Introduction
This page contains a commented collection of publications around superresolution structured illumination microscopy. This is mostly for me to keep track on where to find certain aspects written down and published, but might also be useful to others.
The publications listed here are on the technical side of things, including
 Fundamental papers
 Reviews, Overviews, Protocols
 Building SIM microscopes
 direct/classic SIM reconstruction algorithms
 Software packages
 Nonlinear SIM
I do not try to cover application of SIM to biological problems here, there are just too many papers out there that use SIM as a method for me to really keep track.
I’ll try to update the list on an asneeded basis, but I’ve failed before. If you think anything is missing, or my comments are wrong / off / incomplete, just let me know (main page with contact info, or open an issue on github).
All citations are autogenerated from a bibtex file (using bibtexjs), which can be imported to citation managers. An XML version compatible with current WORD version is semiautomatically generated from it.
Fundamental papers
The standard SRSIM microscope and reconstruction algorithm, in use by all commercial systems and various homebuilt setups, is often attributed to and referred to as GustaffsonHeintzmannSIM:
 Conference proceeding by R. Heintzmann (1999)
 2D SIM by M. Gustafsson (2000):
 3D SIM by M. Gustafsson (2008).
 There is also this PhD thesis (2000):
More precisely, GustaffsonHeintzmannSIM typically refers to sinusoidal SIM illumination pattern, which are amenable to a direct reconstruction approach.
Reviews and Overview
Certainly not a complete list, but the following are reviews, overview articles and protocols that might be helpful:
 A practical guide on how to perform SIM measurements, and how to assess their quality, from the Schermelleh lab. These guys have lots of experience with running OMX microscopes, taking calibration measurements (OTFs, etc.) and checking for / avoiding SIM artifacts.
 An overview focussing on the technical development of SIM microsocpes and reconstruction algorithms
Building microscopes
There are a few papers with details on how groups created homebuilt SIM setups.
 Setup based on a Hamamatsu SLM (thus, nonbinary phase control), 2beam SIM, 4 pattern orientations (0, 45, 90, 135, easy pattern generation). I think this might be first SLMbased SIM paper (2009):
 Setup based on a TI DMD (thus binary), and using incoherent (LED) light. Keep in mind that using incoherent light will not give a full 2x resolution improvement.
 Setup based on the ForthDD ferroelectric SLM (binary, phase shift), device also in use by Betzig, setup very fast:
 Prequel(?) to the fastSIM, giving some more detail on the system
 Addition to the fastSIM paper, making it faster by working with the rolling shutter
 Also interesting: This paper has calculations (raytracing) on how the polarization of the inter fering light influences pattern contrast:
 A videoguide on how to build / align a TIRFSIM based on the ForthDD SLM, by the Kaminsky group:
Multifocal approaches: Diffractive elements
 SIM with multifocal detection, first paper combining the two, by Sara Abrahamssom. This was build by adding her multifocal detection (a lithographed diffractive element, see papers below) with a Zeiss Elysa (commercial) SIM.
 I would assume this is where the idea of producing a phase mask to create a multifocal detection system started, but I am not completely certain:
 This is the main publication featuring the principle…
 … and this paper has nice details on how the elements are actually created, and how to circumvent the problem of chromatic aberration
Multifocal approaches: Changing the detection path length
 The ‘beam splitter’ approach, changing optical path length, here applied to SOFI…
 … which sparked the development of the prismbased realization of the same idea. The publication also merges it with quantitative phase imaging
direct reconstruction algorithms
This describes the direct (now almost somewhat classic) reconstruction approach as introduces by the GustafssonHeitzmannpapers, i.e.: The sample is illuminated with a finite number of overlapping sinusoidal intensity patterns, these become a finite number of deltapeaks in Fourier space, which in turn allows for a direct (noniterative) solution to a set of linear equation. In contrast, newer algorithms use iterative solvers and what could be called deconvolutionlike approaches to SIM, with different advantages and drawbacks over the classic methods.
The direct SIM reconstruction is a multistep process:

Parameter estimation: Obtaining pattern orientation and frequency, obtaining (global and something patternindividual) phase offsets. This can in principle be done through different algorithms, with varying performance and sometimes hardtofind documentation.

Reconstruction: (2a) Band separation, shift and (2b) recombination through filters. This step is usually rather straightforward to implement, though the choice of filters (or regularization) can make a huge difference in image quality.
Parameter estimation
 The SIM pattern causes a peak in the Fourier spectrum of a raw data frame under structured illumination. That peak can in principle be used to obtain pattern orientation, frequency (position of the peak) and phase of the patter (complex phase of the peak). From the analysis in the paper and my experience, this method will work o.k. if the resolution enhancement is not too high, i.e. if the peak associated with the illumination pattern is not dampened too much by the OTF. As an advantage, it is easy to implement.
