Focal Length Research Articles

Quantitative Phase Imaging for Meta‐Lenses by Phase Retrieval

AbstractMeta‐lenses have advanced focusing and imaging capabilities. Traditional methods for assessing meta‐lenses performance, such as focusing light field scanning, are time‐consuming and cannot obtain phase information. Meta‐lenses require accurate and fast phase information measurements for industrial‐level applications. Here, a novel approach is introduced for meta‐lenses phase recovery from defocused images. The precise phase can be obtained by optimizing the complex amplitude of the meta‐lens from the experimentally collected defocused images through complex gradient descent. This method doesn't need complicated experimental setups like traditional off‐axis interferometry. This method is robust and applicable to meta‐lenses with diverse phase modulations. The investigation is extended to measure the phase information of the Pancharatnam‐Berry phase‐based meta‐lens and the achromatic meta‐lens in different incident wavelengths. These results demonstrate that this technique accurately recovers phase information. The 3D intensity profile can be retrieved at arbitrary distances, which is faster and more accurate, enabling the prediction of optical properties such as focal length. This advancement enhances the understanding of meta‐lense behavior in practical scenarios. It provides a foundation for future optimizations in meta‐lenses design, potentially leading to more efficient and versatile optical systems.

Design and analysis of a linear astigmatism-free confocal off-axis reflective collimator for aerial applications

This paper presents the design and analysis of a linear astigmatism-free confocal off-axis reflective collimator for line-of-sight alignment in multi-wavelength/multi-field-of-view optical sensor modules. Comprising two off-axis mirrors and one flat mirror, the collimator has a 73 mm entrance pupil diameter and a 1200 mm focal length. Sensitivity analysis and Monte Carlo simulations using Optic Studio (ZEMAX) confirmed that the design meets all specified requirements. Stray light analysis shows that stray light is effectively blocked by the optomechanical structures only, eliminating the need for additional baffle structures. A semi-kinematic mount ensures assembly precision, while modal analysis indicates a fundamental frequency of 232.55 Hz, ensuring durability in aerial operations.

Color astrophotography with a 100 mm-diameter f/2 polymer flat lens

We demonstrate a 100 mm-diameter, 2.4 μm-thick multilevel diffractive lens (MDL) with a 200 mm focal length, optimized for the 400 to 800 nm wavelength range—specifications that are difficult to achieve even with complex multi-element refractive systems. Created using an inverse-design approach and grayscale lithography, the MDL achieves achromatic focusing, confirmed through hyperspectral point-spread function (PSF) characterization. Imaging experiments resolved spatial frequencies up to 181 lp/mm and demonstrated the MDL's capability in capturing high-quality, full-color images of the moon, sun, and distant terrestrial scenes. Color-enhanced lunar images revealed key geological features, while solar imaging identified visible sunspots. Additionally, the MDL was integrated with a refractive achromatic lens to form a hybrid telescope, significantly reducing weight for airborne and space-based imaging applications. Simulations and experimental results reported here underscore the potential of large-area achromatic flat lenses as lightweight alternatives to conventional refractive systems for astrophotography and other long-range imaging tasks.

Calibrating laser Doppler anemometers utilizing an optical chopper

Abstract Laser doppler anemometers (LDAs) use scattered light to determine velocity components of a flowing fluid. The operating principal of LDAs is simple conceptually; however, it is impractical to trace the LDA-determined velocities to the SI by characterizing the LDA’s subsystems that generate, detect, and process optical signals because these subsystems are complex and include proprietary features. To circumvent this, we calibrated the complete LDA systems utilizing an optical chopper blade as an accurate, SI-traceable velocity standard. The calibrations achieved the expanded velocity uncertainty 0.094 % at a 95 % confidence level. We calibrated two LDAs that differed in manufacturer, focal length (in the ratio 3.3:1), sensing volume (in the ratio 100:1), and orientation (vertical and horizontal bisectors of the LDA's crossing beams). To compare the calibrations, we measured airspeeds in NIST's wind tunnel using both LDAs. The results differed from each other by, at most, 0.2 % throughout the airspeed range 0.5 m/s to 30 m/s.

