating the sigma vectors, which locate the aberration field centers, using the angle between a real-ray trace of the optical axis ray (OAR) and the normal of the local surface where “local” refers to the object and image optical spaces of that surface. Here, we detail the sigma vector calculations for general optical systems and provide an experimental investigation of a misaligned system with a high-precision customized Cassegrain telescope. In the simulations, a Newtonian telescope, a Cassegrain telescope, and a three-mirror anastigmat telescope were misaligned intentionally in ray-tracing software. The sigma vectors were calculated analytically for the third-order aberrations of astigmatism and coma. Experimentally, the same perturbations were implemented for the Cassegrain telescope system, and the aberrations were quantified through interferometric measurements on a grid of field points in the image plane that verified the analytical derivation and simulations.},
keywords = {CeFO related, design},
pubstate = {published},
tppubtype = {article}
}
Nodal Aberration Theory (NAT) was developed to explain the field dependency of aberration field centers in the image plane of nominally rotationally symmetric optical systems that have lost their symmetry through misalignments. A new insight into the theory led to calculating the sigma vectors, which locate the aberration field centers, using the angle between a real-ray trace of the optical axis ray (OAR) and the normal of the local surface where “local” refers to the object and image optical spaces of that surface. Here, we detail the sigma vector calculations for general optical systems and provide an experimental investigation of a misaligned system with a high-precision customized Cassegrain telescope. In the simulations, a Newtonian telescope, a Cassegrain telescope, and a three-mirror anastigmat telescope were misaligned intentionally in ray-tracing software. The sigma vectors were calculated analytically for the third-order aberrations of astigmatism and coma. Experimentally, the same perturbations were implemented for the Cassegrain telescope system, and the aberrations were quantified through interferometric measurements on a grid of field points in the image plane that verified the analytical derivation and simulations.
Xiong, P.; Nikolov, D. K.; Cheng, F.; Rolland, J. P.; Vamivakas, A. N.
All-dielectric hybrid VIS-NIR dual-function metasurface Online
2023, visited: 13.10.2023.
Abstract | Links | BibTeX | Tags: CeFO related, design
@online{Xiong2023,
title = {All-dielectric hybrid VIS-NIR dual-function metasurface},
author = {P. Xiong and D. K. Nikolov and F. Cheng and J. P. Rolland and A. N. Vamivakas },
url = {https://arxiv.org/abs/2310.09393},
doi = {https://doi.org/10.48550/arXiv.2310.09393},
year = {2023},
date = {2023-10-13},
urldate = {2023-10-13},
abstract = {Metasurfaces are a promising technology that can serve as a compact alternative to conventional optics while providing multiple functions depending on the properties of the incident light, such as the wavelength, polarization, and incident angle. Here, we demonstrate a hybrid VIS-NIR dielectriac metasurface that can reflect 940 nm light into a specified direction while transmitting visible light (450-750 nm). The dual functionality is realized by combining an aperiodic distributed Bragg reflector with dielectric meta-tokens. Experimental demonstration is also reported, showing an anomalous reflection of near-infrared (NIR) light within a 20o full field-of-view (FOV) and the transmission of wavelengths from 450 nm to 750 nm.},
keywords = {CeFO related, design},
pubstate = {published},
tppubtype = {online}
}
Metasurfaces are a promising technology that can serve as a compact alternative to conventional optics while providing multiple functions depending on the properties of the incident light, such as the wavelength, polarization, and incident angle. Here, we demonstrate a hybrid VIS-NIR dielectriac metasurface that can reflect 940 nm light into a specified direction while transmitting visible light (450-750 nm). The dual functionality is realized by combining an aperiodic distributed Bragg reflector with dielectric meta-tokens. Experimental demonstration is also reported, showing an anomalous reflection of near-infrared (NIR) light within a 20o full field-of-view (FOV) and the transmission of wavelengths from 450 nm to 750 nm.
