Related Experiment Video
Updated: Jan 30, 2026
06:29
Workflow and Tools for Crystallographic Fragment Screening at the Helmholtz-Zentrum Berlin
Published on: March 3, 2021
6.0K
Transition between paraxial and Helmholtz Fourier spaces
Summary
This study explores mapping functions for correcting paraxial wave solutions. A new mapping method is proposed and compared to existing techniques for wavevector translation.
Area of Science:
- Optics
- Mathematical Physics
Background:
- Paraxial approximations are widely used in wave optics but fail when solutions extend beyond the paraxial regime.
- Correction methods are necessary to extend the validity of paraxial solutions.
Purpose of the Study:
- To analyze the translation of paraxial wavevectors to Helmholtz wavevectors using mapping functions.
- To evaluate existing mapping functions and introduce a novel approach.
Main Methods:
- Examination of two commonly used mapping functions for wavevector translation.
- Development and proposal of a new mapping function.
- Classification of the three mapping functions within full wave correction schemes.
Main Results:
- The study provides a comparative analysis of different mapping functions.
- A new mapping function is introduced, offering a potential improvement for wavevector translation.
Conclusions:
- Mapping functions are crucial for correcting paraxial wave solutions.
- The proposed new mapping offers a valuable addition to the available methods for wavevector translation in optical physics.
Related Concept Videos
02:31Phase Transitions
23.1K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
23.1K
02:58Properties of Transition Metals
29.8K
Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.
29.8K
01:58Cooperative Allosteric Transitions
8.7K
Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
8.7K
02:39Phase Transitions: Vaporization and Condensation
21.2K
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
21.2K
02:33Phase Transitions: Sublimation and Deposition
20.1K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
20.1K
02:39Phase Transitions: Melting and Freezing
15.1K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
15.1K