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Related Concept Videos

Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Sampling Plans01:23

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
Bandpass Sampling01:17

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
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Fixed Target Serial Data Collection at Diamond Light Source
06:19

Fixed Target Serial Data Collection at Diamond Light Source

Published on: February 26, 2021

Adaptive sampling in convergent beams.

Julián Espinosa1, David Mas, Jorge Pérez

  • 1Deparamento Optica, Farmacologia y Anatomia, Universidad de Alicante, Alicante, Spain.

Optics Letters
|September 2, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a method to improve numerical calculations of Fresnel patterns by analyzing wavefront polynomial orders. This optimization relaxes sampling conditions for more efficient algorithms.

Related Experiment Videos

Last Updated: Jul 2, 2026

Fixed Target Serial Data Collection at Diamond Light Source
06:19

Fixed Target Serial Data Collection at Diamond Light Source

Published on: February 26, 2021

Area of Science:

  • Optics and Photonics
  • Computational Physics

Background:

  • Numerical calculation of convergent Fresnel patterns using fast Fourier transform (FFT) demands extensive sampling to meet Nyquist criteria near focal points.
  • The accuracy of these simulations is often limited by computational resources due to high sampling requirements.

Purpose of the Study:

  • To develop a more efficient numerical algorithm for calculating Fresnel patterns.
  • To reduce the computational load in optical simulations by optimizing sampling strategies.

Main Methods:

  • Wavefront analysis using polynomial decomposition to identify dominant contributing orders.
  • Modification of the initial wavefront based on identified polynomial orders.
  • Relaxation of the Nyquist sampling condition through wavefront modification.

Main Results:

  • Identification of specific polynomial orders that significantly influence sampling requirements.
  • Demonstration that wavefront modification can effectively relax the Nyquist condition.
  • Development of a computationally efficient algorithm for Fresnel pattern calculation.

Conclusions:

  • Polynomial decomposition of wavefronts provides a pathway to optimize numerical simulations.
  • The proposed method offers a significant improvement in the efficiency of Fresnel pattern calculations.
  • This approach enables faster and more resource-friendly optical simulations.