CeFO-Related Publications

@article{goodsell_2022,

title = {Method for minimizing lens breathing with one moving group},

author = {J. Goodsell and V. Blahnik and J. P. Rolland},

doi = {https://doi.org/10.1364/OE.457420},

year  = {2022},

date = {2022-05-23},

journal = {Optics Express},

volume = {30},

issue = {11},

pages = {19494-19509},

abstract = {Lens breathing in movie cameras is the change in the overall content of a scene while bringing subjects located at different depths into focus. This paper presents a method for minimizing lens breathing or changing angular field-of-view while maintaining perspective by moving only one lens group. To maintain perspective, the stop is placed in a fixed position where no elements between the scene and the stop can move, thus fixing the entrance pupil in one location relative to the object fields. The result is perspective invariance while refocusing the lens. Using paraxial optics, we solve for the moving group's position to focus on every object position and eliminate breathing between the minimum and maximum object distances. We investigate the solution space for optical systems with two positive groups or a positive and a negative group (i.e., retrofocus and telephoto systems). We explain how to apply this paraxial solution to existing systems to minimize breathing. The results for two systems altered using this method are presented. Breathing improved by two orders of magnitude in both cases, and performance specifications were still met when compared to the initial systems.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Koerber22b,

title = {Reduction of retrace error from broadband variable transmission spheres in Fizeau interferometry},

author = {J. Koerber and G.D. Boreman and T.J. Suleski},

doi = {https://doi.org/10.1364/OPTCON.458860},

year  = {2022},

date = {2022-04-25},

journal = {Optics Continuum},

volume = {1},

number = {5},

pages = {1067-1076},

keywords = {CeFO related, metrology},

pubstate = {published},

tppubtype = {article}

}

@article{karci_2022,

title = {Experimental investigation in nodal aberration theory (NAT): separation of astigmatic figure error from misalignments in a Cassegrain telescope},

author = {O. Karci and M. Yesiltepe and E. Arpa and Y. Wu and M. Ekinci and J. P. Rolland},

doi = {https://doi.org/10.1364/OE.453788},

year  = {2022},

date = {2022-03-28},

journal = {Optics Express},

volume = {30},

issue = {7},

pages = {11150-11164},

abstract = {We present simulations and experimental validations for separating astigmatic figure error from misalignments in Nodal Aberration Theory (NAT) with a high-precision Cassegrain telescope. Both the primary mirror figure error and the secondary mirror misalignments induce binodal astigmatism for the telescope systems. The separation of these two aberration factors plays a crucial role in the telescope alignment process. In this study, the figure error of the aspheric primary mirror of the Cassegrain telescope induced by the mirror mounts was measured interferometrically utilizing a computer-generated hologram (CGH). According to the primary mirror figure error, the astigmatic node locations in the image plane were simulated using real raytracing. The center of the nodes was located on the field center, and the nodes were placed symmetrically with respect to the field center in the image plane. The telescope's alignment was performed using the simulation results, and the node locations were measured on a grid of field points interferometrically. Thereafter, secondary mirror misalignments around the coma-free pivot point were introduced into the optical system, and the node's center was shifted from the field center in the image plane as predicted by NAT. The simulations and interferometric field measurements were performed and compared on a grid of field points for the misaligned state in the presence of primary mirror figure error. The experimental results confirm the predictions from NAT. Statistical analysis was also performed to confirm the accuracy and stability of the measurements.},

keywords = {CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{Koerber22a,

title = {Broadband Variable Transmission Sphere for Fizeau Interferometry},

author = {J. Koerber and G.D. Boreman and T.J. Suleski},

doi = {https://doi.org/10.3390/opt3010011},

year  = {2022},

date = {2022-03-10},

journal = {Optics},

volume = {3},

pages = {88-98},

keywords = {CeFO related, metrology},

pubstate = {published},

tppubtype = {article}

}

@article{falaggis_2022,

title = {Freeform Optics: Introduction},

author = {K. Falaggis and J. P. Rolland and F. Duerr and A. Sohn},

doi = {https://doi.org/10.1364/OE.454788},

year  = {2022},

date = {2022-02-14},

journal = {Optics Express},

volume = {30},

issue = {4},

pages = {6450-6455},

abstract = {This feature issue of Optics Express highlights 28 state-of-the-art articles that capture a snapshot of the recent developments in the field of freeform optics. As an introduction, the editors provide an overview of all published articles, which cover a broad range of topics in freeform optics. The wide variety of applications presented here demonstrates that freeform optics is a growing and vibrant field with many more innovations to come.},

