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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
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 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...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

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Complex-valued Fresnel-transform sampling.

F S Roux

    Applied Optics
    |November 6, 2010
    PubMed
    Summary
    This summary is machine-generated.

    VanderLugt sampling rates accurately capture Fresnel diffraction pattern amplitude but miss phase information. New sampling techniques ensure complete information retention for complex-valued patterns in lensless optical systems.

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    Area of Science:

    • Optics
    • Image Processing
    • Diffraction Theory

    Background:

    • The VanderLugt sampling rates (1990) accurately represent the amplitude of Fresnel diffraction patterns.
    • However, these rates are insufficient for preserving the complete information within complex-valued Fresnel diffraction patterns.

    Purpose of the Study:

    • To demonstrate the inadequacy of existing sampling rates for complex-valued Fresnel diffraction patterns.
    • To develop and validate extended sampling techniques for capturing both amplitude and phase information.
    • To analyze these techniques within the context of lensless optical systems.

    Main Methods:

    • Image reconstruction via backward diffraction of forward diffraction patterns.
    • Extension of VanderLugt sampling principles to include phase information.
    • Numerical computations of Fresnel and rigorous scalar diffraction patterns.

    Main Results:

    • Demonstrated that amplitude-only sampling fails to retain complete information for complex-valued Fresnel diffraction.
    • Developed novel sampling rates that successfully capture both amplitude and phase.
    • Validated the new sampling rates through numerical simulations of forward and backward diffraction.

    Conclusions:

    • Existing sampling rates for Fresnel diffraction patterns are inadequate for complex-valued data.
    • The proposed extended sampling techniques enable reliable capture of both amplitude and phase.
    • These advancements are crucial for accurate reconstruction and analysis in lensless optical systems.