Differential Shack-Hartmann curvature sensor: local principal curvature measurements

Weiyao Zou1, Kevin P Thompson, Jannick P Rolland

  • 1CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL 32816, USA. zouw@indiana.edu

Related Concept Videos

Curvature and Its Interpretation01:25

Curvature and Its Interpretation

Curvature describes how rapidly a curve changes direction at a particular point. A curve with a small curvature bends gently, while a curve with a large curvature turns sharply. For a space curve, the position of a moving object can be described by a vector-valued function r(t), where t often represents time. The direction of motion is determined by the tangent vector, and the unit tangent vector is obtained by normalizing the derivative of the position vector.The unit tangent vector gives the...
Degree of Curvature and Radius of Curvature01:19

Degree of Curvature and Radius of Curvature

The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of curvature as the...
Measurements of Strain01:27

Measurements of Strain

Strain quantifies the deformation of a material under force, typically measured as normal strain, which represents the change in length when compared with the original length. Electrical strain gauges are used for enhanced accuracy. These devices consist of a conductive wire mounted on a paper backing that adheres to the material's surface. These gauges operate on the piezoresistive effect, where the wire's electrical resistance changes in response to mechanical deformation. The strain gauge...
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
Influence of Earth's Curvature and Atmospheric Refraction on Leveling01:26

Influence of Earth's Curvature and Atmospheric Refraction on Leveling

During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference. When the line of sight is leveled, it remains perpendicular to the plumb line only at a single point. Beyond this, it deviates due to the Earth’s curvature, represented by the correction C. For a sight distance D, the deviation can be derived using the relationship:This relationship shows that the deviation increases quadratically with distance. Over a...