9 · References & further reading

What this tool borrows from, and where to read more.

Phasor localization

  • “Phasor based single-molecule localization microscopy in 3D (pSMLM-3D): an algorithm for MHz localization rates using standard CPUs,” K. J. A. Martens, A. N. Bader, S. Baas, B. Rieger, J. Hohlbein, J. Chem. Phys. 148, 123311 (2018). doi:10.1063/1.5005899

  • “Integrating engineered point spread functions into the phasor-based SMLM framework,” K. J. A. Martens et al., Methods (2020).

Aperture photometry (smFRET)

  • The above pSMLM-3D paper’s own Supplementary Information §S11 “Aperture photometry to assess intensity and background levels” describes the circular signal-disk + background-annulus + percentile-background method apertureIntensity() (MODULE: smFRET) ports.

  • “Optimal Background Estimators in Single-Molecule FRET Microscopy,” S. Preus, L. L. Hildebrandt, V. Birkedal, Biophys. J. 111(6), 1278–1286 (2016). doi:10.1016/j.bpj.2016.07.047 — the original source the pSMLM-3D SI’s own method adapts from.

sSMLM pairing — distance-fit background model

  • Philip, J. The Probability Distribution of the Distance Between Two Random Points in a Box. Technical Report TRITA-MAT-07-MA-10, Dept. of Mathematics, Royal Institute of Technology (KTH), Stockholm, 2007. — the rectangle-profile background PDF sSmlmBgPdfRect() (MODULE: sSMLM) uses; this report is widely mis-cited as “1991” (a mixup with an unrelated AMS Mathematics Subject Classification footnote year on the same title page) — 2007 is correct, verified against the report’s own internal references and report number.

  • Solomon, H. Geometric Probability, SIAM, 1978, p. 129 — the circular-profile background PDF sSmlmBgPdfDisk() uses, via Wolfram MathWorld’s “Disk Line Picking” entry.

Spot detection & thresholding

  • “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, G. M. Hagen, Bioinformatics 30(16), 2389–2390 (2014). doi:10.1093/bioinformatics/btu202

  • “Wavelet analysis for single molecule localization microscopy,” I. Izeddin et al., Opt. Express 20(3), 2081–2095 (2012). doi:10.1364/OE.20.002081

  • “Simultaneous multiple-emitter fitting for single molecule super-resolution imaging,” F. Huang, S. L. Schwartz, J. M. Byars, K. A. Lidke, Biomed. Opt. Express 2(5), 1377–1393 (2011). doi:10.1364/BOE.2.001377

Fitting & precision (why LS ≠ MLE)

  • “Precise nanometer localization analysis for individual fluorescent probes,” R. E. Thompson, D. R. Larson, W. W. Webb, Biophys. J. 82(5), 2775–2783 (2002). doi:10.1016/S0006-3495(02)75618-X

  • “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, Nat. Methods 7, 377–381 (2010). doi:10.1038/nmeth.1447

  • “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” C. S. Smith, N. Joseph, B. Rieger, K. A. Lidke, Nat. Methods 7, 373–375 (2010). doi:10.1038/nmeth.1449

  • MLE implementation ported from Picasso’s picasso/gaussmle.py — see Picasso reference below.

Gain/offset estimation (PCFO)

  • “Calibrating photon counts from a single image,” R. Heintzmann, P. K. Relich, R. P. J. Nieuwenhuizen, K. A. Lidke, B. Rieger, arXiv:1611.05654. arxiv.org/abs/1611.05654

Localization precision (NeNA)

  • “A simple method to estimate the average localization precision of a single-molecule localization microscopy experiment,” U. Endesfelder, S. Malkusch, F. Fricke, M. Heilemann, Histochem. Cell Biol. 141, 629–638 (2014). doi:10.1007/s00418-014-1192-3

Image resolution (FRC)

  • “Measuring image resolution in optical nanoscopy,” R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, B. Rieger, Nat. Methods 10, 557–562 (2013). doi:10.1038/nmeth.2448 — also the source for the Render mode section’s (§2) super-resolution-pixel-size-vs-precision guidance (§5.2 of its Supplementary Information).

