Analytic method to optimize aperture design in focal modulation microscopy.

Focal modulation microscopy (FMM) has been demonstrated more effective than confocal microscopy for imaging of thick biological tissues. To improve its penetration depth further, we propose a simple analytical method to enlarge the modulation depth, the unique property of FMM directly linked to its signal-to-noise ratio. The modulation depth increases as the excitation intensity of the binary phase aperture status is pushed further away from the focal region of the detection optics, thereby creating a dark region in the focal volume, which we call maximally flat crater (MFC). By direct algebraic manipulation, MFCs are achieved for both scalar and vector diffraction optics. Numerical results show that the modulation depth from MFC is very close to the maximum values, with a small difference less than 3% for the same number of subapertures. Applications of bifocus produced by MFC apertures are also discussed.