Viscoelasticity is a physical property of a matter which explains how soft, hard, or sticky the matter is. It has two factors; viscosity and elasticity. Viscosity is a factor of how sticky a matter is. Just imagine, honey is stickier than water. That is, the viscosity of honey is higher than that of water. On the other hand, elasticity is a factor of how resilient a matter is. When you push a sponge and a rubber, you may feel the sponge is softer. That is because the sponge has lower elasticity than the rubber.
Imaging vibrating a surface of a viscous or elastic object like poking a pudding. If the pudding is hard, vibration of the surface may not be so much. But if it is softer, the surface must be vibrating more even though you poke it as strong. Then, how to measure it?
Our system utilizes reflection of light on the surface. Placing a screen by the pudding and entering a ray of light onto the surface, we can see the reflection as a point projected on the screen. As the surface vibrates, the point also vibrates because its position is related to the orientation of the surface. As the surface vibrates more, motion of the point on the screen gets larger. If the speed of vibration is enough fast, we, or cameras, just capture it as an ellipsoidal afterimage. Since a larger motion of the point makes a larger ellipsoid, the size of ellipsoid is related to the viscoelasticity of the pudding!