Two simplified versions of the four-flux radiative transfer model (the standard one and a novel extended form) are put into context with respect to the generalized approach. Collimated-collimated, collimated-diffuse, and diffuse-diffuse reflectance and transmittance (R&T) spectra of anatase (TiO2) pigments in a polymeric aqueous medium are generated by these four-flux models. To this end, it has been necessary to evaluate previously the scattering and absorption cross sections, average pathlength parameters, and forward scattering ratios that enter these models. The evaluation has been carried out assuming no interaction between neighboring particles, or assuming the presence of particle aggregates in the composite medium. In the first case, the Lorenz-Mie theory has been applied to obtain the expansion of the phase function in Legendre polynomials. For particulate media containing aggregates, the coefficients in this expansion are derived using a transition matrix formalism. Additionally, parameters such as scattering and absorption cross sections, albedo, and asymmetry parameter have been determined. Evaluating synthetic R&T spectra of these materials can be useful to validate inversion procedures using spectral gradient and simulated annealing methods. Quantifying the dependent scattering effect in R&T spectra, both collimated and diffuse, is now possible. This has been done mostly at the level of cross sections, albedos, and asymmetry parameters of particle aggregates, but not for parameters that can be directly correlated with spectrophotometric measurements like R&T.

We present a robust objective lens optimized for applications requiring both high numerical aperture (NA) and long front working distance imaging, comprised of all commercial-off-the-shelf (COTS) spherical singlet lenses. Unlike traditional designs that require separate collimation and refocusing stages, our approach directly converges imaged light to the back focal plane using a single lens group. Our configuration corrects spherical aberrations and efficiently collects light to achieve diffraction-limited performance across a wide range of wavelengths while simplifying alignment and assembly. Using this approach, we design and construct an example objective lens that features a long front working distance of 61 mm and a clipped NA of 0.30 (limited by an aperture in our experimental setup). We experimentally verify that it achieves monochromatic diffraction-limited resolution at wavelengths from 375 nm to 866 nm without requiring replacement of the lenses or changing the inter-lens spacings, and its performance remains robust across a 46 mm range variation in total length (by adjusting mainly the back working distance). Additionally, we develop a quantitative method to measure the field of view (FOV) using an experimentally calibrated pinhole target. Under 397 nm illumination (i.e., from 40 Ca + ion fluorescence), the objective achieves a resolution of 0.87 μ m with a 540 μ m FOV. This robust, all-COTS, and versatile design is well-suited for a broad range of experiments, supporting high-precision measurements and exploring quantum phenomena.

In this study, we investigate the magnification and angular resolution of a single water droplet positioned on a glass surface, functioning as an optical imaging system. Through theoretical analysis of the droplet’s shape, magnification, and angular resolution, we derive predictions that are subsequently validated through experiments. Our study explores the impact of key parameters, including droplet size, the distance between the droplet and the object, and the contact angle, on the aforementioned optical characteristics. Our findings reveal that smaller droplets exhibit higher magnification at shorter object-to-droplet distances and demonstrate superior resolving capability (i.e., smaller angular resolution).

Spatio-temporal optical coherence tomography (STOC-T) enables high-speed retinal imaging but suffers from limited sensitivity. We present a high-throughput (HT) optical design that improves STOC-T sensitivity by up to 3.5× (5.5 dB). This is achieved by replacing the standard 50/50 beamsplitter with a 90/10 one and using a pupil-plane pick-off mirror to maximize light delivery and signal detection. We validate the design on reflective and scattering phantoms, as well as in vivo human retina, demonstrating significant SNR gains without increasing source power. This simple, light-efficient approach makes STOC-T more suitable for real-time, low-signal imaging applications.

Traditional stone-like camouflage materials often exhibit high exposure probability during engineering terrain restoration due to significant differences in thermal infrared characteristics compared to natural rocks. To address this issue, this study established a thermal radiation model based on the Stefan-Boltzmann law. A low-emissivity coating was prepared using aluminum oxide-graphite powder mixture as functional materials and epoxy resin as binder to reduce the emissivity of stone-like surfaces. Microencapsulated phase-change paraffin was internally incorporated into stone-like materials to regulate temperature variations. Simulation results identified optimal contents of 25% aluminum oxide powder and 5% graphite powder in the stealth coating, with the optimal phase-change material content being 20% of cement mass. Infrared stealth specimens were fabricated according to these optimal ratios for experimental evaluation. Results demonstrate that the external stealth specimen achieves a minimum surface emissivity of 0.643 in the 8–14 μm wavelength range. After 24-hour thermal cycling tests, the mean radiation temperature difference between the specimen and natural marble reached -0.57 K (variance: 0.14 K2), showing negligible discrepancy with natural rock radiation characteristics. Thermal infrared imaging analysis revealed no discernible differences between the stealth specimen and natural marble. The designed infrared stealth specimen demonstrates excellent camouflage performance, providing valuable insights for enhancing infrared stealth capabilities in protective engineering applications.

