The CLOWFS propagation model is similar, but requires a near-field Fresnel integral to compute the defocused sensor field after the coronagraph focal plane. The Fresnel propagation requires us to define several physical dimensions: pupil diameter, focal length, propagation distance (defocus), and wavelength. For these we used the same parameters as for our planned testbed, listed in Table 1. The outer radius of the reflective focal annulus was fixed at $4\lambda /D$, identical to the SAM WFS. We then tuned both the defocus and the inner radius of the annulus by trial and error to give the best performance in terms of $R2$, a metric described in Sec. 3.1. For our coronagraph and range of mode estimation, we found that the CLOWFS worked best without any inner radius, instead leaving the reflective region as a simple disk. We found the best performance at a defocus at 3% of the 200 mm focal length, or 6 mm. For our 550 nm wavelength, and 10 mm diameter pupil, this corresponds to a defocus aberration of 1.88 μm peak to valley, equivalent to 3.4 waves. We note this is very close to the 3.3 waves used by Guyon et al. in their published design.^{11} For both SAM and CLOWFS simulations, the same stellar magnitude, spectral bandwidth, photon counting noise, read noise, and integration time were used.