Dither Offset Reconstruction

Reconstruct absolute planar dither positions from relative offsets and an explicit initial position in a common unit.

Description

A dither log may record relative moves rather than absolute positions.

A dither log may record relative moves rather than absolute positions. Cumulative reconstruction needs an explicit starting point and a common planar unit.^[1]

Reconstruct absolute planar dither positions from relative offsets and an explicit initial position in a common unit.

When to use Dither Offset Reconstruction

Use this tool to reconstruct absolute planar dither positions from relative offsets and an explicit initial position in a common unit.

Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.

How to use Dither Offset Reconstruction and understand its results

Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
Enter incrementX, incrementY, initialX, initialY using the field table and calculation rules, then run the tool.
Read absoluteX, absoluteY. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
incrementX	Increment x	list of number	Required
incrementY	Increment y	list of number	Required
initialX	Initial x	number	Required
initialY	Initial y	number	Required

Enter finite initial x/y and equal-length finite increment lists. The returned x/y arrays start with the initial position and include each cumulative endpoint, so they contain one more entry than the increments. Empty increments return the starting point alone. More than 100,000 generated positions is an error.

absolute_(i+1)=absolute_i+increment_i

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
absoluteX	Absolute x	list of number
absoluteY	Absolute y	list of number

json

{
  "input": {
    "incrementX": [
      1,
      -1
    ],
    "incrementY": [
      0,
      2
    ],
    "initialX": 5,
    "initialY": 3
  },
  "output": {
    "absoluteX": [
      5,
      6,
      5
    ],
    "absoluteY": [
      3,
      3,
      5
    ]
  }
}

Limitations and assumptions

This does not register images, rotate coordinate axes or verify telescope motion. Offsets are literal planar increments; uncertainties and cyclic angle wrapping are not applied.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Shift Stack Rate Offset Grid: Plan every east/north rate-grid shift for exposures relative to a supplied time origin; linear tangent-plane motion is assumed. For a complementary task, use Cd Matrix Image Axis Angles: Infer both image-axis angles in the WCS tangent plane from CD columns, exposing skew rather than assuming an orthogonal scalar rotation.

References

Dither Offset Reconstruction — tool.io

Similar or alternative tools

Shift Stack Rate Offset Grid
Plan every east/north rate-grid shift for exposures relative to a supplied time origin; linear tangent-plane motion is assumed.
Cd Matrix Image Axis Angles
Infer both image-axis angles in the WCS tangent plane from CD columns, exposing skew rather than assuming an orthogonal scalar rotation.