Test a wavelength calibration with an unused spectral reference

1. Define the light and measurement

A spectrum maps detector coordinates to wavelength before physical line interpretation. Reflection, refraction or diffraction can disperse different wavelengths to different positions, but a pixel number is not itself a wavelength. Calibration needs identified reference features and a specified model of the coordinate relation.

2. Connect physical and instrumental mechanisms

The original anchors are 400 nm at pixel 100+o and 700 nm at pixel 400+o, where o is a common detector offset. The fitted linear dispersion is (700−400)/300=1 nm/pixel and intercept 300−o nm. A target at measured coordinate x then has conditional wavelength x+300−o. The calculation uses two anchors exactly and does not yet prove the model is adequate elsewhere.

An unused known 550 nm reference appears at pixel 255+o. The two-anchor fit predicts 555 nm there, leaving a +5 nm residual. A common detector offset does not remove this discrepancy because the anchors and check shift together. The mismatch could reflect nonlinearity, a centroid error or a wrongly identified reference, and requires investigation rather than relabeling the check as exact.

The original calibration packet is separate from the actual SDSS spectrum later in this category. That archive supplies its own per-row logarithmic wavelength coordinates and reduction history. A learner must not attach this fictional linear scale to those source pixels. Calibration validation, not merely fitting a line, is part of a reproducible spectral inference.

3. Work the evidence

At offset o=10, anchors are pixels 110 and 410 and the fitted relation is λ=x+290 nm. A target at x=300 gives 590 nm conditionally. The unused check at x=265 predicts 555 rather than its known 550 nm, retaining a +5 nm validation residual.

4. Predict and investigate

Can a perfect fit to two calibration anchors establish that every other wavelength is correctly calibrated?

Reconstruct slope and intercept, then evaluate the unused reference before trusting the target result. Change the common pixel offset and explain why the check residual persists; propose a discriminating additional reference.

Source and boundaries

Primary source. Checked 30 October 2026. Original teaching and fictional numerical models are separate from the explicitly labeled actual SDSS archive; no direct observing, radiation experiment or instrument operation is requested.