Lens Aberrations and Distortion

Lens aberrations

Opti­cal aber­ra­tions are imper­fec­tions in the way lens­es con­verge rays of light to a point. Lens aber­ra­tions can be divid­ed into two types: imper­fect con­verg­ing of light to a focused point (which affects sharp­ness) and flawed geo­met­ric pro­jec­tion of the scene (which man­i­fest as dis­tor­tions or warp­ing). When design­ing a lens, an opti­cal engi­neer is faced with mak­ing a series of com­plex com­pro­mis­es to lim­it aber­ra­tions. Since there’s no such thing as a per­fect lens, engi­neers must make the best pos­si­ble com­pro­mis­es giv­en the restric­tions of the intend­ed use, fea­tures, pro­duc­tion costs, and mar­ketable price. While there’s lit­tle you can do about aber­ra­tions in your lens­es (except for stop­ping down the aper­ture), it’s help­ful to know what they are when set­ting out to make a new pur­chase. More impor­tant­ly, as a pho­tog­ra­ph­er, you should be aware of the lim­i­ta­tions of your lens­es; this allows you to exploit their strengths and avoid empha­siz­ing their weak­ness­es.

Types of lens aberrations

Aber­ra­tions are the pri­ma­ry cause of reduced acu­ity in lens­es that are cor­rect­ly focused. There are five types you should know about, chro­mat­ic aber­ra­tion, spher­i­cal aber­ra­tion, cur­va­ture of field, coma, and astig­ma­tism.

Chro­mat­ic aber­ra­tions man­i­fest them­selves as fringes of colour on high-con­trast edges. They are caused by dif­fer­ent wave­lengths of light (i.e., dif­fer­ent colours) under­go­ing vary­ing degrees of refrac­tion and being focused at dif­fer­ent posi­tions as they pass through the lens. Two types of chro­mat­ic aber­ra­tion exist: lon­gi­tu­di­nal and lat­er­al. Lon­gi­tu­di­nal aber­ra­tions are caused by dif­fer­ent wave­lengths of light focus­ing to vary­ing dis­tances from the lens. Blue-vio­let light focus­es clos­er to the lens than red, with green com­ing into focus between them. Lon­gi­tu­di­nal aber­ra­tions can be min­i­mized by stop­ping down your aper­ture, which brings the wave­lengths into accept­able focus. Lat­er­al aber­ra­tions occur when dif­fer­ent wave­lengths of light focus on dif­fer­ent posi­tions of the focal plane (i.e., on the image sen­sor). These typ­i­cal­ly hap­pen with short-focus, and espe­cial­ly, ultra-wide angle lens­es. Lat­er­al aber­ra­tions can­not be dimin­ished by stop­ping down the aper­ture, but are effec­tive­ly min­i­mized by some pho­to-edit­ing soft­ware.

Chromatic aberrations

Example of lateral chromatic aberrations in photography.
In this exam­ple, the Canon EF 16–35 mm f/2.8 L II shows sig­nif­i­cant lat­er­al chro­mat­ic aber­ra­tions at the branch edges. This is from the very cor­ner of the frame at 16 mm on a full-frame cam­era. To empha­size the fact that lat­er­al chro­mat­ic aber­ra­tions are not min­i­mized by using small­er aper­tures, this image was shot at f/11.
Example of longitudinal chromatic aberrations in photography.
This pho­to was cap­tured using the Canon EF 35 mm f/1.4 lens at f/1.4. Wide open, the lens exhibits a tremen­dous amount of lon­gi­tu­di­nal chro­mat­ic aber­ra­tion, which becomes neg­li­gi­ble with larg­er f-num­bers.

Spher­i­cal aber­ra­tions cause soft-focused images that lack fine con­trast. They occur when light pass­ing through the edges of a lens focus­es clos­er to the lens than light pass­ing through its cen­tre. In most lens­es, the pres­ence of spher­i­cal aber­ra­tion is an unde­sir­able tech­ni­cal flaw; how­ev­er, in the past, delib­er­ate and con­trolled spher­i­cal aber­ra­tion was imple­ment­ed for use in “soft-focus” por­trait lens­es. Spher­i­cal aber­ra­tion can be reduced by stop­ping down the aper­ture.

Spherical aberrations

Example of spherical aberrations in photography.
Spher­i­cal aber­ra­tions often present as slight halos about high­lights, such as on the crown of this statue’s head.
Example of spherical aberrations in photography.
Spher­i­cal aber­ra­tions also result in a loss of micro con­trast across the image.

Cur­va­ture of field occurs when a lens can­not focus a flat sub­ject nor­mal to its opti­cal axis onto a flat image plane. To a cer­tain degree, this aber­ra­tion isn’t prob­lem­at­ic for por­trait, land­scape, and street pho­tog­ra­phy; how­ev­er, it’s high­ly unde­sir­able in fields apt to fea­ture promi­nent flat planes, such as archi­tec­tur­al, tech­ni­cal, and macro pho­tog­ra­phy. The effects of cur­va­ture of field can be reduced by stop­ping down the aper­ture.

Coma describes the reduced abil­i­ty of a lens to ren­der a sharp point image that orig­i­nates away from the lens axis. As the name implies, the ren­di­tion of such a point source is char­ac­ter­ized by a shape sim­i­lar to a comet’s tail. Coma may be min­i­mized by stop­ping down the aper­ture.

In pho­tog­ra­phy, astig­ma­tism caus­es a sub­ject point orig­i­nat­ing away from the lens axis to ren­der as a high­ly stretched oval at one focus dis­tance, as a high­ly stretched oval per­pen­dic­u­lar to the first at anoth­er focus dis­tance, and as a blur­ry disc in between. There are two types, tan­gen­tial and sagit­tal astig­ma­tism. In tan­gen­tial astig­ma­tism, the elon­ga­tion of the sub­ject points occurs along an imag­i­nary line radi­at­ing from the opti­cal axis, where­as in sagit­tal astig­ma­tism, the elon­ga­tion is nor­mal to this, appear­ing to fol­low imag­i­nary rings cir­cling the opti­cal axis. Much like most of the oth­er types of aber­ra­tion, astig­ma­tism may be reduced by stop­ping down the aper­ture.

 

Example of optical astigmatism in photography.
A real-life exam­ple of sagit­tal astig­ma­tism: notice the slight diag­o­nal halation/smearing around the high­lights. The red line indi­cates the path from the opti­cal cen­tre of the lens to the upper right cor­ner. Sagit­tal astig­ma­tism results in hala­tion per­pen­dic­u­lar to such imag­i­nary lines about the opti­cal axis.

Linear distortion

Lin­ear dis­tor­tions are devi­a­tions from an ide­al rec­ti­lin­ear pro­jec­tion. Recall that rec­ti­lin­ear lens­es are designed to ren­der the straight ele­ments found in a scene as straight lines in the image. There are three types of dis­tor­tions: bar­rel (con­vex), pin­cush­ion (con­cave), and com­plex.

Barrel distortion correction on super wide-angle lens in Prague intersection
Bar­rel dis­tor­tion. This image demon­strates the pres­ence and sub­se­quent soft­ware cor­rec­tion of a super wide-angle lens’ dis­tor­tion.
pincushion distortion of telephoto lens image Lisbon street.
Pin­cush­ion dis­tor­tion. This image demon­strates the pres­ence and sub­se­quent soft­ware cor­rec­tion of a long focus lens’ dis­tor­tion.

Unlike the aber­ra­tions above, dis­tor­tions do not gen­er­al­ly affect image sharp­ness; fur­ther­more, dis­tor­tions can­not be min­i­mized by stop­ping down a lens. Despite this, bar­rel and pin­cush­ion dis­tor­tions are effi­cient­ly cor­rect­ed using soft­ware, and some cam­eras auto­mat­i­cal­ly apply the appro­pri­ate cor­rec­tions when tak­ing a pic­ture. Cor­rect­ing com­plex dis­tor­tions is also pos­si­ble, but requires a cor­rec­tion pro­file that knows the exact struc­ture of the warped geom­e­try.

Bar­rel and pin­cush­ion dis­tor­tion are often asso­ci­at­ed with spe­cif­ic focal lengths. For instance, short-focus lens­es tend to exhib­it bar­rel dis­tor­tion, while long-focus lens­es are more sus­cep­ti­ble to pin­cush­ion dis­tor­tion. Zoom lens­es are com­mon­ly afflict­ed by both, show­ing bar­rel dis­tor­tion on their wide end and tran­si­tion­ing to pin­cush­ion dis­tor­tion on the long end of the zoom range. This behav­iour is present regard­less of the absolute focal length of the zoom lens. For exam­ple, both 16–35 mm and 70–200 mm lens­es will show bar­rel dis­tor­tion at 16 mm and 70 mm, respec­tive­ly, and pin­cush­ion dis­tor­tion at 35 mm and 200 mm, respec­tive­ly.

Despite the pres­ence of opti­cal dis­tor­tions in many lens­es, the effects are hard to notice in most pho­tographs. Images where opti­cal dis­tor­tions are most evi­dent often fea­ture straight lines run­ning par­al­lel and close to the edges of the frame.