Related Experiment Video
Updated: Jun 7, 2026

06:48
Surface Mapping of Earth-like Exoplanets using Single Point Light Curves
Published on: May 10, 2020
Calculation of the power spectral density from surface profile data
Applied Optics
|October 22, 2010
Summary
This study provides correct methods for calculating one-dimensional power spectral density (PSD) from surface profile data. It addresses issues with standard routines and offers techniques to reduce PSD estimate variance for accurate surface texture analysis.
Area of Science:
- Metrology and Surface Engineering
- Signal Processing and Data Analysis
Background:
- Surface roughness specification is transitioning to a 2D power spectral density (PSD) standard.
- Accurate calculation of 1D PSD from discrete profile data is crucial for this transition.
- Existing methods in reference books may contain inaccuracies.
Purpose of the Study:
- To provide a correct method for calculating 1D PSD from discrete surface profile data.
- To identify and flag problems with common fast Fourier-transform routines for PSD estimation.
- To suggest methods for reducing the variance of PSD estimates.
Main Methods:
- Derivation of correct normalizing factors for 1D PSD calculation.
- Analysis of discrepancies in standard fast Fourier-transform implementations.
- Proposal of two variance reduction techniques for PSD estimation.
Main Results:
- A validated method for calculating 1D PSD with correct normalization is presented.
- Common pitfalls in using standard FFT routines for PSD are identified.
- Demonstrated examples of significant variance reduction in PSD estimates.
Conclusions:
- The provided method ensures accurate 1D PSD calculation for surface texture analysis.
- Awareness of FFT routine issues is critical for reliable surface roughness metrology.
- Variance reduction techniques enhance the precision of surface texture characterization using PSD.
Related Concept Videos
Complex Power
Power engineers have introduced the concept of complex power to determine the cumulative effect of parallel loads. This idea plays a crucial role in power analysis because it encompasses all the details related to the power consumed by a specific load.
Complex power is defined as the multiplication of the voltage and the complex conjugate of the current. The magnitude of this power, known as apparent power, is measured in volt-amperes (VA). Notably, the angle of the complex power equates to the...
Complex power is defined as the multiplication of the voltage and the complex conjugate of the current. The magnitude of this power, known as apparent power, is measured in volt-amperes (VA). Notably, the angle of the complex power equates to the...
Power Factor
The power factor is defined as the ratio of average (or active) power to apparent power, as illustrated by the relation
Area of a Surface of Revolution
Surfaces of revolution are formed when a two-dimensional curve is rotated around an axis, producing a three-dimensional shape. This concept is used in engineering tasks like determining the surface area of a rocket nozzle, where precise calculations are critical for applying uniform heat-resistant coatings. When a curve is revolved about the x-axis, it sweeps out a continuous surface whose area must be calculated accurately to estimate material requirements.Approximating with Conical BandsTo...
Parseval's Theorem for Fourier transform
Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
Parseval's Theorem
Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...
Simpson's Rule II
In warehouse roofing applications, corrugated or curved metal sheets are commonly used to improve structural strength, water drainage, and ventilation efficiency. To accurately estimate material requirements and optimize design parameters, engineers must determine the curved surface area of these sheets. Because the sheet profiles often repeat smoothly along their length, they can be effectively approximated by parabolic curves, enabling the use of numerical integration techniques for area...

