Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Transfer function and Bode Plots-I

Transfer function and Bode Plots-I

A transfer function presented in its standard form integrates elements' constant gain, the zeros, and poles at the origin, simple zeros and poles, and quadratic poles and zeros. The transfer function can be written as H(ω):

You might also read

Related Articles

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

Sort by

Same author

Optical path length difference of ray paths inside a reference sphere: a new approach for determining wavefront aberrations in axially symmetrical systems with an object at infinity.

Journal of the Optical Society of America. A, Optics, image science, and vision·2025

Same author

Wavefront aberration determination in non-axially symmetrical optical systems.

Journal of the Optical Society of America. A, Optics, image science, and vision·2024

Same author

Transverse ray aberrations determination in non-axially symmetrical optical imaging systems using Taylor series expansion.

Applied optics·2023

Same author

The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems.

Heliyon·2022

Same author

Differential method for determining third-order derivative matrix of ray with respect to source ray variables at spherical boundary.

Optics express·2020

Same author

Third-order derivative matrix of a skew ray with respect to the source ray vector at a flat boundary.

Journal of the Optical Society of America. A, Optics, image science, and vision·2020

Search research articles

Related Experiment Video

Updated: Jun 1, 2026

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Published on: May 20, 2013

Calculation of the modulation transfer function for object brightness distribution function oriented along any

Psang Dain Lin¹, Wei Wu

¹National Cheng Kung University, Department of Mechanical Engineering, Tainan 70101, Taiwan. pdlin@mail.ncku.edu.tw

|June 16, 2011

Summary

This study introduces a new method for calculating the geometrical modulation transfer function (MTF) for any object brightness distribution function (OBDF) orientation. It reveals that MTF values are not monotonic and can peak at arbitrary OBDF directions, requiring only a 90° rotation for full analysis.

More Related Videos

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Oligomerization Dynamics of Cell Surface Receptors in Living Cells by Total Internal Reflection Fluorescence Microscopy Combined with Number and Brightness Analysis

Oligomerization Dynamics of Cell Surface Receptors in Living Cells by Total Internal Reflection Fluorescence Microscopy Combined with Number and Brightness Analysis

Published on: November 6, 2019

Related Experiment Videos

Last Updated: Jun 1, 2026

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Published on: May 20, 2013

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Oligomerization Dynamics of Cell Surface Receptors in Living Cells by Total Internal Reflection Fluorescence Microscopy Combined with Number and Brightness Analysis

Oligomerization Dynamics of Cell Surface Receptors in Living Cells by Total Internal Reflection Fluorescence Microscopy Combined with Number and Brightness Analysis

Published on: November 6, 2019

Area of Science:

Optical Engineering
Image Quality Assessment
Geometrical Optics

Background:

Existing literature on modulation transfer function (MTF) primarily considers object brightness distribution functions (OBDFs) along meridional and sagittal directions.
There is a need for a generalized method to compute geometrical MTF for arbitrary OBDF orientations, especially for off-axis sources.

Purpose of the Study:

To develop and present a method for computing the geometrical modulation transfer function (MTF) for an off-axis source point with an arbitrarily oriented object brightness distribution function (OBDF).
To analyze the behavior of MTF and phase shift variations with respect to OBDF orientation, translation, and rotation.

Main Methods:

The study employs a recent irradiance method for MTF computation, avoiding ray-hit counting on meshes.
This approach enhances accuracy and eliminates grid-size dependency, improving upon traditional methods.

Main Results:

The geometrical MTF is not a monotonic function of OBDF direction; extreme values can occur at orientations between meridional and sagittal.
Four theorems are established for MTF and phase shift variations under OBDF translation and rotation.
MTF and phase shift exhibit symmetry or antisymmetry about specific directions, necessitating only a 90° rotation of the OBDF for comprehensive analysis.

Conclusions:

The developed method provides accurate geometrical MTF computation for arbitrary OBDF orientations.
Understanding the non-monotonic behavior and symmetries of MTF is crucial for optical system characterization.
The irradiance-based method offers a robust and accurate alternative to traditional MTF computation techniques.