lessons from decam active optics - project.lsst.org · mapping of wavefront zernikes to control...

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


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)


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 #


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

<latexit sha1_base64="JbvFF6x9KsfwO1UXgJQVZ0d9pe0=">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</latexit>

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


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



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



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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Reference Wavefront

Measured Wavefront does not perfectly match Zemax model

i Band Data

Zemax Model


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


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

]


Image Sequence: Focus Zernike CoefficientsDefocus [microns]


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!


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


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


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.


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

lessons from decam active optics - project.lsst.org · mapping of wavefront zernikes to control...

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