Eye Retroreflector Research Articles

Transverse dynamical response of laser frequency-shifted feedback with mode mismatch

The transverse mode mismatch between the echo wave and optical fields in the laser cavity substantially impacts the responses of the laser frequency-shifted feedback (LFSF) system. This mismatch widely exists in experiments, which limits the detection sensitivity and degrades the signal-to-noise ratio. However, current research on the dynamic response of LFSF has predominantly concentrated on longitudinal modes and intensity modulation, with a lack of quantitative analysis regarding the dynamic response of the transverse modes. In this paper, we establish a transverse dynamical response model of LFSF considering the mode-mismatch. A calculation method of the effective reflectivity (ER) and mode-matching factor (MMF) is presented by decomposing the echo wave to the eigenmodes of the laser. The theoretical model is highly consistent with the experimental data. Finally, with this transverse dynamical response model, we develop a simple scheme to calibrate the effective reflectivity of scattering surfaces by employing a cat's eye retroreflector. Overall, this paper provides a detailed demonstration of the mismatch, which promises an effective theoretical basis to make full use of the high sensitivity of LFSF and apply it over a long distance.

Distance and Efficiency Enhancement With Aspherical Retroreflectors for Resonant Beam SWIPT

The resonant beam system (RBS) with double spherical retroreflectors presents a potential mobile simultaneous wireless information and power transfer (SWIPT) technology without any tracking control. However, the movement distance and performance are limited due to the effect of spherical aberration. To improve mobility performance in RBS, including movement distance and output power, we adopt an aspherical lens as the focusing mirror in a retroreflector. By shifting the beam phase distribution, the aspherical lens focuses all passing beams, particularly edge beams, on the focal mirror, enhancing energy concentration in the resonant cavity. The beam field propagation through cat’s-eye retroreflectors, gain medium, and air is studied for analyzing the transfer efficiency and output power, and we demonstrate that the axial movement distance in the aspherical resonator is about 7 m, which is more than twice as far away as the spherical resonator. Within a field of view of 3° at a distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1~\rm {m}$ </tex-math></inline-formula> , the output power of the aspherical resonator is greater than that of the spherical resonator with the same movement angle, up to two times. The maximum output electric power and spectral efficiency are approximately <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4~\rm {W}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$12~\rm {bps/Hz}$ </tex-math></inline-formula> , respectively.

Charging a Smartphone Over the Air: The Resonant Beam Charging Method

Wireless charging for mobile Internet of Things (IoT) devices such as smartphones is extremely difficult. To reduce energy dissipation during wireless transmission in mobile scenarios, laser or narrow radio beams with sophisticated tracking control are typically required. However, reaching the necessary tracking accuracy and reliability is really difficult. In this article, inspired by the features of optical resonators and retroreflectors, we develop an experiment on a self-aligned resonant beam charging system for long-distance mobile power transfer. It exploits light resonances inside a double-retroreflector-based spatially separated laser resonator (SSLR), which eliminates the requirement for any kind of tracking control. Focal telecentric cat’s eye retroreflectors are employed here. The SSLR was investigated by both theoretical calculation and experiment. We also well assembled the transmitter and the receiver and demonstrated its application in mobile smartphone charging. The results show that above 5-W optical power (also obtained more than 0.6-W electrical power) transferring with negligible diffraction loss to a few-centimeter-size receiver is realized while the receiver moves arbitrarily within 2-m vertical distance and 6° field of view from the transmitter. The maximum horizontal moving range is up to ±18 cm. This wireless charging system empowers a smartphone in mobile operation with unlimited battery life without the need for a cable.

Novel laser tracking measurement system based on the position sensitive detector.

The rapid development of modern industrial technology has led to the increase of machinery precision. Laser tracking measurement systems represent a novel type of coordinate measurement method, which was developed on the basis of metrology. In this paper, we aim to define a single-station 3D coordinate rotating laser tracking measurement system based on the principle of the space coordinate method. In view of the current architecture and optical path of the system, we establish the ideal mathematical model of the system and derive the coordinate expression for arbitrary measured points in the measurement space. The output response of the photoelectric position detector to the rotating laser and the linearity of the position signal in the detection circuit have been detected via a concrete experiment. A laser tracking system was used to track the target mirror mounted on the coordinate measuring machine measuring spindle. It is shown that stable tracking is possible during the 3D movement of a cat's eye retroreflector if its velocity is 0.2 m/s and the distance to the moving object is 1-2 m. The corresponding velocity of the object must be 0.4 m/s. Our system provides a feasible implementation method for the tracking of the moving target space position.

