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#### Optical Path Difference

This interactive tutorial explores optical path differences for phase objects as a function of specimen and surround refractive index variations. Instructions for operation of the tutorial are given below the applet window.

In this tutorial, the phase object has a thickness (t), adjustable with the Thickness slider, and a refractive index, n(s), which is also adjustable with the Specimen RI slider. The refractive index of the surrounding media is n(m) is adjustable with the Surround RI slider. The equation below the image calculates the Optical Path Difference (OPD) between the specimen and its surround according to the formula:

OPD = (tn(s) - tn(m)) = t(n(s) - n(m))

With the phase difference being:

d = (2p/l)(OPD)

where p is a constant (3.14159265) and l is the wavelength of light illuminating the specimen. The optical path difference is the product of two terms: the thickness (t) and the difference in refractive index (n). The OPD can often be quite large even though the thickness of the object is quite thin. On the other hand, when the refractive indices of the specimen and the surrounding medium are equal, the OPD is zero even if the specimen thickness is very large. In this case, light traveling through the object is merely delayed (a phase difference) relative to the light passing an equal thickness of the surround. Phase differences are not detectable by the human eye.

Contributing Authors

Mortimer Abramowitz - Olympus America, Inc., Two Corporate Center Drive., Melville, New York, 11747.

Matthew J. Parry-Hill and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

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