The Berek compensator, capable of accurately measuring optical delay, is a compensator invented in the early twentieth century. Although the instrument has been widely used so far, the lack of a comprehensive internal job description based on basic principles in modern literature makes the instrument difficult for novice students and researchers to access. In this tutorial, we first established the basic relationship through geometric optics, that is, the delay of the variable induced by the compensator varies with its tilt angle. We then elaborate on the general relationships generally given in the manufacturer's manuals, which do not appear to have been updated since the ruler era. We then discuss the third tilt-delay relationship, which is obtained within a more rigorous wave optics framework. Finally, we explain in detail how the instrument works.
In a Berek compensator tuned to zero delay, the direction of a single birefringent uniaxial crystal plate is perpendicular to the crystal surface and parallel to the optical axis of the microscope. The polarized light passing through the sample encounters the compensator at normal incidence (zero degrees) and propagates through the compensator at a speed independent of the polarization direction. In other words, when the birefringent plate is perpendicular to the optical axis of the microscope, the Berek compensator is like a normal isotropic material and therefore has no effect on the polarized light that passes through.
When the compensation plate tilt adjustment knob is rotated in the direction relative to the incident polarized light (and the optical axis of the microscope) (see Figure 1), the incident surface coincides with the refractive index surface of the extraordinary axis, changing the speed of light through the crystal. In general, the polarization wavefront is delayed by a measurable amount that depends on the tilt angle and the illumination wavelength. At the same time, light polarized perpendicular to the incident plane continues to propagate through the compensation plate along the normal axis, regardless of the tilt angle. As a result, when polarized light passes through the tilted Berek compensator from the sample, it is additionally delayed by the compensator and accumulates a relative phase shift (dependent on the tilt angle), which can be measured by the device. The optical path difference introduced by the Berek compensator is determined by the thickness of the birefringence plate, the illumination wavelength, the difference in refractive index between the ordinary and extraordinary axes of the compensation crystal, and the tilt angle. Most manufacturers combine all these quantities into a constant that is used to calibrate the deceleration micro scale.
As shown in Figures 1 and 2, the Berek compensator is equipped with an inclinable calcite slab, mounted within a rectangular frame and controlled by a rotary drum knob fixed to the vernier scale. The compensator is located in the middle tube of the microscope at a 45-degree angle to the polarization direction of the polarizer and analyzer, and the delay is adjusted by rotating the compensation knob. The vernier on the rotary compensator tilts the birefringence plate relative to the optical axis of the microscope (see Figure 2 (a)). Delay value increases as the sheet is tilted
In effect, the birefringent sample (usually a crystal) is placed on the microscope table and rotated until it reaches the extinction position (i.e. the feature of interest dims). Next, rotate the stage by +45 degrees and clamp it in place. The compensation drum knob is set to 30 degrees (rotate the knob unidirectionally to avoid recoil) and inserted into the microscope intermediate tube. Finally, rotate the compensation knob to confirm that the black tassel intersects the center of the field of view. If the tassel does not intersect the center, the stage rotates 90 degrees and reclamps. Interferometric filters with transmission bandwidths between 540 and 570 nanometers can improve the accuracy of measurements, but in addition to the black fringes that are visible when there is no filter, multiple black fringes are created. The reference table shows the optical path difference of the tilt angle when compensation is achieved.
Figure 3 shows a typical series of measurements taken with a Berek compensator. The mineral sheet in Figure 3 (a) shows the performance of the grain structure under cross-polarized illumination, either without a compensator or when the delay plate is perpendicular to the optical axis (without delay). By inserting the Berek compensator and rotating the fine-tuning dial, the central grain tends to dissipate (see Figure 3 (b)), thereby measuring birefringence. Typical analysis of the lamellar fiber thickness for cross-polarized light only is shown in Figures 3 (c) and 3 (d), and the compensator is inserted and the delay plate is tilted to the maximum extinction angle (Figure 3 (d)).
Similarly, other birefringent fibers can also be evaluated by Berek compensators over a wide range of delay values (see Figures 3 (e) and 3 (f)). The synthetic fibers shown in Figure 3 (e) exhibit positive birefringence, and when a low-resistance (0-3 wavelength) Berek compensator is inserted into the optical path, the central part presents a uniformly distributed extinction band, and the background interference color is higher. Alternatively, the high-value compensator (0-20 wavelength) produces a skewed extinction band inside the fiber, and the background produces a low-order interference pattern (see Figure 3 (f)). Note that for fibers exhibiting negative birefringence, the order of interference fringes is reversed in Figures 3 (e) and 3 (f). In general, Berek compensators with low latency measurement ranges are manufactured using calcite/magnesium fluoride sheets, while compensators designed to measure high latency values are manufactured using calcite sheets.
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