... dimensions of the various sensor formats for both aspect ratios used in broadcast cameras [3]. Table 1 - Dimensions of CCD television camera sensors. Sensor ...

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With nearly all illumination systems, one goal is to maximize the throughput of the system. Since most sources emit into a wide distribution, this usually means increasing the size of the freeform surface to increase the collection angle and gather more light. This is an effective approach, but it can have drawbacks.

Y.Z., Y.O. and A.L.G conceived the project. Y.Z. and J.K.J. performed the theoretical analysis. Y.Z., J.K.J. and G.J.B. performed the experiment. Y.Z., J.K.J., Y.O. and A.L.G. performed the data analysis with input from all authors. X.J. and K.J.M. fabricated the silicon-nitride devices under the supervision of M.L. Y.Z., J.K.J. and A.L.G. wrote the manuscript with feedback from all authors. M.L. and A.L.G. supervised the project.

This work was performed in part at the Cornell Nano-Scale Facility, which is a member of the National Nanotechnology Infrastructure Network, supported by the NSF and in part at the CUNY Advanced Science Research Center NanoFabrication Facility. We acknowledge computing resources from Columbia University’s Shared Research Computing Facility project, which is supported by NIH Research Facility Improvement Grant 1G20RR030893-01 and associated funds from the New York State Empire State Development, Division of Science Technology and Innovation (NYSTAR) Contract C090171, both awarded 15 April 2010. We thank T. Schibli, Y. Levin, K. Bergman and M. Hattink for helpful discussions. This work was supported by Defense Advanced Research Projects Agency of the US Department of Defense (Grant No. HR0011-22-2-0007), Army Research Office (ARO) (Grant No. W911NF-21-1-0286) and Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-20-1-0297).

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The use of freeform optical elements in illumination applications has received a great deal of attention in recent years. For applications with specific target requirements and relatively compact sources, freeform optics offer the ability to precisely tailor the resulting illumination pattern to meet system requirements, enhance the visual appeal, and improve energy efficiency.

Drake, T. E., Stone, J. R., Briles, T. C. & Papp, S. B. Thermal decoherence and laser cooling of Kerr microresonator solitons. Nat. Photon. 14, 480–485 (2020).

Jake Jacobsen is technical marketing manager and William Cassarly is a scientist at Synopsys, Mountain View, CA; e-mail: [email protected]; https://optics.synopsys.com.

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For refractive surfaces, the collection issue is somewhat different. As with reflective elements, increasing the collection angle increases the size of the optic, but also increases the collected energy. The limitations come when the incident angles at the edge of the optic approach the critical angle. At this point, increasing the collection angle further will cause rays at the edge of the optic to undergo total internal reflection. Even for rays approaching the critical angle but still refracting, the Fresnel losses become significant and require active compensation.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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JAKE JACOBSEN and WILLIAM CASSARLYThe use of freeform optical elements in illumination applications has received a great deal of attention in recent years. For applications with specific target requirements and relatively compact sources, freeform optics offer the ability to precisely tailor the resulting illumination pattern to meet system requirements, enhance the visual appeal, and improve energy efficiency.Calculation techniques and the resulting design software have been available for years.1 However, it was only recently that the capability to design freeform surfaces was effectively integrated into a fully capable illumination-design software package. Because of this integration, the design and use of reflective and refractive freeform optical elements has become a practical endeavor for a wide range of illumination applications and designers. The inclusion of a freeform design capability in an illumination-design software package allows the designer to integrate freeform elements with other optical components to build more complex systems, add real sources, and use automated tools to analyze the resulting illumination pattern.As part of its LightTools illumination design software, Synopsys recently introduced the Freeform Designer as an integrated capability in the software's Advanced Design Module. The Freeform Designer can be used to calculate freeform reflective and refractive surfaces based on an illuminance or intensity target distribution, source collection angle and distribution, and several other geometrical settings. The following examples highlight some practical considerations when designing freeform illumination optics.Target mappingThe calculation of the shape of a freeform surface is based on a mapping of a known source angular distribution to a desired target distribution. That target distribution can be angular or spatial, depending on the need. If we know the distribution of light on the freeform surface as a function of position on the surface and incoming angle, then we can tailor that surface so that the outgoing light meets the desired target distribution either on a specified surface, or in angle space (see Fig. 1).While this is conceptually simple, implementing it in the general case—where symmetries cannot be assumed—can be complex. Nevertheless, the problem is tractable, and surfaces can be computed for both simple and complex targets (see Fig. 2).

Since the angular size of the source as seen from the freeform surface directly affects the extent of the blur, a good method for reducing the blur size is simply to place the freeform surface farther away from the source. This reduces the apparent source angular extent, which reduces the target blur. Of course, the tradeoff is that the optic will increase in size.

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The calculation of the shape of a freeform surface is based on a mapping of a known source angular distribution to a desired target distribution. That target distribution can be angular or spatial, depending on the need. If we know the distribution of light on the freeform surface as a function of position on the surface and incoming angle, then we can tailor that surface so that the outgoing light meets the desired target distribution either on a specified surface, or in angle space (see Fig. 1).

