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<p>We present a comparison between the step transmission filter in the frequency domain and the Gaussian filter in the time domain for measuring surface roughness in real-time, in accordance with the ISO 4287 standard. The sample being measured consists of reflective gold bumps with an average roughness of 4.46&#xa0;μm and a precision of ± 0.35&#xa0;μm along a length of 3.55&#xa0;mm, as measured by the Taylor Hobson Surtronic 25 Stylus Profilometer. A custom Toymen-Green interferometer is used to analyze the sample. The results computed with the step transmission filter indicate that the average roughness of the gold bumps is 4.65&#xa0;μm with a precision of ± 0.31&#xa0;μm over a length of 3.55&#xa0;mm. The results obtained using the Gaussian filter show an average roughness of 5.32&#xa0;μm with a precision of ± 0.35&#xa0;μm over the same length. The step transmission filter in the frequency domain overcomes the limitations of the Gaussian filter in the time domain, including distortion near edges, the inability to track texture in large forms, and sensitivity to outliers.</p>

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Comparison of a step transmission filter in the frequency domain and the gaussian filter in the time domain for surface roughness measurement

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  • 发表日期：

    2026年4月1日

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  • Dahi Ghareab Abdelsalam Ibrahim,
  • Hesham Mahmoud

摘要

We present a comparison between the step transmission filter in the frequency domain and the Gaussian filter in the time domain for measuring surface roughness in real-time, in accordance with the ISO 4287 standard. The sample being measured consists of reflective gold bumps with an average roughness of 4.46 μm and a precision of ± 0.35 μm along a length of 3.55 mm, as measured by the Taylor Hobson Surtronic 25 Stylus Profilometer. A custom Toymen-Green interferometer is used to analyze the sample. The results computed with the step transmission filter indicate that the average roughness of the gold bumps is 4.65 μm with a precision of ± 0.31 μm over a length of 3.55 mm. The results obtained using the Gaussian filter show an average roughness of 5.32 μm with a precision of ± 0.35 μm over the same length. The step transmission filter in the frequency domain overcomes the limitations of the Gaussian filter in the time domain, including distortion near edges, the inability to track texture in large forms, and sensitivity to outliers.