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Phase unwrapping still plays an important role in optical metrology field. The phase unwrapping process has direct influence on the accuracy of final results. This is why many algorithms have been proposed for phase unwrapping. In spite of this, there is no agreement between the current phase unwrapping algorithms for different applications. This is due to the existence of disturbance in the measured phase data. In the case that there is no disturbance in the phase data, the unwrapped phase can be obtained by integrating the phase gradients over the whole data set which is independent from the integration path. However, there are several sources of errors. Firstly, phase aliasing occurs when the true phase changes by more than one cycle (2π radian) between samples, which was caused by long baselines, objects discontinuities or high deformation. The second source is noise, which may be caused by speckle noise, electronic noise and/or fringe breaks. In the presence of these errors, it is hard to unwrap a phase map correctly.

Recurve bows that are used in competitions like the Olympic Games are high-technology products. Good risers are lightweight but retain a high stiffness. The aim of this study was to design a riser with a stiffness comparable to that of the lightest riser currently used by the archers of the German National Archery Team, but with a considerably reduced weight. We computed the loads that are applied to a riser of a drawn recurve bow (the RADIAN model used by the German team) and created a 3-D solid CAD model of a riser with 24 variable parameters. We used evolutionary computing to optimize the 24 parameters of the model according to these criteria. We selected the most optimal riser out of the 1650 CAD models generated, manufactured it, and had it tested by three archers of the German National Archery Team. The mass of our manufactured riser is 871g, which is 243g or 22% less mass than the RADIAN riser.

The strength and rigidity of wide flange beam to rectangular tube column joints are reduced significantly if the connections are not reinforced. However, the reinforcement for the connections can be complex and increase the fabrication costs significantly because the tube columns are closed sections. This paper describes the force transfer mechanism and the cyclic performance of wide flange beam to concrete-filled rectangular tube column joints reinforced with stiffening plates. The first phase of this research program was to assess the force transfer mechanism at the joint using an analytical yield line method. An experimental program was conducted to verify the proposed model. The test results showed that the derived nominal strength equation provided a reasonable prediction. The second phase of the research program was to assess the cyclic performance of the joints by full-scale joint subassemblage tests. A total of five specimens were tested under cyclic loading. Test results showed that plastic rotation of 0.02 radian which is required for Intermediate Moment Resisting Frames could be obtained.

In transect relascope sampling, a wide‐angle relascope is used along survey lines for selecting a sample of objects that extend linearly in the plane, e.g. downed logs. The method is closely related to line intersect (intercept) sampling. In this article, a special case of the transect relascope technique is studied. Using a π/2 radian relascope angle, the method becomes invariant to the orientation of the line objects in the population. The reason is that the area of inclusion around objects, through which a survey line should pass for an object to be included, turns out to be circular. In analytical studies and Monte Carlo simulations, the cost‐efficiency of transect relascope and line intersect sampling is evaluated. It is found that transect relascope sampling is a competitive alternative to line intersect sampling in inventories of the total volume of coarse woody debris (in the form of downed logs) in forest compartments.

I was thinking of the curve traced by a particle on a wheel mounted on a wheel mounted on a wheel, each turning at a different rate. The first term represents the largest wheel, of radius 1, turning counter-clockwise at one radian per second. The second term represents a smaller wheel centered at the edge of the first, turning 7 times as fast. The third term is for the smallest wheel centered at the edge of the second, turning 17 times as fast as the first, clockwise and out of phase. See FIGURE 1. As you can notice from FIGURE 2, this curve displays a 6-fold symmetry, a fact that one would probably not guess by looking at the formulas.

Phase shifting shearography is achieved by translating the wedge at the iris plane of the image-shearing camera parallel to the shearing direction. For a particular wedge angle used, the amount of phase shift is linearly proportional to the amount of wedge translation. Furthermore, the sensitivity of the phase shift increases with wedge angle. The experimental results for the wedge translation corresponding to a 2π radian phase shift deviate by less than 7% from the derived theoretical prediction for a range of wedge angles used. This technique is particularly developed for the determination of fractional fringe order in real-time shearography.

In recent years, neutron experiments have provided valuable data for particle physics and for astrophysics. Neutrons are an important tool in this field because they react to all known forces except the long-range electrostatic force. Experimental techniques available with cold and ultracold neutrons make them unrivaled in experimental physics. For instance, with the momentum resolution achieved today, a change in a neutron trajectory of one A, over a beam length of 10 meters can be detected. And with today's energy sensitivity, changes in the neutron interaction energy of 10−21eV are measurable. Further, neutrons are easily polarized to 98 percent over large beam cross-sections, and the direction of polarization can be controlled to better than 10−6 radian.

We describe electro-optic phase shifters at a carrier frequency of 95 GHz using LiNbO3 in an H-guide configuration. We have observed induced phase shifts of ∼1 radian at an applied frequency of 1 kHz.

A 2-identical-unit system, with either 1 or 2 repair facilities, is considered. Initially, only the existence of the unit failure and repair time densities is assumed. Equations are derived describing the distributions of the system up, down and total repair times, number of repairs, times of the nth unit failure and nth repair completion, and the probability that i units are operating at time t. These equations are then solved under the assumption that the unit times to failure have a density which is a linear combination of EBXA radian densities. For some arrangements of the system, the first moments arc exhibited for arbitrary failure/repair distributions.

Modifications to iterative procedures for recovering phase information from recorded electron intensity distributions, which are applicable to strong, periodic phase objects are considered. Test calculations involving functions resembling those encountered when studying magnetic thin films in the electron microscope are made, and in particular the success or otherwise in recovering the original phase function, when only imperfectly recorded electron intensities are available, is discussed. For objects with peak-to-peak phase shifts less than 10 radian considerable success is achieved, but only if some a priori knowledge of the nature of the specimen is available have satisfactory results been obtained for stronger phase modulators. Under suitable conditions rapid and accurate results may be obtained for objects with peak-to-peak phase shifts of 30 radian using an appropriate iterative technique.

Interferometric and optical studies on a twinned diamond reveal the presence of true crystallographic slip on two opposite faces of the twin. Slip occurs parallel to a (111) plane, in both cases, making thus an angle of 70 1/2° with the surface. An internal optical opacity is found associated with the slip. The two faces on either side of one slip line are not parallel but inclined at the very small angle of 10-5 radian.

Detailed descriptions are given of experimental investigations on how closely an electron gun of rotational symmetry can focus an electron beam into an image having a peak density equal to the theoretical maximum defined by Langmuir Particular stress is laid on the difficulty of making this study if the cathode is non-uniform in emission density or shows irregularities in emission velocity over its active surface Within the errors occasioned by such lack of uniformity and uncertainty as to the precise cathode area, the measurements to date are consistent with the following statements: (a) If the image is formed only by a ray pencil of sufficiently narrow angle (d here approximately 2 × 10−3 radian or less), then for all practical purposes the measured density reaches the theoretical maximum. This result is substantially independent of grid bias or geometry (b) The value of θ at which the gun begins to fall appreciably below the theoretical performance diminishes as the current from the cathode is...

The design and construction of a completely screened variable mutual inductance of high stability are described. The instrument has a range of 10,000 μH., and changes of 0·01 μH. can be read. Double screening renders the properties of the instrument independent of the circuit in which it is used. A novel method of adjustment of the sections is described, together with a novel form of inductance slide-wire. The instrument is compensated for phase defect, which even at 3000 cycles per second is only 0·0005 radian at the maximum setting. The variation of mutual inductance with frequency is also low, being less than 4 parts in 104 at 1000 cycles per second. The method of calibration is described, the limits of error being ±0·02 μH. throughout the range. The instrument is admirably suited for high precision a.c. bridge measurements of all kinds.

An optical waveguide balanced modulator was constructed with passive niobium oxide strip waveguides on a LiNbO3 substrate. Modulation was produced via the r 33 term of the electro-optic coefficient of the substrate. Full-on, full-off switching could be produced by 17 volts dc, leading to a power bandwidth characteristic of 200 microwatts per mega-hertz for a modulation index of 1 radian over the measured 1.5 GHz bandwidth of the device.

(1912). The Word “Radian”. The American Mathematical Monthly: Vol. 19, No. 10-11, pp. 166-166.