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Self-interference digital holography (SIDH) can image incoherently emitting objects over large axial ranges with sub-diffraction resolution in all three dimensions from three two-dimensional images. By combining SIDH with single-molecule localization microscopy (SMLM), incoherently emitting objects can be localized with nanometer precision over a wide axial range without mechanical refocusing. Simulations show that SIDH can achieve sub-20 nm precision with only a few thousand photons. However, background light substantially degrades the performance of SIDH due to the relatively large size of the hologram. Therefore, to achieve the best results, the background must be reduced, and the hologram size must be optimized to increase the signal-to-noise ratio (SNR) and maximize the light efficiency of the SIDH optical system. To optimize the performance of SIDH, we performed simulations to study the optimal hologram radius (𝑅𝑅ℎ) for different levels of background photons. The results show that the reduction of the hologram size improves the localization precision of SIDH. For a given hologram size under different background noise levels, a lower background noise level provides a higher localization precision. By reducing the radius of the entry hologram to 1.4 mm and optimizing the SIDH design, we can achieve a localization precision of better than 60 nm laterally and 80 nm axially over a 10 μm axial range under the conditions of low signal level (6000 photons) with ten photons/pixel of background noise.
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