Modulation enhanced single-molecule localization microscopy (meSMLM) methods improve the localization precision by using patterned illumination to encode additional position information. Iterative meSMLM (imeSMLM) methods iteratively generate prior information on emitter positions, used to locally improve the localization precision during subsequent iterations. The Cramér-Rao lower bound cannot incorporate prior information to bound the best achievable localization precision because it requires estimators to be unbiased. By treating estimands as random variables with a known prior distribution, the Van Trees inequality (VTI) can be used to bound the best possible localization precision of imeSMLM methods. An imeSMLM method is considered, where the positions of in-plane standing-wave illumination patterns are controlled over the course of multiple iterations. Using the VTI, we analytically approximate a lower bound on the maximum localization precision of imeSMLM methods that make use of standing-wave illumination patterns. In addition, we evaluate the maximally achievable localization precision for different illumination pattern placement strategies using Monte Carlo simulations. We show that in the absence of background and under perfect modulation, the information content of signal photons increases exponentially as a function of the iteration count. However, the information increase is no longer exponential as a function of the iteration count under non-zero background, imperfect modulation, or limited mechanical resolution of the illumination positioning system. As a result, imeSMLM with two iterations reaches at most a fivefold improvement over SMLM at 8 expected background photons per pixel and 95% modulation contrast. Moreover, the information increase from imeSMLM is balanced by a reduced signal photon rate. Therefore, SMLM outperforms imeSMLM when considering an equal measurement time and illumination power per iteration. Finally, the VTI is an excellent tool for the assessment of the performance of illumination control and is therefore the method of choice for optimal design and control of imeSMLM methods.

调制增强单分子定位显微镜（meSMLM）方法通过使用图案照明来编码附加位置信息来提高定位精度。迭代 meSMLM (imeSMLM) 方法迭代生成有关发射器位置的先​​验信息，用于在后续迭代期间局部提高定位精度。Cramér-Rao 下界无法合并先验信息来限制可实现的最佳定位精度，因为它要求估计器无偏。通过将估计量视为具有已知先验分布的随机变量，范树不等式 (VTI) 可用于限制 imeSMLM 方法的最佳可能定位精度。考虑 imeSMLM 方法，其中面内驻波照明图案的位置在多次迭代过程中受到控制。使用 VTI，我们分析地近似了利用驻波照明模式的 imeSMLM 方法的最大定位精度的下限。此外，我们使用蒙特卡洛模拟评估不同照明图案放置策略可最大实现的定位精度。我们表明，在没有背景和完美调制的情况下，信号光子的信息内容作为迭代计数的函数呈指数增加。然而，在非零背景、不完善的调制或照明定位系统的机械分辨率有限的情况下，信息增加不再是迭代次数的指数函数。因此，具有两次迭代的 imeSMLM 在每像素 8 个预期背景光子和 95% 调制对比度下最多比 SMLM 提高五倍。此外，imeSMLM 增加的信息通过降低的信号光子速率来平衡。因此，当考虑每次迭代的测量时间和照明功率相等时，SMLM 优于 imeSMLM。最后，VTI 是评估照明控制性能的出色工具，因此是 imeSMLM 方法优化设计和控制的首选方法。当考虑每次迭代的测量时间和照明功率相等时，SMLM 优于 imeSMLM。最后，VTI 是评估照明控制性能的出色工具，因此是 imeSMLM 方法优化设计和控制的首选方法。当考虑每次迭代的测量时间和照明功率相等时，SMLM 优于 imeSMLM。最后，VTI 是评估照明控制性能的出色工具，因此是 imeSMLM 方法优化设计和控制的首选方法。