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Volume change of graphite leads to change in thickness of battery storage layers during discharging and charging. Pouch cell lithium ion batteries are used in the field of electric vehicles and solar home storage. This paper shows a measurement setup for the three-dimensional measurement of thickness change on a flat 6.7mm thick pouch cell using a white light interferometer. With a measuring field of 7.05mm diameter the resulting 3D thickness change record contains 226000 3D readings. The measuring points have a lateral distance of 13.1μm. The repeatability of the measurement is 312.8nm for the individual values and 64.1nm for the average value. In addition, this paper shows how the storage capacity of this pouch cell drops over 30 charge cycles.