In the cases of interest to this investigation, the Einstein radius is comparable to the radius of the white dwarf, which is the lens. Finite-lens effects must therefore be considered; they diminish the magnification and make the signatures of lensing more subtle. This is not the only complication, since the Einstein ring is smaller than the lensed star. Finite-source-size and limb darkening also influence the value of the peak magnification and the shape of the light curve. A set of instructive examples that take these effects into account can be found in the pioneering investigation of Sahu & Gilliland (2003), which studied the detectability of binary self-lensing during transits, as observable by Kepler. 

While the transiting mass blocks light from the star it orbits, its action as a lens increases the amount of light we receive. Sahu & Gilliland (2003) found that, for low-mass white dwarfs in close orbits, the transit signature dominates. As the mass and/or orbital separation increases, lensing begins to play a larger role and can effectively balance the diminuation of light associated with the transit. The transits of some white dwarfs will therefore not be detectable, even though the cancellation is not exact. As the mass and separation continue to increase, the lensing magnification dominates. During transit, and for an interval both before and afterward, there is a highly significant increase in the received light. For systems in which the influence of lensing can be photometrically detected, model fits can provide estimates of the white dwarf’s mass and radius. 

Sahu and Gilliland (2003) showed that Kepler would be likely to detect lensing by white dwarfs, but did not have a detailed model of white-dwarf/main-sequence binaries and could therefore not predict the rates. The population calculations of the previous section can be used as a basis to compute the expected rates. Ideally, the light curves of each transiting system formed in the population calculation would be computed. This is a large project, because a variety of other effects must also be included; in addition, the age of the white dwarf influences its radius. Here we attempt a simple estimate, with the goal of determining how frequently signals of lensing in the light curve may eliminate confusion with planets. We utilize the value of R$_{E}$/R$_{WD}$ to test the detectability of lensing effects, using guidelines derived from the work of Sahu & Gilliland (2003). Note that, at almost the same time as Sahu & Gilliland (2003), Farmer & Agol (2003) took an alternative approach to incorporating the effects of lensing, in the context of a population synthesis analysis. Although they did not classify systems by their previous evolution (common envelope versus stable mass transfer), they did provide numerical results which can be compared with our totals (see § 5). 

We computed the value of R$_{E}$/R$_{WD}$ for every white dwarf in our simulations, using an empirically-derived approximation to estimate the radius of a white dwarf of given mass M$_{WD}$. From Parsons et al. 2010 we use: R$_{WD}$ = [0 . 014 − 0 . 012 ( M$_{WD}$ − 0 . 5)] . The results are shown in Figure 4 for the same simulation that produced Figure 3. Note that Figure 4 