Goodsell, J.; Xiong, P.; Nikolov, D. K.; Vamivakas, A. N.; Rolland, J. P.
Metagrating meets the geometry-based efficiency limit for AR waveguide in-couplers Journal Article
In: Optics Express, vol. 31, iss. 3, pp. 4599-4614, 2023.
Abstract | Links | BibTeX | Tags: CeFO related, design
@article{Goodsell2023,
title = {Metagrating meets the geometry-based efficiency limit for AR waveguide in-couplers},
author = {J. Goodsell and P. Xiong and D. K. Nikolov and A. N. Vamivakas and J. P. Rolland},
doi = {https://doi.org/10.1364/OE.480092},
year = {2023},
date = {2023-01-24},
urldate = {2023-01-24},
journal = {Optics Express},
volume = {31},
issue = {3},
pages = {4599-4614},
abstract = {Recently, augmented reality (AR) displays have attracted considerable attention due to the highly immersive and realistic viewer experience they can provide. One key challenge of AR displays is the fundamental trade-off between the extent of the field-of-view (FOV) and the size of the eyebox, set by the conservation of etendue sets this trade-off. Exit-pupil expansion (EPE) is one possible solution to this problem. However, it comes at the cost of distributing light over a larger area, decreasing the overall system's brightness. In this work, we show that the geometry of the waveguide and the in-coupler sets a fundamental limit on how efficient the combiner can be for a given FOV. This limit can be used as a tool for waveguide designers to benchmark the in-coupling efficiency of their in-coupler gratings. We design a metasurface-based grating (metagrating) and a commonly used SRG as in-couplers using the derived limit to guide optimization. We then compare the diffractive efficiencies of the two types of in-couplers to the theoretical efficiency limit. For our chosen waveguide geometry, the metagrating's 28% efficiency surpasses the SRG's 20% efficiency and nearly matches the geometry-based limit of 29% due to the superior angular response control of metasurfaces compared to SRGs. This work provides new insight into the efficiency limit of waveguide-based combiners and paves a novel path toward implementing metasurfaces in efficient waveguide AR displays.},
keywords = {CeFO related, design},
pubstate = {published},
tppubtype = {article}
}
Recently, augmented reality (AR) displays have attracted considerable attention due to the highly immersive and realistic viewer experience they can provide. One key challenge of AR displays is the fundamental trade-off between the extent of the field-of-view (FOV) and the size of the eyebox, set by the conservation of etendue sets this trade-off. Exit-pupil expansion (EPE) is one possible solution to this problem. However, it comes at the cost of distributing light over a larger area, decreasing the overall system's brightness. In this work, we show that the geometry of the waveguide and the in-coupler sets a fundamental limit on how efficient the combiner can be for a given FOV. This limit can be used as a tool for waveguide designers to benchmark the in-coupling efficiency of their in-coupler gratings. We design a metasurface-based grating (metagrating) and a commonly used SRG as in-couplers using the derived limit to guide optimization. We then compare the diffractive efficiencies of the two types of in-couplers to the theoretical efficiency limit. For our chosen waveguide geometry, the metagrating's 28% efficiency surpasses the SRG's 20% efficiency and nearly matches the geometry-based limit of 29% due to the superior angular response control of metasurfaces compared to SRGs. This work provides new insight into the efficiency limit of waveguide-based combiners and paves a novel path toward implementing metasurfaces in efficient waveguide AR displays.
2019
ALEMÁN-CASTAÑEDA, LUIS A.; ALONSO, MIGUEL A.
Study of reflectors for illumination via conformal maps Journal Article
In: Optics Letters, vol. 44, no. 15, pp. 3809-3812, 2019.
