We show a digital holographic approach for polarimetric characterization of a twisted nematic liquid crystal spatial light modulator (TNLC-SLM). An experimental scheme is designed to perform polarization analysis of the SLM with gray levels. This is realized by simultaneous detection of the polarization states of the light from the SLM for a given gray level with the help of a specially designed spatial-frequency multiplex polarization interferometer. This provides amplitude and phase characteristics of the SLM in a single shot. In order to characterize the SLM, we perform Jones matrix imaging at its various gray values (driving voltages), and corresponding results are presented. These results are expected to be useful in designing and developing various SLM-based experiments in the scalar and vectorial domain.Deflectometry has been widely used to detect defects on specular surfaces. However, it is still very challenging to detect defects on semispecular or diffuse surfaces because of the low contrast and low signal-to-noise ratio. To address this challenge, we proposed a phase-modulation combined method for accurate defect detection. Based on the phase and modulation of captured fringes, a dual-branch convolutional neural network is employed to simultaneously extract geometric and photometric features from the phase-shifting pattern sequence and modulation, which improves the defect detection performance significantly. Compared to state-of-the-art methods, we believe the results demonstrated the proposed method's effectiveness and capability to reduce false positives.A phase imaging technique based on the transport of intensity equation with polarization directed flat lenses is demonstrated. Transport-of-intensity phase imaging enables one to obtain a phase distribution from through-focus intensity distributions by solving the transport of intensity equation. In general, the through-focus intensity distributions are obtained by mechanical scanning of an image sensor or target object. Therefore, a precise alignment of an optical system is required. To solve this issue, the introduction of polarization directed flat lenses is presented. In the proposed method, two intensity distributions at different depth positions on the optical axis are obtained without mechanical scanning by changing polarization states of incident light. The feasibility of the proposed method is confirmed by an optical experiment.Spectrum-fingerprint anti-counterfeiting fiber with double luminous centers was tentatively prepared using $\rm SrAl_2\rm O_4\rm Eu^2 + ,\rm Dy^3 + $SrAl2O4Eu2+,Dy3+, $\rm Sr_2\rm MgSi_2\rm O_7\rm Eu^2 + ,\rm Dy^3 + $Sr2MgSi2O7Eu2+,Dy3+, and PAN powder as main raw materials by wet spinning. The microstructure and spectral properties of the fiber were studied by means of scanning electron microscope (SEM), x-ray diffractometer (XRD), and a fluorescence spectrophotometer. The results showed that the two rare-Earth luminous materials were randomly dispersed on the interior and surface of the fiber. Due to the spinning process, the luminescent materials were agglomerated in fiber, and there were many voids in the fiber. Compared with pure rare-Earth luminous materials, the emission wavelength of the spectrum-fingerprint anti-counterfeiting fiber has no obvious shift, but the addition proportion and amount of two rare-Earth luminous materials have great influence on the spectral curve of the fiber. This fiber with two luminous centers maintains the basic characteristics of spectrum-fingerprint anti-counterfeiting fiber and is a new, to the best of our knowledge, type of anti-counterfeiting fiber with high anti-counterfeiting application potential.The paper presents a detailed theoretical analysis of two-component optical systems of Petzval objective, tele-objectives, reverse tele-objectives, and objectives of anallactic type. This type of optical system is popular in practice, especially in the field of photographic technologies and surveying devices (theodolites, levelling devices, etc.), where anallactic telescopes with inner focusing are used. The paper presents methods of designing of fundamental parameters of the objective, i.e., focal distances of the objective's components and their mutual distance, and radii of curvatures of individual surfaces if the components are cemented doublets. Further, a detailed analysis of aberration properties of those optical systems is presented.An ultracompact and polarization-insensitive power splitter using a subwavelength-grating-based multimode interference (MMI) coupler on an SOI platform is proposed and analyzed in detail. selleck chemical By properly tailoring the structural parameters of the subwavelength gratings embedded in the center of the MMI coupler, the effective reflective indices for TE and TM modes supported by this MMI coupler can be engineered, leading to equal coupling lengths for the two polarizations and an efficient reduction in length for the used MMI coupler. As a result, an ultracompact polarization-insensitive power splitter can be realized. Moreover, to effectively minimize the loss, tapered waveguides are used, and two right angles are cut at both corners of the used MMI coupler. Results show that a footprint of $2.2\;\unicodex00B5 \rm m \times 3.8\;\unicodex00B5 \rm m$2.2µm×3.8µm for the MMI region is achieved with an insertion loss of 0.07 dB for both TE and TM modes (polarization dependent loss $\sim\;0\;\rm dB $∼0dB) and a reflection loss of $ - 28.29\;\rm dB$-28.29dB ($ - 31.25\;\rm dB$-31.25dB) for TE mode at the wavelength of 1.55 µm. Insertion loss below 0.3 dB is obtained over the bandwidth of 200 nm, covering the C-band. In addition, fabrication tolerances to the structural parameters are analyzed, and the injected light propagating through the power splitter is also presented.The displacement measuring technique is prone to failure within the industrial environment due to the influence of dust, oil, and other contaminants that stain the equipment. There is urgent demand for new anti-stain techniques. In today's image angular displacement measurement technology, the pixel array is used instead of the traditional photoelectric conversion element; this creates room for anti-stain improvement based on the image processing components. Based on a previous study on image-type angular displacement measurement technology, a single head image-type anti-stain algorithm is proposed in this paper that can remove the interference of small stains and ensure correct measurement value outputs. The influence of the stain on the calibration grating is first assessed based on the principle of image angular displacement measurement technology. An anti-stain algorithm based on the metal grating and multi-line fusion is proposed accordingly. The proposed algorithm is then tested on a circular grating with 38 mm diameter and $2^N\; = \;256$2N=256 lines in the circle.