Figure 1.1 Comparison of a mammalian cell imaged with (A) brightfield and (B) phase contrast light microscopy.

1.2.1 Basic Overview

Brightfield transmitted light microscopy has a fundamental weakness in the study of thin transparent biological specimens: they generally absorb little light to provide limited contrast by this means alone. The samples do however interact with light in ways other than absorption, and phase contrast is a method to exploit this and turn these interactions into observable contrast.

What does happen to light as it passes through transparent biological material such as the cell in Figure 1.1? Though transparent, the cell will cause diffraction and scatter of some of the light that passes through it. This process causes deviation and a phase shift of λ/4 between the small amounts of light that is deviated relative to the undeviated wave. A cell is far from homogeneous. The variety of components of the cell and the molecular, macromolecular, and organelle level structures into which they are arranged provide a complex landscape of changes in refractive index, and this variation will also have an effect on the light passing through the different parts of the cell.

Refractive index of a medium is defined as the ratio of speed of light in a vacuum to the speed of light in a medium.

(1.1)

A vacuum therefore has a refractive index of 1.0000, air 1.0003, water 1.33, cytosol 1.35, and the glass most commonly used to make optics 1.52. The refractive index of a medium is an aspect of the interaction between the light and the electrical and magnetic susceptibilities of the medium. Overall the cell has a different refractive index than the surrounding medium. Finer scale differences within the cell provide observable subcellular resolution: different constituents such as lipids, proteins, and nucleic acids and different concentrations of these in an organelle or region produce local changes in refractive index. In a transmitted light image, some of the light will have passed through a cell and will have interacted with this complex refractive index topology and have been affected. Both the occurrence of diffraction of the light and the refractive index differences produce phase shifts which can be exploited to produce contrast.

This and the consequent means of exploiting the effects in a phase contrast microscope are most easily explained pictorially with a series of annotated diagrams.

Figure 1.2 shows schematically a phase shift by a sample. Reducing the sample to a gray box that represents an object, such as a cell, of a different refractive index to its surroundings and having a propensity to diffract and deviate some of the light we see light 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 λ/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.)

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 λ/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.

(1.2)

(1.3)

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

(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 μm, it can be calculated that the phase shift from optical path length differences are generally smaller than λ/4. Figure 1.3 shows the phase shift between the undeviated surround wave and the deviated wave shifted by around 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. The small phase difference between the S- and the P-waves is shown in Figure 1.3B and the amplitudes of the S- and the P-waves are essentially the same so we are still not provided with contrast to distinguish the object from background. This is essentially the state in brightfield illumination. How could a greater magnitude of interference be produced?

If we are able to produce an additional relative phase shift of λ/4 by advancing the S-wave, the total will be ~λ/2 (Figure 1.4C), thus presenting the maximal destructive interference potential. If we are also able to make the two waves of more equal amplitude, the efficiency of extinction through interference will be higher. This situation providing very high extinction is shown in Figure 1.4.

Should you prefer these concepts in vector diagram form where phase is presented by angle (retardation is clockwise, an advance is anticlockwise) and the amplitude by length of the line—the two situations of modest phase shift (Figure 1.3) and very high extinction (Figure 1.4) in phasor diagrams are shown in Figure 1.5.