Abstract | Links | BibTeX | Tags: design, related
@article{ALONSOALEMAN2019,
title = {Study of reflectors for illumination via conformal maps},
author = {LUIS A. ALEMÁN-CASTAÑEDA AND MIGUEL A. ALONSO},
editor = {Optical Society of America },
doi = {https://doi.org/10.1364/OL.44.003809},
year = {2019},
date = {2019-07-02},
urldate = {2019-07-02},
journal = {Optics Letters},
volume = {44},
number = {15},
pages = {3809-3812},
abstract = {We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map that transforms the reflector’s shape into a curve that describes light’s direction after reflection. Both segmented reflectors and continuous reflectors are discussed, illustrating how certain reflector characteristics become apparent under this transformation. This method can also be used to study extended sources via translations.},
keywords = {design, related},
pubstate = {published},
tppubtype = {article}
}
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map that transforms the reflector’s shape into a curve that describes light’s direction after reflection. Both segmented reflectors and continuous reflectors are discussed, illustrating how certain reflector characteristics become apparent under this transformation. This method can also be used to study extended sources via translations.
2018
Schiesser, Eric M.; Bahk, Seung-Whan; Bromage, Jake; Rolland, Jannick P.
Gaussian curvature and stigmatic imaging relations for the design of an unobscured reflective relay Journal Article
In: Optics Letters, no. 20, pp. 4855-4858, 2018.
Abstract | Links | BibTeX | Tags: CeFO related, design
@article{Schiesser2018,
title = {Gaussian curvature and stigmatic imaging relations for the design of an unobscured reflective relay},
author = {Eric M. Schiesser and Seung-Whan Bahk and Jake Bromage and Jannick P. Rolland},
url = {https://doi.org/10.1364/OL.43.004855},
doi = {10.1364/OL.43.004855},
year = {2018},
date = {2018-10-03},
journal = {Optics Letters},
number = {20},
pages = {4855-4858},
abstract = {We derive the relationship between Coddington's equations and the Gaussian curvature for a stigmatic reflective imaging system. This relationship allows parameterizing off-axis conic optical systems using traditional first-order optics by considering the effective curvature at the center of the off-axis sections. Specifically, we demonstrate parameterizing the system requirements of a 2{texttimes} achromatic image relay for a terawatt laser system. This system required both collimation (far-field) and pupil imaging (near-field) simultaneously. Long working distances and specific spatial constraints limited the available layout options for the imaging components. By parameterizing these system requirements and packaging constraints, the final specifications could be quickly iterated, while allowing for flexibility in the layout of the system during a multi-year conceptual period.},
keywords = {CeFO related, design},
pubstate = {published},
tppubtype = {article}
}
We derive the relationship between Coddington's equations and the Gaussian curvature for a stigmatic reflective imaging system. This relationship allows parameterizing off-axis conic optical systems using traditional first-order optics by considering the effective curvature at the center of the off-axis sections. Specifically, we demonstrate parameterizing the system requirements of a 2{texttimes} achromatic image relay for a terawatt laser system. This system required both collimation (far-field) and pupil imaging (near-field) simultaneously. Long working distances and specific spatial constraints limited the available layout options for the imaging components. By parameterizing these system requirements and packaging constraints, the final specifications could be quickly iterated, while allowing for flexibility in the layout of the system during a multi-year conceptual period.
Papa, Jonathan C.; Howard, J.; Rolland, J. P.
Starting point designs for freeform four-mirror systems Journal Article
In: Optical Engineering, vol. 57, no. 10, pp. 101705, 2018.
