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Lessons from DECam Active Optics

Aaron Roodman LSST Project & Community Workshop

August 14, 2019

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

DECam Active Optics: Wavefront Sensors

F&A Sensors: 8 CCDs (2Kx2K) 1.5mm above/below focal plane

FN4

FN3

FN2

FN1 FS1

FS2

FS3

FS4

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

DECam Forward Donut Model

I(x, y) ⇥ PSF�Atmos� Pixel

Model Wavefront at the pupil plane as a sum of Zernike terms

Calculate Donut image via Fourier Transform from pupil ⟹Focal plane

Convolute with smearing for Seeing, Pixelate.

Non-linear χ2 fit (MINUIT) to determine Zernike coefficients Detailed model of DECam/Blanco shadow for pupil function Fit to 9 Zernike terms online; 12 Zernike terms offline Fix Seeing kernel online; Float Kolmogorov kernel offline

Algorithm based on work of Fienup 1982,1993; Heathcote, Tokovinin 2006 Fast algorithm - 0.5 cpu sec/donut for 9 Zernike terms

PSF(x, y) ����F

⇥P(u, v)ei 2⇥

� W(u,v)⇤���

2

W(u, v) =10

Âi=2

aiZi(r, q)

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

DECam AOSActive Control of Camera Hexapod degrees of freedom (5)

Focus, Tip/Tilt, Decenter Active Control of Blanco Primary Astigmatism (2) Look-up Tables for those 7 degrees of freedom vs. (Alt,Az) Active (closed-loop), unsupervised, operational since 2013

Exposure Id269.5 269.55 269.6 269.65 269.7 269.75

310×

m]

µFo

cus [

-250-200-150-100-50

050

100150200250

Exposure Id269.5 269.55 269.6 269.65 269.7 269.75

310×

m]

µFo

cus A

OS

[

-750

-700

-650

-600

-550

-500

-450

-400

-350

-300 Focus Trim

Focus Error

Image #

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Mapping of Wavefront Zernikes to Control D.O.F.Prime Focus system simpler than 3-mirror LSST

Sensitivity Matrix is diagonal for Hexapod Focus, Primary Astigmatism:

Matrix nearly diagonal for Hexapod Tip/Tilt & Decenter

�zHexapod = 172[µm/�]Da4(x, y)� aReference

4 (x, y)E

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m]µX [Δ-6000-4000-2000 0 2000 4000 6000

