Power Spectral Density: Understanding Surfaces at Different Scales

The concept of Power Spectral Density (PSD) is extremely beneficial when specifying optics of various types, with PSD proving to be a useful metric in laser fusion and other extreme application spaces.

This specification method can also be applied to demanding applications such as high-energy laser (HEL) optics because it can assist developers in better understanding and optimizing the quality of optical surfaces that more conventional methods cannot accommodate.

This article looks at why PSD is such a valuable tool.

Understanding Surfaces at Varying Scales

Examining the surface of a high-energy laser system’s mirror or lens can pose specific challenges.

For example, the surface may appear smooth to the naked eye, but it may possess a range of tiny imperfections or rough sections that are only visible on a microscopic level. These imperfections can cause light to scatter, causing problems in applications requiring precise laser beam control.

Power Spectral Density:  Understanding Surfaces at Different Scales

Image Credit: GIPHOTOSTOCK/SCIENCE PHOTO LIBRARY

Several optical specifications describe the overall smoothness and figure of optical surfaces, such as Peak-to-Valley (PV), Root Mean Square (RMS) roughness, power, and irregularity.

These metrics are useful in more general commercial applications. PV can show the maximum height difference between the surface’s lowest and highest points, while RMS can provide a statistical average of surface deviations. Irregularity offers a useful measurement of deviation from the best-fit sphere.

These metrics only offer a limited perspective. They provide a summary view that lacks detailed insight into how different-sized surface features contribute to surface texture.

Figure 1 illustrates how aberrations caused by surface figure error can impact a beam’s energy distribution - an especially important consideration in HEL applications.

Examples of low order figure errors and their effect on energy distribution of a focused beam

Figure 1. Examples of low-order figure errors and their effect on the energy distribution of a focused beam. Image Credit: Zygo Corporation

However, PSD offers more detailed insights and can effectively analyze an optical component’s surface features by transforming surface topography data from the spatial domain into the frequency domain.

This change in analytical approach breaks down the surface texture into its constituent spatial frequencies, affording users a far more detailed analytical perspective.

PSD provides information on the contribution of each different-sized surface feature to the surface’s overall roughness. This data is essential for HEL and other high-precision applications where a system’s efficiency is a key driver of energy demand and, therefore, cost.

Unlike conventional metrics like RMS or PV, PSD can facilitate identifying and controlling certain surface imperfections that can adversely affect a laser’s propagation and quality. PSD also offers a more robust framework for predicting and optimizing optical performance in various advanced applications.

Figure 2 shows a PSD plot for a polished surface measured using multiple interferometers and atomic force microscopes. The plot covers a wide range of spatial periods from 10 mm to 10 nm, or six orders of magnitude. This data offers useful information about various scales of surface artifacts that impact scatter and haze.

Example of composite 1D PSD information measured using a combination of interferometers and atomic force microscopes

Figure 2. Example of composite 1D PSD information measured using a combination of interferometers and atomic force microscopes. Image Credit: Zygo Corporation

Enhancing Laser Performance and Predictability

PSD allows developers and manufacturers to specify how smooth or rough an optical component’s surface must be to perform optimally in a high-energy laser system. This is important for several reasons.

High-energy lasers are required to precisely focus intense light beams. Even minute amounts of scattered light can result in performance issues, inefficiencies, or damage to other parts of the optical system. Using PSD, engineers can characterize and minimize this scattering by controlling the different surface imperfections.

PSD as a specification tool helps ensure that high standards are maintained for every optical component produced. Consistency remains a key consideration in systems where high performance is essential, and PSD can assist where it is necessary to troubleshoot or refine the production process.

Contemporary manufacturing techniques rely on precise measurements, particularly those designed to improve the surface quality of laser optics. PSD offers a quantitative means of assessing improvements and informing manufacturing processes to achieve their desired outcomes, such as polishing and coating.

Summary

PSD can be understood as having access to a detailed map that shows the valleys and mountains on an optical surface, but also the fine details of the terrain.

Using this map enables improved design, more efficient manufacturing, and the effective application of high-energy laser optics—key considerations in ensuring that these systems are effective and efficient in their roles.

This information has been sourced, reviewed and adapted from materials provided by Zygo Corporation.

For more information on this source, please visit Zygo Corporation.

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