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A point-like astronomical source has an angular extent negligible for the calculation or measurement being considered. The ideal mathematical limit concentrates its luminosity at one source-plane position. In gravitational lensing, this approximation permits divergent formal magnifications on a caustic; a finite source averages the magnification over its emitting area. An unresolved source need not have negligible size compared with the lens's caustic scale.

Primordial-tensor foreground separation is the attempt to distinguish a polarization signal from early-universe gravitational waves from other signals in microwave observations. A measured B-mode polarization pattern can contain polarized Galactic emission and conversion of other Cosmic microwave background polarization by gravitational lensing, as well as a possible primordial contribution.

Frequency coverage helps because the cosmic microwave background, dust and synchrotron radiation do not share one emission spectrum. Spatial correlations and instrumental tests provide additional information. A joint component fit must propagate uncertainty in the foreground model; a B-mode excess at one frequency is not by itself a detection of cosmic inflation.^[ref]

An astrophysicist whose work connects models of gravity with astronomical observations. His lectures with Matthias Bartelmann develop gravitational lensing from the deflection of individual light rays to images made by galaxies and galaxy clusters. A useful example is the thin gravitational lens equation: an observed image position combines the deflection angle with the geometry between observer, lens and source. This turns a distorted image into information about the intervening mass distribution.^[ref]

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]

The gravitational lensing approximation in which deflection is concentrated in a plane whose thickness is small relative to the relevant observer-lens-source distances. The reduced angular deflection includes the distance ratio. A projected surface mass density then determines the lensing potential and the image-to-source mapping. This is distinct from a refracting thin optical lens.

When gravitational lensing gives small angular distortions without generic multiple imaging, its deflection field changes source positions, magnification and shear. Angular derivatives of the lensing potential determine these distortions. Ensemble galaxy-shape distortions and cosmic microwave background remapping probe the foreground gravitational field.

The average of the two conformal Newtonian gauge potentials controls scalar gravitational lensing. A conformal rescaling makes the spatial optical metric flat and its time component $1+4\Psi$ to first order. Vanishing scalar anisotropic stress makes $\varphi =\psi$ in general relativity, but lensing depends on their sum even when they differ.