Focus (geometry)In geometry, focuses or foci (ˈfəʊkaɪ; : focus) are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian oval, and more than two foci are used in defining an n-ellipse.
Power ruleIn calculus, the power rule is used to differentiate functions of the form , whenever is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function's derivatives. Let be a function satisfying for all , where . Then, The power rule for integration states that for any real number . It can be derived by inverting the power rule for differentiation.
Cartesian ovalIn geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points (foci). These curves are named after French mathematician René Descartes, who used them in optics. Let P and Q be fixed points in the plane, and let d(P, S) and d(Q, S) denote the Euclidean distances from these points to a third variable point S. Let m and a be arbitrary real numbers. Then the Cartesian oval is the locus of points S satisfying d(P, S) + m d(Q, S) = a.
KeratoconusKeratoconus (KC) is a disorder of the eye that results in progressive thinning of the cornea. This may result in blurry vision, double vision, nearsightedness, irregular astigmatism, and light sensitivity leading to poor quality-of-life. Usually both eyes are affected. In more severe cases a scarring or a circle may be seen within the cornea. While the cause is unknown, it is believed to occur due to a combination of genetic, environmental, and hormonal factors.
Tilt (optics)In optics, tilt is a deviation in the direction a beam of light propagates. Tilt quantifies the average slope in both the X and Y directions of a wavefront or phase profile across the pupil of an optical system. In conjunction with piston (the first Zernike polynomial term), X and Y tilt can be modeled using the second and third Zernike polynomials: X-Tilt: Y-Tilt: where is the normalized radius with and is the azimuthal angle with . The and coefficients are typically expressed as a fraction of a chosen wavelength of light.
