# Technical note: A universal method for measuring the thickness of microscopic calcite crystals, based on bidirectional circular polarization

Coccoliths are major contributors to the particulate inorganic carbon in the ocean that is a key part of the carbon cycle. The coccoliths are a few micrometres in length and weigh a few picogrammes. Their birefringence characteristics in polarized optical microscopy have been used to estimate their mass. This method is rapid and precise because camera sensors produce excellent measurements of light. However, the current method is limited because it requires a precise and replicable set-up and calibration of the light in the optical equipment. More precisely, the light intensity, the diaphragm opening, the position of the condenser and the exposure time of the camera have to be strictly identical during the calibration and the analysis of calcite crystal. Here we present a new method that is universal in the sense that the thickness estimations are independent from a calibration but result from a simple equation. It can be used with different cameras and microscope brands. Moreover, the light intensity used in the microscope does not have to be strictly and precisely controlled. This method permits the measurement of crystal thickness up to 1.7 inline-formulaµm. It is based on the use of one left circular polarizer and one right circular polarizer with a monochromatic light source using the following equation:

disp-formulaCh1.Ex1 $M2blockscrollmathmld=true\frac{\mathrm{italic \lambda }}{\mathrm{italic \pi }\mathrm{normal \Delta }n}\mathrm{normal arctan}\left(\right)\left(\sqrt{true\frac{{I}_{\mathrm{normal LR}}}{{I}_{\mathrm{normal LL}}}}\right),$
131pt42ptsvg-formulamathimgf4dd413876fdda2d026fc76d2022df04 bg-18-775-2021-ue00001.svg131pt42ptbg-18-775-2021-ue00001.png

where inline-formulad is the thickness, inline-formulaλ the wavelength of the light used, inline-formulaΔn the birefringence, and inline-formulaILR and inline-formulaILL the light intensity measured with a right and a left circular polarizer. Because of the alternative and rotational motion of the quarter-wave plate of the circular polarizer, we coined the name of this method “bidirectional circular polarization” (BCP).

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Beaufort, Luc / Gally, Yves / Suchéras-Marx, Baptiste / et al: Technical note: A universal method for measuring the thickness of microscopic calcite crystals, based on bidirectional circular polarization. 2021. Copernicus Publications.

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