On the Application of Integral Field Unit Design Theory for Imaging Spectroscopy

Integral field spectroscopy is a powerful tool for astronomical observation, of particular importance to large telescopes. In this paper, different techniques for the design and construction of integral field units (IFUs) are described, concentrating on the use of lenslet arrays coupled to fibers. The theory of the design of the foreoptics, lenslets, and fibers is presented. The effects of the fiber oversizing and focal ratio degradation on IFU performance are described. A mathematical model is developed that can be used to calculate the optimized fiber core size according to the required coupling efficiency. A figure of merit for the IFU system is also derived, which can be used to estimate and compare the performance of different IFU systems. Finally, a design example is given to demonstrate the applications of this theory.