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HOCUS FOCUS

George Hilios

NEAIC, Suffern NY

April 14, 2023

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The Science of Star Measurement for

Auto-Focusing and Tilt Correction

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Familiar Situation?

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Hocus Focus

  • Optimize performance for amateur astronomy
    • Pinpoint focus
    • Fast: Minimize image acquisition impact
    • Sophisticated: Fine tune back-focus and tilt
  • Promote scientific discourse and discovery
    • No ivory towers: test theories with data
  • Transparent algorithms
    • No magic parameters!
    • Fully open source (MPLv2)

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About Myself

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NINA Contributions

  • Dome support, including scope synchronization
  • Center after Drift
  • MetaGuide integration
  • SBIG CCD native support
  • Plugins
    • Orbitals: tracking and imaging comets, asteroids, planets
    • 10u Tools: building models for 10 micron mounts
    • Hocus Focus: Auto focus, PSF measurement, aberration inspection

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AGENDA

Scientific Workbench

Star Measurement

Finding Optimal Focus

Tilt and Backfocus

Future Work

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SCIENTIFIC WORKBENCH

Collect the right tools to iterate on new methods

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  • View measurements per star
  • No magic knobs, all parameters configurable
  • Re-analyze with different approaches
  • Visual inspection of each step of the process

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Star Annotation

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Star Rejection

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Tunable Parameters

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Test and Iterate

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Autofocus Replay

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Development Debugging

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MEASURING STARS

Size, Shape, Center Position, etc

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Goals

  • Identify star candidates
  • Reject low-quality or poor matches
    • Double stars
    • Distorted
    • Flat discs
  • Measure heuristic for star focus
    • FWHM or HFR?

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1 – Hotpixel Filtering

Simple (low-overhead) – 3x3 Median Blur

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Thresholding (preferred) – Filter when large diff

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2 – Noise Reduction

Gaussian Convolution

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Stdev = Radius * 2 + 1

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3 – Structure Detection

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Wavelet to extract structures

Larger = bigger stars = longer focal length

Kappa Sigma background noise estimate

Larger = higher background noise

Dilate star candidate structures

Off by default

Binarize

Noise Clipping Multiplier * noise estimate

Star candidate boxes

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4 - Rejection

  1. Has saturated pixels
  2. Touching border of image
  3. Elongated/Distorted
  4. Too dim
  5. Centroid not centered
  6. Too flat/no peak

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5 – HFR Measurement

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Sum of pixel brightness * center distance

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Sum of pixel brightness

Distance containing half of star brightness

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6 – FWHM Measurement

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Point Spread Function

Non-linear optimization. No direct solution

B = background ADU

A = center ADU

x0, y0 = center

β = Moffat Beta (1.4)

σx, σy = FWHM sigma (solving for)

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Convert sigma to FWHM pixels

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AUTOFOCUS

Finding Optimal Focus

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Hyperbolic Fit

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HFR Std Dev

Minima

Goodness of Fit

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Doesn’t fit?

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Improvements

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Outlier rejection

Hyperbola with different slopes

Minima changed by 34 steps

Higher error = lower weight

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Options

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ABERRATION INSPECTION

Measuring and correcting tilt and back-focus

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Background

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Back-focus

Tilt

Similar, but at a gradient

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Corners Analysis

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Credit: Chris White

Cloudy Nights Thread - https://www.cloudynights.com/topic/809050-tilt-discussion-astap/

  1. Divide sensor into grid (3x3)
  2. Calculate optimal focus in center and corners
  3. No tilt = corners arrive at focus together
  4. Perfect backfocus = corners arrive at focus with center

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Automated in NINA

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Replay or run live

Large tilt!

Tilt and back-focus mixed together…

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Sensor Model

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Credit: Frank Freestar8n

Observations

  • Calculate focus position for every star
  • Fit a 3d paraboloid across the sensor
  • Include a tilt plane to calculate both at the same time

Approach

  • Corners model coarse due to averaging across regions
  • Tilt must be corrected to measure back-focus error

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Mathematical Model

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Distance from sensor center

Offset from curvature

Offset from tilt

Total offset

x0, y0 Sensor Center

c Positive or negative curvature inverse radius. Smaller = flatter

Θ, Φ Tilt plane rotation, amount (radians). Θ = 0 = no tilt

Variables

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Techniques Applied

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  • Non-linear optimization - Levenberg-Marquardt
    • Implemented with Alglib
  • Naïve star registration – Quad Trees
    • Use RANSAC instead
  • Deal with outliers – Iterative reweighting (IRLS)

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FUTURE WORK

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Future Work

Autofocus

  • Fourier transformation method
    • Credit: Cheng-Yan Tang
  • 2-pass AF with FWHM and small step-size
  • Planetary AF in Fourier domain

Aberration Inspection

  • Guidance for which screws to turn
    • Calculate tilt adjuster screw locations
    • Motorized tilt adjusters?
  • Evaluate interpolation instead of outlier rejection
    • Ie, Kriging and RBF

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THANK YOU

George Hilios

jokogeo (Discord)

ghilios (Cloudy Nights)

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