1. Deflectometry-based Measurement And Correction Of Mirror Misalignment
Joel Berkson
Large Optics Fabrication and Testing (LOFT) Group
Mentor: Dae Wook Kim

2. What is Deflectometry? Object Optics Image
How did we get from object to image?

3. General Deflectometry
Display
Sample
Input data
Measured data
Camera

4. Sheared Fourier Transform for Phase Data
Sheared Pattern
g(x+Δ)-g(x)
Measured Pattern
Show subtraction of waves/general FT idea Δ
Heejoo Choi, et al. Proc. SPIE G, G (2017)

5. Benefits and Applications
High updating time (~10Hz)
Scalable to monitor multiple mirrors simultaneously
JWST (James Webb Space Telescope)
GMT (Giant Magellan Telescope)
Can achieve mrad and μrad relative misalignment measurement
Scalable by camera and display pixel size/geometry of setup
Closed loop monitoring and correction of mirror segments

6. Test Procedure Closed Loop Control LCD Tilt Mounted Mirror
Display and image initial pattern
Start monitoring process
External mirror misalignment
Capture image
Analyze pattern
Evaluate tilt
Move motor
Test Procedure
Closed Loop Control
Computer
LCD
Motorized Rotation Stage
Camera
Laser
Tilt Mounted Mirror
Motor Driver

7. Results
(μrad)

8. Results
Manual mirror tilt
(μrad)

9. Results
Compensate tilted mirror
(μrad)

10. Results
Return position
(μrad)

11. Conclusions
Deflectometry for mirror orientation has potential to be used in active control systems in both fabrication and assembly stages of an optical system
Future work
Absolute as well as relative tilt measurement
Using voice coil actuators for quick correction
Adjust for non-static alignment disruption

12. Acknowledgements NASA Space Grant Consortium
Dae Wook Kim, Heejoo Choi, LOFT group

13. Thank You!

14. Sheared Fourier Transform for Phase Data
Measured Pattern
Sheared Pattern
g(x+Δ)-g(x) Δ
Show subtraction of waves/general FT idea
∆= 1 2𝜋𝑓 𝑎𝑟𝑐𝑐𝑜𝑠 1− 𝐹𝑇 𝑔 𝑥+∆ −𝑔 𝑥 𝐹𝑇[𝑔 𝑓 ] 2
Heejoo Choi, et al. Proc. SPIE G, G (2017)

15. Angle Calculation
𝑥 𝑓 = 𝑥 𝑖 + Pixel pitch in physical units × number of pixels for one period × shifted phase (D)
𝜃= 𝑎𝑟𝑐𝑡𝑎𝑛 x 𝑓 − x 0 z 𝑑 −𝑎𝑟𝑐𝑡𝑎𝑛 x 𝑖 − x 0 z 𝑑 ,
Heejoo Choi, et al. Proc. SPIE G, G (2017)