Lensless efficient snapshot hyperspectral imaging using dynamic phase modulation

Snapshot hyperspectral imaging based on a diffractive optical element (DOE) is increasingly featured in recent progress in deep optics. Despite remarkable advances in spatial and spectral resolutions, the limitations of current photolithography technology have prevented the fabricated DOE from being designed at ideal heights and with high diffraction efficiency, diminishing the effectiveness of coded imaging and reconstruction accuracy in some bands. Here, we propose, to our knowledge, a new lensless efficient snapshot hyperspectral imaging (LESHI) system that utilizes a liquid-crystal-on-silicon spatial light modulator (LCoS-SLM) to replace the traditionally fabricated DOE, resulting in high modulation levels and reconstruction accuracy. Beyond the single-lens imaging model, the system can leverage the switch ability of LCoS-SLM to implement distributed diffractive optics (DDO) imaging and enhance diffraction efficiency across the full visible spectrum. Using the proposed method, we develop a proof-of-concept prototype with an image resolution of 1920×1080 pixels, an effective spatial resolution of 41.74 μm, and a spectral resolution of 10 nm, while improving the average diffraction efficiency from 0.75 to 0.91 over the visible wavelength range (400–700 nm). Additionally, LESHI allows the focal length to be adjusted from 50 mm to 100 mm without the need for additional optical components, providing a cost-effective and time-saving solution for real-time on-site debugging. LESHI is the first imaging modality, to the best of our knowledge, to use dynamic diffractive optics and snapshot hyperspectral imaging, offering a completely new approach to computational spectral imaging and deep optics.

Adaptive Fresnel lens: basic theory

We present a design for an adaptive Fresnel lens. The focal length can be altered by rotating two components relative to each other, each comprising modified cylindrical lenses wound into spirals. The main light-ray-direction change is due to transmission through pairs of parallel cylindrical lenses whose focal lengths have equal magnitude but opposite signs. Shifting the cylindrical lenses relative to each other perpendicular to the common cylinder-axis direction changes the directions of transmitted light rays, and by designing each component to be one long, thin, cylindrical lens whose focal length changes along its length and is bent into a suitable spiral, rotation of the components relative to each other shifts the cylindrical lenses as required. Adding the thickness profiles of the two parts of a cylindrical Alvarez–Lohmann lens to those of the two cylindrical lenses significantly improves the optical performance. We support our construction with raytracing simulations and discuss potential applications.

Liquid lens with a large aperture and a wide zoom range by using a flexible retractable pipe

In this work, a large-aperture and wide zoom range liquid lens based on a flexible retractable pipe is proposed. It mainly consists of a flexible corrugated pipe, transparent filling liquid, elastic film, and electromagnetic actuator. By applying different currents, the pipe stretches or compresses along the axial direction, changing the curvature of the elastic membrane instead of driving by the filling liquid flow, and ultimately realizing the continuous tuning of the focal length. In the experiment, a 20 mm aperture liquid lens prototype is fabricated and tested. As the current changes from −300 to 300 mA, the negative focal length varies from −∞ to −46.25mm, while the positive focal length ranges from 44.25 mm to +∞. When the current is 300 mA, the lens achieves 45.30 lp/mm resolution and exhibits 1.73× magnification. Additionally, its response time is less than 8 ms.

Fluid‐Induced Reconfigurable Polarization‐Insensitive Metasurfaces for Optical Wireless Communications

AbstractIn optical wireless communication (OWC), the adaptability of infrared and visible spectra is attracting growing interest. These technologies are promising solutions for various real‐world applications, including indoor, underwater, vehicular, and IoT systems. However, conventional OWC systems are constrained by their bulky structures and fixed optical properties, which limit their ability to provide on‐demand communication services and integrate with on‐chip technologies. Therefore, the demand for ultrathin, reconfigurable devices with real‐time adaptability is becoming increasingly urgent to ensure efficient and reliable communication. Here, this study introduces a fluid‐induced reconfigurable, polarization‐insensitive metasurface to enhance the performance and flexibility of OWC networks. A key feature is its ability to adjust diffracted light to meet communication requirements, irrespective of the polarization state of the incident light. This metasurface utilizes infrared light at a wavelength of 1550 nm to enhance signal transmission and reduce environmental interference. In a proof‐of‐concept, a 0.5 mm × 0.5 mm metasurface is fabricated, and its focal length variation is verified in three different fluidic environments: Air (n = 1), Polymethyl methacrylate (PMMA) (n = 1.491), and AZ‐GXR (n = 1.602). The proposed design offers reconfigurability, reduced polarization sensitivity, and consistent signal quality, making it ideal for next‐generation OWC applications.

