Innovations Foresight Introduction to optimal autoguiding The AstroImaging

Innovations Foresight Introduction to optimal auto-guiding The Astro-Imaging Channel June 17 th, 2018 Dr. Gaston Baudat Innovations Foresight, LLC (c) Innovations Foresight 2016 - Dr. Gaston Baudat 1

Why auto-guiding? Innovations Foresight • Stay on target within a fraction of an arc-second all the time. - Could become challenging for long focal lengths (>1 m). • Correct for mount and/or model errors, such: - Drifts, noises, artefacts, flexures, accidents, unforeseen. . . guide star open loop error (c) Innovations Foresight 201 - Dr. Gaston Baudat 2

Deterministic setup tracking errors (open loop) Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 3

Random setup tracking errors (open loop) Innovations Foresight • Mount gear mechanical noise after PEC: • Random errors ~0. 1” to 1” rms (bandwidth ~ 0. 001 Hz) • Minimized with a good mount (almost gone with direct drive and/or high resolution encoders) • Wind burst, accidents (bumping mount, cables, mirror flop, …): • Minimized by dropping frames • Unforeseen (Mr. Murphy is very creative and works in team) • Minimized by dropping frames • All of those errors are fully correlated across the all FOV! (c) Innovations Foresight 2016 - Dr. Gaston Baudat 4

The different types of noise Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 5

Innovations Foresight Mount mechanical noise (after PEC, no drift) • Low frequency (“pink”) noise (RA in the plot below) (almost gone with high resolution encoders and/or direct drive) Time constant t = 122 seconds (c) Innovations Foresight 2016 - Dr. Gaston Baudat 6

Seeing limited conditions Innovations Foresight • Astronomical seeing is the blurring of astronomical objects caused by Earth's atmosphere turbulence • It impacts the intensity (scintillation) and the shape (phase) of the incoming wave front • Scintillation is usually Star under seeing limited condition (short exposure << 1 s) Credit: John Hayes not a major problem, at least for exposures above one second. Phase is the main concern (wandering stars) since the wavefront tilt/tip contribution >85% of the total seeing phase variance (c) Innovations Foresight 2016 - Dr. Gaston Baudat 7

Wavefront and phase distortion Innovations Foresight An incoming plane wave (star) is perturbed by the Earth atmosphere turbulent structure leading to phase errors. l l (c) Innovations Foresight 2016 - Dr. Gaston Baudat 8

The Fried’s parameter Innovations Foresight FWHM [“] 1 1. 5 2 2. 5 3 110 / 4. 3 74 / 2. 9 56 / 2. 2 44 / 1. 7 37 / 1. 5 (c) Innovations Foresight 2016 - Dr. Gaston Baudat 9

Seeing versus diffraction limit Innovations Foresight FWHM [“] 1 1. 5 2 2. 5 3 110 / 4. 3 74 / 2. 9 56 / 2. 2 44 / 1. 7 37 / 1. 5 (c) Innovations Foresight 2016 - Dr. Gaston Baudat 10

Aberrations and seeing Innovations Foresight Wave-front Zernike’s decomposition Zernike’s polynomials: F. Zernike (1934) Type of aberration Phase variance contribution Tilt/tip (wandering star) ~87% Defocus ~2% Astigmatism ~2% Coma (3 rd order) ~2% Spherical (4 th order) <1% Trefoild (3 rd order) <1% (c) Innovations Foresight 2016 - Dr. Gaston Baudat 11

Isoplanatic patch Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 12

Effect of the isoplanatic angle on AO Innovations Foresight AO operation is usually only effective in a very narrow FOV. IR bands: 1200 nm, 1600 nm, and 2200 nm Credit R. Dekany, Caltec Palomar AO system (c) Innovations Foresight 2016 - Dr. Gaston Baudat Guide star offset FWHM [“] 0 0. 2 5. 5 0. 3 13 0. 45 0. 59 23 0. 51 0. 68 13

Isokinetic patch (wavefront tilt/tip component) Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 14

Seeing wavefront tilt/tip (wandering star) power spectrum Innovations Foresight • The wavefront tilt/tip seeing component is the dominant effect • The tilt/tip component is a large (“white”) bandwidth noise (c) Innovations Foresight 2016 - Dr. Gaston Baudat 15

Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 16

Total open loop noise (PEC, accidents & drift removed) Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 17

Innovations Foresight Auto-guiding error (close loop) on a target (c) Innovations Foresight 2016 - Dr. Gaston Baudat 18

Understanding the auto-guiding (proportional control) Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 19

Auto-guiding system stability (step response diverged) Innovations Foresight K K K (c) Innovations Foresight 2016 - Dr. Gaston Baudat 20

Innovations Foresight Auto-guiding analysis 3 basic situations (c) Innovations Foresight 2016 - Dr. Gaston Baudat 21

Auto-guiding The step response Innovations Foresight K = 0. 5 K = 0. 8 Close loop error (c) Innovations Foresight 2016 - Dr. Gaston Baudat 22

Auto-guiding The drift response Innovations Foresight K = 0. 5 K = 0. 8 Close loop error (c) Innovations Foresight 2016 - Dr. Gaston Baudat 23

Innovations Foresight Auto-guiding The “white” noise response K=0. 8 Close loop error K = 0. 8 (c) Innovations Foresight 2016 - Dr. Gaston Baudat 24

Auto-guiding The “pink” noise response Innovations Foresight K=0. 8 (c) Innovations Foresight 2016 - Dr. Gaston Baudat K=0. 8 25

Optimal auto-guiding Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 26

Auto-guiding loop: The big picture Innovations Foresight + - + + Perfect ++ Mount & Setup Actual Mount & Setup Proportional Corrector Guider + Centroid Auto-Guiding System (c) Innovations Foresight 2016 - Dr. Gaston Baudat 27

Target error on imager Final FWHM Innovations Foresight + + Imager (c) Innovations Foresight 2016 - Dr. Gaston Baudat 28

Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 29

Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 30

Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 31

Innovations Foresight Asymptotic mount error (c) Innovations Foresight 2016 - Dr. Gaston Baudat 32

Aggressiveness & close loop target FWHM mid-range mount (4” peak-peak, after PEC) Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 33

Aggressiveness & close loop target FWHM high-end mount (1” peak-peak, after PEC) Innovations Foresight • A lower mount error leads to smaller close loop target FWHM under same seeing. Most guide exposures give the same result. Improvement between 1 s and 10 s = ~0. 02” (c) Innovations Foresight 2016 - Dr. Gaston Baudat 34

Innovations Foresight + 2. 5 mag. + 2 mag. + 1 mag. Not recommended (c) Innovations Foresight 2016 - Dr. Gaston Baudat 35

Open loop seeing error scatter plot Innovations Foresight Perfect mount open loop error scatter plot (100 samples). SNR=6 d. B (2 x), 4 stars (same mag. ), seeing 2 pixel rms. Red diamond: One star centroid. Green dot: Full frame guiding ADIC (uses the all frame). Blue dot: Multi-star centroids (uses 4 star centroids). (c) Innovations Foresight 2016 - Dr. Gaston Baudat 36

Close loop target FWHM v. s. information in guider FOV mid-range mount (4” peak-peak, after PEC) Innovations Foresight Target FWHM for various number of guide star in the guider FOV (same mag. ) One guide star Four guide stars (c) Innovations Foresight 2016 - Dr. Gaston Baudat 37

Lucky imaging and seeing Innovations Foresight (c) Innovations Foresight 2016 - Dr. Gaston Baudat 38

Innovations Foresight FWHM improvement ~40% before processing M 83 with full spectrum guiding (OAG) M 83 with NIR guiding >750 nm (ONAG) (c) Innovations Foresight 2015 - Dr. Gaston Baudat (c) Innovations Foresight 2016 - Dr. Gaston Baudat 39

Optimal-guiding calculator (Excel spreadsheet) Innovations Foresight • An optimal guiding calculator can be downloaded from here: https: //www. innovationsforesight. com/support/download/ (c) Innovations Foresight 2016 - Dr. Gaston Baudat 40

Thank you! Innovations Foresight, LLC Clear skies! (c) Innovations Foresight 2016 - Dr. Gaston Baudat 41