keywords = {CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{takaki_cub2022,

title = {Schemes for cubature over the unit disk found via numerical optimization},

author = {N. Takaki and G. W. Forbes and J.P. Rolland},

doi = {https://doi.org/10.1016/j.cam.2021.114076},

isbn = {0377-0427},

year  = {2022},

date = {2022-01-03},

journal = {Journal of Computational and Applied Mathematics},

volume = {407},

pages = {114076},

abstract = {Cubature schemes, in this case for uniformly weighted integration over the unit disk, enable exact evaluation of numerical integrals of polynomials but have been explicitly constructed for only low or moderate degrees. In this paper, cubature formulae are discovered for a wider range of degrees by leveraging numerical optimization. These results include a degree-17 cubature scheme with fewer points than existing solutions and up to a degree-77 solution with 1021 cubature points. Optimization heuristics and patterns in the distributions of cubature points are discussed, which serve as vital guides in this work. For example, these heuristics leverage a connection to circle-packing configurations to facilitate the discovery of fully symmetric cubature schemes.},

keywords = {CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{Hu2021,

title = {Morphology and waveguiding properties of ultrafast-laser-inscribed type-II waveguides in IG2},

author = {W. Hu and M. Kilinc and W. Gebremichael and C. Dorrer, and J. Qiao},

url = {https://opg.optica.org/ome/fulltext.cfm?uri=ome-12-1-360&id=466364},

year  = {2021},

date = {2021-12-24},

urldate = {2021-12-24},

journal = {Optical Materials Express},

volume = {12},

number = {1},

pages = {360-373},

abstract = {Ultrafast-laser-inscribed type-II waveguides inside the chalcogenide glass IG2 and the morphology of the inscribed tracks are presented for the first time to our knowledge. Self-organized periodic structures induced by the ultrafast laser in the tracks are characterized. The near-infrared waveguiding properties are studied for various pulse energies, durations, repetition rates, and polarization states, as well as different separations between the two written tracks. A propagation loss of ∼ 2.3 dB/cm is demonstrated in a type-II waveguide formed in IG2.},

keywords = {manufacturing, related},

pubstate = {published},

tppubtype = {article}

}

@article{Feng2021,

title = {Femtosecond-Laser-Ablation Dynamics in Silicon Revealed by Transient Reflectivity Change},

author = {T. Feng and G. Chen and H. Han and J. Qiao},

url = {https://www.mdpi.com/2072-666X/13/1/14#

https://centerfreeformoptics.org/wp-content/uploads/2023/02/micromachines-13-00014-v2.pdf},

doi = {https://doi.org/10.3390/mi13010014},

year  = {2021},

date = {2021-12-23},

urldate = {2021-12-23},

journal = {Micromachines},

volume = {13},

number = {1},

abstract = {The dynamics of ablation in monocrystalline silicon, from electron-hole plasma generation to material expansion, upon irradiation by a single femtosecond laser pulse (1030 nm, 300 fs pulse duration) at a wide range of fluences is investigated using a time-resolved microscopy technique. The reflectivity evolution obtained from dynamic images in combination with a theoretical Drude model and a Two-Temperature model provides new insights on material excitation and ablation process. For all fluences, the reflectivity increased to a temporary stable state after hundreds of femtoseconds. This behavior was predicted using a temperature-dependent refractive index in the Drude model. The increase in velocity of plasma generation with increasing fluence was theoretically predicted by the Two-Temperature model. Two ablation regimes at high fluences (>0.86 J/cm2) were identified through the measured transient reflectivity and ablation crater profile. The simulation shows that the fluence triggering the second ablation regime produces a boiling temperature (silicon, 2628 K).},

