Pixel Scale from CD Matrix Elements Derivation Calculator
Both WCS CD column norms separately, anisotropic/skewed matrices retained; not determinant-area square root substituted for both pixel axes. Caller independently establishes frames, units, epoch, covariance and instrument context; not an identity, association or astrometric quality certification.
Description
CD-matrix column norms describe local image-axis scales.
CD-matrix column norms describe local image-axis scales.1
They need not be equal and do not describe projection distortion everywhere in an image. Use Pixel Scale from CD Matrix Elements Derivation Calculator to evaluate the supplied inputs under the model explained below.
When to use Pixel Scale from CD Matrix Elements Derivation Calculator
Use Pixel Scale from CD Matrix Elements Derivation Calculator to evaluate the supplied inputs under the model explained below. Establish the units, measurement scope and model assumptions before entering values.
How to use Pixel Scale from CD Matrix Elements Derivation Calculator and understand its results
- Establish the units, measurement scope and model assumptions before entering values.
- Enter Caller wcs cd degrees per pixel using the field table and validation rules below, then run the tool.
- Read Image column pixel scale arcsec, Image row pixel scale arcsec; interpret the units, signs, ordering and unknown-value placeholders described below.
- Correct reported input errors and rerun. Apply successful results according to their specific meanings and check the assumptions before using them in a decision.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerWcsCdDegreesPerPixel | Caller wcs cd degrees per pixel | array of array | Required; constraints below |
Enter an exact 2×2 finite CD matrix in degrees/pixel with rows [a,b] and [c,d]. Return 3600×hypot(a,c) for the image-column scale and 3600×hypot(b,d) for the row scale in arcsec/pixel. A zero or singular matrix is accepted; no orthogonality or celestial-projection correction occurs.
columnScale=3600hypot(a,c); rowScale=3600hypot(b,d) Use the field order, units and branch conditions described above.
| Output field | Meaning | Value type |
|---|---|---|
| imageColumnPixelScaleArcsec | Image column pixel scale arcsec | number |
| imageRowPixelScaleArcsec | Image row pixel scale arcsec | number |
{
"input": {
"callerWcsCdDegreesPerPixel": [
[
3,
0
],
[
4,
2
]
]
},
"output": {
"imageColumnPixelScaleArcsec": 18000,
"imageRowPixelScaleArcsec": 7200
}
}Limitations and assumptions
They need not be equal and do not describe projection distortion everywhere in an image. Apply the exact scope and assumptions explained above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are explained above; extremely large inputs or outputs can also be rejected. Input errors differ from successful false results, empty match lists and unknown-evidence placeholders.
Alternative or Complementary methods
Use WCS CD Matrix Determinant Orientation Sign Checker for a related task: A WCS CD matrix maps image-axis increments to declared coordinate increments.
Use Plate Scale arcsec per Pixel CCD Calculator for a related task: Pixel pitch and focal length determine a small-angle plate scale.
References
Similar or alternative tools
- WCS CD Matrix Determinant Orientation Sign Checker
A WCS CD matrix maps image-axis increments to declared coordinate increments.
- Plate Scale arcsec per Pixel CCD Calculator
Pixel pitch and focal length determine a small-angle plate scale.