Mirror Edges Research Articles

Weakly-Supervised Mirror Detection via Scribble Annotations

Mirror detection is of great significance for avoiding false recognition of reflected objects in computer vision tasks. Existing mirror detection frameworks usually follow a supervised setting, which relies heavily on high quality labels and suffers from poor generalization. To resolve this, we instead propose the first weakly-supervised mirror detection framework and also provide the first scribble-based mirror dataset. Specifically, we relabel 10,158 images, most of which have a labeled pixel ratio of less than 0.01 and take only about 8 seconds to label. Considering that the mirror regions usually show great scale variation, and also irregular and occluded, thus leading to issues of incomplete or over detection, we propose a local-global feature enhancement (LGFE) module to fully capture the context and details. Moreover, it is difficult to obtain basic mirror structure using scribble annotation, and the distinction between foreground (mirror) and background (non-mirror) features is not emphasized caused by mirror reflections. Therefore, we propose a foreground-aware mask attention (FAMA), integrating mirror edges and semantic features to complete mirror regions and suppressing the influence of backgrounds. Finally, to improve the robustness of the network, we propose a prototype contrast loss (PCL) to learn more general foreground features across images. Extensive experiments show that our network outperforms relevant state-of-the-art weakly supervised methods, and even some fully supervised methods. The dataset and codes are available at https://github.com/winter-flow/WSMD.

Toward Autonomous Field Inspection of CSP Collectors With a Polarimetric Imaging Drone

We developed a polarimetric imaging drone to perform field inspections of heliostats and carried out field tests at Sandia’s National Solar Thermal Test Facility (NSTTF). The preliminary results show that Degree of Linear Polarization (DOLP) and Angle of Polarization (AOP) images greatly enhanced the edge detection results compared with the conventional visible images, supporting fast and accurate detection of heliostat mirror edges and cracks. The system holds the promise to enable future automated detection of heliostats optical errors and mirror defects.

Structure constants of operators on the Wilson loop from integrability

We study structure constants of local operators inserted on the Wilson loop in mathcal{N}=4 super Yang-Mills theory. We conjecture the finite coupling expression of the structure constant which is interpreted as one hexagon with three mirror edges contracted by the boundary states. This is consistent with a holographic description of the correlator as the cubic open string vertex which consists of one hexagonal patch and three boundaries. We check its validity at the weak coupling where the asymptotic expression reduces to the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factor. For this purpose, we compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the Wilson loop and the open spin chain. The result is nicely matched with our conjecture at the weak coupling regime.

Open Resonators with Conducting Cylindrical Inserts. 2. Resonators with Finite-Length Mirrors

We present the results of experimental studies of controlling the spectrum and Q-factors of modes in an open resonator with a conducting cylindrical insert. The phenomenon of an increase in the diffraction Q-factor is experimentally observed for the fundamental TEM00q mode for two resonant diameters of the conducting cylindrical insert located inside the open resonator. The features of excitation of modes in an open resonator with smooth cylindrical finite-length mirrors and in an open resonator with cutoff bevels at the mirror edges are studied. Prospects for using open resonators with conducting inserts in quasi-optical devices in the millimeter-wave range are discussed.

Hole coupling resonator for free electron lasers

The performance of two mirror resonators with holes for output coupling is studied for free electron laser application using a Fox-Li type code. The mode profiles inside and outside the cavity, the diffraction losses at the mirror edges and apertures, the amount of useful power coupled through the hole, etc., are calculated for the dominant mode for different hole and mirror dimensions. It is found that resonators in near concentric geometry can develop a mode degeneracy in certain cases, which should be avoided for the stability of the free electron laser gain and output. A resonator configuration for a free electron laser at Lawrence Berkeley Laboratory was found which can provide satisfactory performance over a wavelength range from 25 to 50 μm. The possibility of further increasing the tuning range by an adjustable intracavity aperture is discussed.

Conditions for cw lasing in a filled open telescopic resonator

The condition ensuring cw lasing is derived and the normal oscillation modes are found for an unstable telescopic resonator filled with an amplifying medium. The diffraction of light at the mirror edges is allowed for. The problem of the normal oscillations is solved for a resonator with cylindrical mirrors. The selected properties of such resonators are considered.

Use of indeterminate Padè approximations in the analysis of diffraction at the mirror edges of an optical resonator

A method is presented for analysis of the diffraction of waveguide modes at the open end of a two-dimensional metallic waveguide, based on a rational approximation of the field diffracted outside the open end. We believe that this method can be used for waveguides with nonplane walls, and it should prove a useful tool in the analysis of optical resonators.

Ray-optical calculation of eigenmode behavior of unstable laser resonators with rounded edges

The eigenmode resonance equation, previously developed by the ray-optical method of analysis for unstable symmetric bare resonators with strip and spherical mirrors, is employed here to establish the basic properties of resonators with rounded mirror edges. The numerical results obtained in this manner are far more comprehensive than those presented earlier from a waveguide model approach to the resonator problem. As in this earlier study, edge rounding is found to improve mode separation and to shift the onset of low-loss mode detachment to lower Fresnel numbers. It is also found that a simple closed form expression predicts accurately the low-loss mode behavior after it has detached from the remaining mode spectrum.

