Editing Refractive index (section)

==Refractive index measurement==

===Homogeneous media===
{{Main|Refractometry|Refractometer}}
[[File:Pulfrich refraktometer en.png|thumb|alt=Illustration of a refractometer measuring the refraction angle of light passing from a sample into a prism along the interface|The principle of many refractometers]]

The refractive index of liquids or solids can be measured with [[refractometer]]s. They typically measure some angle of refraction or the critical angle for total internal reflection. The first [[Abbe refractometer|laboratory refractometers]] sold commercially were developed by [[Ernst Abbe]] in the late 19th century.<ref>{{cite web |url = http://www.humboldt.edu/scimus/Essays/EvolAbbeRef/EvolAbbeRef.htm |title = The Evolution of the Abbe Refractometer |publisher = Humboldt State University, Richard A. Paselk |year = 1998 |access-date = 2011-09-03 |url-status = live |archive-url = https://web.archive.org/web/20110612000645/http://www.humboldt.edu/scimus/Essays/EvolAbbeRef/EvolAbbeRef.htm |archive-date = 2011-06-12 }}</ref>
The same principles are still used today. In this instrument, a thin layer of the liquid to be measured is placed between two prisms. Light is shone through the liquid at incidence angles all the way up to 90°, i.e., light rays [[parallel (geometry)|parallel]] to the surface. The second prism should have an index of refraction higher than that of the liquid, so that light only enters the prism at angles smaller than the critical angle for total reflection. This angle can then be measured either by looking through a [[telescope]],{{clarify|date=June 2017}} or with a digital [[photodetector]] placed in the focal plane of a lens. The refractive index {{mvar|n}} of the liquid can then be calculated from the maximum transmission angle {{mvar|θ}} as {{math|1=''n'' = ''n''{{sub|G}} sin ''θ''}}, where {{math|''n''{{sub|G}}}} is the refractive index of the prism.<ref>{{cite web | url = http://www.refractometer.pl/ | title = Refractometers and refractometry | publisher = Refractometer.pl | year = 2011 | access-date = 2011-09-03 | url-status = live | archive-url = https://web.archive.org/web/20111020123455/http://www.refractometer.pl/ | archive-date = 2011-10-20 }}</ref>

[[File:Refractometer.jpg|thumb|alt=A small cylindrical refractometer with a surface for the sample at one end and an eye piece to look into at the other end|A handheld refractometer used to measure the sugar content of fruits]]

This type of device is commonly used in [[chemistry|chemical]] laboratories for identification of [[chemical substance|substances]] and for [[quality control]]. [[Digital handheld refractometer|Handheld variants]] are used in [[agriculture]] by, e.g., [[wine maker]]s to determine [[Brix|sugar content]] in [[grape]] juice, and [[inline process refractometer]]s are used in, e.g., [[chemical industry|chemical]] and [[pharmaceutical industry]] for [[process control]].

In [[gemology]], a different type of refractometer is used to measure the index of refraction and birefringence of [[gemstones]]. The gem is placed on a high refractive index prism and illuminated from below. A high refractive index contact liquid is used to achieve optical contact between the gem and the prism. At small incidence angles most of the light will be transmitted into the gem, but at high angles total internal reflection will occur in the prism. The critical angle is normally measured by looking through a telescope.<ref>{{cite web |url = http://gemologyproject.com/wiki/index.php?title=Refractometer |title = Refractometer |publisher = The Gemology Project |access-date = 2011-09-03 |url-status = live |archive-url = https://web.archive.org/web/20110910082406/http://www.gemologyproject.com/wiki/index.php?title=Refractometer |archive-date = 2011-09-10 }}</ref>

===Refractive index variations===
{{Main|Phase-contrast imaging}}
[[File:S cerevisiae under DIC microscopy.jpg|thumb|alt=Budding yeast cells with dark borders to the upper left and bright borders to lower right|A [[differential interference contrast microscopy]] image of [[budding yeast]] cells]]

Unstained biological structures appear mostly transparent under [[bright-field microscopy]] as most cellular structures do not attenuate appreciable quantities of light. Nevertheless, the variation in the materials that constitute these structures also corresponds to a variation in the refractive index.  The following techniques convert such variation into measurable amplitude differences:

To measure the spatial variation of the refractive index in a sample [[phase-contrast imaging]] methods are used. These methods measure the variations in [[phase (waves)|phase]] of the light wave exiting the sample. The phase is proportional to the [[optical path length]] the light ray has traversed, and thus gives a measure of the [[integral]] of the refractive index along the ray path. The phase cannot be measured directly at optical or higher frequencies, and therefore needs to be converted into [[intensity (physics)|intensity]] by [[interference (optics)|interference]] with a reference beam. In the visual spectrum this is done using Zernike [[phase-contrast microscopy]], [[differential interference contrast microscopy]] (DIC), or [[interferometry]].

Zernike phase-contrast microscopy introduces a phase shift to the low [[spatial frequency]] components of the [[Real image|image]] with a phase-shifting [[annulus (geometry)|annulus]] in the [[Fourier optics|Fourier plane]] of the sample, so that high-spatial-frequency parts of the image can interfere with the low-frequency reference beam. In {{abbr|DIC|differential interference contrast microscopy}} the illumination is split up into two beams that are given different polarizations, are phase shifted differently, and are shifted transversely with slightly different amounts. After the specimen, the two parts are made to interfere, giving an image of the derivative of the optical path length in the direction of the difference in the transverse shift.<ref name=Carlsson/> In interferometry the illumination is split up into two beams by a [[Beam splitter|partially reflective mirror]]. One of the beams is let through the sample before they are combined to interfere and give a direct image of the phase shifts. If the optical path length variations are more than a wavelength the image will contain fringes.

There exist several [[phase-contrast X-ray imaging]] techniques to determine 2D or 3D spatial distribution of refractive index of samples in the X-ray regime.<ref>{{Cite journal | first = Richard | last = Fitzgerald | title = Phase-Sensitive X-Ray Imaging | journal = Physics Today | volume = 53 | page = 23 | date = July 2000 | doi = 10.1063/1.1292471|bibcode = 2000PhT....53g..23F | issue = 7 | s2cid = 121322301 | doi-access = free }}</ref>