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Primordial abundances require extrapolation to material minimally processed by stars. Helium is inferred from hydrogen and helium emission in low-metallicity ionized regions, with ionization and temperature corrections. Deuterium is inferred from isotope-shifted absorption in low-metallicity quasar systems. Lithium is measured in old metal-poor stellar atmospheres and requires a correction, or a bound, for stellar depletion. These observables probe different astrophysical environments and systematic errors.

The quasar proximity effect is a reduction of nearby Lyman-alpha forest absorption caused by extra photoionization from the quasar. At fixed density and temperature in photoionization equilibrium, an added rate ${\Gamma }_Q$ changes the neutral fraction by the factor ${\Gamma }_{\mathrm{bg}}/({\Gamma }_{\mathrm{bg}}+{\Gamma }_Q)$. A host environment with positive density contrast can mask this reduction, and a variable or anisotropic source complicates its interpretation.

In photoionization equilibrium at fixed gas density and temperature, the extra quasar photoionization rate reduces neutral-hydrogen column density by the displayed factor. Its local rate is calculated from the quasar flux, while the isotropic background rate is ${\Gamma }_{\mathrm{bg}}=4\pi \int J_{\nu }{\sigma }_{\mathrm{HI}}(\nu )/(h\nu )d\nu$. Fitting the absorption suppression versus proper distance constrains the cosmic ionizing background. For an unperturbed column-density distribution proportional to $N^{-p}$ with $p>1$, the line abundance above a fixed threshold is reduced by $(1+\omega {)}^{1-p}$. Density enhancement, quasar age, anisotropy and redshift errors must be distinguished from this ionization effect.

For nearby redshifts in a homogeneous expanding universe, the comoving radial distance increment is $c\delta z/H(z)$. Multiplying by the scale factor at the absorber's epoch gives the displayed proper distance in cosmology. The conversion neglects peculiar velocities; observed redshift differences can also contain such velocities and errors in the quasar emission redshift.

The Sandage-Loeb test seeks the spectroscopic velocity drift of stable cosmological absorption features over an observer-time baseline. Many Lyman-alpha forest lines in bright distant quasars can be combined, but wavelength calibration, instrumental stability and peculiar accelerations must be controlled below the tiny cosmological signal. The absorption-template proposal is developed in the original 1998 redshift-drift study.

The two resolved quasar images of 0957+561 provide an observational question: are they separate sources, or different light paths from one source? In May 1979, spectrophotometry used the McDonald Observatory 2.7 m reflecting telescope, the UVITS spectrograph, and an intensified dissector scanner at the f/9 focus of the Cassegrain reflector. A 600-groove-per-millimetre diffraction grating produced 4100-7100 ångström scans sampled every 2 ångströms, with about 7 ångström resolution over most of that range. Two spectrograph slits, about 52 arcseconds apart, recorded object and sky background simultaneously for subtraction. Interleaving observations of the two images reduced instrumental and atmospheric gain changes.^[ref]

The readout was received light versus wavelength for each image. Closely matching absorption line redshifts supported a common source and absorber; differences in continua and line strengths motivated differential interstellar extinction. Spectral agreement supplied evidence for gravitational lensing, rather than proving the point-mass gravitational lens model. The authors discussed a physical double and discrepant optical and radio light ratios. Their note added in proof attributed the redder spectrum to foreground galaxy contamination and emphasized an extended mass distribution.^[ref]