Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Integration by Parts: Indefinite Integrals01:26

Integration by Parts: Indefinite Integrals

173
Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...
173
Integration by Parts: Definite Integrals01:23

Integration by Parts: Definite Integrals

80
Definite integrals involving the product of two functions over a fixed interval can be evaluated using integration by parts. This method rewrites the integral as the difference of a product evaluated at the endpoints and a remaining definite integral that is often simpler to compute.A representative example is the definite integral of the inverse tangent function. Since there is no direct integration formula for arctan ⁡x, the integrand is rewritten as a product of arctan⁡ x and the...
80
Integrator and Differentiator01:13

Integrator and Differentiator

1.4K
Op-amp circuits have significant applications in various fields, including automotive engineering. One such application is cruise control systems in cars, where op-amp circuits are integral for maintaining a constant speed. In these systems, op-amps function as both integrators and differentiators.
An integrator within an op-amp circuit produces an output directly proportional to the integral of the input signal. This is achieved by replacing the feedback resistor in a typical inverting...
1.4K
Definite Integral01:29

Definite Integral

71
Consider a real-valued function defined on a closed interval. One of the fundamental objectives in calculus is to determine the area under the graph of such a function. When an exact computation is not readily available, this area can be estimated by dividing the interval into a finite number of equal subintervals. Each subinterval corresponds to a rectangle whose width is the length of the subinterval and whose height is determined by the value of the function at a selected point within that...
71
Indefinite Integrals01:25

Indefinite Integrals

71
The water inflow rate into a storage tank is not constant but increases over time. Initially, the pump delivers water at a rate of 5 L/min. However, the inflow rate increases by 2 L/min for each additional minute due to rising pressure or system adjustments. This scenario can be described mathematically by a linear function:It is necessary to integrate the inflow rate function to measure the total volume of water added to the tank over time. The total water volume V(t) is obtained by performing...
71
Integration by Parts: Problem Solving01:29

Integration by Parts: Problem Solving

68
Smart speakers process voice commands by modeling audio inputs as piecewise functions and analyzing them through integration against trigonometric functions, such as cosine. This mathematical approach is fundamental in signal processing, where complex sound waves are decomposed into simpler frequency components.Consider a definite integral involving a piecewise function multiplied by a cosine function. Because the function is defined differently over separate intervals, the integral is split...
68

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The impact of legal expertise on moral decision-making biases.

Humanities & social sciences communications·2024
Same author

Surface Bragg gratings of proteins patterned on integrated waveguides for (bio)chemical analysis.

Mikrochimica acta·2023
Same author

Discovery of tight-binding competitive inhibitors of dipeptidyl peptidase IV.

International journal of biological macromolecules·2021
Same author

Advanced and versatile interferometric technique for the characterization of photonic integrated devices.

Optics express·2021
Same author

BIO bragg gratings on microfibers for label-free biosensing.

Biosensors & bioelectronics·2021
Same author

Reconfigurable reflective arrayed waveguide grating using optimization algorithms.

Optics express·2020

Related Experiment Video

Updated: Feb 2, 2026

Fabrication and Characterization of Thickness Mode Piezoelectric Devices for Atomization and Acoustofluidics
10:39

Fabrication and Characterization of Thickness Mode Piezoelectric Devices for Atomization and Acoustofluidics

Published on: August 5, 2020

7.4K

Integrated optical frequency domain reflectometry device for characterization of complex integrated devices.

Luis A Bru, Daniel Pastor, Pascual Muñoz

    Optics Express
    |November 25, 2018
    PubMed
    Summary

    We developed an integrated optical frequency domain reflectometry (OFDR) device for precise photonic integrated circuit measurements. This compact system enhances performance for characterizing fabrication deviations in advanced optical devices.

    More Related Videos

    Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography
    11:21

    Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography

    Published on: January 15, 2013

    12.0K
    Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points
    09:30

    Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points

    Published on: March 2, 2011

    16.2K

    Related Experiment Videos

    Last Updated: Feb 2, 2026

    Fabrication and Characterization of Thickness Mode Piezoelectric Devices for Atomization and Acoustofluidics
    10:39

    Fabrication and Characterization of Thickness Mode Piezoelectric Devices for Atomization and Acoustofluidics

    Published on: August 5, 2020

    7.4K
    Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography
    11:21

    Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography

    Published on: January 15, 2013

    12.0K
    Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points
    09:30

    Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points

    Published on: March 2, 2011

    16.2K

    Area of Science:

    • Photonics
    • Integrated Optics
    • Optical Metrology

    Background:

    • Advanced measurement systems are crucial for modern photonic integrated circuits.
    • Optical frequency domain reflectometry (OFDR) offers robust characterization of design-to-fabrication deviations.
    • Existing methods may lack compactness or integrated functionality.

    Purpose of the Study:

    • To report a novel OFDR device with monolithic integration of the interferometric component and the device under test.
    • To highlight the advantages of this integrated approach, including improved compactness and performance.
    • To emphasize the significance of an incorporated dispersion de-embedding mechanism.

    Main Methods:

    • Monolithic integration of the OFDR interferometric system with the device under test.
    • Development and implementation of a dispersion de-embedding mechanism.
    • Experimental validation using an arrayed waveguide grating on a silicon nitride platform.

    Main Results:

    • Demonstration of a compact and high-performance integrated OFDR device.
    • Successful characterization of design-to-fabrication deviations in an arrayed waveguide grating.
    • Validation of the dispersion de-embedding mechanism's effectiveness.

    Conclusions:

    • The proposed integrated OFDR device represents a significant advancement in testing photonic integrated circuits.
    • This work is a foundational step towards a universal test structure for integrated optical devices.
    • The integrated approach offers a promising solution for efficient and accurate characterization in photonic manufacturing.