If you found our previous section on super resolution interesting, you may be curious for a more detailed explanation behind some of the techniques.

## Introduction to this counterintuitive method

Of the super-resolution microscopy techniques, structured illumination microscopy (SIM) is arguably the most counterintuitive to grasp. Of course, that’s what makes it so much fun! To understand how it works we’ll have to think about the nature of information and how it can move between real and Fourier space. Further, we’ll discuss the mechanics of generating the structured illumination lightpath, and how the super-resolution images are reconstructed.

## 1.  It’s a digital camera, so we only collect amplitude

Structural information of any real image (such as your sample) can be described as a mix of sinusoidal modulations in the amplitude of the light- in other words, a wave form which varies in height.  In truth, it is also a mixture of phase values, spectra, and quantum effects, but since our readout is a digital camera we can only collect amplitude values.

## 2. The low and high frequencies are invisible

The information in these amplitude modulations may also be considered as frequencies through use of a Fourier Transform (FT) – visible or diffraction-limited structures are in a certain frequency range, while frequencies in the lower and higher ranges are obscured and normally invisible. By this framework, very small structures in real space (e.g. sub-diffraction details in your sample <200 nm in size) are represented by very high frequencies.

## 3. Patterns of illumination equal encoded information

The beauty of SIM is that by creating patterns in the illuminating light and thus the frequency patterns of light emitted from the sample, high frequency information becomes encoded in those patterns. This high frequency information, and therefore the sub-diffraction structures, can be extracted by deconvolving the patterns in light emitted from the sample from the patterns you introduced to the illumination.

## 4. Unique patterns also equal a reconstructed image

Normally, these higher frequency emissions from the sample would be unable to enter the microscopes’ back focal plane and cause smearing in the image. By applying many unique patterns to the same area of sample, SIM reconstructs where those emissions would come from, allowing us to see structures which are up to 100 nm below the diffraction limit.

## How it actually works

A polarized laser beam is directed through a transmitting phase grating (i.e. a glass plate with etched or coated stripes) to be separated into many diffraction ordered beams all emanating from the diffraction grating at different angles. The three beams closest to the center (0, +1 and -1 orders, respectively) are then brought together in the focal plane of the microscope to generate a very fine-striped illumination pattern.

As in early implementations, this pattern can be formed with only two beams to create patterning the X and Y directions, but requires the third central beam for patterning in Z. The pattern is then shifted laterally by modulating the phase of the beams and acquiring an image at each step. This is usually accomplished by physically moving the grating in the lateral direction.

The pattern is then rotated, generally by physically rotating the grating, and more images are acquired. Each z-stack usually contains 15 raw images per plane as the pattern is shifted in five steps (five different phases) and rotated at three different angles. The sample is then moved through the focal plane and a z-stack of images assembled, usually with a spacing of 125 nm between z-section, as with other optical sectioning techniques.

## Back to the math

(a)  A reconstruction algorithm combines the information from all 15 images in each z-section in Fourier space. As each image has a different location of the pattern relative to the sample, the Fourier representations of each image are arranged in a way such that higher-order information can be determined when compared to the Fourier-space information of the pattern itself. That information (of the pattern itself) is referred to as the Optical Transfer Function or OTF, and is similar to the Point Spread Function or PSF upon which conventional deconvolution algorithms are based.

(b)  The higher-order information from the sample is isolated and shifted into real space, made visible once the image is transformed back into the mixture of amplitude patterns we would recognize as an image of the sample. The algorithm also takes information from the sections above and below the section of interest, allowing for an increase in resolution in the Z axis as well. Overall this strategy currently achieves an 8-fold volumetric reduction of a resolvable structure.

## Coming next…

In the near future we’ll discuss the differences between commercially available SIM platforms from GE/Applied Precision, Nikon, and Zeiss, as well as some exciting future directions. We’ll also look at technical considerations – such as sample preparation and system calibration – to keep in mind when imaging with this exquisitely clever and sensitive technique.

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