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Detectors
Published in C. R. Kitchin, Astrophysical Techniques, 2020
A quadrant detector is one whose detecting area is divided into four independent sectors (i.e., a 2 × 2-pixel array), the signal from each of which can be separately accessed. If the image is centred on the intersection of the sectors, then their signals will all be equal. If the image moves, then at least two of the signals will become unbalanced and the required error signal can then be generated. A variant of this system uses a pyramidal ‘prism’. The image is normally placed on the vertex and so is divided into four segments each of which can then be separately detected. When guiding on stars by any of these automatic methods, it may be advantageous to increase the image size slightly by operating slightly out of focus, scintillation ‘jitter’ then becomes less important.
Wavefront sensors
Published in Pablo Artal, Handbook of Visual Optics, 2017
In a later work [110], an approach was described of making the procedure of target alignment automatic. Two beams are projected into the eye alternately, the first one as a reference and another one as a test beam (Figure 2.8). A quadrant detector “looks” into the eye, measures relative positions of the test beam, and controls its positioning and tilt until the coordinates of its projection on the retina coincide with the coordinates of the reference beam.
Construction of rhombic triacontahedron discrete global grid systems
Published in International Journal of Digital Earth, 2022
Xiaoyu Liang, Jin Ben, Rui Wang, Qishuang Liang, Xinhai Huang, Junjie Ding
The derivation of the above equation is based on a basic unit as an example. This necessitates the use of the symmetry characteristics of the rhombus to convert a given point into the basic unit. Given the azimuth angle and the given point in the first and third quadrants, the azimuth angle can be adjusted directly according to the symmetry characteristics to ensure it falls within the interval , and the adjusted angle is recorded, as shown in Figure 6 (a). When the azimuth angle of the given point is in the second and fourth quadrants, it is necessary to adjust the azimuth angle according to . The azimuth angle in the fourth quadrant and in the second quadrant helps it fall within the interval , and the adjusted angle needs to be recorded, as shown in Figure 6(b). Finally, the equal-area mapping of the rhombus can be realized using the equations derived by considering the basic unit as an example.
Plane-wave scattering by chirally coated orthorhombic dielectric-magnetic sphere
Published in Waves in Random and Complex Media, 2022
Muhammad Aqeel Ahmed, Allah Ditta Ulfat Jafri, Qaisar Abbas Naqvi, Shakeel Ahmed
By exploiting the closed-form vector spherical wavefunctions pertinent to orthorhombic dielectric–magnetic material, the electric and magnetic field phasors (specified by the subscript qualifier ) inside the core, can be obtained as [14] where is the relative impedance of the medium. The vector spherical wavefunctions and appearing in above expressions are given as [26] and where The angle must lie in the same quadrant as its argument. The expansion coefficients and are not known.
Promoting uncertainty to support preservice teachers’ reasoning about the tangent relationship
Published in International Journal of Mathematical Education in Science and Technology, 2019
David Glassmeyer, Aaron Brakoniecki, Julie M. Amador
As they completed the series of tasks, all PSTs were observed to make statements about the tangent relationship in ways attending to all three Mental Actions of the covariational framework. For example, in Group 2 all three PSTs made verbal and written comments in the Day 2 task describing how a change in one quantity (angle, measured from the 3 o’clock position counterclockwise, ranging between 0° and 90°) influences a change in the other quantity (slope of the terminal ray). Each PST in Group 2 then wrote down the relationship between the angle measure and resulting slope, which they label as ‘ratio’ in their work (Figure 4). Note at this point in this activity they are focused on angle measures in the first quadrant. These statements were coded as evidence of PSTs attending to the tangent relationship using covariational reasoning Mental Action 2 (coordinating the direction of change of one variable with changes in the other variable). Similar statements were made by PSTs in other groups, such as when Moises said to his group, ‘This angle increases with the slope increase, is the ratio’, and a peer responded, ‘Together … as the angle increases, the slope will change.’