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

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Computed Tomography01:10

Computed Tomography

Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

You might also read

Related Articles

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

Sort by
Same author

Simultaneous imaging and optode calibration with diffuse optical tomography.

Optics express·2009
Same author

A shape-based reconstruction technique for DPDW data.

Optics express·2009
Same author

Design and evaluation of a continuous-wave diffuse optical tomography system.

Optics express·2009
Same author

Systematic diffuse optical image errors resulting from uncertainty in the background optical properties.

Optics express·2009
Same author

Diffuse optical reflection tomography using continuous wave illumination.

Optics express·2009
Same author

Introduction.

Optics express·2009

Related Experiment Video

Updated: Jun 23, 2026

Computed Tomography-guided Time-domain Diffuse Fluorescence Tomography in Small Animals for Localization of Cancer Biomarkers
12:24

Computed Tomography-guided Time-domain Diffuse Fluorescence Tomography in Small Animals for Localization of Cancer Biomarkers

Published on: July 17, 2012

A fundamental limitation of linearized algorithms for diffuse optical tomography.

D Boas

    Optics Express
    |April 21, 2009
    PubMed
    Summary

    Linear approximations in Diffuse Optical Tomography (DOT) prevent accurate imaging of tissue optical properties. This study demonstrates why these assumptions fail for quantitative analysis in scattering media, impacting future DOT algorithm development.

    Area of Science:

    • Biophotonics and Biomedical Imaging
    • Medical Physics
    • Optical Engineering

    Background:

    • Diffuse Optical Tomography (DOT) is an emerging imaging technique for analyzing light-scattering media like biological tissues.
    • Current DOT algorithms often employ linear approximations to simplify the relationship between optical properties and measured signals.
    • The development of advanced DOT algorithms is crucial for accurate characterization of tissue optical properties.

    Purpose of the Study:

    • To investigate the limitations of linear approximations in Diffuse Optical Tomography.
    • To demonstrate the impossibility of quantitative imaging of spatially varying optical properties using linear models.
    • To discuss the implications of these findings for the future development of DOT imaging algorithms.

    Main Methods:

    More Related Videos

    Near Infrared Optical Projection Tomography for Assessments of β-cell Mass Distribution in Diabetes Research
    15:18

    Near Infrared Optical Projection Tomography for Assessments of β-cell Mass Distribution in Diabetes Research

    Published on: January 12, 2013

    Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
    10:20

    Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

    Published on: September 5, 2019

    Related Experiment Videos

    Last Updated: Jun 23, 2026

    Computed Tomography-guided Time-domain Diffuse Fluorescence Tomography in Small Animals for Localization of Cancer Biomarkers
    12:24

    Computed Tomography-guided Time-domain Diffuse Fluorescence Tomography in Small Animals for Localization of Cancer Biomarkers

    Published on: July 17, 2012

    Near Infrared Optical Projection Tomography for Assessments of β-cell Mass Distribution in Diabetes Research
    15:18

    Near Infrared Optical Projection Tomography for Assessments of β-cell Mass Distribution in Diabetes Research

    Published on: January 12, 2013

    Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
    10:20

    Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

    Published on: September 5, 2019

    • Theoretical analysis of the relationship between optical contrast and perturbed signals in scattering media.
    • Mathematical derivation to show the breakdown of linear assumptions.
    • Discussion of the impact of non-linear effects on quantitative imaging accuracy.

    Main Results:

    • The linear approximation commonly used in DOT algorithms is fundamentally flawed for quantitative imaging.
    • This linear model prevents accurate characterization of spatially varying optical properties in scattering media.
    • The study provides a clear explanation for the failure of these simplified models.

    Conclusions:

    • Quantitative imaging in Diffuse Optical Tomography is impossible with current linear approximation-based algorithms.
    • Future DOT algorithm development must move beyond linear assumptions to achieve accurate quantitative results.
    • This research highlights critical challenges and directions for advancing DOT technology.