Comparing intrinsic and received brightness
Under an appropriate propagation model, a source of fixed luminosity appears fainter at greater distance. An independently established luminosity can therefore be compared with received brightness to infer distance.
The calibration is essential. Equally faint sources can be a nearby weak emitter and a distant powerful one. An image alone does not separate distance from radiated power.
References: [1]
Cepheids and linked distance methods
Cepheid pulsation periods correlate with luminosity. Repeated photometry supplies the period, and a calibrated period–luminosity relation supplies the expected luminosity; the method does not assume identical power for all Cepheids.
Parallaxes or eclipsing-binary distances can anchor the calibration. Cepheids in more distant galaxies then help calibrate Type Ia supernovae, linking methods into a distance ladder whose uncertainties propagate between steps.
References: [1]
Dust and passbands affect calibration
Circumstellar and intervening dust alter received light. Spitzer observations of Delta Cephei showed how a wind and surrounding material could affect different passbands and the resulting distance interpretation.
Standard candles remain calibrated tools with uncertainties. Source class, passband, extinction and the calibration relation must be checked rather than treating the word standard as a guarantee of zero systematic error.