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Related Concept Videos

Passive Filters01:27

Passive Filters

1.0K
Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff...
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Active Filters01:25

Active Filters

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Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Partial Fractions01:28

Partial Fractions

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A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
227
Trial and Error and Algorithm01:12

Trial and Error and Algorithm

429
A problem-solving strategy is a plan of action used to find a solution. Different strategies have distinct action plans. Trial and error involves trying different solutions until one works. For instance, to fix a broken printer, you might check ink levels, ensure the paper tray isn't jammed, and verify the printer's connection to your laptop. This method can be time-consuming but is commonly used. Thomas Edison, for example, used trial and error to find a suitable filament for the light...
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Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions03:03

Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

44.3K
Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other’s pressure. Each gas in a mixture exerts the same pressure that it would exert if it were present alone in the container. The pressure exerted by each individual gas in a mixture is called its partial pressure.
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Automated 3D Optical Coherence Tomography to Elucidate Biofilm Morphogenesis Over Large Spatial Scales
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Multi-focus TIE algorithm including partial spatial coherence and overlapping filters.

Alberto Eljarrat, Johannes Müller, Michael R S Huang

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    Summary

    A new multi-focus transport of intensity equation (MFTIE) method simplifies phase retrieval by avoiding specific imaging planes and incorporating partial spatial coherence. This approach enhances accuracy in optical and electron microscopy phase imaging.

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    Area of Science:

    • Wave optics
    • Phase retrieval algorithms
    • Microscopy techniques

    Background:

    • The transport of intensity equation (TIE) relates wave-front intensity changes to phase.
    • Experimental TIE applications suffer from artefacts due to axial derivative estimation errors and noise amplification.
    • Existing multi-focus TIE (MFTIE) methods require precise image acquisition at specific focal planes.

    Purpose of the Study:

    • To develop a simplified and more robust MFTIE implementation for accurate phase retrieval.
    • To address limitations of current MFTIE methods regarding experimental flexibility and noise sensitivity.
    • To incorporate partial spatial coherence into the MFTIE framework.

    Main Methods:

    • A convenient MFTIE implementation using overlapping spatial frequency cut-offs, eliminating the need for precisely positioned focal planes.
    • Integration of simulated and experimental data from optical and electron microscopy.
    • Application of a flux-preserving framework to account for partial spatial coherence.

    Main Results:

    • The proposed MFTIE algorithm efficiently recovers a broad spectrum of phase spatial frequencies.
    • The method simplifies experimental procedures by allowing images from non-specific focal planes.
    • Iterative refinement further extends the recovered phase information.

    Conclusions:

    • The developed MFTIE method offers a practical and effective solution for phase retrieval in microscopy.
    • This approach enhances the accuracy and applicability of TIE-based phase imaging.
    • The technique is validated across diverse microscopy modalities and data types.