This case records deterministic conversion of a Ø82 mm optical component from a spherical precursor to the target aspheric form. The vertex radius was R = -230 mm. The published record states that three MRF polishing cycles were completed on the PKC500Q with approximately 20 hours of polishing time. Relative to the target asphere, the initial figure error was approximately 10.992 µm PV and 3.093 µm RMS; the final result was approximately 142.538 nm PV and 7.224 nm RMS.
Item | Published Record |
Customer Requirement | Convert a spherical precursor toward the specified asphere and reduce the residual error through repeated deterministic correction |
Workpiece diameter | Ø82 mm optical component; vertex radius R = -230 mm; sphere-to-asphere correction |
Vertex radius | R = -230 mm |
Correction type | Sphere to asphere |
MRF cycles | 3 |
Published polishing time | Approximately 20 h |
Initial Condition | PV 10.992 µm; RMS 3.093 µm relative to the target asphere |
Final Result | PV reduced from 10.992 µm to 142.538 nm (about 98.70%); RMS reduced from 3.093 µm to 7.224 nm (about 99.77%). Results are case-specific |
Processing platform | PKC500-Q magnetorheological finishing machine |
Measurement | Final PV 142.538 nm and RMS 7.224 nm are reported. The material, effective aperture, instrument, wavelength, fit, removed terms, filtering, wheel/fluid and uncertainty were not disclosed. Approximately 20 h refers to published polishing time for the three cycles, not total project turnaround. |
Sphere-to-asphere correction requires more than reduction of random residual error. The process must remove a controlled low-spatial-frequency shape difference defined by the target aspheric equation. When the starting deviation is in the micrometer range, removal efficiency, removal-function stability, path coverage, and iterative convergence must be managed together to avoid local over-correction and the introduction of mid-spatial-frequency structure.
• Micrometre-scale nominal shape correction: The starting error of approximately 10.992 µm PV and 3.093 µm RMS had to be converted into a stable localized removal plan.
• Multi-cycle convergence: Each of the three polishing cycles required remeasurement and an updated dwell-time solution.
• Residual-error control: After the major shape conversion, the process still had to reduce the final PV and RMS rather than merely generate the nominal aspheric form.
The PKC500-Q combines an X/Y/Z/A/B/C six-axis architecture with MRF process software for figure-data processing, removal-function management, dwell-time solution, and coordinated path execution. The target asphere was used as the reference surface. The initial error map was translated into a material-removal map and reduced through three measurement–calculation–polishing–remeasurement cycles.
1. Define the target asphere: Import or define the nominal aspheric equation and establish a common workpiece coordinate system, data aperture, and fit convention.
2. Measure the initial error: Generate PV and RMS error maps relative to the target aspheric surface.
3. Calibrate the removal function: Characterize the localized removal function for the selected process settings.
4. Calculate dwell time and path: Convert the target removal map into dwell-time distribution and multi-axis motion.
5. Complete three MRF cycles: Remeasure after each cycle and update the next correction based on the remaining error.
6. Final verification: Evaluate the final surface against the same nominal asphere and data-processing convention.
PV decreased from 10.992 µm (10,992 nm) to 142.538 nm, a calculated reduction of approximately 98.70% and an improvement factor of about 77. RMS decreased from 3.093 µm (3,093 nm) to 7.224 nm, a calculated reduction of approximately 99.77% and an improvement factor of about 428. The result demonstrates that, with a suitable starting condition and process configuration, MRF can perform substantial sphere-to-asphere shape correction as well as nanometer-scale residual finishing.
Initial: 10.992 µm PV and 3.093 µm RMS. Final: 142.538 nm PV and 7.224 nm RMS.
• Deterministic conversion of a spherical precursor to a target asphere.
• Multi-cycle convergence from micrometer-scale starting error to nanometer-scale RMS.
• Coordination of removal-function calibration, dwell-time solution, and multi-axis path execution.
• Process planning under constraints for correction cycles and polishing time.
• Aspheric lenses and mirrors
• Infrared aspheric optics
• Pre-correction of freeform surfaces
• Precision optics requiring convergence from a pre-generated form
Data and Metrology Note: The published record does not disclose the workpiece material, effective aperture, metrology instrument, wavelength, fit reference, removed terms, spatial filtering, polishing head, MRF fluid, or measurement uncertainty. The approximately 20-hour value is reported as the polishing time for three MRF cycles and should not automatically be interpreted as including all fixturing, metrology, cleaning, and project turnaround activities.
Case boundary Final performance is application-specific and depends on workpiece material, geometry, initial condition, fixturing, process parameters, environmental control and metrology. Numerical results apply only to this cited record and its disclosed conditions.
