Shear amount in differential interference

1. Shear amount

Differential interference is a phenomenon used to observe contrast in specimens such as extremely fine structures or transparent biological specimens (phase specimens) for which conventional human sight or microscope cameras cannot discern contrast. Differential interference contrast (DIC) microscopy involves optical techniques not used in brightfield microscopy, the most important of which is a special crystal prism in the light path.

In conventional brightfield microscopy, light passes through the objective to bounce off the specimen and back through the objective to form the image. In DIC microscopy, a special crystal prism is inserted before the objective (Figure 1). This has the following effect:

  • 1.The prism splits the light into two paths.
  • 2.The light paths split by the prism diverge by a very slight amount, called a “shear amount”. These split light rays will bounce off the specimen at different points, separated only by the shear amount, and back through the object lens to the viewer.
  • 3.Light rays passing back through the objective overlap in the prism. The spatial difference between the points at which the two light paths reflected off the specimen result in an optical path difference (phase difference) which results in interference when they overlap again within the prism, imparting contrast equivalent to the difference of the light paths.

The spatial difference between the points at which the two light paths reflected off the specimen result in an optical path difference (phase difference) which results in interference when they overlap again within the prism, imparting contrast equivalent to the difference of the light paths.

[fig.]
Figure 1. Shear amount in differential interference (reflective) microscopy

This technique allows contrast that would be nearly invisible in brightfield microscopy to be viewed in DIC microscopy, lending high contrast sensitivity to phase specimens that are difficult to view. However, resulting images have directionality, and contrast is visualized only in the direction that the light paths diverge. This is called the “shear direction”.

2. Shear amount and resolution

It is important to keep in mind that the shear amount is extremely small. Since the shear amount is equivalent to the amount of horizontal deviation, if the shear amount is large, image resolution deteriorates. (Points and lines look fatter due to the horizontal deviation.) If the shear amount becomes too great, the horizontal deviation is such that it makes the image appear double.

Figure 2. Example of image appearing double due to excessive shear amount

[fig.]
From left, Grid viewed under brightfield illumination, Grid viewed with small shear, Grid viewed with large shear

Images do not appear double when observing a grid micrometer with a prism that has little shear, but when a prism with a large shear amount is used, the calibrations appear double. Also, the image appears double only in the direction of the shear (along the diagonal from upper left to lower right), and the lines that are perpendicular to these lines do not appear double.

Sample: Grid micrometer
Magnification: 10x
Conventional reflected brightfield microscope images

[Note] To make the phenomenon that occurred in both grids viewed with small and large shear easy to see and describe, we only inserted a DIC prism into the brightfield optical path. Since interference was not induced, these are not true differential interference images.

To avoid this, in DIC (differential interference contrast) microscopes, their share amount is generally set to smaller than the human eye's resolving power. The difference in height between two points in the image being viewed in DIC observations is therefore sufficiently small spatially. In other words, we know that this is the gradient for each minute portion, or differential. This is the origin of the term “differential” in “differential interference.”

3. Shear amount and contrast

While the resolving power of an image deteriorates when the shear amount is large, the contrast of the image, on the other hand, actually increases.

This is easy to understand when we consider a sloping specimen as shown in Figure 3. Contrast increases, because the difference (D) in the optical path of light that is split in two also increases when the shear amount is large. (Figure 4)

Figure 3. Difference in contrast between small shear amount and large shear amount

[fig.]
Figure 4. Example of image where contrast of DIC image changes with the shear amount
[fig.]
From left, IC viewed under brightfield, IC viewed under small shear, IC viewed under large shear

The pattern is not clearly visible in the brightfield image, but in the DIC image it is clearly visible with greater contrast. The contrast in images with a large shear amount is greater than the contrast in images with a small shear amount .

Sample: IC pattern
Magnification: 10x

In addition, strength profiles for the lines between points A and B in an IC image viewed with different amounts of shear in Figure 4 are given below. (Figure 5)

[fig.]
Figure 5. Line profiles between points A and B in an IC image viewed with different amounts of shear in Figure 4

The graph above shows that while contrast in the image with a large shear amount is greater than the contrast in the image with a small shear amount, the line in the former image is wider, indicating this image has lower resolution than the image with the small shear amount.

The images and the graph show that instead of low contrast, images with a small shear amount have a narrower line, i.e. high resolution, while images with a large shear amount have a wider line, i.e. low resolution, instead of high contrast.

Resolution and contrast in DIC observation thus have a trade-off relationship that is determined by the shear amount . In general DIC microscopes, the shear amount is determined after a balance between resolution and contrast is considered, but since different specimens require different balances of resolution and contrast, some products allow the user to make selections that give priority to either high resolution or high contrast.

Though we based these explanations on a reflection-type microscope configuration, the principles are exactly the same in the case of transmitted-light type microscopes. With the transmitted-light type, however, a total of two prisms needs to be inserted into the optical path, one that splits the illuminating beam and another that recombines the observation light after it has passed through the specimen.