# Presentation: 190572

## AMSD Alignment Sensitivity Analysis

- Patrick J. Reardon (UAH-CAO)
- reardonp@email.uah.edu
- H. Philip Stahl (NASA-SOMTC)
- Phil.Stahl@msfc.nasa.gov
- May 10, 2001

## Goals of Analysis

- Verify the measurement process
- Specify necessary stage resolutions
- Determine and minimize measurement uncertainty

## Outline

- Geometry for analysis
- Error budget matrix
- Contributions calculated for several elements
- Alignment Sensitivity
- Perfect mirror
- Radius error
- Conic error
- Simulated gravity sag
- Aberration evolution
- Next steps

## Geometry for Analysis

## Terms and Conditions

- Mirror segment is circular
- Diameter = 1.5m
- Everything is in P-V OPD waves, not surface
- Optical model used is not final design
- Measurement wavelength is 632nm

## Error Budget

## Error Budget

## Null Errors

- Null pattern yields “large” minimum features (~0.011mm)
- Easily manufactured
- Pixelization errors should be negligible
- Substrate transmitted wavefront distortion less than /10
- zero order transmission can be measured and subtracted

## Window Errors

- Initial modeling indicates no perceptible distortions due to pressure differential
- Testing is underway at SOMTC to characterize wedge and distortions of window at ambient and under vacuum

## Null Misalignments

- Null Lens Set: two kinematically mounted plates:
- the Null and an Alignment Mask
- Alignment mask used to align null stages, then null replaces alignment mask.
- Manufacturing tolerances limit registration between two plates to ~0.003mm laterally and ~0.01mm in focus.
- Lateral misalignments yield immeasurable errors: simple tilts in spherical wave space
- Given focus error:
- If mirror is exactly laterally aligned to fiducials, 0.09 
- If mirror is misaligned by 0.04mm, 0.04 

## Null Misalignments

## Null Misalignments

- Error Reduction:
- Error between alignment and null masks is determined.
- Quantify focus difference before test.
- Compensate during alignment phase.
- Reduce position uncertainty by a factor of >2
- Reduces wavefront error to <0.05 .

## Window Misalignments

- Null designed to compensate for aberrations from window.
- Window tilted ~0.4 degrees from central ray
- Arbitrarily set in optical design model for null (default)
- Produces three primary aberrations
- 	0.056  spherical aberration
- 	0.056 /degree coma
- 	2 * 0.014 / degree2 astigmatism
- Misalignments generate uncompensated aberrations
-   	Spherical aberration unchanged
-    0.056 / degree coma
- 	* 0.028 /degree2 astigmatism

## Window Misalignments

- Window is AR coated, in widely diverging beam, so tilting may be  unnecessary
- Tilt errors can be kept to <<0.1 degree using a dedicated region of null plate

## Uncompensated Mirror Misalignments

- 6-DoF misalignments yield 3 aberration decomposition groups
- {x, y}  {0.07 /m, 0.72 /rad}
- {y, x, z}  {0.06 /m, 0.56 /rad, 0.07 /rad}
- {z} {0.01 /m}
- Tilt removed from these analyses
- ~0.5 /m for x and y
- ~4.6 /rad for x and y
- ~0.6 /rad for z

## Uncompensated Mirror Misalignments

## Apparent Mirror Errors

- Alignment sensitivity depends on modeled mirror surface
- Misalignments can yield incorrect mirror errors
- 4 surfaces were analyzed:
- 	Perfect mirror
- 	Radius error
- 	Conic error
- 	Simulated gravity sag

## Apparent Mirror Errors :Perfect Mirror

- Specific lateral errors were applied
- Aberrations compensated with mirror tilt
- {x, y}, {y, x}
- “Measured” wavefront error varies with misalignment
- ~2.4 /mm decenter
- Primary Zernike term is astigmatism

## Apparent Mirror Errors :Perfect Mirror

## Apparent Mirror Errors :Radius Error

- A 1mm radius error was applied to surface (10001mm)
- Model optimized to reduce aberrations
- Case 1:  Mirror completely free to move
- Measures ~0.03  aberration
- Primary Zernike component horizontal coma
- Case 2:  Mirror constrained to stay aligned to lateral fiducials
- Measures ~0.14  aberration
- Primary Zernike component horizontal astigmatism
- Difference between Case 1 and Case 2:
- 0.05mm   lateral displacement (2.2 /mm)

## Apparent Mirror Errors :Radius Error

## Apparent Mirror Errors :Conic Error

- A 0.001 error was applied to surface conic
- Model optimized to reduce aberrations
- Case 1:  Mirror completely free to move
- Measures ~0.35  aberration
- Primary Zernike component coma
- Case 2:  Mirror constrained to stay aligned to lateral fiducials
- Measures ~1.57  aberration
- Primary Zernike astigmatism
- Matches geometrical difference
- Difference between Case 1 and Case 2:
- 0.7mm   lateral displacement (1.74 /mm)

## Apparent Mirror Errors :Conic Error

## Apparent Mirror Errors :Simulated Gravity Sag

- A 5m cylindrical deformation was applied to surface
- Model optimized to reduce aberrations
- Case 1:  Mirror completely free to move
- Measures ~3.90 aberration
- Primary Zernike component coma
- Case 2:  Mirror constrained to stay aligned to lateral fiducials
- Measures ~16.54 aberration
- Primary Zernike astigmatism
- Closely matches geometrical difference
- Difference between Case 1 and Case 2:
- 6.4mm lateral displacement (1.96/mm)

## Apparent Mirror Errors :Simulated Gravity Sag

## Alignment Accuracy

- Perceived surface shape depends on aberrations
- Given:
- 1kx1k camera
- 1/10th pixel
- Alignment accuracy is ~0.14mm
- Perfect Mirror: 0.33  uncertainty
- Radius Error 1mm: 0.31  uncertainty
- Conic Error 0.001: 0.24  uncertainty
- Gravity Sag 0.005: 0.27  uncertainty

## Aberration Evolution

- Measurement approach will utilize aberration evolution
- Align and measure
- Translate sensor pallet a known amount
- Tilt mirror to minimize aberrations and re-measure
- Repeat
- Evaluate evolution of aberrations through test space to determine “true” alignment position and/or actual surface shape
- Analytical solution?
- Least Squares Fit approach?

## Aberration Evolution

## Aberration Evolution

## Aberration Evolution

## Future (Immediate) Efforts

- Error Budget Analysis
- Fill in any incomplete error budget boxes
- Convert P-V OPD errors to RMS Surface Zernikes
- Compute final Error Budget value or function
- Complete investigation of aberration evolution and finalize alignment procedure.