Specimen Optical Path Length Variations

Phase contrast microscopy interprets differences in specimen optical path length as fluctuations in light intensity, which are readily observed as variations in contrast through the microscope. This interactive tutorial explores the effects of refractive index and thickness changes on the apparent overall optical path length, and demonstrates how two specimens can have different combinations of these variables but still display the same path length.

The tutorial initializes with two specimens (represented by gray boxes) appearing in the window, each having the same optical path length, but with a different combination of refractive index and thickness. Twin coherent planar wavefronts (entitled Waves In Phase) are incident on the left-hand faces of the specimens, and are modified in phase according to the variables set by the sliders as they pass through. Upon exiting the specimen, the wavefronts can be in phase if the optical path length of the two specimens is approximately equal, or out of phase if the path length difference exceeds more than a few tenths of a micrometer. The wavefronts are blue in color when they are in phase, but turn red when shifted out of phase. In addition, the specimens are assumed to be surrounded by air, which has a refractive index of 1.00 for the purposes of the tutorial. Note that the actual number of wavefronts passing through the specimen is exaggerated for ease of illustration.

In order to operate the tutorial, use the mouse cursor to translate the Refractive Index and Specimen Thickness sliders for both the top and bottom specimens. As the slider values are altered, the resulting specimen optical path length (which equals the refractive index multiplied by the thickness) changes. The gray-level intensity of the specimen box also decreases (becomes darker) as the refractive index is increased. Although most slider values will result in the waves passing through the specimens becoming out of phase (and titled Waves Out Of Phase), several combinations of the slider settings will produce identical specimen optical path lengths where the waves exiting the two specimens are in phase. The visitor is encouraged to experiment with a variety of slider settings and observe how a wide range of refractive index and thickness values can result in the specimens having equal optical path lengths. Note that the size of the wavefronts in relation to the actual specimen dimensions are exaggerated for ease of illustration in the tutorial.

In terms of the optical path difference between the specimen and its surrounding medium, the portion of the incident light wavefront that traverses the specimen, but does not pass through the surrounding medium, is slightly retarded. For arguments in phase contrast microscopy, the role of the specimen in altering the optical path length (in effect, the relative phase shift) of waves passing through is of paramount importance. In classical optics, the optical path length (OPL) through an object or space is the product of the refractive index (n) and the thickness (t) of the object or intervening medium as described by the relationship:

Formula 1 - Optical Path Length

Optical Path Length (OPL) = n × t

When light passes from one medium into another, the velocity is altered proportionally to the refractive index differences between the two media. Thus, when a coherent light wave emitted by the focused microscope filament passes through a phase specimen having a thickness t and refractive index (n), the wave is either increased or decreased in velocity. If the refractive index of the specimen is greater than that of the surrounding medium, the wave is reduced in velocity while passing through the specimen and is subsequently retarded in relative phase when it emerges from the specimen. In contrast, when the specimen refractive index is less than that of the surrounding medium, the wave is advanced in phase upon exiting the specimen. The difference in location of an emergent wavefront between the specimen and surrounding medium is termed the phase shift (δ) and is defined in radians as:

Formula 2 - Phase Shift

δ = 2πΔ/λ

In the equation above, the term Δ is referred to as the optical path difference, which is similar to the optical path length:

Formula 3 - Optical Path Difference

Optical Path Difference (OPD) = Δ = (n2 - n1) × t

where n(2) is the refractive index of the specimen and n(1) is the refractive index of the surrounding medium. In positive phase contrast systems (where the undiffracted light wavefronts are advanced by the phase plate), if the specimen has a greater optical path length (higher refractive index) than the surrounding medium, it is imaged as a dark object on a neutral gray background. The situation is reversed when the surrounding medium has a higher refractive index than the specimen. In effect, the specimen appears bright on a darker background.

As demonstrated above, the optical path difference results from the product of two terms: the thickness of the specimen, and its difference in refractive index with the surrounding medium. In many cases, the optical path difference can be quite large even though the thickness of the specimen is small. On the other hand, the optical path difference can be zero even for large specimen thickness, when the refractive index of the specimen equals that of the surrounding medium.

For individual cells in tissue culture, the optical path difference is relatively small. A typical cell in monolayer culture has a thickness around 5 micrometers and a refractive index of approximately 1.36. The cell is surrounded by a nutrient medium having a refractive index of 1.335, which yields an optical path difference of 0.125 micrometer, or about a quarter wavelength. Subcellular structures produce much smaller retardations. These small optical path differences produce a linear reduction in intensity with increasing phase shift (the image grows progressively darker) up to a point (depending upon phase plate configuration), after which, the specimen image becomes brighter through reversal of contrast. In phase contrast microscopy, the intensity of an image does not bear a simple linear relationship to the optical path difference produced by the specimen for the entire thickness and refractive index range. Instead, intensity is dependent on a variety of factors including absorption at the phase plate, the degree of phase advancement or retardation at the phase plate, and the relative sign of this phase shift.

Contributing Authors

Douglas B. Murphy - Department of Cell Biology and Anatomy and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205.

Matthew 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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Specimen Optical Path Length Variations