Effects of incident beam deviation from the center of a cat's eye retro-reflector on the measurement accuracy of a laser tracing system

This paper proposed a method of analyzing the measurement accuracy of a laser tracing system using the deviation of the incident beam from the center of a cat's eye retro-reflector. Based on the laser tracing system's measurement principle, a corresponding model is established to analyze the influence of the incident beam deviation from the center of cat's eye retro-reflector at the initial measurement position on the measurement accuracy. The measurement experiments verified that the influence was significant. When the deviation between the incident beam and the center of the cat's eye retro-reflector was -50 μm, the displacement measurement error was 3.5867 ± 0.0260 μm. When the deviation was 50 μm, the displacement measurement error reached 3.5939 ± 0.0189 μm. The relative displacement error between the cat's eye retro-reflector and the laser tracing system decreased the measurement system's accuracy. This study provides an important theoretical basis for evaluating and improving the accuracy and reliability of laser tracing measurement systems.

Frequency shifts due to Stark effects on a rubidium two-photon transition

The $5S_{1/2}\rightarrow 5D_{5/2}$ two-photon transition in Rb is of interest for the development of a compact optical atomic clock. Here we present a rigorous calculation of the 778.1~nm ac-Stark shift ($2.30(4) \times10^{-13}$(mW/mm$^2$)$^{-1}$) that is in good agreement with our measured value of $2.5(2) \times10^{-13}$(mW/mm$^2$)$^{-1}$. We include a calculation of the temperature-dependent blackbody radiation shift, we predict that the clock could be operated either with zero net BBR shift ($T=495.9(27)$~K) or with zero first-order sensitivity ($T=368.1(14)$~K). Also described is the calculation of the dc-Stark shift of 5.5(1)$\times 10^{-15}$/(V/cm$^2$) as well as clock sensitivities to optical alignment variations in both a cat's eye and flat mirror retro-reflector. Finally, we characterize these Stark effects discussing mitigation techniques necessary to reduce final clock instabilities.

Magnetically Driven MEMS Cat’s Eye Array as an Optical Identification

We report a micro-electro-mechanical system tunable cat's eye retroreflector array for optical identification. A rotational concave mirror is employed in the retroreflector to achieve modulability of the retroreflected optical intensity. The magnetic force between the permanent magnet and magnetic beads on the rotatable concave mirror unit enables magnetic actuation and accomplishes modulation. The magnetically actuated mirror achieves a large tilt angle. The tilt angle of the concave mirror can change from 0° to 12°, with the retroreflection efficiency varying from 19% to 5% correspondingly. The retroreflection efficiency versus the position of the permanent magnet is characterized. A dynamic image can be generated by applying magnetic force individually to each cat's eye in the array.

Deep turbulence effects mitigation with coherent combining of 21 laser beams over 7 km.

We demonstrate coherent beam combining and adaptive mitigation of atmospheric turbulence effects over 7km under strong scintillation conditions using a coherent fiber array laser transmitter operating in a target-in-the-loop setting. The transmitter system is composed of a densely packed array of 21 fiber collimators with integrated capabilities for piston, tip, and tilt control of the outgoing beams wavefront phases. A small cat's-eye retro reflector was used for evaluation of beam combining and turbulence compensation performance at the target plane, and to provide the feedback signal for control of piston and tip/tilt phases of the transmitted beams using the stochastic parallel gradient descent maximization of the power-in-the-bucket metric.

Pseudo-cat's eye for improved tilt-immune interferometry.

We present a new simple optical design for a cat's eye retroreflector. We describe the design of the new optical configuration and its use in tilt-immune interferometry where it enables the tracking of the displacement of a plane target mirror with minimum sensitivity to its tilt about axes orthogonal to the interferometer's optical axis. In this application the new cat's eye does not behave as a perfect retroreflector and we refer to it as a "pseudo"-cat's eye (PCE). The device allows, for the first time, tilt-immune interferometric displacement measurements in cases where the nominal distance to the target mirror is significantly larger than the length of the cat's eye. We describe the general optical characteristics of the PCE and compare its performance in our application with that of a conventional cat's eye optical configuration using ABCD matrices and Zemax analyses. We further suggest a simple modification to the design that would enable the PCE to behave as a perfect cat's eye, and this design may provide an advantageous solution for other applications.

Tunable Micro Cat's Eye Array in an Optical Identification System and Comparison of Different ID Tags

An optical identification (ID) system has been built, and dynamic ID tags are compared, which include a home-made tunable cat's eye retroreflector array, a liquid crystal (LC) spatial light modulator (SLM) combined with a retroreflective tape, a LC SLM combined with a plane mirror, and a LC SLM combined with normal white paper. Performance comparisons indicate that the tag implemented with the microtunable cat's eye retroreflector array offers the best system security. The image produced by the ID tag is also accurately recognized by the identification system.

