NASA’s Neil Gehrels Swift Observatory is an agile satellite designed to swing around rapidly whenever a gamma-ray burst detonates in deep space.
Its Ultraviolet/Optical Telescope (UVOT) is capable of capturing incredible images. But during high reaction-wheel momentum or attitude limit cycling, the satellite can experience mechanical shudder, tracing out erratic serpentine streaks across the detector that can exceed 400 pixels.
If you combine the raw exposure with standard pipeline stacking, point-source stars don’t look like stars; they look like blurry ribbons of spaghetti.
To rescue these observations, we developed UNJITR (UV/Optical Nonlinear Jitter & Instability Trajectory Recovery). Here is the core math behind how it works.
Photons Are Free Time Slices
Most digital cameras integrate light into fixed frames (e.g., 30 frames per second). UVOT, however, operates in photon-counting mode: every detected ultraviolet photon is recorded with microsecond timestamps and detector coordinates (x, y, t).
Because we have individual photons, we can slice time however we want. We break the raw photon continuum into overlapping 1.0-second time slabs.
Sub-Pixel Fourier Registration
For each time slab, we compute the 2D cross-correlation against a stable reference template in the Fourier domain:
Finding the integer peak of that correlation surface gives the coarse pixel shift. To achieve diffraction-limited precision, we fit a closed-form 1D parabola through the peak’s cardinal neighbors:
This gives sub-pixel trajectory tracking (±0.10 pixels) at 6.7 Hz with zero expensive non-linear optimization.
282 Galaxies Later
Once the continuous trajectory ΔX(t), ΔY(t) is solved and smoothed, we invert it against every raw photon event in the FITS table:
Across 282 Swift UVOT galaxy observations, this delivered a 99.7% archive recovery rate, collapsing 450-pixel serpentine tracks back into tight 2.94″ Airy diffraction cores and recovering light curves that astronomers had written off as lost.