In applications such as optical data storage or laser direct write, one wishes to use a mechanical feedback system to keep a focused laser \"in focus on an optical surface. This requires generating some error signal that is negative when the focus is above the surface, zero when the focus is on the surface and positive when the focus is below the surface. Consider generating a focus with a small amount of astigmatism, B_3 h in x and 3 times this in y. Imagine that this has been reflected from the surface and imaged back to a camera that can detect the shape of the focus. In reality one would use a quadrant photodiode with just four pixels. Assuming the distance from the exit pupil to the focus is R, write a formula for the distance between the sagittal and meridional focus (as a positive number assuming B is positive). Hint: Look first at the linear term for the defocus aberration and establish how a transverse ray aberration that is proportional to pupil coordinate determines the distance from the measurement plane to the plane of best focus. Then apply this relationship to both the x and y directions of the astigmatic beam