External cavity diode laser with frequency drift following natural variation in air pressure.

A compact and mechanically very robust external cavity diode laser was made by removing any position adjusters such as precision screws and piezo actuators, taking advantage of a cat's eye retroreflector insensitive to misalignment. Under free-running operation during 150h, the frequency drift followed natural variation in air pressure with a ratio of -66.6±0.1 MHz/hPa in a range between 1001.5 and 1013.6hPa. The ratio was in good agreement with that estimated from variation in the effective cavity length derived from the relation between the pressure and the refractive index of air. These results indicate that an external cavity diode laser with predictable frequency drift was successfully created.

Design, Fabrication, and Characterization of Tunable Cat's Eye Retroreflector Arrays as Optical Identification Tags

This study has developed an independently-addressed tunable cat's eye retroreflector array for an optical identification system. Switchable cat's eye retroreflectors are achieved by incorporating polymer dispersed liquid crystal film and indium tin oxide (ITO) electrodes into the cat's eye structure. Experiments show that the gap between the front and back units of the cat's eye retroreflector plays a role in the optical performance of the device. The second-generation device is used to realize the optical ID tag. By controlling the ON-OFF state of each pixel, the tunable optical device can generate a dynamic image which carries temporal and spatial codes for the purpose of identification. The ID tag (cat's eye retroreflector array) can operate at two orientations.

Interferometric measurement of angular motion

This paper describes the design and realization of a homodyne polarization interferometer for measuring angular motion. The optical layout incorporates carefully designed cat's eye retroreflectors that maximize the measurable range of angular motion and facilitate initial alignment. The retroreflectors are optimized and numerically characterized in terms of defocus and spherical aberrations using Zemax software for optical design. The linearity of the measurement is then calculated in terms of the aberrations. The actual physical interferometer is realized as a compact device with optical components from stock and without relying on adjustable holders. Evaluation of its performance using a commercial autocollimator confirmed a reproducibility within 0.1%, a non-linearity of less than 1 ppm with respect to the autocollimator, an upper limit to its sensitivity of about 5 × 10(-11) rad/Hz from audioband down to 100 mHz and an angular measurement range of more than ±1°.

Integral wide-field spectroscopy in astronomy: the Imaging FTS solution

Long-slit grating spectrometers in scanning mode and Fabry–Perot interferometers as tunable filters are commonly used to perform integral wide-field spectroscopy on extended astrophysical objects as HII regions and nearby galaxies. The goal of this paper is to demonstrate, by comparison, through a thorough review of the imaging Fourier transform spectrometer (IFTS) properties, that this instrument represents another interesting solution. After a brief recall of the performances, regarding FOV and spectral resolution, of the grating spectrometer, without and with integral field units (IFU), and of the imaging Fabry–Perot, it is demonstrated that for an IFTS the product of the maximum resolution R by the entrance beam etendue U is equal to $2.6\,N\times S_I$ with $N\,\times \,N$ the number of pixels of the detector array and S $_I$ the area of the interferometer beamsplitter. As a consequence, the IFTS offers the most flexible choice of field size and spectral resolution, up to high values for both parameters. It also presents on a wide field an important multichannel advantage in comparison to integral field grating spectrometers, even with multiple IFUs. To complete, the few astronomical IFTSs, built behind ground-based telescopes and in space, for the visible range up to the sub-millimetric domain, are presented. Through two wide-field IFTS projects, one in the visible, the other one in the mid-infrared, the question is addressed of the practical FOV and resolution limits, set by the optical design of the instrument, which can be achieved. Within the 0.3 to $\sim $ 2.5 $\upmu$ m domain, a Michelson interferometer with wide-field diopric collimators provides the easiest solution. This design is illustrated by a $11^{\prime}\times 11^{\prime}$ -field IFTS in the 0.35–0.90 $\upmu$ m range around an off-axis interferometer, called SITELLE, proposed for the 3.6-m CFH Telescope. At longer wavelengths, an all-mirror optics is required, as studied for a spaceborne IFTS, H2EX, for the 8–29 $\upmu$ m range, a $20^{\prime} \times 20^{\prime}$ field, and a high resolution of $\simeq 3\times 10^4$ at 10 $\upmu$ m. To comply with these characteristics, the interferometer is designed with cat’s eye retroreflectors. In the same domain and up to the far infrared, if the instrument aims only at a low spectral resolution (few thousands) and a smaller field (few arcmins $^2$ ), roof-top or corner cube mirrors, as for the IFTS SPIRE on the Herschel space telescope, are usable. At last, perspectives are opened, behind an ELT in the visible and the near infrared with the SITELLE optical combination, in the 2–5 $\upmu$ m on the Antarctic plateau or in space up to longer wavelengths, with the H2EX design, to provide the missing capability of global high spectral resolution studies of extended sources, from comets to distant galaxy clusters.