Continuous Fourier-transform spline solution of unstable resonator-field distribution

To deal with sharply cut off fields at mirror edges, a continuous Fourier integration procedure is described. A spline fit is made to the discrete data, followed by analytic integration of the spline functions. End corrections associated with the difference between spline functions near the edges and the remaining uniform splines are made. This procedure permits an accurate integration of the paraxial equation in the thin-gain-sheet approximation.

Eigenvalues of a nonconfocal laser resonator with an output-coupling aperture

A nonconfocal laser resonator that has output-coupling apertures has been analyzed using the matrix eigenvalue technique. Numerical calculations of eigenvalues and eigenfunctions are performed for the interesting resonator consisting of one plane mirror with a coupling aperture and one spherical mirror. The effects of the coupling aperture are also discussed for several kinds of modes when both the mirror and coupling- aperture Fresnel numbers vary. It is found that the power loss of the TEM(00) mode becomes nearly constant in a finite range of the mirror Fresnel number. In such a range, the major source of a resonator loss is the power coupling through an aperture, and the coupling loss can be estimated independently of the loss caused by the spillover at mirror edges.

Unstable strip resonators with misaligned circular mirrors

The waveguide approach developed previously by the authors is here applied to unstable strip resonators with unequal sharp-edged circular mirrors that have been tilted with respect to the resonator axis. An equivalent resonator with nontilted mirrors is defined wherein the mirror edges form asymmetrically placed terminations of the open-ended transverse waveguide. The eigenmode losses are found by calculating the waveguide mode reflection coefficients for each pair of edges and inserting these into the previously derived resonance equation. Numerical calculations for the low-loss detached mode are presented for the special case of symmetrical resonators with equally tilted mirrors since results for this configuration, for moderately large Fresnel numbers, have previously been given by Sanderson and Streifer. Our solutions agree with those of Sanderson and Streifer but accommodate also the range of large Fresnel numbers. It is found that misalignment introduces additional ripples into the power loss vs Fresnel number curves. A ray-optical interpretation in terms of edge diffraction is shown to account for this behavior.

Mode losses in unstable resonators with rounded edges

The waveguide approach to unstable resonators is employed for determining the eigenmode losses in unstable 2-D and 3-D resonators with perfectly reflecting round-edged mirrors. It is found that edge rounding in cylindrical mirror configurations leads to mode detachment at lower Fresnel numbers than for the sharp-edged case and that the loss behavior approaches more closely the geometric optical limit for infinite mirrors. Similar effects are observed in resonators with circular mirrors, where mode detachment does not occur at all when the mirror edges are sharp. It is also shown that edge rounding improves the separation between the low-loss detached mode and the next higher order modes.

Unstable open resonators: two-dimensional and three-dimensional losses by a waveguide analysis

Previous calculations performed by a waveguide approach to unstable open resonators with cylindrical hyperbolic mirrors are further refined. By this approach, the resonator is regarded as a waveguide transverse to the resonator axis, and resonance is established by self-consistent reflection of a single waveguide mode, or of two selectively coupled waveguide modes, from the mirror edges and from the axial region. The refinement refers to improved values for the modal reflection coefficients that appear in the resonance equation. The theory is now shown to be capable of predicting the eigenmode loss behavior in resonators with large Fresnel numbers, as verified by comparisons with published numerical solutions of the resonator integral equation. The theory is also extended successfully to circular hyperbolic mirrors. Finally, the waveguide model is utilized to derive known equivalence relations, previously deduced from the integral equation, between resonators with symmetrical mirrors and those with other arrngements. Thus, the results in this paper lend further support to the validity of the coupled-mode waveguide model for unstable resonators.

Theory of open resonators with cylindrical mirrors

A theoretical analysis is made of resonators with cylindrical mirrors. Analytic expressions are obtained for the fields of the oscillation modes and the corresponding losses in unstable resonators, in the case of high equivalent Fresnel numbers. The influence of smoothing of the mirror edges on the mode losses is discussed.

Improved mode properties of unstable resonators with tapered reflectivity mirrors and shaped apertures

The use of tapered reflectivity mirrors and shaped apertures in unstable resonators is shown to be an effective method for improving the mode properties. Mode intensity and phase profiles are smoothed and the mode discrimination ratio is increased. Results are presented illustrating the importance of diffracted waves from sharp mirror edges in determining these mode properties. A simple expression for estimating the diffractive contribution is given and is used to determine optimum mirror designs. Shaped mirrors and mirrors having amplitude and phase reflectivity tapers are studied. The concept of equivalent Fresnel zones is used to gain physical insight into the mode properties.

PROPERTIES OF UNSTABLE RESONATORS WITH LARGE EQUIVALENT FRESNEL NUMBERS

The results are given of numerical calculations of oscillation modes in unstable resonators. It is shown that slight smoothing of the mirror edges leads to a considerable improvement of the selective properties of a resonator. It is shown that, contrary to the predictions of the theory of unstable resonators with sharp-edged mirrors, oscillation in the lowest transverse mode described by the geometrical approximation is possible in real resonators with large equivalent Fresnel numbers.

Influence of the edge effects on the properties of unstable resonators

The diffraction problem is considered in the case of normal oscillations in open resonators. In the case of unstable resonators with large equivalent Fresnel numbers, the standard approach to the idealization of the boundary conditions gives rise to an unwarranted complication of the mathematical model. The properties of systems with smoothed mirror edges are considered.