Optical true-time-delay devices based on the White cell can be divided into two general types: polynomial cells, in which the number of delays that can be obtained is related to the number of times m that a beam bounces in the cell raised to some power, and exponential cells, in which the number of delays is proportional to some number raised to the power of m. In exponential cells, the topic to be addressed, the spatial light modulator switches between a delay element and a null path on each bounce. We describe an improved design of this switching engine, which contains a liquid-crystal switch and a White cell. We examine astigmatism and corrections for it and present a specific design.