keywords = {manufacturing, related},

pubstate = {published},

tppubtype = {article}

}

@article{papa_OE21,

title = {Survey of the four-mirror freeform imager solution space},

author = {J. C. Papa and J. M. Howard and J. P. Rolland},

doi = {https://doi.org/10.1364/OE.442943},

year  = {2021},

date = {2021-12-06},

journal = {Optics Express},

volume = {29},

issue = {25},

pages = {41534-41551},

abstract = {We present the results and methods of a survey of the four-mirror freeform imager solution space. This survey is a grid search over the parameters that remain after reducing the solution space’s degrees of freedom using first-, second-, and third-order aberration theory. We then optimize the systems’ higher-order surface shapes through sixth-order. Finally, we discuss general trends in the systems’ performance versus volume and etendue and their utility in trade studies.},

keywords = {CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{Swain2021,

title = {Telephoto-lens-based Optical Differentiation Wavefront Sensor for freeform metrology},

author = {BR Swain and C. Dorrer and J. Qiao},

url = {https://opg.optica.org/oe/fulltext.cfm?uri=oe-29-23-38395&id=464483},

doi = {https://doi.org/10.1364/OE.443558},

year  = {2021},

date = {2021-11-03},

urldate = {2021-11-03},

journal = {Opt. Express},

volume = {29},

number = {23},

pages = {38395-38403},

abstract = {We report an Optical Differentiation Wavefront Sensor based on a telephoto lens system and binary pixelated filters. It provides a five-fold reduction in the system length compared to a 4f system with identical effective focal length. Measurements of phase plates with this system are compared to measurements performed with a commercial low-coherence interferometer. The telephoto-lens-based system can measure wavefronts with accuracy better than λ/10 Root Mean Squared (RMS) at λ=633 nm. Experimental investigation shows that the system has a high tolerance to components alignment errors.},

keywords = {metrology, related},

pubstate = {published},

tppubtype = {article}

}

@article{karci_NAT21,

title = {Experimental investigation of binodal astigmatism in nodal aberration theory (NAT) with a Cassegrain telescope system},

author = {O. Karci and E. Arpa and M. Ekinci and J. P. Rolland},

doi = {https://doi.org/10.1364/OE.427164},

year  = {2021},

date = {2021-06-21},

journal = {Optics Express},

volume = {29},

issue = {13},

pages = {19427-19440},

abstract = {We present simulations and an experimental investigation of binodal astigmatism in

nodal aberration theory (NAT) for a customized, high-precision Cassegrain telescope system. The

telescope system utilizes a five-axis, piezo-actuated flexural mechanism to introduce secondary

mirror misalignments and generate aberrations intentionally. The induced aberrations are

measured interferometrically and quantified for a grid of field points on the telescope system’s

image plane. For this purpose, a coma-free pivot point of the secondary mirror was simulated for

isolating the binodal astigmatism field response. The separation of the nodes is proportional to

the introduced misalignments. A simulation of Fringe Zernike coma and binodal astigmatism

was generated using a real ray trace model of the optical system and analyzed to compare to

the experimental results. A statistical analysis of the measurements was performed to show the

experimental results’ accuracy and stability. The experimental results were consistent with the

simulations, hence experimentally validating NAT for binodal astigmatism for the first time.

},

keywords = {CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{nokey,

title = {Metaform optics: Bridging nanophotonics and freeform optics},

author = {Daniel K. Nikolov and Aaron Bauer and Fei Cheng and Hitoshi Kato and A. Nick Vamivakas and Jannick P. Rolland},

url = {https://www.science.org/doi/abs/10.1126/sciadv.abe5112},

doi = {10.1126/sciadv.abe5112},

year  = {2021},

date = {2021-04-30},

urldate = {2021-04-30},

journal = {Science Advances},

volume = {7},

number = {18},

pages = {eabe5112},

abstract = {The demand for high-resolution optical systems with a compact form factor, such as augmented reality displays, sensors, and mobile cameras, requires creating new optical component architectures. Advances in the design and fabrication of freeform optics and metasurfaces make them potential solutions to address the previous needs. Here, we introduce the concept of a metaform—an optical surface that integrates the combined benefits of a freeform optic and a metasurface into a single optical component. We experimentally realized a miniature imager using a metaform mirror. The mirror is fabricated via an enhanced electron beam lithography process on a freeform substrate. The design degrees of freedom enabled by a metaform will support a new generation of optical systems.},