Abstract | Links | BibTeX | Tags: CeFO related, design
@article{Papa_IODC2017,
title = {Starting point designs for freeform four-mirror systems},
author = {Jonathan C. Papa and J. Howard and J. P. Rolland},
url = {https://doi.org/10.1117/1.OE.57.10.101705},
doi = {10.1117/1.OE.57.10.101705},
year = {2018},
date = {2018-06-21},
journal = {Optical Engineering},
volume = {57},
number = {10},
pages = {101705},
abstract = {Driven by the development of freeform four-mirror solutions, we review and compare analytical methods to generate starting point designs with various states of correction, surface types, symmetry, and obscuration. The advantages and disadvantages of each are examined. We have combined several concepts and techniques from the literature to analytically generate unobscured freeform starting point designs that are corrected through the third-order image degrading aberrations. The surfaces in these starting point designs are described as base off-axis conics that image stigmatically for the central field point, also known as Cartesian reflectors, with an aspheric departure “cap” (quartic with the aperture) added to the Cartesian reflectors. Tilt angles are chosen to cancel field-asymmetric field-linear astigmatism and unobscure the system. Paraxial data from an equivalent on-axis system are used to solve a system of linear equations to determine the magnitude of the aspheric departure “caps” that are placed on top of the base Cartesian reflectors, in order to eliminate the remaining third-order image degrading aberrations. In this approach, each aspheric departure “cap” is centered about the intersection of the optical-axis-ray, also known as the base ray, with the base surface, rather than being centered about the axis of rotational invariance.},
keywords = {CeFO related, design},
pubstate = {published},
tppubtype = {article}
}
Driven by the development of freeform four-mirror solutions, we review and compare analytical methods to generate starting point designs with various states of correction, surface types, symmetry, and obscuration. The advantages and disadvantages of each are examined. We have combined several concepts and techniques from the literature to analytically generate unobscured freeform starting point designs that are corrected through the third-order image degrading aberrations. The surfaces in these starting point designs are described as base off-axis conics that image stigmatically for the central field point, also known as Cartesian reflectors, with an aspheric departure “cap” (quartic with the aperture) added to the Cartesian reflectors. Tilt angles are chosen to cancel field-asymmetric field-linear astigmatism and unobscure the system. Paraxial data from an equivalent on-axis system are used to solve a system of linear equations to determine the magnitude of the aspheric departure “caps” that are placed on top of the base Cartesian reflectors, in order to eliminate the remaining third-order image degrading aberrations. In this approach, each aspheric departure “cap” is centered about the intersection of the optical-axis-ray, also known as the base ray, with the base surface, rather than being centered about the axis of rotational invariance.
Rolland, J. P.
Engineering the ultimate augmented reality display: Paths towards a digital window into the world Miscellaneous
2018.
Links | BibTeX | Tags: design, related
@misc{RollandLFW,
title = {Engineering the ultimate augmented reality display: Paths towards a digital window into the world},
author = {J. P. Rolland},
url = {http://digital.laserfocusworld.com/laserfocusworld/201806/MobilePagedArticle.action?articleId=1404125#articleId1404125},
year = {2018},
date = {2018-06-20},
issuetitle = {Laser Focus World},
volume = {June 2018},
pages = {31-34},
keywords = {design, related},
pubstate = {published},
tppubtype = {misc}
}
2017
Papa, J.; Howard, J. M.; Rolland, J. P.
Four-Mirror Freeform Design Conference
Mirror Tech/SBIR/STTR Workshop 2017, 2017.
Links | BibTeX | Tags: CeFO related, design, related
@conference{Papa_nasa,
title = {Four-Mirror Freeform Design},
author = {J. Papa and J. M. Howard and J. P. Rolland},
url = {https://spie.org/Documents/ConferencesExhibitions/Tech-Days-2017-Presentations-DRAFT.pdf},
year = {2017},
date = {2017-11-15},
booktitle = {Mirror Tech/SBIR/STTR Workshop 2017},
keywords = {CeFO related, design, related},
pubstate = {published},
tppubtype = {conference}
}
Papa, J.; Howard, J. M.; Rolland, J. P.
Starting Point Designs for Freeform Four-Mirror Systems Conference
Proceedings of the International Optical Design Conference 2017, Optical Society of America, 2017, ISBN: 978-1-943580-31-6.
