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MetroPro PSD Analysis

Introduction

In many industries, a powerful method of quantifying surface texture on smooth surfaces is Power Spectral Density (PSD) analysis. This method uses Fourier analysis to convert the spatial domain measurement data of a surface into its frequency components. Spectral analysis of this type is extremely useful in describing how a polished surface will scatter incident radiation – a critical performance metric in optical, semiconductor, and precision machining applications.
MetroPro™ software has built in tools for PSD analysis that are very simple to set up and use. For users in the precision optics industry, ISO 10110-8 compliant units are available.

What is a PSD?

When manufacturing a smooth surface such as a silicon wafer or an optical surface, the finishing process can create a repetitive structure – a ripple – on the surface
(see the inset of Figure 1). The frequency and magnitude of these ripples have a direct impact on the way the surface will scatter incident radiation. For an optical surface this scattering may degrade imaging or performance of the system. On a semiconductor surface, this ripple could limit the size of the features that can be printed on the surface.


Figure 1.

Figure 1 – A PSD created from a 10 pixel wide trace through the surface area shown in the inset



PSD analysis examines the power of surface variations as a function of frequency.
An example is shown in Figure 1. To properly measure the surface, a band pass filter must be applied that restricts the data to frequencies of interest. The specific cutoffs that are applied depend on the optical resolution of the system as well as the intended function of the surface.

Once filtered, a profile slice is taken across the data perpendicular to the direction of the structure (the lay). This profile data is Fourier transformed into its spectral components, and the square of the magnitude is plotted against frequency creating the PSD chart. Typically, the rms surface roughness of the filtered data is the calculated parameter of interest; and spikes in the plot show where dominant surface ripple occurs.

Why PSD?

PSD is a valuable analysis tool particularly when regularity of the surface needs to be minimized. It is possible for both a virtually random and an extremely regular surface to produce the same rms roughness value. However, a random surface will have essentially no peaks in the PSD plot, while a very regular surface will show strong peaks. By placing limits on the power measured in the PSD, a desired level of randomness in the surface can be ensured.

Using PSD analysis in MetroPro

MetroPro™ 8.1.5 includes PSD analysis in all profile data windows. In order to adhere to the standards defined by ISO 10110-8 for PSD analysis, the profiles should be perpendicular to the dominant lay of the surface. Profiles running at an angle to the dominant lay will not be correct in power or frequency. Similarly, if the slices were to run parallel to the lay, then they will not see the repeated structure at all, and the PSD analysis would be useless from a metrological view!

Second, PSD analysis requires band pass filtering. For compliance with ISO10110-8, the filter should be an FFT with a Gaussian cutoff – the standard form of an FFT in MetroPro™. While not strictly an ISO 10110-8 filter, the Gaussian spline filter can also be a good choice, particularly when working with more complex surface shapes. In order to perform the PSD analysis, a simple line profile needs to be created in a filled plot. This line profile will be the source of the data for the PSD analysis.

While only a single trace is required, using only one slice is susceptible to small local variation in the measurement surface. In order to avoid these problems, MetroPro™ enables the averaging of parallel slices in the spatial domain by setting the width of the slice. Figure 1 shows a typical PSD and the two dimensional surface used to generate it. Notice the peak at approximately 2 cycles / mm. This represents the dominant frequency for the slice.

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