keywords = {Aberration correction, augmented reality, CeFO manufacturing, CEFO metrology, freeform, head display, Image quality, Optical design, relay optics, rolland, tomography},

pubstate = {published},

tppubtype = {article}

}

@article{Horvath_2021a,

title = {Advancing lightweight mirror design: a paradigm shift in mirror preforms by utilizing design for additive manufacturing},

author = {Nicholas Horvath and Matthew Davies},

doi = {https://doi.org/10.1364/AO.410350},

year  = {2021},

date = {2021-01-18},

urldate = {2021-01-18},

journal = {Applied Optics},

volume = {60},

issue = {3},

pages = {681-696},

abstract = {Additive manufacturing is a disruptive technology that can be leveraged by the redesign of components in most engineering fields. Fundamental engineering resources for lightweight mirrors were developed more than 30 years ago with a main design limitation, state of the art manufacturing. Here, we present two design methodologies for the design of lightweight mirrors. The first method utilizes analytical expressions to design a traditional isogrid mirror, which provided the foundation for most lightweight mirrors to date. The second method employs a combination of topology optimization, lattice infill, and analytical estimation to develop an advanced lightweight mirror designed for additive manufacturing. The advanced mirror design outperforms the traditional design for each functional requirement, including a 94% reduction in predicted surface quilting and a higher specific stiffness. The manufacturing of the advanced mirror is only possible with an additive manufacturing process.},

keywords = {CeFO related, manufacturing},

pubstate = {published},

tppubtype = {article}

}

@article{Sahoo2020,

title = {Dynamic pulse propagation modelling for predictive femtosecond-laser-microbonding of transparent materials},

author = {Pankaj K. Sahoo and Tao Feng and Jie Qiao},

doi = {https://doi.org/10.1364/OE.402493},

year  = {2020},

date = {2020-10-02},

urldate = {2020-10-02},

journal = {Opt. Express},

volume = {28},

number = {21},

pages = {31103-31118},

abstract = {A dynamic pulse propagation modeling for femtosecond laser bonding of Borofloat glass is presented. The temperature evolution and internal modifications are predicted by incorporating the nonlinear electron dynamics along with temperature dependent thermal properties. The modelling predicts the spatial and temporal distribution of absorption coefficient and plasma density that gives quantitative estimations of the heat affected zone and weld geometry. The impact of focusing condition on heat affected zone and weld geometry is investigated, which for the first time to our knowledge allows to numerically determine the desired relative position between the geometrical focus of a femtosecond-laser-pulse and the interface of the two substrates to be welded. The prediction of the modelling on the offset distance is applied to weld Borofloat glass plates having optical contact and can be applied to other dielectric solids.},

keywords = {manufacturing, related},

pubstate = {published},

tppubtype = {article}

}

@article{Horvath19-ab,

title = {Grinding of additively manufactured silicon carbide surfaces for optical applications},

author = {Nicholas Horvath and Andrew Honeycutt and Matthew A. Davies},

url = {https://doi.org/10.1016/j.cirp.2020.04.079},

year  = {2020},

date = {2020-05-19},

journal = {CIRP Annals},

volume = {69},

pages = {509-512},

abstract = {Many of the properties of Silicon carbide (SiC) are advantageous for optical applications, such as telescope mirrors and industrial laser systems. However, the base shapes of complex components are costly and difficult to manufacture. Leveraging additive manufacturing, near net complex components are readily processed. Here, we investigate the post processing of additively manufactured SiC (AM SiC) compared to chemical vapor deposited (CVD) SiC. The specific grinding energy for the AM SiC was lower than CVD, however the trends were the same. A specular finish was observed on both materials but the AM SiC finish was limited due to residual porosity.},

keywords = {manufacturing, related},

pubstate = {published},

tppubtype = {article}

}

@article{DeMars_02,

title = {Single-Shot Phase Calibration of a Spatial Light Modulator using Geometric Phase Interferometry},

author = {L. A. DeMars and M. Mikula-Zdankowska and K. Falaggis and R. Porras-Aguilar},