Abstract | Links | BibTeX | Tags: design, related
@conference{PapaIODC17,
title = {Starting Point Designs for Freeform Four-Mirror Systems},
author = {J. Papa and J. M. Howard and J. P. Rolland},
url = {https://doi.org/10.1364/IODC.2017.ITu2A.4},
doi = {10.1364/IODC.2017.ITu2A.4},
isbn = {978-1-943580-31-6},
year = {2017},
date = {2017-07-13},
urldate = {2017-07-13},
booktitle = {Proceedings of the International Optical Design Conference 2017},
publisher = {Optical Society of America},
abstract = {Driven by the development of freeform four-mirror solutions, we compare analytical methods to generate starting point designs with various states of correction, surface types, symmetry, and obscuration. The advantages and disadvantages of each are examined.},
keywords = {design, related},
pubstate = {published},
tppubtype = {conference}
}
Driven by the development of freeform four-mirror solutions, we compare analytical methods to generate starting point designs with various states of correction, surface types, symmetry, and obscuration. The advantages and disadvantages of each are examined.
Shultz, J. A.; Suleski, T. J.
Design of a Variable Toric Lens Using Laterally Shifted Freeform Elements Conference
Freeform 2017 (Freeform, IODC, OFT), Optical Society of America, 2017.
Abstract | Links | BibTeX | Tags: design, related
@conference{Suleski17_2,
title = {Design of a Variable Toric Lens Using Laterally Shifted Freeform Elements},
author = {J. A. Shultz and T. J. Suleski },
doi = {https://doi.org/10.1364/FREEFORM.2017.JW2C.2},
year = {2017},
date = {2017-07-13},
urldate = {2017-07-13},
booktitle = {Freeform 2017 (Freeform, IODC, OFT)},
publisher = {Optical Society of America},
abstract = {We present a design process for a variable lens pair where the x and y focal lengths are varied independently of each other using laterally shifted freeform surfaces. Examples are presented.},
keywords = {design, related},
pubstate = {published},
tppubtype = {conference}
}
We present a design process for a variable lens pair where the x and y focal lengths are varied independently of each other using laterally shifted freeform surfaces. Examples are presented.
HIPPOLYTE DOURDENT ANTHONY VELLA, LUKAS NOVOTNY; ALONSO, MIGUEL A.
Birefringent masks that are optimal for generating bottle fields Journal Article
In: Optics Express, vol. 25, no. 8, pp. 9318-9332, 2017.
Abstract | Links | BibTeX | Tags: design, related
@article{AlonsoVella2017,
title = {Birefringent masks that are optimal for generating bottle fields},
author = {ANTHONY VELLA, HIPPOLYTE DOURDENT, LUKAS NOVOTNY, AND MIGUEL A. ALONSO},
editor = {OSA},
doi = {https://doi.org/10.1364/OE.25.009318},
year = {2017},
date = {2017-04-17},
journal = {Optics Express},
volume = {25},
number = {8},
pages = {9318-9332},
abstract = {An optical bottle field containing a three-dimensional intensity null at the focal point can be generated by placing a spatially inhomogeneous birefringent mask at the pupil of an aplanatic high-NA focusing system. We derive the optimal birefringence distribution for which a uniformly polarized input beam is converted into a bottle field with the sharpest possible null in intensity. We show that a stress engineered optical (SEO) window, which has a radially varying retardance, followed by a half-wave plate, performs nearly as well as the optimal solution. Experimental results corroborate that an SEO element can be used to generate a bottle field.},
keywords = {design, related},
pubstate = {published},
tppubtype = {article}
}
An optical bottle field containing a three-dimensional intensity null at the focal point can be generated by placing a spatially inhomogeneous birefringent mask at the pupil of an aplanatic high-NA focusing system. We derive the optimal birefringence distribution for which a uniformly polarized input beam is converted into a bottle field with the sharpest possible null in intensity. We show that a stress engineered optical (SEO) window, which has a radially varying retardance, followed by a half-wave plate, performs nearly as well as the optimal solution. Experimental results corroborate that an SEO element can be used to generate a bottle field.
2016
Papa, J.; Rolland, J. P.; Howard, J.
