According to one embodiment of the present invention, a method of constructing a fluid lens is provided. The method comprises establishing a generalized sidewall profile function and converting the generalized sidewall profile function to a plurality of lens sidewall contact angle functions defined by different combinations of sidewall profile parameters. Thereafter, the method comprises determining respective degrees of operational linearity of the lens sidewall contact angle functions over a range of positions along the x axis by assessing derivative uniformity of each of the lens sidewall contact angle functions within an established slope flatness metric ε. The respective degrees of operational linearity of the lens sidewall contact angle functions are then evaluated to identify an optimized sidewall profile. A fluid lens is then constructed by forming the fluid lens reservoir having at least one sidewall with the optimized sidewall profile.