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.

Description

Shift-and-stack planning tests candidate tangent-plane motion rates across exposures.

Shift-and-stack planning tests candidate tangent-plane motion rates across exposures. The offset for each exposure is linear rate times elapsed time relative to an explicit origin.^[1]

Plan every east/north rate-grid shift for exposures relative to a supplied time origin; linear tangent-plane motion is assumed.

When to use Shift Stack Rate Offset Grid

Use this tool to plan every east/north rate-grid shift for exposures relative to a supplied time origin; linear tangent-plane motion is assumed.

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 Shift Stack Rate Offset Grid 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 eastRatesArcsecPerHour, northRatesArcsecPerHour, exposureOffsetsHours using the field table and calculation rules, then run the tool.
Read candidateRates, eastShiftArcseconds, northShiftArcseconds. 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
eastRatesArcsecPerHour	East rates arcsec per hour	list of number	Required
northRatesArcsecPerHour	North rates arcsec per hour	list of number	Required
exposureOffsetsHours	Exposure offsets hours	list of number	Required

Enter nonempty strictly increasing east/north rate axes in arcsec/hour and increasing exposure offsets in hours. The Cartesian product may contain at most 128 candidate rates and at most 128 times. East rate is the outer loop and north rate the inner; returned shift matrices have candidate rows and exposure columns. Signed rates and offsets are allowed.

Sequences checked for increasing order must be nonempty and strictly increasing; additional calculation rules may require more samples.

eastShift=rateEast × time; northShift=rateNorth × time

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

Output field	Meaning	Value type
candidateRates	Candidate rates	list of list of number
eastShiftArcseconds	East shift arcseconds	list of list of number
northShiftArcseconds	North shift arcseconds	list of list of number

json

{
  "input": {
    "eastRatesArcsecPerHour": [
      0,
      1
    ],
    "northRatesArcsecPerHour": [
      0,
      1
    ],
    "exposureOffsetsHours": [
      0,
      1
    ]
  },
  "output": {
    "candidateRates": [
      [
        0,
        0
      ],
      [
        0,
        1
      ],
      [
        1,
        0
      ],
      [
        1,
        1
      ]
    ],
    "eastShiftArcseconds": [
      [
        0,
        0
      ],
      [
        0,
        0
      ],
      [
        0,
        1
      ],
      [
        0,
        1
      ]
    ],
    "northShiftArcseconds": [
      [
        0,
        0
      ],
      [
        0,
        1
      ],
      [
        0,
        0
      ],
      [
        0,
        1
      ]
    ]
  }
}

Limitations and assumptions

This plans numeric shifts without resampling or stacking images. Motion is constant on a tangent plane; acceleration, image-axis orientation and registration uncertainty are not modeled.

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 Moving Source Trail Pixels: Project tangent-plane motion onto a detector trail length and position angle for a supplied exposure and pixel scale. For a complementary task, use Dither Offset Reconstruction: Reconstruct absolute planar dither positions from relative offsets and an explicit initial position in a common unit.

References

Shift Stack Rate Offset Grid — tool.io

Similar or alternative tools

Moving Source Trail Pixels
Project tangent-plane motion onto a detector trail length and position angle for a supplied exposure and pixel scale.
Dither Offset Reconstruction
Reconstruct absolute planar dither positions from relative offsets and an explicit initial position in a common unit.