Rendering (Render mode)

  • “Super-resolution microscopy with DNA-PAINT,” J. Schnitzbauer, M. T. Strauss, T. Schlichthaerle, F. Schueder, R. Jungmann, Nat. Protoc. 12, 1198–1228 (2017). doi:10.1038/nprot.2017.024 — Picasso’s own default per-localization Gaussian rendering, the model for precision mode’s splat.

  • “Raw Data to Results: A Hands-On Introduction and Overview of Computational Analysis for Single-Molecule Localization Microscopy,” K. J. A. Martens, B. Turkowyd, U. Endesfelder, Front. Bioinform. 1, 817254 (2022). doi:10.3389/fbinf.2021.817254 — histogram-vs-Gaussian rendering trade-offs, including the √2 resolution loss precision mode’s own docs cite.

  • “Averaged shifted histograms: effective nonparametric density estimators in several dimensions,” D. W. Scott, Ann. Statist. 13(3), 1024–1040 (1985). projecteuclid.org/euclid.aos/1176349654 — the statistical basis for dither mode: shift-and-bin converges to a kernel density estimate.

  • “Random average shifted histograms,” M. Bourel, R. Fraiman, B. Ghattas, Comput. Stat. Data Anal. 79, 149–164 (2014). doi:10.1016/j.csda.2014.05.004 — the randomized-shift refinement dither mode’s single seeded jitter per localization is closer in spirit to.

Temporal median filtering (FTM)

  • Originates with the Nieuwenhuizen et al. paper above; ported from the Hohlbein Lab’s own newer implementation, FTM2, used in “Enabling single-molecule localization microscopy in turbid food emulsions,” A. Jabermoradi, S. Yang, M. I. Gobes, J. P. M. van Duynhoven, J. Hohlbein, Phil. Trans. R. Soc. A 380(2220), 20200164 (2022). doi:10.1098/rsta.2020.0164

Drift correction (AIM)

  • “Toward drift-free high-throughput nanoscopy through adaptive intersection maximization,” H. Ma, M. Chen, P. Nguyen, Y. Liu, Sci. Adv. 10(21), eadm7765 (2024). doi:10.1126/sciadv.adm7765

  • Adapted from Picasso’s picasso/aim.py (parabolic sub-pixel peak fit replaces the FFT phase refinement; linear interpolation replaces the spline) — see Picasso reference below.

Nuclear pore complex (NPC) simulation

  • “Nuclear pores as versatile reference standards for quantitative superresolution microscopy,” J. V. Thevathasan et al., Nat. Methods 16, 1045–1053 (2019). doi:10.1038/s41592-019-0574-9

  • “CIR4MICS: simulating structurally variable nuclear pore complexes for microscopy,” R. Wanninger et al., Bioinformatics 39(10), btad587 (2023). doi:10.1093/bioinformatics/btad587

COMET drift

  • “Cost-function Optimized Maximal Overlap Drift Estimation for Single Molecule Localization Microscopy,” L. Reinkensmeier, S. Aufmkolk, I. Farabella, A. Egner, M. Bates, bioRxiv (2026). doi:10.64898/2026.03.27.714864. Reference implementation (MIT): github.com/gpufit/comet; webSMLM’s cometDrift() is written from the published description, not ported from that code.

Picasso (reference implementation for the ported MLE and AIM drift code above, github.com/jungmannlab/picasso)

  • “Super-resolution microscopy with DNA-PAINT,” J. Schnitzbauer, M. T. Strauss, T. Schlichthaerle, F. Schueder, R. Jungmann, Nat. Protoc. 12, 1198–1228 (2017). doi:10.1038/nprot.2017.024

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