Two-photon nanolithography of sub-micrometer thickness microlenses designed by NPCC assisted Rayleigh Sommerfeld diffraction integral

Recent development of artificial neural networks (ANNs) and inverse design methods have demonstrated their prospective significance for planar diffractive lens design, with a plethora of optical lenses designed for wavelengths ranging from visible to Thz wavelengths. However, previous research to design planner diffractive lenses only considers the maximum intensity in the focus area or its derivatives as the optimization function, leaving the intensity outside the focus area unconsidered. We proposed and investigated a two-dimensional (2D) physics-driven ANN method assisted by the negative Pearson correlation coefficient (NPCC) to design microlenses with varied focusing distances, which takes the entire 2D intensity distribution at the focus plane as an optimization function. Taking advantage of 3D two-photon nanolithographic technology, sub-micrometer thickness microlenses with varied focusing lengths are designed and fabricated, achieving an average focusing efficiency of around 35%, and an average focusing spot size of about 1 µm. Furthermore, a microlens array (19 by 19 microlenses with a total size of 4 mm2) with a curved focusing plane was fabricated and integrated into a CMOS sensor, achieving direct object imaging under incoherent white light illumination. Our results demonstrate that the NPCC is a very useful optimization function for designing planar diffractive lenses, and the use of NPCC in ANNs is of great potential for the future design of functional diffractive optical elements in optics and nanophotonics.

Continuous varifocal metalens based on phase-change material

Abstract Metasurfaces have provided new opportunities for the realization of flat lenses, among which tunable metalenses have garnered considerable attention due to their flexible functionalities. In this paper, we present a continuously tunable metalens based on the phase-change material Sb2S3, which enables precise and continuous focal length control through the transition of states. Under the excitation of linearly polarized light at 1550 nm, phase compensation is provided by changing the crystallization state of the Sb2S3 nanopillars, allowing the focal length to continuously shift between 36 µm and 48 µm. At the same time, the metalens maintains a high focusing efficiency over 75%. This approach provides greater design flexibility and broader applicability across diverse applications. By reducing the reliance on polarized light sources, it enhances device integration and tunability, paving the way for new opportunities in the practical implementation of metalenses in advanced optical imaging and nanophotonics.

Design of a Freeform Surface Optical Detection System with a Square Aperture

To meet the demands for heightened detection sensitivity in satellite-based space target detection systems, we introduce an innovative square aperture diaphragm system utilizing freeform surfaces for detecting targets in the visible light spectrum. Characterized by a 40 mm × 40 mm square entrance pupil, a 4° × 4° field of view (FOV), and a 150 mm focal length, this system achieves a spot size of 2 × 2 pixels with 85% energy concentration within 18.4 μm, showcasing exceptional performance. Our design, compared to a circular aperture system of similar specifications, increases the entrance pupil area by 27% while having a smaller volume, resulting in a 0.24 magnitude improvement in the detection of space targets. This advancement significantly enhances our ability to detect fainter space targets with high sensitivity. The findings of this study pave the way for advancements in satellite-based space target detection technology.

Analysis of two-element optical system composed of membrane fluidic lenses with variable focal length

Analysis of two-element optical system composed of membrane fluidic lenses with variable focal length

Unique thermal characteristics of polarization-insensitive metalenses over traditional refractive and diffractive lenses

The thermal characteristics of lenses play an essential role in the performance of optical systems, particularly infrared detection systems. Metalenses, composed of sub-wavelength nanostructured surfaces, have recently emerged as a promising technology to realize flat, lightweight, and mass-producible lenses. However, their thermal behavior remains largely unexplored. This study examines the impact of uniform temperature variations (both theoretically and experimentally) and laser heating (theoretically) on the performance of polarization-insensitive metalens (PIM) at a representative wavelength of 10.6 µm. We compare the thermal performance of PIMs with refractive and diffractive lenses, by a comprehensive structural, thermal, and optical performance (STOP) analysis through finite-element analysis (FEA) and finite-difference-time-domain (FDTD) simulations. A comprehensive analysis of various thermal aberration indicators reveals that the PIM exhibits smaller thermal aberrations than both the aspheric lens and the harmonic diffractive lens, and its performance is closer to that of a traditional diffractive optical element (DOE). We also find that the unique nanostructures of PIM make it highly sensitive to the refractive index change induced by temperature variations, allowing the PIM to achieve unique capabilities compared to other lenses. A typical example is that the PIM consistently demonstrates an opposite shift in focal length and depth of focus, contrary to conventional cases. We also experimentally verify the near-athermal properties of 5-centimeter-aperture metalens, confirming the advantages of large-aperture PIMs over refractive lenses in athermal infrared imaging applications. Additionally, our numerical analysis demonstrates that the broadband achromatic metalens notably outperforms the DOE in simultaneously achromatic (8 to 12 µm) and athermal (-60 to 80°C) performance. It is reasonable to speculate that the thermal diffraction efficiency of the achromatic metalens is likely superior to that of the achromatic multi-level diffractive lens (MDL). Our results confirm the strong potential of metalenses in athermal imaging applications.