Starting Points for Designing Freeform Four-Mirror Telescopes Conference
2016.
BibTeX | Tags: design, related
@conference{Papa2016a,
title = {Starting Points for Designing Freeform Four-Mirror Telescopes},
author = {Papa, J. and J.P. Rolland and J. Howard },
year = {2016},
date = {2016-00-00},
keywords = {design, related},
pubstate = {published},
tppubtype = {conference}
}
2015
Kitt, A.; Rolland, J. P.; Vamivakas, A. N.
Visible metasurfaces and ruled diffraction gratings: a comparison Journal Article
In: Opt. Express, vol. 5, no. 12, pp. 2895-2901, 2015.
Abstract | Links | BibTeX | Tags: design, related
@article{Kitt15,
title = {Visible metasurfaces and ruled diffraction gratings: a comparison},
author = {Kitt, A. and J. P. Rolland and A. N. Vamivakas},
doi = {https://doi.org/10.1364/OME.5.002895},
year = {2015},
date = {2015-11-23},
urldate = {2015-11-23},
journal = {Opt. Express},
volume = {5},
number = {12},
pages = {2895-2901},
abstract = {Metasurface based and physical ruling based diffraction gratings function by controlling the phase of light, but the origin of the phase control is different. Here we compare the simulated optical response of a 1800 lines/mm ruled diffraction grating blazed for 650 nm light to the response of a 1800 lines/mm phase grating meta-surface designed for efficiency in the visible. The efficiencies are comparable; the transverse electric polarized efficiency of the meta-surface based grating is similar to the transverse magnetic polarized efficiency of the ruled-grating. However, due to the different mechanisms of phase accrual, the meta-surface based grating does not exhibit grating anomalies and has low efficiency for transverse magnetic polarized light.},
keywords = {design, related},
pubstate = {published},
tppubtype = {article}
}
Metasurface based and physical ruling based diffraction gratings function by controlling the phase of light, but the origin of the phase control is different. Here we compare the simulated optical response of a 1800 lines/mm ruled diffraction grating blazed for 650 nm light to the response of a 1800 lines/mm phase grating meta-surface designed for efficiency in the visible. The efficiencies are comparable; the transverse electric polarized efficiency of the meta-surface based grating is similar to the transverse magnetic polarized efficiency of the ruled-grating. However, due to the different mechanisms of phase accrual, the meta-surface based grating does not exhibit grating anomalies and has low efficiency for transverse magnetic polarized light.
Gray, R.
2015.
Abstract | Links | BibTeX | Tags: design, related
@phdthesis{GRAY-THESIS,
title = {Investigation of the Field Dependence of the Aberration Functions of Rotationally Nonsymmetric Optical Imaging Systems},
author = {Gray, R.},
url = {https://urresearch.rochester.edu/institutionalPublicationPublicView.action?institutionalItemId=29981&versionNumber=1},
year = {2015},
date = {2015-11-06},
urldate = {2015-11-06},
abstract = {It is shown how Shack’s vector product (SVP) can be used to express the expansion of the monochromatic wavefront aberration function for rotationally symmetric optical imaging models using the H. H. Hopkins’ expansion coefficients. As a result of this research it was discovered that SVP fits naturally within the framework of 2-dimensional Geometric Algebra (GA). It is further shown how SVP can be used to define two-dimensional vectors in terms of the Zernike polynomials. The wavefront aberration function expansion is then expressed in terms of these Zernike vectors. A method for calculating the H. H. Hopkins’ expansion coefficients is described, including the calculation of the per surface, sphere/asphere, intrinsic/extrinsic expansion coefficient contributions. Methods for converting the Zernike expansion coefficients into the H. H. Hopkins’ expansion coefficients have been developed and are presented in this work. Nodal aberration theory (NAT), now well established in the literature, is presented in terms of these mathematical developments. As a quantitative validation of the NAT predications of an optical system’s field dependence, comparisons are made between the full field displays (FFDs) produced by using a double Zernike expansion of the wavefront aberration function and by application of NAT to rotationally symmetric optical imaging systems having one or more surfaces decentered and/or tilted. Validation of these developments is provided using idealized computer models of several space telescopes having one or more optical surfaces decentered and/or tilted. Initial steps toward one approach for extending NAT to include optical imaging systems containing freeform surface shapes defined by Zernike polynomials is also provided.},
