Author: Site Editor Publish Time: 2026-09-21 Origin: Site
Causes Measurement and Process Control
A reduction in total surface RMS does not mean that errors at every spatial scale have decreased. For optics with imaging or beam-quality requirements, form correction also needs to address the distribution of error within specified frequency bands. Control of mid-spatial-frequency errors connects the target band, removal function, tool path and metrology method.
Mid-spatial frequency, commonly abbreviated MSF, describes a range between longer-scale form variation and shorter-scale texture. Its boundaries must be defined for the optical application, drawing requirements and metrology capability. There is no fixed boundary suitable for every optical component. [1,5]
For a periodic variation along one direction, spatial frequency f is the reciprocal of spatial period L. With L in mm, f can be expressed in cycles/mm:
This describes variation per unit distance on the surface and differs from the temporal vibration frequency of a machine in Hz. MSF identifies a band; RMS is an amplitude statistic. Interpreting an RMS value requires the evaluation region, reference processing and frequency range.
Figure 1 Two synthetic sinusoidal profiles have zero mean and RMS equal to 1 over the same normalized interval, but different spatial periods. The figure explains the difference between amplitude statistics and spatial scale. It does not define MSF boundaries or represent measured workpieces.
Grinding or other preceding operations may leave periodic texture. Whether existing errors can be corrected depends on the tool’s spatial response, an executable dwell solution and measurement capability. A form-correction pass should not be assumed to remove every shorter-period structure.
Finishing can also introduce structured residuals. Regular path spacing combined with a finite removal footprint affects local coverage; speed or execution errors, removal-function drift and ribbon fluctuations can map process variations onto the surface. Original studies of magnetorheological finishing have investigated both path effects and ribbon fluctuations in relation to MSF errors. [2,3]
These mechanisms suggest diagnostic questions, but a surface map alone does not establish the root cause. Compare the observed direction and spacing with the tool path, machine and process records, and repeat measurements.
Power spectral density, or PSD, describes how surface-height variation is distributed across spatial frequencies. Narrow peaks in particular directions can indicate periodic structure; broader distributions require evaluation across a band. PSD does not retain all spatial-location information, so also inspect surface maps, relevant directional profiles and local defects.
With consistent processing and normalization, integrating PSD over a specified frequency domain gives a band mean-square value; taking its square root gives band-limited RMS. Distinguish one-dimensional PSD, two-dimensional PSD and radial statistics. A radially averaged two-dimensional PSD cannot be integrated as an ordinary one-dimensional curve while omitting the appropriate weighting. Comparing just one peak or total RMS can miss changes in other bands or directions. [7]
Define the following before evaluating results:
· Clear aperture or measurement region, sampling interval, analysis direction and coordinate registration.
· Form removal, detrending, filtering, window function, and the dimensionality, units and normalization of PSD.
· PSD limits or band-limited RMS requirements over the specified band, including directional requirements where needed.
· Reliable spatial bandwidth, noise and repeatability for the instrument configuration. Sampling pitch is not the same as lateral resolving capability; more pixels alone do not ensure reliable high-frequency data. [4]
Evaluate path spacing together with the removal function, target frequency band and dwell distribution. Smaller spacing, a changed scan direction or a nonperiodic path may improve particular structures, but can also increase processing time or redistribute energy to other bands. Validate the strategy on the relevant machine and workpiece; neither a randomized path nor a smaller step is a universal guarantee. [2]
Also verify removal-function stability during processing and whether the motion system can execute the computed dwell solution. If ribbon or process-state fluctuations occur, investigate their origin and relationship to surface structure before taking action under the manufacturer’s procedure. Path changes do not replace control of an unstable process. [3]
Use consistent aperture, detrending, filtering and bandwidth in post-process metrology. Check improvement in the target band, possible degradation elsewhere and any new directional structure. Different tool scales or process combinations may warrant evaluation, with stock allowance, surface texture and defect requirements considered together.
ISO 10110-8:2019 addresses drawing indications for optical surface texture, including statistical description of the residual surface after form removal. ISO 25178-2:2021 defines areal surface-texture parameters. Each has its own scope. Neither establishes that a machine can eliminate MSF, and compliance with one parameter limit does not establish acceptance across all frequency bands. [5,6]
Project documents should identify the evaluation aperture, spatial band, direction, limits, instrument configuration, processing method and acceptance decision procedure. Define surface-height and wavefront evaluation separately. Ra is a profile parameter and Sq an areal parameter; their evaluation domains and filtering conditions also need to be stated.
APEX supports magnetorheological finishing equipment selection and project coordination. For an MSF-sensitive project, provide the material and geometry drawing, shareable starting surface data, target frequency band, available metrology and acceptance requirements. A request for “lower RMS” alone cannot determine the equipment configuration or process. Capability and acceptance conditions are governed by the technical documents and written agreement.
Contact APEX to discuss your magnetorheological finishing equipment project.
[1] Pohl, M., Kukso, O., Boerret, R., and Rascher, R. (2020). Mid-spatial frequency error generation mechanisms and prevention strategies for the grinding process. Journal of the European Optical Society–Rapid Publications, 16, 19. Source
[2] Chen, C., Dai, Y., Hu, H., and Guan, C. (2024). Study on the influence of a magnetorheological finishing path on the mid-frequency errors of optical element surfaces. Optics Express, 32(11), 19133–19145. Source
[3] Wang, B., Shi, F., Tie, G., Zhang, W., Song, C., Tian, Y., and Shen, Y. (2022). The Cause of Ribbon Fluctuation in Magnetorheological Finishing and Its Influence on Surface Mid-Spatial Frequency Error. Micromachines, 13(5), 697. Source
[4] Lehan, J. P., Griesmann, U., and Chu, J. (2010). Power Spectral Density: Is it right? Optical Fabrication and Testing, paper OWE1. OSA Technical Digest. Source
[5] ISO 10110-8:2019. Optics and photonics — Preparation of drawings for optical elements and systems — Part 8: Surface texture. Source
[6] ISO 25178-2:2021. Geometrical product specifications (GPS) — Surface texture: Areal — Part 2: Terms, definitions and surface texture parameters. Source
[7] Sidick, E. (2009). Power spectral density specification and analysis of large optical surfaces. Proceedings of SPIE, 7390, 73900L. Source
This article provides general technical information and does not replace workpiece-specific process documents, inspection reports or safe operating procedures. Literature findings and illustrations do not establish the performance of APEX-supplied equipment or create an additional warranty. Obligations imposed by applicable law remain unchanged.
