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

Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

308
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
308
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

271
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
271
Focusing of Light in the Eye01:16

Focusing of Light in the Eye

2.6K
Light rays enter the eye through the cornea, a transparent dome-shaped tissue that is the eye's outermost layer. The cornea bends or refracts, light rays traveling to the pupil. The shape of the cornea determines how much of the light is bent and whether the image will be focused correctly on the retina at the back of the eye. Once the light has passed through both refraction layers, it converges into a single focal point onto a small area. This is where photoreceptors start transforming...
2.6K
Properties of the z-Transform II01:16

Properties of the z-Transform II

111
The property of Accumulation in signal processing is derived by analyzing the accumulated sum of a discrete-time signal and using the time-shifting property to determine its z-transform. This principle reveals that the z-transform of the summed signal is related to the z-transform of the original signal by a multiplicative factor.
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...
111
Properties of the z-Transform I01:17

Properties of the z-Transform I

173
The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
173
Definition of z-Transform01:26

Definition of z-Transform

415
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
415

You might also read

Related Articles

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

Sort by
Same author

Hybrid zeolitic imidazolate frameworks with catalytically active TO4 building blocks.

Angewandte Chemie (International ed. in English)·2010
Same author

Whiter matter abnormalities in medication-naive subjects with a single short-duration episode of major depressive disorder.

Psychiatry research·2010
Same author

A new comorbidity index: the health-related quality of life comorbidity index.

Journal of clinical epidemiology·2010
Same author

S-adenosylmethionine inhibits the growth of cancer cells by reversing the hypomethylation status of c-myc and H-ras in human gastric cancer and colon cancer.

International journal of biological sciences·2010
Same author

Nano-sized SnSbAgx alloy anodes prepared by reductive co-precipitation method used as lithium-ion battery materials.

Journal of nanoscience and nanotechnology·2010
Same author

Complementary diffusion tensor imaging study of the corpus callosum in patients with first-episode and chronic schizophrenia.

Journal of psychiatry & neuroscience : JPN·2010
Same journal

Denoising algorithm of Φ-OTDR systems based on adaptive fractional wavelet transform denoising.

Optics express·2026
Same journal

Millisecond photon-to-photon latency and high-speed volumetric projection system for optogenetics.

Optics express·2026
Same journal

Polarization-encoded coaxial structured light for high-precision 3D surface profilometry.

Optics express·2026
Same journal

Discrete freeform optical design based on collaborative optimization of point cloud and local normals.

Optics express·2026
Same journal

Ultrafast ghost imaging with 25 GHz speckle switching and wavelength-division multiplexing.

Optics express·2026
Same journal

Atomic vapor cells fabricated by femtosecond laser welding of standard-optical-quality glass.

Optics express·2026
See all related articles

Related Experiment Video

Updated: Jun 16, 2025

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

9.4K

Optimize progressive addition lens by Zernike polynomials.

Yuechen Shen, Yunhai Tang, Quanying Wu

    Optics Express
    |June 14, 2025
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an efficient method for optimizing progressive addition lenses (PALs) using Zernike polynomials and the Analytic Hierarchy Process (AHP). The new approach significantly reduces computation time and improves lens performance.

    More Related Videos

    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
    08:39

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

    Published on: January 28, 2019

    9.8K
    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution
    08:41

    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution

    Published on: August 16, 2012

    11.5K

    Related Experiment Videos

    Last Updated: Jun 16, 2025

    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
    09:04

    Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

    Published on: February 23, 2018

    9.4K
    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
    08:39

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

    Published on: January 28, 2019

    9.8K
    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution
    08:41

    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution

    Published on: August 16, 2012

    11.5K

    Area of Science:

    • Optics and Photonics
    • Computational Design
    • Ophthalmic Lens Technology

    Background:

    • High-precision modeling of progressive addition lens (PAL) surfaces traditionally requires a large number of Zernike polynomials (231), leading to significant computational challenges.
    • Existing optimization methods for PALs can be computationally intensive and time-consuming, hindering rapid design iterations and manufacturing.

    Purpose of the Study:

    • To develop an innovative and computationally efficient method for optimizing progressive addition lens (PAL) surfaces.
    • To enhance the performance of PALs by improving the width of the distance and near vision zones.
    • To reduce the computational time required for PAL surface optimization.

    Main Methods:

    • Utilized Zernike polynomial coefficients within commercial optical design software for PAL surface modeling.
    • Employed the Analytic Hierarchy Process (AHP) for systematic weight allocation within the merit function.
    • Introduced a novel technique to minimize the number of optimization variables, thereby increasing efficiency.

    Main Results:

    • Achieved a 79.6% reduction in computation time compared to traditional optimization methods.
    • Demonstrated a 17.2% increase in the width of the distance vision zone in manufactured lens samples.
    • Observed a 15.9% increase in the width of the near vision zone in manufactured lens samples.

    Conclusions:

    • The proposed method offers a significant improvement in computational efficiency for PAL optimization.
    • The optimized PALs exhibit enhanced visual performance with wider distance and near vision zones.
    • This approach provides an effective strategy for the design and manufacturing of advanced progressive addition lenses.