/mm

]λ [ x

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006 / ndf 2χ 256.2 / 9

offset 2.48e-06± 0.0003539 slope 7.731e-10± 6.824e-09

/ ndf 2χ 256.2 / 9offset 2.48e-06± 0.0003539 slope 7.731e-10± 6.824e-09

m]µY [Δ-6000-4000-2000 0 2000 4000 6000

/mm

]λ [ x

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006 / ndf 2χ 1148 / 9

offset 2.401e-06± 0.0003024 slope 7.675e-10± 4.247e-07

/ ndf 2χ 1148 / 9offset 2.401e-06± 0.0003024 slope 7.675e-10± 4.247e-07

X [arcsec]θ-200 -100 0 100 200

/mm

]λ [ x

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006 / ndf 2χ 12.56 / 3

offset 3.16e-06± -0.000101 slope 1.859e-08± -2.18e-05

/ ndf 2χ 12.56 / 3offset 3.16e-06± -0.000101 slope 1.859e-08± -2.18e-05

Y [arcsec]θ-300 -200 -100 0 100 200 300

/mm

]λ [ x

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006 / ndf 2χ 313.5 / 4

offset 2.778e-06± 0.0003337 slope 1.583e-08± 7.795e-09

/ ndf 2χ 313.5 / 4offset 2.778e-06± 0.0003337 slope 1.583e-08± 7.795e-09

m]µX [Δ-6000-4000-2000 0 2000 4000 6000

/mm

]λ [ y

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

/ ndf 2χ 2925 / 9offset 2.483e-06± -0.0002902 slope 7.744e-10± 3.867e-07

/ ndf 2χ 2925 / 9offset 2.483e-06± -0.0002902 slope 7.744e-10± 3.867e-07

m]µY [Δ-6000-4000-2000 0 2000 4000 6000

/mm

]λ [ y

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

/ ndf 2χ 7982 / 9offset 2.398e-06± -0.000339 slope 7.648e-10± -9.758e-09

/ ndf 2χ 7982 / 9offset 2.398e-06± -0.000339 slope 7.648e-10± -9.758e-09

X [arcsec]θ-200 -100 0 100 200

/mm

]λ [ y

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

/ ndf 2χ 470.6 / 3offset 3.157e-06± -0.0008744 slope 1.858e-08± -1.738e-07

/ ndf 2χ 470.6 / 3offset 3.157e-06± -0.0008744 slope 1.858e-08± -1.738e-07

Y [arcsec]θ-300 -200 -100 0 100 200 300

/mm

]λ [ y

Θ

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

/ ndf 2χ 288.5 / 4offset 2.781e-06± 0.0006582 slope 1.586e-08± 2.174e-05

/ ndf 2χ 288.5 / 4offset 2.781e-06± 0.0006582 slope 1.586e-08± 2.174e-05

m]µX [Δ-6000-4000-2000 0 2000 4000 6000

]λ [

Z7Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 2.052e+04 / 9

offset 0.0001836± -0.2458 slope 6.757e-08± 0.0002109

/ ndf 2χ 2.052e+04 / 9offset 0.0001836± -0.2458 slope 6.757e-08± 0.0002109

m]µY [Δ-6000-4000-2000 0 2000 4000 6000

]λ [

Z7Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 2.13e+04 / 9

offset 0.0001688± -0.1771 slope 6.642e-08± 2.474e-06

/ ndf 2χ 2.13e+04 / 9offset 0.0001688± -0.1771 slope 6.642e-08± 2.474e-06

X [arcsec]θ-200 -100 0 100 200

]λ [

Z7Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 6732 / 3

offset 0.0001857± -0.2236 slope 1.108e-06± 5.333e-05

/ ndf 2χ 6732 / 3offset 0.0001857± -0.2236 slope 1.108e-06± 5.333e-05

Y [arcsec]θ-300 -200 -100 0 100 200 300

]λ [

Z7Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 2.377e+04 / 4

offset 0.0001598± -0.3018 slope 8.752e-07± -0.0005089

/ ndf 2χ 2.377e+04 / 4offset 0.0001598± -0.3018 slope 8.752e-07± -0.0005089

m]µX [Δ-6000-4000-2000 0 2000 4000 6000

]λ [

Z8Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 1.738e+04 / 9

offset 0.0001498± -0.09783 slope 5.194e-08± -3.94e-06

/ ndf 2χ 1.738e+04 / 9offset 0.0001498± -0.09783 slope 5.194e-08± -3.94e-06

m]µY [Δ-6000-4000-2000 0 2000 4000 6000

]λ [

Z8Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 1.293e+04 / 9

offset 0.0001743± -0.1119 slope 7.315e-08± -0.0002263

/ ndf 2χ 1.293e+04 / 9offset 0.0001743± -0.1119 slope 7.315e-08± -0.0002263

X [arcsec]θ-200 -100 0 100 200

]λ [

Z8Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 7655 / 3

offset 0.0001634± -0.1058 slope 9.787e-07± -0.0006105

/ ndf 2χ 7655 / 3offset 0.0001634± -0.1058 slope 9.787e-07± -0.0006105

Y [arcsec]θ-300 -200 -100 0 100 200 300

]λ [

Z8Δ

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2 / ndf 2χ 1.347e+04 / 4

offset 0.0001505± -0.0908 slope 8.264e-07± 7.03e-05

/ ndf 2χ 1.347e+04 / 4offset 0.0001505± -0.0908 slope 8.264e-07± 7.03e-05

Hexapod d.o.f.