Modeling of micro cat’s eye retroreflectors using a matrix-based three-dimensional ray tracing technique

In this paper we develop a three-dimensional (3D) ray tracing tool based on the ABCD ray transfer matrices. With symmetric optical components and under paraxial approximation, two sets of 2×2 ABCD matrices, each for a two-dimensional subspace, can be used to describe the 3D ray propagation completely. Compared to commercial ray-tracing software packages, our tool requires no tedious drawing, and the results for various conditions, such as different device dimensions and incident angles, can be easily obtained by simply changing the parameter values used for the calculation. We have employed this matrix-based 3D ray tracing tool to model cat's eye retroreflectors. The cat's eye performance, including the retroreflection efficiency, acceptance angle (i.e., field of view), and beam divergence and deviation, is fully studied. The application of this 3D ray tracing technique can be further extended to other optical components.

Fabrication and characterization of a micro tunable cat's eye retro-reflector

In this paper, we report on a micro tunable cat's eye retro-reflector. The tunability is obtained through the use of a smart film, a polymer dispersed liquid crystal device (PDLC). The cat's eye device consists of three subassemblies, a front-side focusing unit, the smart film, and a back-side reflecting unit. The characterization of the device, considering possible fabrication inaccuracy such as misalignment, is presented. Such a device can be used in a free-space communication system, or more specifically, an optical identification system.

Mirror tilt immunity interferometry with a cat’s eye retroreflector

This paper describes the behavior of a cat's eye retroreflector, which is incorporated in a novel way in a double-pass homodyne polarization interferometer. The amount of mirror tilt immunity a cat's eye provides is calculated within the paraxial approximation using 4×4 ABCD matrices. It is found that there is a position of the target mirror in which the tilt immunity is at a maximum. A real cat's eye, which is affected by aberrations, is optimized and examined using Zemax software for optical design. The maximum amount of mirror tilt immunity is numerically calculated and written in terms of defocus and spherical aberration. Finally, for the purposes of comparison, the amplitude of the Lissajous pattern as the target mirror tilts is calculated for both an interferometer with an integrated cat's eye and an interferometer with a cube corner.

Novel moving cat's-eye-pair interferometer

A novel type of cat's-eye interferometer, the novel moving cat's-eye-pair interferometer, is presented. It has neither tilt nor shearing problems. It consists of one moving cat's-eye-pair (MCEP), i.e. two identical cat's-eye retro-reflectors fixed together back to back in a rigid structure as a single moving element, four fixed plane mirrors and one beam-splitter. The optical path difference (OPD) is created by the straight reciprocating motion of the MCEP, and the OPD value is eight times the displacement of the MCEP. The new interferometer is suitable for very-high resolution Fourier transform spectrometers for any wave-number region from the far infrared down to the visible if the cat's-eye retro-reflector comprises a parabolic primary and a spherical secondary.

Free-space optical communication link across 16 kilometers over the Chesapeake Bay to a modulated retroreflector array

This paper presents the results of a successful bidirectional free-space optical link across 16 km to a modulated retroreflector array. The link was implemented at the Naval Research Laboratory's Chesapeake Bay Detachment laser test range. A 6-W cw 1550-nm class 1 M interrogation beam was used to illuminate an array of three modulated cat's-eye retroreflectors located on a tower across the Chesapeake Bay on Tilghman Island. The modulated retroreflectors had a diameter of 16 mm and were arranged in a triangular pattern with a spacing of 30 cm. The interrogating terminal employed a 100-µrad divergence and a high-speed pointing and tracking system to maintain link alignment. Link testing occurred over 12 days in the months of September, October, and November of 2006. Topics presented in this paper include the link scenario for the 16-km free-space optical link, the link budget, and terminal designs, as well as link acquisition and performance. Link performance results presented include data transmission throughput, scintillation data, and pointing and tracking results.

General method for determining the sensor readings of motion measurement systems by using skew-ray tracing method

High-accuracy laser-based optoelectronic motion- and position-measuring systems typically utilize light rays that travel from one optical boundary surface to another to perform motion and/or position measurements. It is not a simple task to accurately determine the equations of these sensor readings in terms of positional/angular motions. This problem is addressed in this paper by application of the analytic skew-ray tracing methodology as computed by the finite-difference methodology. An illustrative example of a motion-measurement system and comparison of the position-sensing detector (PSD) readings are given to validate the proposed methodology. It is shown that the proposed methodology can provide accurate expressions of PSD readings. It is also shown that the performance of a corner-cube retro-reflector is better than a cat's eye retro-reflector in positional/angular motion measurement systems.