High‐Isolation Multidimensional Holography Multiplexing in Non‐Interleaved Metasurfaces

AbstractMetasurfaces have revolutionized holography by enabling high‐density channel multiplexing, positioning them as promising candidates for applications in full‐color holographic imaging, optical data storage, and encryption. However, conventional non‐interleaved metasurfaces face limitations in the number of controllable dimensions, restricting the channels available in each dimension. Here, a novel high‐dimensional multiplexing scheme is introduced that significantly enhances both the channel multiplexing capacity and isolation in non‐interleaved metasurfaces. By integrating the Rayleigh‐Sommerfeld diffraction (RSD) formula into the Gerchberg‐Saxton (GS) algorithm and incorporating gradient descent optimization, the approach achieves precise phase profile control across multiple dimensions—extending the controllable parameters to include wavelength, polarization state, and spatial distance. This method enables simultaneous multiplexing of three polarization channels, three wavelength channels, and two focal plane distances, producing a total of 18 distinct, well‐isolated holographic channels with minimal crosstalk. These results showcase the powerful channel multiplexing and isolation capabilities of this non‐interleaved metasurface design, underscoring its potential to advance optical color imaging, secure data storage, and high‐capacity information transmission, thereby contributing to the development of next‐generation intelligent optical devices.

Ultrasound liquid–gel hybrid lens using acoustic radiation forces

Conventional camera modules use a mechanical system comprising moving parts to change the focal length of the lens by moving it along the optical axis, increasing the volume of the camera. Here, the potential of compact variable-focus lenses was examined to enhance response speed and robustness via a combination of viscoelastic gel films, liquids, and acoustic radiation forces. The optical properties of the lenses were evaluated using a wavefront sensor. Focal lengths could be controlled by changing the lens shape via acoustic radiation forces generated by ultrasound vibrations. The response time of the lens was dependent on the thickness of the gel film on the lens surface; a thinner film thickness resulted in a shorter response time. The response times for hybrid lenses with gel film thickness of , 0.8 mm, 1 mm, and 2 mm were 58 ms, 68 ms, 82 ms, and 172 ms, respectively.

Vehicle speed measurement method using monocular cameras

This paper proposes a method for fast and accurate vehicle speed measurement based on a monocular camera. Firstly, by establishing a new camera imaging model, the calibration method for variable focal lengths is optimized, simplifying the transformation process between the four coordinate systems in traditional camera imaging models, and the method does not need to restore the pixel coordinates to dedistortion. Secondly, based on the camera imaging model, a two-dimensional positioning algorithm is proposed. By leveraging the characteristics of the speed measurement problem, the complex three-dimensional positioning problem is simplified into a two-dimensional model, reducing the overall computational complexity of the positioning problem. Finally, the algorithm is combined with You Only Look Once version 7 (YOLOv7) and Deep Simple Online and Realtime Tracking (DeepSORT) algorithms, integrating multiple model structures to optimize the network, achieving precise multi-target speed measurement. Experiments show that under frame-by-frame measurement conditions, the minimum and average accuracies of this method reach 95.1% and 97.6%, respectively. Compared with other methods, it has significant advantages in speed measurement accuracy and computational efficiency. Therefore, this research outcome is expected to play an important role in intelligent transportation systems and road safety management.

