Quantitative phase imaging with using orientation‐independent differential interference contrast (
OI
‐
DIC
) microscopy
Authors: Michael Shribak 
Published: December 2016

Conventional differential interference contrast (DIC) microscope shows the two‐dimensional distribution of optical phase gradient encountered along the shear direction between two interfering beams. Therefore, contrast of DIC images varies proportionally to cosine of the angle made by azimuth of the phase gradient and the direction of wavefront shear. The image contrast also depends on the initial phase difference (bias) between the interfering beams. To overcome the limitations of DIC systems, we have developed a quantitative orientation‐independent differential interference contrast (OI‐DIC) microscope, which allows the bias to be modulated and shear directions to be switched rapidly without mechanically rotating the specimen or the prisms [1]. A set of raw DIC images with orthogonal shear directions and different biases is captured within a second. Specialized software computes the phase gradient vector map and then the quantitative phase image.

The new OI‐DIC beam‐shearing assembly is shown in
Fig.1.
It consists of two standard DIC prisms with a liquid crystal 90º polarization rotator in between. The shear plane of the first prism DIC1 is oriented at 0º, and the shear plane of the second prism DIC2 is oriented at 90º. Another liquid crystal cell works as a phase shifter, which modulates the bias. Its principal plane is oriented at 0º. We employed a twisted‐nematic liquid crystal cell as 90º rotator and an untwisted nematic cell as phase shifter. The OI‐DIC technique can use any high‐NA objective lens at the full aperture and provides an optical path length (OPL) or phase map with the highest resolution. Unlike other phase mapping techniques, the OI‐DIC does not require phase unwrapping and calibration. The OI‐DIC can also be combined with other imaging modalities such as fluorescence and polarization.

An example of the computed OPL gradient map is shown in
Fig. 2
. The image displays a 4‐µm thick glass rod that is embedded in immersion liquid with refractive index 1.47. The image brightness is linearly proportional to OPL gradient magnitude. White level corresponds to gradient magnitude 200 nm/nm. The hue depicts the gradient direction, as it is illustrated by the color wheel in the left bottom corner. We used microscope Olympus BX61 equipped with objective lens UPlanSApo 100x/1.40 Oil.

The obtained OPL gradient map was processed by Fourier integration to compute the OPL (phase) map, which is represented in
Fig. 3
.The image brightness is linearly proportional to OPL and phase. White corresponds to 500nm (OPL) and 5.75rad (phase) at wavelength λ=546 nm.

Fig.4
displays cross‐sections of the OPL and phase maps of 4‐µm thick glass rods in immersion liquids with the refractive indices 1.47 (red curve), 1.51 (orange curve), 1.54 (blue curve), 1.56 (violet curve), and 1.58 (green curve). Refractive index of the glass is 1.56. An extremum OPL is determined by formula:

where n
r
and n
im
are refractive indices of rod and immersion, respectively, d is diameter of the rod. As one can see, the OPL maxima and minimum are practically equal to the theoretical values 360nm, 200nm, 80nm, 0nm, and ‐80nm.

The OI‐DIC assemblies fit into existing slots of a regular research grade microscope. We confirmed that a microscope upgraded with the OI‐DIC provides lateral resolution ~200 nm and axial resolution ~100 nm at wavelength 546 nm. The OPL noise level was ~0.5nm. According our best knowledge, the images with such high level of resolution cannot be produced by any other currently available interference and phase microscopy techniques.