自由曲面の製造
Manufacturing of free-formoptics
Mikio Kurita
Kyoto Univ.

可視赤外線観測装置ワークショップ2022
京都大学 セミナーハウス
20221223

Introduction:
Potential of Free-form Optics

Conventional Optical DesignKorsch FoV ～Φ1 deg

Three Mirror Anastigmat
TMA (designed by us) FoV ～Φ4 deg

Introduction
Limitation of Interferometer• Interferometer is a powerful tool for a test of optics.
• requiring an accurate and custom-made reference
surface (null optics)• requiring a stable and large space equivalent to theradius of curvature (RoC) of the test mirror• challenging to test a large flat, and convex surface
nearly impossible to test free-form optics highly asphericInterferometer

Interferometer

Interferometer

Concave

ConvexFree-form

Introduction
Limitation of CMM/Mechanical method• Coordinate measurement machine is a powerfultool for testing free-form optics.
• limited to size up to 1 m• very few tools which can both test and polish
1000
700

Off-axis four mirror optics
ALOS-3 (JAXA), Watarai+2018“A-Ruler” developed by Canon Inc
Watarai+2018

Three Point Method (TPM)• Three-sensor unit travels with linear guide• Sag or hump (local curvature) is obtained with
2s2-s1-s3• Local curvatures are doubly integrated along thescanning path
• The cross-sectional shape of the test surface isobtained☺
• Measuring local curvature is insensitive to motion error of the unit

• Precise reference (null optics) is not required → Free-form• Low spatial resolution• Sensor noise is also magnified with the integration process.
• Inapplicable to surface departing from flat

Dragging TPM• Dragging TPM drags a probe unit on the test surface.

• Difference of the local curvature from the design value is
integrated along the path for obtaining the figure error.
Dragging TPM☺
A linear guide is not required.
A large measurement range of sensors is not required.
Resistant to temperature changes and vibration
It can be mounted on a polishing machine.
→Measurable range is not limited

Robot Arm System• Polish & Profilometer• Work Area: φ1.8m• Small space• Robust• Cost saving

PolishMeasurement

Data Stitching Algorithm• Sensor error is emphasized with the integral procedure.
• The cross-sectional data is inconsistent with each other atthe intersection after least squares.
• New algorithm deals with the data as a deformable linear
elastic body and stitches the data without inconsistency.
• The solver is based on FEM (minimum energy).

Image of stitching elastic bodies

Simulation
True

Stitched
Raw data
Stitched with circle pathRaw data is made using a three-point method with a sensor noise of 1 nm and 100 steps.
Raw data has inconsistencies at the intersections and has a discontinuous surface.
Stitched surface reduces figure error and has a continuous surface.
The circle path at the edge dramatically improves the figure error.

Repeatability on flat mirror
Polishing flat mirror

1m

Motion of robot-armand table

RMS < 10 nm

Convex Aspheric
1m

After grindingSeimei Telescope

Flat mirror

NGC6946

Seimei 3.8 m telescope
The largest telescope in East-Asia

Convex AsphericHartmann Test

Current and Future Work• 2-m off axis parabola• Telescope for observing
planets in our solar system• Three mirror anastigmat(TMA) telescope
2-m off axis parabola for PLANETS• 0.5 m aperture• FoV of Φ4 deg• Off-axis and good MTF

Conclusion• We developed new manufacturing system for freeform and one-meter scale optics.
• The system figured out the M2 and M3 mirrors ofSeimei telescope.
• The system finished 1m convex M2 within one
month with the figure error of 35 nm RMS.
• We confirmed the optical performance of M2 andM3 with the Shack Hartmann test and obtained theHartmann constant of 0”.26.