doi = {https://doi.org/10.1364/AO.383610},

year  = {2020},

date = {2020-01-01},

urldate = {2020-01-01},

journal = {Appl. Opt.},

volume = {59},

issue = {13},

pages = {D125-D130},

abstract = {A vibration-insensitive, single-shot phase-calibration method for phase-only spatial light modulators (SLM) is reported. The proposed technique uses a geometric phase lens to form a phase-shifting radial shearing interferometer to enable common-path measurements. This configuration has several advantages: (a) unlike diffraction-based SLM calibration techniques, this technique is robust against intensity errors due to misalignment; (b) unlike two-beam interferometers, this technique offers a high environmental stability; and (c) unlike intensity-based methods, the phase-shifting capability provides a phase uncertainty routinely in the order of 2𝜋/100

. The experimental results show a significantly higher accuracy when compared to the diffraction-based approaches.},

keywords = {CEFO metrology, CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{Swain2019,

title = {High-performance optical differentiation wavefront sensing towards freeform metrology},

author = {Biswa Ranjan Swain and Christophe Dorrer and Jie Qiao},

doi = {https://doi.org/10.1364/OE.27.036297},

year  = {2019},

date = {2019-12-09},

urldate = {2019-12-09},

journal = {Opt. Express},

volume = {27},

number = {25},

pages = {36297-36310},

abstract = {We report the demonstration of freeform optics metrology with an optical differentiation wavefront sensor that relies on spatially dithered distributions of binary pixels to synthesize a far-field amplitude filter. Analysis of experimental results and comparison with a commercial low-coherence-length interferometer shows that freeform phase plates with different magnitude of wavefront slopes can be accurately characterized. RMS accuracy of ∼ λ/10 and precision of ∼ λ/70 at 633 nm were achieved with pixelated filters having 2.5-µm pixels. Simulations that describe the characterization of a freeform optical component in the presence of photodetection noise and filter nonlinearity demonstrate the robustness of this wavefront-sensing approach for freeform optics characterization.},

keywords = {CeFO related, metrology},

pubstate = {published},

tppubtype = {article}

}

@article{lineark,

title = {Absolute linear-in-k spectrometer designs enabled by freeform optics},

author = {C. Yoon and A. Bauer and D. Xu and C. Dorrer and J. P. Rolland},

url = {https://doi.org/10.1364/OE.27.034593},

year  = {2019},

date = {2019-11-25},

journal = {Optics Express},

volume = {27},

number = {24},

pages = {34593-34602},

abstract = {Linear-in-wavenumber, k, spectrometers have the merits of saving signal processing time and improving the sensitivity of spectral-domain optical coherence tomography (SD-OCT) by avoiding post-k-interpolation. We report on an approach leveraging freeform optics to linearize spectrometers in k to achieve an extremely low residual k-nonlinearity in design. A freeform lens reduced the k-nonlinearity from 2.47% for a benchmark spectrometer to 2.79 × 10−5% and 3.36 × 10−9% using the Fringe Zernike coefficients up to the 16th term and 37th term, respectively. A simulation model was developed to evaluate the performance of SD-OCT with the designed spectrometers. Without the k-interpolation in software, results show that the two freeform spectrometers achieve a roll-off gain of 5.24 dB over the imaging depth from 0.5 to 5.5 mm, while the maximum imaging depth is 5.8 mm. Finally, a 4.2-µm-FWHM axial PSF was maintained throughout the imaging depth in air.},

keywords = {CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{Alonso2019b,

title = {Effects on the OTF of MSF structures with random variations},

author = {Kevin Liang; Miguel A. Alonso },

doi = {10.1364/OE.27.034665},

year  = {2019},

date = {2019-11-11},

urldate = {2019-11-11},

journal = {Optics Express},

volume = {27},

number = {24},

pages = {34665-34680},

abstract = {In diamond-machined freeform manufacturing processes, a tool-tip often leaves behind characteristic mid-spatial frequency (MSF) structures on the optical surface. Unwanted movement between the tool-tip and the part results in MSF structures with random variations. Here, we analyze the effects of these MSF structures on the system’s optical performance and derive simple analytic estimates for the optical transfer function in terms of the parameters of these structures. These expressions are expected to aid in MSF tolerancing.},

