[1][2] Volkert was born in Rockanje, son of the minister Johannes van der Willigen (1777–1857)[3] and his wife Gerarde Maria Elsabé Bodde (1795–1865).

[5] When the Athenaeum Illustre of Deventer was abolished in 1864, he was appointed conservator of the Physical Cabinet of the Teylers Museum in Haarlem where Jacob Gijsbertus Samuël van Breda had resigned his post nine months earlier.

[6][7] Thus free to devote himself to the instrument collection and physics experiments, in the years that he spent at Teylers, Van der Willigen published 51 papers.

Inspired by this discussion and a publication by the Swedish scientist Anders Ångström in 1855, Van der Willigen decided to dedicate himself first to the determination of the refractive index and the wavelength of light, in order to be able to more accurately define the unit of length.

In the inner garden of the Museum, he had a small observatory built in 1866/1867, where he set up several precision instruments to determine the latitude (zenith telescope) and time (clock).