Chromatic aberration

An optical camera can focus a white object sharply in one colour while leaving coloured fringes around its edges in another. Chromatic aberration is the dependence of image position or image scale on wavelength, caused by optical dispersion in the optical lens materials. Axial chromatic aberration separates the optical foci along the optical axis; lateral chromatic aberration changes the transverse magnification with wavelength. Moving the receiving plane can favour one colour without bringing all colours into focus. ^[ref]; ^[ref].

For ordinary optical glass in the visible range, the blue refractive index exceeds the red refractive index. For a fixed positive thin lens in air, the lensmaker's equation then givesHere $\lambda$ is wavelength, $n$ is refractive index, $\Phi$ is optical power, $f$ is focal length, and $R_a,R_b$ are the signed surface radius of curvature values in the lensmaker's equation. The blue light rays therefore bend more strongly and meet sooner. This ordering is a statement about ordinary visible optical dispersion, not a universal rule for every material and every spectral range. ^[ref].

For a worked example, take a single positive thin lens with reference optical power ${\Phi }_d=5\mathrm{D}$ and Abbe number $V_d=60$, hence reference focal length $f_d=0.2\mathrm{m}$. Its F–C optical power difference is $\Delta \Phi ={\Phi }_F-{\Phi }_C={\Phi }_d/V_d=5/60\mathrm{D}\approx 0.08333\mathrm{D}$, by the achromatic doublet power balance relation below. This difference alone does not locate the reference optical power within the F–C interval. To draw a transparent example, introduce a synthetic colour coordinate $q$, a dimensionless quantity, with red $q=-1/2$, reference $q=0$, and blue $q=+1/2$, and choose the toy optical dispersion modelThe diagram's red and blue endpoints represent the C and F endpoints of this toy model. Its reference point is placed symmetrically in optical power by construction; $q$ is not a measured wavelength scale, and the model is not measured optical glass data. The endpoint focal lengths areThus the axial chromatic aberration in this example separates the endpoint optical foci by about $3.334\mathrm{mm}$. A single receiving plane cannot coincide with both optical foci.

The useful design idea is to cancel changes of optical power while retaining a positive total optical power. An achromatic lens does this with materials having different Abbe numbers. It greatly reduces chromatic aberration, but correcting two chosen wavelengths still leaves the possibility of a secondary spectrum.