�z 7,�

z 8,⇥

x(z

5,z

6),⇥

y(z

5,z

6)

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�z7 =Da7(x, y)� aReference

7 (x, y)E

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Reference wavefront determined from Data

�z8 =Da8(x, y)� aReference

8 (x, y)E

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Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Reference Wavefront

Measured Wavefront does not perfectly match Zemax model

i Band Data

Zemax Model

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Covariance of Zernike Wavefront termsLSST Atmospheric Simulations

19 Zernike terms

In each of 4 Wavefront

Sensors

Zernike Sigma[nm]Focus 39AstigY 87AstigX 105ComaY 30ComaX 28TrefoilY 44TrefoilX 44

Spherical 6

Correlation Matrix

⇢iZ ,jZ ⇠ 0.7<latexit sha1_base64="McwP0pSbYg92Z3Wo/iIsm0WBUS0=">AAACAHicbVC5TsNAEF2HKyQcBgoKmhUBiQJZdihCGUFDGSRyKLFlrTfrZMn60O46UmS54VdoKECIhoKWP6DjQ6BmcxSQ8KSRnt6b0cw8L2ZUSNP81HJLyyura/n1QnFjc2tb39ltiCjhmNRxxCLe8pAgjIakLqlkpBVzggKPkaY3uBz7zSHhgkbhjRzFxAlQL6Q+xUgqydX3bd6P3JS67dNbt51BW9AAmkbF1UumYU4AF4k1I6Xq0dfr+7D4XXP1D7sb4SQgocQMCdGxzFg6KeKSYkaygp0IEiM8QD3SUTREARFOOnkgg8dK6UI/4qpCCSfq74kUBUKMAk91Bkj2xbw3Fv/zOon0z52UhnEiSYini/yEQRnBcRqwSznBko0UQZhTdSvEfcQRliqzggrBmn95kTTKhnVmlK9VGhdgijw4AIfgBFigAqrgCtRAHWCQgXvwCJ60O+1Be9Zepq05bTazB/5Ae/sB9COZwQ==</latexit>

Each Zernike term is highly correlated between Wavefront Sensors

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Blanco+DECam Covariance of Zernike WavefrontEngineering images with DECam out-of-focus by +1.5mm AOS in open-loop, only LUT used 100 Image sequence taken tracking on the sky

very small slews, to dither donuts 30 second exposures Use Wavefront values in 4 corners of DECam

Image #

ComaYAstigYFocus

highly stochastic large correlation between 4 corners

Zern

ike

[nm

]

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Image Sequence: Focus Zernike CoefficientsDefocus [microns]

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Blanco+DECam Covariance of Zernike Wavefront

Zernike Sigma[nm]Focus 57AstigY 35AstigX 35ComaY 19ComaX 17TrefoilY 14TrefoilX 16

Spherical 13

30 sec Blanco (3.6m) ~ 15 sec LSST (6.5m) Wavefront error larger in Focus & Spherical, smaller in other terms, compared to LSST simulation Additional errors from LUT errors, slews, hysteresis ~0.8-0.9 correlation between 4 corners

Ground layer dominates Qualitative agreement with LSST Atmospheric Simulation!

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

DECam Delivered AOS performanceDES wide-field r, i, z images Images from all 5.5 years Includes all size slews

Delivered Focus Zernike Wavefront Error = 91 nm

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Active Control: PID loop

Since Wavefront errors are completely dominated by random Atmospheric variation, need a control loop Each D.O.F. has its own PID loop

Gains are roughly P: 0.3 ; I: 0.1 ; D: 0.1 Tuned on open-loop data Results quite insensitive to exact gains

DECam AOS control applied using results from Image i on Image i+1

Donuts fit, Wavefront analyzed, Hexapod & Primary Astigmatism commanded in <10sec Larger deviations observed after large slews, but PID loop is not reset following large slews

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Blanco-DECam Look-Up Tables

nm

Focus Decenter

Tip/Tilt Astigmatism

LUTs built from 3 years of Science observations, both DES & community. LUTs

from sky scans had significant systematic

deviations.

Aaron Roodman SLAC National Accelerator Laboratory DECam Active Optics

Conclusions

Ideal Wavefront may vary from Optical Model Procedure to create ideal Wavefront, combining images & applying corrections corresponding to d.o.f.

Atmospheric Turbulence Wavefront Error dominates, for very stable observing conditions highly correlated between Wavefront sensors

Delivered focus performance has 60% additional contributions LUT errors Hysteresis

LUTs were derived from Science images Engineering sky scans had significant systematics