keywords = {design, related},
pubstate = {published},
tppubtype = {phdthesis}
}
It is shown how Shack’s vector product (SVP) can be used to express the expansion of the monochromatic wavefront aberration function for rotationally symmetric optical imaging models using the H. H. Hopkins’ expansion coefficients. As a result of this research it was discovered that SVP fits naturally within the framework of 2-dimensional Geometric Algebra (GA). It is further shown how SVP can be used to define two-dimensional vectors in terms of the Zernike polynomials. The wavefront aberration function expansion is then expressed in terms of these Zernike vectors. A method for calculating the H. H. Hopkins’ expansion coefficients is described, including the calculation of the per surface, sphere/asphere, intrinsic/extrinsic expansion coefficient contributions. Methods for converting the Zernike expansion coefficients into the H. H. Hopkins’ expansion coefficients have been developed and are presented in this work. Nodal aberration theory (NAT), now well established in the literature, is presented in terms of these mathematical developments. As a quantitative validation of the NAT predications of an optical system’s field dependence, comparisons are made between the full field displays (FFDs) produced by using a double Zernike expansion of the wavefront aberration function and by application of NAT to rotationally symmetric optical imaging systems having one or more surfaces decentered and/or tilted. Validation of these developments is provided using idealized computer models of several space telescopes having one or more optical surfaces decentered and/or tilted. Initial steps toward one approach for extending NAT to include optical imaging systems containing freeform surface shapes defined by Zernike polynomials is also provided.
Gray, R.; Rolland, J. P.
Wavefront aberration function in terms of R.V. Shack’s vector product and Zernike polynomial vectors Journal Article
In: JOSA A, vol. 32, no. 10, pp. 1836-1847, 2015.
Abstract | Links | BibTeX | Tags: design, related
@article{GRAY15,
title = {Wavefront aberration function in terms of R.V. Shack’s vector product and Zernike polynomial vectors},
author = {Gray, R. and J. P. Rolland},
doi = {https://doi.org/10.1364/JOSAA.32.001836},
year = {2015},
date = {2015-08-18},
urldate = {2015-08-18},
journal = {JOSA A},
volume = {32},
number = {10},
pages = {1836-1847},
abstract = {Previous papers have shown how, for rotationally symmetric optical imaging systems, nodes in the field dependence of the wavefront aberration function develop when a rotationally symmetric optical surface within an imaging optical system is decentered and/or tilted. In this paper, we show how Shack’s vector product (SVP) can be used to express the wavefront aberration function and to define vectors in terms of the Zernike polynomials. The wavefront aberration function is then expressed in terms of the Zernike vectors. It is further shown that SVP fits within the framework of two-dimensional geometric algebra (GA). Within the GA framework, an equation for the third-order node locations for the binodal astigmatism term that emerge in the presence of tilts and decenters is then demonstrated. A computer model of a three-mirror telescope system is used to demonstrate the validity of the mathematical development.},
keywords = {design, related},
pubstate = {published},
tppubtype = {article}
}
Previous papers have shown how, for rotationally symmetric optical imaging systems, nodes in the field dependence of the wavefront aberration function develop when a rotationally symmetric optical surface within an imaging optical system is decentered and/or tilted. In this paper, we show how Shack’s vector product (SVP) can be used to express the wavefront aberration function and to define vectors in terms of the Zernike polynomials. The wavefront aberration function is then expressed in terms of the Zernike vectors. It is further shown that SVP fits within the framework of two-dimensional geometric algebra (GA). Within the GA framework, an equation for the third-order node locations for the binodal astigmatism term that emerge in the presence of tilts and decenters is then demonstrated. A computer model of a three-mirror telescope system is used to demonstrate the validity of the mathematical development.