... Ring + 55 cm Ring + 40 cm Ring, Deckenplatte ∅ 20 cm - Dimmbar mit ... Eine Leuchte besteht aus 3 Ringen: 70cm + 55cm + 40cm. Farbwiedergabeindex. CRI ...

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While increasing the number of grid points on the surface does increase target resolution, it can substantially increase the amount of time needed to calculate the freeform surface—from much less than a minute in many simple cases to many minutes for complex cases. The times cited here are for a midrange laptop where the calculation algorithm uses a single CPU.

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(a), Homodyne setup for thermal noise characterization of microresonators. DUT, device under test. (b), Measured thermal noise of the SiN device at room temperature (0V) and when a heating voltage is applied using a commercial arbitrary-waveform generator (1.3 V).

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Calculation techniques and the resulting design software have been available for years.1 However, it was only recently that the capability to design freeform surfaces was effectively integrated into a fully capable illumination-design software package. Because of this integration, the design and use of reflective and refractive freeform optical elements has become a practical endeavor for a wide range of illumination applications and designers. The inclusion of a freeform design capability in an illumination-design software package allows the designer to integrate freeform elements with other optical components to build more complex systems, add real sources, and use automated tools to analyze the resulting illumination pattern.

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The code used to plot the data is available in the Zenodo repository. Simulation code may be obtained from the authors upon reasonable request.

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Supplementary Figs. 1–3 and sections I–IV regarding theoretical model and numerical simulations: I, Schawlow–Townes linewidth of optical parametric oscillator; II, Classical phase-noise sources of optical parametric oscillator; III, Numerical model of synchronization; IV, Design example of the athermal waveguide.

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The integration of a capability that quickly and easily calculates freeform surfaces in the LightTools design software environment will allow for greater use of freeform optics in illumination by facilitating their design and analysis.

Inherent in the approach is a one-to-one mapping. Rays incident on a given point of the freeform surface are assumed to have the same angle of incidence. This implies a point source or, alternatively, a collimated source. Rays emitted by an extended source will strike a given point on the freeform surface at different angles and thus will strike the target at slightly different locations (or slightly different angles for intensity targets), causing a blur in the target pattern. The extent of this effect is dependent on the angular size of the source as seen from the freeform surface. Because of this, smaller sources such as LEDs and discharge sources tend to produce less blur.

Mar 24, 2020 — The first problem we want to solve is understanding the movement of pixels from one frame to another. Optical flow estimations can be done in a ...

2024114 — Focal length isn't just a technical detail or a number printed on your lens; it's essentially the DNA of how your lens sees the world. Think of ...

Present address: John Hopcroft Center for Computer Science, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, China

These include the linear magnification, numerical aperture value, optical corrections, microscope body tube length, the type of medium the objective is ...

Zhao, Y., Jang, J.K., Beals, G.J. et al. All-optical frequency division on-chip using a single laser. Nature 627, 546–552 (2024). https://doi.org/10.1038/s41586-024-07136-2

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As part of its LightTools illumination design software, Synopsys recently introduced the Freeform Designer as an integrated capability in the software's Advanced Design Module. The Freeform Designer can be used to calculate freeform reflective and refractive surfaces based on an illuminance or intensity target distribution, source collection angle and distribution, and several other geometrical settings. The following examples highlight some practical considerations when designing freeform illumination optics.

Nature thanks Olivier Llopis, Florian Sedlmeir and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Liu, F., Menyuk, C. R. & Chembo, Y. K. A stochastic approach to phase noise analysis for microwaves generated with Kerr optical frequency combs. Commun. Phys. 6, 117 (2023).

The generation of spectrally pure microwave signals is a critical functionality in fundamental and applied sciences, including metrology and communications. Optical frequency combs enable the powerful technique of optical frequency division (OFD) to produce microwave oscillations of the highest quality1,2. Current implementations of OFD require multiple lasers, with space- and energy-consuming optical stabilization and electronic feedback components, resulting in device footprints incompatible with integration into a compact and robust photonic platform3,4,5. Here we demonstrate all-optical OFD on a photonic chip by synchronizing two distinct dynamical states of Kerr microresonators pumped by a single continuous-wave laser. The inherent stability of the terahertz beat frequency between the signal and idler fields of an optical parametric oscillator is transferred to a microwave frequency of a Kerr soliton comb, and synchronization is achieved via a coupling waveguide without the need for electronic locking. OFD factors of N = 34 and 468 are achieved for 227 GHz and 16 GHz soliton combs, respectively. In particular, OFD enables a 46 dB phase-noise reduction for the 16 GHz soliton comb, resulting in the lowest microwave noise observed in an integrated photonics platform. Our work represents a simple, effective approach for performing OFD and provides a pathway towards chip-scale devices that can generate microwave frequencies comparable to the purest tones produced in metrological laboratories.

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