keywords = {CeFO design},

pubstate = {published},

tppubtype = {article}

}

@article{BauerARRI,

title = {All-reflective electronic viewfinder enable by freeform optics},

author = {A. Bauer and M. Pesch and J. Muschaweck and F. Leupelt and J. P. Rolland},

url = {https://doi.org/10.1364/OE.27.030597},

year  = {2019},

date = {2019-10-14},

journal = {Optics Express},

volume = {27},

number = {21},

pages = {30597-30605},

abstract = {Refractive eyepiece design forms are often limited by chromatic aberrations and require a mix of glass types to achieve sufficient correction, thus they are not conducive to manufacture in volume. Reflective surfaces are inherently achromatic and can be produced in volume, but rotationally symmetric reflective surfaces are either used with lossy obscurations or are incapable of correcting rotationally variant aberrations when used in an unobscured form. Freeform optics enable unobscured reflective design forms with excellent image quality. Here, we document the design, fabrication, and assembly of an all-reflective high-end electronic viewfinder that shows the applicability of freeform surfaces to eyepiece design forms.},

keywords = {CeFO design, CeFO related},

pubstate = {published},

tppubtype = {article}

}

@article{TAYLOR2019,

title = {Femtosecond laser polishing of germanium},

author = {LAUREN L. TAYLOR, JING XU, MICHAEL POMERANTZ, THOMAS

R. SMITH, JOHN C. LAMBROPOULOS, AND JIE QIAO},

url = {https://doi.org/10.1364/OME.9.004165},

year  = {2019},

date = {2019-10-02},

journal = {Optical Materials Express},

volume = {9},

number = {11},

pages = {4165-4177},

abstract = {Freeform optics can reduce the cost, weight, and size of advanced imaging systems,

but it is challenging to manufacture the complex rotationally asymmetric surfaces to optical

tolerances. To address the need for disruptive, high-precision sub-aperture forming and finishing

techniques for freeform optics, we investigate an alternative, non-contact polishing methodology

using femtosecond lasers, combining modeling, experiments, and demonstrations. Femtosecondlaser-

based polishing of germanium was investigated using an experimentally-validated twotemperature

model of laser/germanium interaction to guide the understanding and selection of

laser parameters to achieve near-nonthermal ablation for polishing and figuring. For the first time

to our knowledge, model-guided femtosecond laser polishing of germanium was successfully

demonstrated, achieving precision material removal while maintaining single-digit nanometer

optical surface quality. The demonstrated femtosecond-laser-based polishing technique lays the

foundation for semiconductor optics polishing/fabrication using femtosecond lasers and opens a

viable path for high-precision, complex sub-aperture optical polishing tasks on various materials.},

keywords = {CeFO manufacturing, CEFO metrology, fabrication, Freeform surfaces, manufacturing, Mid-Spatial Frequency error},

pubstate = {published},

tppubtype = {article}

}

@article{Feng2019,

title = {Pulse-Propagation Modeling and Experiment for Femtosecond-Laser Writing of Waveguide in Nd:YAG},

author = {Tao Feng and Pankaj K. Sahoo and Francisco R. Arteaga-Sierra and Christophe Dorrer and Jie Qiao},

doi = {https://doi.org/10.3390/cryst9080434},

year  = {2019},

date = {2019-08-20},

urldate = {2019-08-20},

journal = {Crystals },

volume = {9},

number = {8},

pages = {434},

abstract = {In this work, unidirectional pulse propagation equation (UPPE) modeling is performed to study the nonlinear laser-mater interaction in silicon and Nd:Y3Al5O12 (Nd:YAG) crystals. The simulation results are validated with reported experimental results for silicon and applied to Nd:YAG crystals with experimental validation. Stress-induced waveguides are written in Nd:YAG crystals using 515 nm, 300 fs pulses at a 1 kHz repetition rate. Waveguides having a mean propagation loss of 0.21 ± 0.06 dB/cm are obtained, which is lower than the previous reported values for Type-II waveguides written in Nd:YAG crystals. The modeling and experimental results consistently show that the modification (waveguide track) depth increases with input energy. A detailed analysis is presented to control the modal properties of the waveguide in the context of UPPE simulation.},

keywords = {CeFO related, manufacturing},

pubstate = {published},

tppubtype = {article}

}

@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}

}