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Related Concept Videos

Graphical and Analytic Representation of Sinusoids01:20

Graphical and Analytic Representation of Sinusoids

Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
Sinusoidal Sources01:18

Sinusoidal Sources

Direct current (DC) refers to an electric current that flows in a single direction, maintaining a constant polarity. This is in contrast to alternating current (AC), which periodically changes its direction and magnitude. AC forms the backbone of modern electricity transmission and distribution systems due to its efficient long-distance transmission capabilities.
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Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Phase Contrast and Differential Interference Contrast Microscopy01:26

Phase Contrast and Differential Interference Contrast Microscopy

Phase-Contrast Microscopes
In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...
Phasor Arithmetics01:13

Phasor Arithmetics

Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
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Updated: Jun 12, 2026

Implementation of a Reference Interferometer for Nanodetection
16:11

Implementation of a Reference Interferometer for Nanodetection

Published on: April 26, 2014

Sinusoidal phase modulating Fizeau interferometer.

O Sasaki, T Okamura, T Nakamura

    Applied Optics
    |June 18, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Sinusoidal phase modulation interferometry using Fizeau interferometers is demonstrated. This technique accurately measures surface profiles and wafer movements, proving its practical applications in precision engineering.

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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Precision Measurement

    Background:

    • Fizeau interferometers are optical instruments used for surface analysis.
    • Achieving precise phase modulation is crucial for advanced interferometric measurements.
    • Existing methods may lack accuracy in phase modulation control.

    Purpose of the Study:

    • To demonstrate sinusoidal phase modulating interferometry with a Fizeau interferometer.
    • To establish a method for precise phase modulation generation and measurement.
    • To validate the technique's utility in surface profiling and motion detection.

    Main Methods:

    • Utilizing a Fizeau interferometer with a vibrating reference plate to generate sinusoidal phase modulation.
    • Measuring the amplitude and phase of the modulation in-situ for exact phase determination.
    • Applying the technique to measure surface profiles of plate glasses and integrated circuit (IC) wafers.

    Main Results:

    • Successful implementation of sinusoidal phase modulation in a Fizeau interferometer.
    • Accurate determination of phase modulation parameters through self-measurement.
    • Demonstrated capability in high-resolution surface profile measurements (80-mm diameter optics).
    • Effective application in measuring the movement of integrated circuit wafers.

    Conclusions:

    • Sinusoidal phase modulating Fizeau interferometry is a viable and accurate technique.
    • The method provides precise control and measurement of phase modulation.
    • The interferometer is useful for critical applications like semiconductor manufacturing and optical component inspection.