Practical error prediction in UAV imagery-based 3D reconstruction: assessing the impact of image quality factors

ABSTRACT Over the past decade, Structure-from-Motion (SfM) and Multi-View Stereo (MVS) techniques have been highly effective in generating high-quality 3D point clouds, especially when integrated with Unmanned Aerial Vehicles (UAVs). However, accurately predicting errors in these point clouds remains challenging. This study introduces a predictive model for quantifying errors in point clouds generated using SfM-MVS, based on 2D image error propagation. We analysed the impact of four key image quality factors – exposure, resolution, blur (including motion and out-of-focus blur), and noise – on 2D image errors. These factors are determined using nine practical parameters belonging to camera settings (ISO, shutter speed, F-number, and pixel resolution), UAV flight methods (speed and distance), camera specifications (sensor size and focal length), and illumination conditions. To account for variations in SfM-MVS output quality due to software and camera model differences, we introduced two experimentally calibratable constants: the maximum template size and the noise sensitivity coefficient. We validated our error prediction model by comparing the predicted errors with observations from a reference indoor target, utilizing a total of 258 image sets acquired with varying parameter combinations. The model demonstrated high predictive accuracy, achieving an R2 value of 0.84. This confirms the effectiveness and feasibility of our model in accurately predicting point cloud errors using the nine parameters.

Compact High-Zoom-Ratio Mid-Wavelength Infrared Zoom Lens Design Based on Particle Swarm Optimization.

This paper presents an automated method for solving the initial structure of compact, high-zoom-ratio mid-wave infrared (MWIR) zoom lenses. Using differential analysis, the focal length variation process of zoom lenses under paraxial conditions is investigated, and a model for the focal power distribution and relative motion of three movable lens groups is established. The particle swarm optimization (PSO) algorithm is introduced into the zooming process analysis, and a program is developed in MATLAB to solve for the initial structure. This algorithm integrates physical constraints from lens analysis and evaluates candidate solutions based on key design parameters, such as total lens length, zoom ratio, Petzval field curvature, and focal length at tele end. The results demonstrate that the proposed method can efficiently and accurately determine the initial structure of compact MWIR zoom lenses. Using this method, a mid-wave infrared zoom lens with a zoom ratio of 50×, a total length of less than 530 mm, and the ratio of focal length to total length approximately 2:1 was successfully designed. The design validates the effectiveness and practicality of this method in solving the initial structure of zoom lenses that meet complex design requirements.

Depth‐Modulus Engineered Meta‐Elastomers for Multiaxial Strain Programming in Stretchable Displays

With the growing demand for displays with diverse form factors, stretchable displays are at the forefront of this evolution garnering significant interest. One challenge is image warping caused by the high Poisson's ratio (ν) of conventional elastomers during stretching, meta‐elastomer (ME) substrates incorporating high‐modulus mechanical metamaterial frames with a negative ν have emerged as promising solutions. However, the modulus mismatch between the frame and matrix results in undesirable thickness variations in ME substrates under tensile stress, degrading image quality by distorting the focal length. In this study, depth‐modulus engineered MEs that achieve near‐zero ν under multiaxial strain are reported. By infiltrating a vaporized cross‐linker, a continuous depth‐modulus gradient in the ME substrates is created, effectively minimizing Poisson's effects and z‐axis deformation simultaneously. These continuous gradient depth‐modulus engineered ME (C‐GDME) substrates reduce the in‐plane ν to 0.09 and exhibit thickness variation close to half that of pristine ME substrates without modulus tailoring. Furthermore, C‐GDME substrates demonstrate excellent mechanical durability and ≈90% visible‐light transmittance. The integrated light‐emitting diode arrays on the C‐GDME substrates display linear and predictable pixel displacement under stretching, highlighting their potential for stretchable displays.

Continuously focus tunable 2D/3D switchable cylindrical liquid crystal microlens arrays for autostereoscopic displays.

Cylindrical microlens arrays are important optical elements for autostereoscopic display. Conventional fixed focal length cylindrical microlens arrays do not allow switching between 2D mode and 3D mode when constructing a 3D viewing zone. In contrast, cylindrical liquid crystal microlens arrays with zoom characteristics allow switching between 2D and 3D states, as well as adjusting the width of the sub-viewing zone. Therefore, based on the quantitative analysis of the geometrical structure of the viewing zone in different states, this paper proposes a continuous zoom type cylindrical liquid crystal microlens array structure, which is a liquid crystal cell composed of an array of plano-concave glass substrates and planar glass substrates. Theory and experiments show that it is close to a favorable parabolic phase profile at different driving voltages, and at the same time, it can realize a zoom range of 1.6mm-36 mm at a smaller driving voltage. The wide zoom range and excellent zoom effect make this structure particularly suitable for autostereoscopic display, and this characteristic can achieve the effect of switching between 2D and 3D by adjusting the shape of the central viewing zone.