Tan Wcs Pixel To Sky

Apply inverse gnomonic TAN projection after a CD transform; pixel and reference-pixel values must use the same indexing convention, and SIP is not applied here.

Description

A TAN world-coordinate projection maps a detector's tangent plane onto the celestial sphere.

A TAN world-coordinate projection maps a detector's tangent plane onto the celestial sphere. The CD matrix first converts reference-pixel offsets into angular tangent-plane offsets; distortion correction is a separate step.^[1]

Apply inverse gnomonic TAN projection after a CD transform; pixel and reference-pixel values must use the same indexing convention, and SIP is not applied here.

When to use Tan Wcs Pixel To Sky

Use this tool to apply inverse gnomonic TAN projection after a CD transform; pixel and reference-pixel values must use the same indexing convention, and SIP is not applied here.

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 Tan Wcs Pixel To Sky 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 pixelX, pixelY, referencePixelX, referencePixelY, referenceRaDegrees, referenceDecDegrees, cdMatrix using the field table and calculation rules, then run the tool.
Read raDegrees, decDegrees. 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
pixelX	Pixel x	number	Required
pixelY	Pixel y	number	Required
referencePixelX	Reference pixel x	number	Required
referencePixelY	Reference pixel y	number	Required
referenceRaDegrees	Reference ra degrees	number	Required
referenceDecDegrees	Reference dec degrees	number	Required
cdMatrix	Cd matrix	list of list of number	Required

Enter pixel/reference positions using the same indexing convention, a nonsingular finite 2×2 CD matrix in degrees/pixel, and reference RA/Dec in degrees with Dec within ±90. The tool subtracts reference pixels, applies CD and uses atan2-based inverse TAN equations. Return RA wrapped to [0,360) and declination degrees. At the reference pixel, the reference direction is recovered.

(ξ,η)=CD × (pixel−referencePixel), in radians; inverse gnomonic projection gives RA/Dec

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

Output field	Meaning	Value type
raDegrees	Ra degrees	number
decDegrees	Dec degrees	number

json

{
  "input": {
    "pixelX": 10,
    "pixelY": 20,
    "referencePixelX": 10,
    "referencePixelY": 20,
    "referenceRaDegrees": 120,
    "referenceDecDegrees": 30,
    "cdMatrix": [
      [
        0.01,
        0
      ],
      [
        0,
        0.01
      ]
    ]
  },
  "output": {
    "raDegrees": 120,
    "decDegrees": 29.999999999999993
  }
}

Limitations and assumptions

SIP distortion, other WCS projections, frame/epoch transformations and FITS header parsing are not applied. The matrix and coordinate conventions must be established independently.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Sip Distortion Evaluation: Validate and evaluate forward SIP distortion terms for reference-pixel offsets; linear and constant terms belong in WCS, not SIP. 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

Tan Wcs Pixel To Sky — tool.io

Similar or alternative tools

Sip Distortion Evaluation
Validate and evaluate forward SIP distortion terms for reference-pixel offsets; linear and constant terms belong in WCS, not SIP.
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.