This paper presents what we believe to be a novel theoretical framework for analyzing two-dimensional (2D) diffraction phenomena using biquaternions. We introduce a rigorous mathematical development of the 2D integral theorem of Helmholtz and Kirchhoff, the 2D biquaternionic Fresnel-Kirchhoff diffraction formula, and the 2D biquaternionic Rayleigh-Sommerfeld diffraction formula. The proposed approach offers several advantages over traditional methods, including a more concise and elegant representation of the diffraction process.

In this work, we present an experimental investigation of the temperature-dependent transmission characteristics of a low-birefringence Sagnac interferometer incorporating a double-sense twisted fiber loop. The study focuses on the influence of wave retarder adjustments within the loop on the interferometric response over a temperature range of 25°C to 50°C. A 10-meter fiber loop, optimized for maximum transmission, exhibited an approximately linear transmission profile, achieving a sensitivity of 10.62µW/°C within the 35–50°C interval. In contrast, the 300-meter loop demonstrated a sinusoidal transmission behavior, with a sensitivity of approximately 140.03µW/°C observed between 30°C and 35°C. The comparative analysis reveals that the short-loop configuration offers stable and predictable linear response characteristics. In contrast, the higher sensitivity of the longer loop restricts its utility to narrower temperature windows. Hysteresis effects were consistently recorded in both configurations, suggesting dynamic thermal responses attributable to coil-induced birefringence. These results underscore the significant influence of temperature on the performance of Sagnac interferometers across a variety of industrial and scientific scenarios.

A reconfigurable silicon-photonic filter stage for the processing and monitoring of input signals is demonstrated and employed. The device consists of a balanced Mach-Zehnder interferometer with two ring resonators nested in each arm and built-in germanium photodetectors at its output ports. The transfer function of the device is adjustable through thermo-optic tuning of optical phase delays within each of the four resonators and between the two interferometer arms. Response examples include bandpass filters of variable bandwidth, as well as narrow bandpass and narrow band-stop shapes. The device is used in the wavelength division demultiplexing of a 16 Gbit/s on-off-keying data channel, with spacing of only 26 GHz between adjacent channels. A basic optical spectrum analyzer is realized by scanning the transmission wavelength of a narrowband filter response and reading the output from the on-chip detector. The device supports agile processing and monitoring input signals.

To mitigate severe thermal challenges within co-packaged optics (CPO) modules and prevent adverse effects on electrical or silicon photonic chip performance, the optical transmitter can effectively utilize an external laser source (ELS). This article presents the design, fabrication, and testing methodology of a four-channel coarse wavelength division multiplexing (CWDM) cooled distributed feedback laser diode (DFB-LD) module explicitly developed for CPO ELS applications. We selected AlGaInAs multiple quantum well (MQW) DFB-LDs with nominal wavelengths of 1265 nm, 1285 nm, 1305 nm, and 1325 nm to meet the requirements of O-band CWDM systems. Thermoelectric coolers (TECs) and thermistors are integrated into the module to achieve precise temperature control and stable monitoring of the DFB-LDs’ operating temperature, which is crucial for maintaining laser performance. To optimize fiber coupling efficiency, lenses are placed at the LD output facet, and optical isolators are incorporated to prevent back-reflections from the fiber from negatively impacting the DFB-LD chips. The electrical interface of this module complies with the Octal Small Form-factor Pluggable (OSFP) specification, a design choice aimed at facilitating commercialization and simplifying system integration. At a 200 mA bias current, the coupled output power of each channel through a standard single-mode fiber (SMF) exceeds 30 mW, with a coupling efficiency of approximately 50%, demonstrating the module’s potential as an external light source in CPO systems. This paper elaborates on the key steps from design considerations to practical manufacturing, assembly, and performance verification, aiming to provide valuable practical guidance for engineers and researchers in related fields.

We assume a bundle of rays propagating parallel to the optical axis incident on aspheric converging Fresnel-type reflectors (ACFR), to study the formation of caustic surfaces produced by reflection. Subsequently, we evaluate the circle of least confusion (CLC) produced by ACFR. Alternatively, varying the design parameters, it is possible to reduce the size and modify the shape of the caustic surfaces, which have wide potential applications for both imaging and non-imaging optical systems. We ideally provide a formula to evaluate the optical concentration ratio produced by ACFR. If we demand that the absorber is placed at CLC, we can optimize the design for ACFR by increasing its optical concentration ratio. Finally, an ACFR prototype is designed to minimize its CLC and consider the properties of caustic surfaces.