Phase Contrast Microscopy - Biomedical Optical Phase Microscopy and Nanoscopy - page 4

that passes through it becomes phase shifted relative to a reference wave that passes around
the object unaffected. The phase shift has two components: (1) diffraction causes a /4

phase shift and (2) the difference in refractive index and optical path length changes the
speed of the wave and so the transit time across the object relative to the surround which
causes a typically small phase shift between the deviated wave passing through the sample
and reference surround wave. The object here has a higher refractive index, a lower speed
of transmission of the wavefront, so the phase is retarded slightly. It is noted that no
difference in amplitude is produced—there is no absorption—and so no contrast is provided
by this means alone. Our eyes and digital cameras are insensitive to phase or differences in
phase of light, and we are unable to distinguish the object from the surrounding background
without further action. (Objects such as our limiting case example which produce a phase
shift but no absorption are called “phase objects”; at the other extreme, objects which
produce strong absorption but little phase interaction are termed “amplitude objects” but of
course nearly everything really lies somewhere between these two extremes.)

λ

The change in phase presents some possibility for interference between the light that is
shifted and that which is not. An observable difference in intensity could be produced in
this way. To provide a very simple example consider the wavefronts occurring in
Figure 1.2 . Of the light illuminating the sample and surrounding, most of the light is
undeviated (the zeroth-order light) and has no phase shift. Some of the light passes through
the sample and is diffracted and phase shifted, by an amount of around /4. The precise

magnitude of the phase shift is the sum of the phase shift from diffraction (

λ

/4) and the
effect of a difference in the optical path length—the product of refractive index and
thickness.

λ

Optical Path Length 5 n 3 t (1.2)

Optical Path Difference ; Δ 5 ðn sample n surround Þ 3 t (1.3)

The relationship between the optical path difference and the phase shift of a wave in
radians is

Phase shift 5 2 πΔ=λ (1.4)

Using examples of refractive index of the cytosol (1.35) and culture medium (1.33) and a
range of thickness of the cell up to 10 µ m, it can be calculated that the phase shift from
optical path length differences are generally smaller than /4. Figure 1.3 shows the phase

shift between the undeviated surround wave and the deviated wave shifted by around

λ

λ /4.

Because of the limited extent of the phase shift (shown in Figure 1.3A ) and the difference
in amplitude of the two waves (which to underscore is due to only a small fraction of the
light being diffracted rather than this light being attenuated) the difference between the
observed interfered output (the particle wave) and unaltered surround wave is very minimal.