Shell thickness (including membrane) was traditionally measured with a micrometer after rinsing the shell to remove any adhering albumen.

See eg this publication

Article Effect on performance of a low level mixture of organochlori...

Typically shell membrane is included in shell thickness measurements.

The tools have changed now that there are some nice electronic micrometers on the market, but the method is about the same. The equatorial region of the egg has the most consistent thickness. Once we wash out the albumen and let the shells dry for at least a day, we measure thickness at 3 spots and take the average. You will need to state in your Materials and Methods if the thickness includes shell membranes or if they have been removed. We have tested the measurements with or without membranes present and both methods work equally well in detecting treatment-based differences in shell thickness.

There is a machine called a Texture Analyzer (http://www.stablemicrosystems.com/frameset.htm?http://www.stablemicrosystems.com/TAXTplus.htm) that can be used and is great for both accuracy and precision of your measurements. It requires attachments for different the different types of material you use. It is quite expensive but does avoid operator error, such as how hard the operator may squeeze the digital micrometers (suggested above). The Texture Analyzer has a program that takes many other types of measurements as well as it is not only used for egg quality measurements. We also use the machine for egg breaking force. 

Problably you need to mantain the shell membrane, but nedd to care bout removing egg White (using water and fingers), then keep it drying in a place dry without sun light. and use the micrometer measuring in the equatorial region of the egg. But I believe that could be useful to analyse the egg using light to try to find any internal (shell membrane) or external defects (thin shell) before egg were broken.

Eggshell thickness typically includes the membrane using a modified micrometer and averaging three measurements around the blow-hole near the equator of the egg (Klaas et al. 1974). Newer instruments are available that reduce the error associated with a mechanical measuring device (Santolo et al. 2016).

Article Avian eggshell thickness: variability and sampling

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Dear Bijaya

There is two types of measurements for shell thickness : shell thickness including shell membranes and shell thickness without shell membranes.

You can use a micrometer to measure the shell thickness.

Good Luck