2014
Thompson, K. P.; Rolland, J. P.
Cost-driven self-consistent fabrication and assembly tolerance classes Conference
Proceedings of the SPIE, vol. 9633, no. 96330U, 2014.
Abstract | Links | BibTeX | Tags: assembly, design, related
@conference{Thomsponoptifab15b,
title = {Cost-driven self-consistent fabrication and assembly tolerance classes},
author = {Thompson, K.P. and J.P. Rolland},
doi = {https://doi.org/10.1117/12.2195783},
year = {2014},
date = {2014-10-11},
urldate = {2014-10-11},
booktitle = {Proceedings of the SPIE},
volume = {9633},
number = {96330U},
abstract = {At the 1994 International Optics Design Conference, a paper was presented by the author that proposed that optics costs are often driven by the fabrication and assembly tolerances. In addition, that these tolerances fall into groups (classes) that for any given shop are set typically by the capital investment in measurement equipment that the shop has access to. The premise is then that it is essential that the optical system tolerances on fabrication, e.g. radii, element thickness, wedge, surface figure, and surface finish and on assembly e.g. component tilt and decenter and spacer thickness and wedge that are assigned by the optical designer be self-consistent with the capabilities of the shops that are solicited to provide a quotation.
In the 1994 paper, five classes of optical fabricators were identified; catalog, regular, select, premium, and ultimate (lithography). For each of these classes, representative minimum tolerances were published along with estimates of the cost increment. An important concept is that if any one tolerance falls into a tighter class, then the optical system must be built in a shop capitalized to provide that one minimum tolerance and as a result all the other tolerances can typically be moved to the tighter class with little cost impact. The primary cost impact then is driven by the class of shop dictated by the minimum tolerance. In this talk, a primary purpose is to revisit the tolerances associated with a given class of shop and update the numbers to reflect advances in the intervening two decades.},
keywords = {assembly, design, related},
pubstate = {published},
tppubtype = {conference}
}
At the 1994 International Optics Design Conference, a paper was presented by the author that proposed that optics costs are often driven by the fabrication and assembly tolerances. In addition, that these tolerances fall into groups (classes) that for any given shop are set typically by the capital investment in measurement equipment that the shop has access to. The premise is then that it is essential that the optical system tolerances on fabrication, e.g. radii, element thickness, wedge, surface figure, and surface finish and on assembly e.g. component tilt and decenter and spacer thickness and wedge that are assigned by the optical designer be self-consistent with the capabilities of the shops that are solicited to provide a quotation.
In the 1994 paper, five classes of optical fabricators were identified; catalog, regular, select, premium, and ultimate (lithography). For each of these classes, representative minimum tolerances were published along with estimates of the cost increment. An important concept is that if any one tolerance falls into a tighter class, then the optical system must be built in a shop capitalized to provide that one minimum tolerance and as a result all the other tolerances can typically be moved to the tighter class with little cost impact. The primary cost impact then is driven by the class of shop dictated by the minimum tolerance. In this talk, a primary purpose is to revisit the tolerances associated with a given class of shop and update the numbers to reflect advances in the intervening two decades.
In the 1994 paper, five classes of optical fabricators were identified; catalog, regular, select, premium, and ultimate (lithography). For each of these classes, representative minimum tolerances were published along with estimates of the cost increment. An important concept is that if any one tolerance falls into a tighter class, then the optical system must be built in a shop capitalized to provide that one minimum tolerance and as a result all the other tolerances can typically be moved to the tighter class with little cost impact. The primary cost impact then is driven by the class of shop dictated by the minimum tolerance. In this talk, a primary purpose is to revisit the tolerances associated with a given class of shop and update the numbers to reflect advances in the intervening two decades.