Related Experiment Video
Updated: Jul 7, 2026
16:11
Implementation of a Reference Interferometer for Nanodetection
Published on: April 26, 2014
Some considerations of reduction of reference phase error in phase-stepping interferometry
J Schwider1, T Dresel, B Manzke
1Lehrstuhl für Optik, Universität Erlangen-Nürnberg Staudtstrasse 7, D-91058 Erlangen, Germany.
Applied Optics
|February 29, 2008
Summary
Phase-stepping errors in interferometers cause systematic errors. This study unifies error-compensating algorithms and shows experimental removal of these errors a posteriori using a Twyman-Green interferometer.
Area of Science:
- Optical metrology
- Interferometry
- Precision engineering
Background:
- Phase-stepping interferometry is susceptible to positioning errors and miscalibrations.
- These errors introduce systematic phase deviations, distorting measurements.
- Accurate phase retrieval is crucial for optical testing and characterization.
Purpose of the Study:
- To provide a unified mathematical framework for phase-shift error-compensating algorithms.
- To experimentally validate the a posteriori removal of systematic errors in phase-stepping measurements.
- To analyze the impact of positioning errors on phase-stepping interferometry.
Main Methods:
- Review and unification of historical phase-shift algorithms.
- Experimental implementation using a Twyman-Green type microlens test interferometer.
- Development and application of a posteriori error correction techniques.
Main Results:
- Systematic errors are shown to be proportional to twice the measured phase distribution.
- A unified mathematical perspective on error-compensating algorithms is presented.
- Experimental demonstration of successful a posteriori systematic error removal.
Conclusions:
- Systematic errors in phase-stepping interferometry can be effectively compensated.
- The proposed unified approach offers a comprehensive understanding of error correction.
- A posteriori correction provides a practical method for enhancing measurement accuracy.
Related Concept Videos
01:24Time 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.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
01:17Common Leveling Mistakes and Errors
A survey team is tasked with determining the elevation difference between points Point A and Point B, separated by uneven terrain. They use a leveling instrument and a leveling rod.Common MistakesMisreading the Rod: During a backsight reading at Point A, the instrumentman observes the rod partially obscured by tall grass. Instead of reading 1.135 m, they mistakenly record 1.735 m due to the misalignment of the crosshair with the wrong graduation. This error adds 0.600 m to all subsequent...
01:10Interference: Path Lengths
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
01:26Phase 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...
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...
01:20The Phase Rule
The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
01:21Time 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,...
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...