 Approach by crosscorrelation of separated bands. The idea here is that the separated spectra have overlapping regions, so the correct shift (angle, frequency, global phase, modulation depth) can be found by maximizing the crosscorrelation of these bands in respect to a complex shift vector. To my knowledge, this is the method of choice to obtain SIM reconstruction parameters, in use e.g. even for the current work of nonlinear SIM. It is also the only method I know to obtain pattern frequency and angle, while the phases can be refined by further means. The idea is already explained in one paragraph in Gustafsson 2008, but not written down in detail. A quite detailed description can however be found in this review:
 Iterative phase optimization: The crosscorrelation will only yield one global phase, with phase differences between patterns assumed as fixed (and set in the band separation matrix). The iterative approach optimizes these phases by analyzing their shift through crosscorrelation in the raw data. It seems like a very sound approach, but it probably takes some time to implement correctly.
 NonIterative phase optimization: A followup to the last paper, this performs phase optimization in a single step. The algorithm is easy to understand and implement, the paper provides comparisons to the iterative method (performance similar for realistic SNRs). fairSIM has some code to run this optimization, though it is currently not accessible directly through the GUI.
Filters
The last step of a SIM reconstruction is the recombination of frequency bands. Since the bands are OTFcorrected, a suitable filter needs to be applied. Typically (i.e., in the original publications), this is a modified/generalized Wienertype filter, however other regularization methods can be applied.
There is often some discussion about “linearity” of filters, i.e. if they can change relative intensities, which might be seen as a disadvantage of e.g. RichardsonLucylike iterative deconvolution methods.
 For good cameras, photon counts are highly dominated by Poisson noise (photon count statistics) compared to Gaussian noise (electron readout noise). Since the Wiener filter is not tuned to that, other filter approaches might yield better results. Again, I am not aware of any implementation of this in use.
 Using RichardsonLucy for both sectioning and also filtering.
 A Hessianbased (2nd derivative) based regularization filter that offers an impressive cleanup of noise, as it promotes “smoothness” in the result. Especially useful in combination with videoimaging, as the smoothness criterion can also be used along the time axis.
Optical sectioning (in singleslice / 2D SIM)
SIM reconstructions can be done in either 2D (single slice, one focal plane) or 3D (requires zstack and 3D OTF). Single slice reconstructions are independent of the illumination mode (2beam or 3beam interference), and even profit of 3beam illumination for the following trick: To reduce the outoffocus light, i.e. to introduce optical sectioning, the 2D OTF is reweighted in such a way that SIM bands do not contribute around their missing cone. To use this trick, one either needs threebeam data (which has the medium band overlapping all missing cones) or twobeam data set to less than the maximum resolution improvement. The idea is mentioned in the appendix of the noniterative phase optimization paper, and documented in two more papers:
 The approach itself:
 Application to highspeed singleslice SIM:
Another more recent approach is to use RichardsonLucy filtering on both the SIM raw input data, and as a replacement of the Wiener filtering step in the results. This allows for sectioning even without the OTF overlap, and in my experience yields very nice result as long as the SNR is good enough (i.e. it can remove outoffocus background, but relies on data with good signal / low noise).
Optimization and checks
Work that deals with aspects of optimizing and checking the quality of the SIM reconstruction process, but does not fit the other categories:
 Optimization of modulation depth, spatially varying illumination intensity and such. A very early paper (2004), I don’t know if and where any of this has been implemented.
 Detecting motion artifacts in SIM reconstructions
Software
SIM image reconstruction
 Of course fairSIM. Currently singleslice (3D is in progress), with crosscorrelation parameter estimation, handles twobeam and threebeam data (more bands work, but not through GUI), and offers optical sectioning through both OTF attenuation and RLdeconvolution.
 Also, there is OpenSIM,
 And another, bigger Matlabbased software, where however the direct “stardard” SIM reconstruction approach does not seem not to be their main focus:
SIM analysis / quality checks
 The “SIMcheck” plugin. Thorough analysis of the input data quality. Last time I’ve checked, mainly for 3D SIM:
General image processing for microscopy
The publications to cite when using ImageJ and Fiji:
 ImageJ:
 Fiji:
 MicroManager (2014)
 MicroManager (2010)
 StackReg / TurboReg are based on:
 bUnwarpJ
Localization microscopy
Not related to SIM, but included here for (my) convenience, popular papers around software packages for localization microscopy:
 rapidSTORM (github by maintainer / first author):
 Comparison of localization microscopy software packages (with a comprehensive list):
Nonlinear SIM
This is not a very complete list, but the milestone papers on extending SIM with “nonlinear techniques” towards more than the 2× resolution enhancement:
 Arguably among the first papers that promoted the idea
 Early work on nonlinear SIM by Gustaffson
 One of the main papers on nonlinear by Gustaffson
 Betzig’s 2015 big (see length of supplementals) Science paper on nonlinear SIM: