This sheet focusses on the use of spherical lenses in opto-mechanical applications, not on the design of a lens itself. The thin lens equation, chromatic and spherical aberrations, wave lengths and the use of GRIN lenses is discussed.
Spherical lenses have a focal region (see ‘Spherical aberrations’) whereas parabolic lenses comprise an exact focal point. However a spherical surface is much more cost-efficient to manufacture (grinding/polishing) and therefore they are (still) often used.
= focal length (average)
= refractive index of lens, medium
= incoming radius, outgoing radius
= object distance, image distance
Further from the lens axis the refraction of light due to a spherical shaped lens is larger. Therefore the rays do not focus in the same point causing the image to become blurry.
Minimize this effect via a good choice for and :
The refractive index decreases with increasing wavelength. Therefore the image becomes `fringed’. Therefore suppliers often specify the focus distance per wavelength ().
Minimize this effect by minimizing the spectrum of wavelengths of the light source.
|X-ray||0.01 - 10|
|UV-ray (far - near)||10 - 390|
|Indigo||390 - 450|
|Blue (cyan = 490)||450 - 490|
|Green||490 - 580|
|Yellow||580 - 600|
|Orange||600 - 620|
|Red (dark red > 700)||620 - 770|
|Fiber optics (infrared)||800 - 1e6|
|Infrared (near far)||1800 - 4e4|
GRIN lenses are treated such that they comprise a GRadient in the INdex of refraction over the lens axis. This gradient may be designed in circular, parabolic or sinusoidal shapes, whereby the possibility arises to place and arbitrary.