Structured Illumination Microscopy - Fundamentals and Applications

SAHLGRENSKA ACADEMY
STRUCTURED ILLUMINATION MICROSCOPY
FUNDAMENTALS AND APPLICATIONS
RAFAEL CAMACHO | SCIENTIFIC OFFICER - IMAGE ANALYSIS | CENTRE FOR CELLULAR IMAGING

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Resolution of an optical microscope
The resolution of an optical microscope is limited due to light diffraction to about 200 nm.
CENTRE FOR CELLULAR IMAGING (CCI)
NATIONAL MICROSCOPY INFRASTRUCTURE
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The resolution limit
From the perspective of wave theory
The larger the numerical aperture of the lens, the larger the resolution
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The image of a point source is
called the Point Spread
Function (PSF) of the
microscope.
𝑁𝐴 = 𝑛 sin 𝜃 ≈ 𝑛
𝐷
2𝑓
Numerical Aperture
Image attribution disclaimer: all figures marked by come from https://commons.wikimedia.org
Task: Which PSF belongs to
the upper and bottom diagram?

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The resolution limit
What are the actual numbers
1873 Ernst Abbe empirically
defined resolution as:
𝑑 =
𝜆
2 𝑁𝐴
Rayleigh criterion,
based on human vision:
𝑑 =
1.22 𝑓 × 𝜆
𝐷
Considering both,
Abbe and Rayleigh:
𝑑 =
0.61 𝜆
𝑁𝐴
Vangindertael, J., Camacho, R., Sempels, W., Mizuno, H., Dedecker, P., & Janssen,
K. P. F. (2018). Methods and Applications in Fluorescence, 6(2), 022003.
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Methods Appl. Fluoresc. 6(2018), 022003.
Nyquist-Shannon sampling theorem
Analog image pixels: 10 x 10 500 x 500 1000 x 1000
Does it make sense to have as many pixels as possible?
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Nyquist-Shannon sampling theorem dictates that a continuous analog signal should be
oversampled by at least a factor of two to obtain an accurate digital representation.
If we don’t sample properly we get Aliasing. This is when
different signals become indistinguishable after sampling

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Super-resolution microscopy
Brief history
Over the last two decades, a number of pioneering scientists and
technological advancements have found ways to go around the
resolution limit. One of these pioneers was Matt Gustafsson:
“Even though the classical resolution limits are imposed by physical law, they
can, in fact, be exceeded. There are loopholes in the law or, more precisely, the
limitations are true only under certain assumptions. Three particularly important
assumptions are that observation takes place in the conventional geometry in
which light is collected by a single objective lens; that the excitation light is
uniform throughout the sample; and that fluorescence takes place through
normal, linear absorption and emission of a single photon”
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Gustafsson M G 1999 Extended resolution fluorescence microscopy.
Curr. Opin. Struct. Biol. 9 627–34

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Brief history – time line
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1989, Moerner reports the first optical detection of single molecules via absorption.
1990, Orrit reports the optical detection of single molecules via fluorescence.
Early 90s, Stefan Hell postulates that samples could be observed by two
opposing objectives.
2000, Gustafsson demonstrates 2 fold resolution enhancement of lateral
resolution via Structured Illumination Microscopy (SIM).
2000, Stefan Hell demonstrates super-resolution via Stimulated Emission
Depletion (STED) microscopy.
2006, Betzig demonstrates super-resolution via Single Molecule Localization
Microscopy, specifically by photo activation (PALM).

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Brief history
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https://www.nature.com/articles/nmeth.1612
Matt Gustafsson,
1960–2011.
Photo by Paul Fetters

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Methods we will cover
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Structured Illumination Microscopy – SIM
https://giphy.com/gifs/animated-gif-processing-creative-coding-10DhrOkl4VnHfq
Stimulated Emission Depletion Microscopy – STED
https://giphy.com/gifs/doughnut-N04Fkkzhf9slO
https://www.youtube.com/watch?v=RE70GuMCzww
Single Molecule Localization Microscopy – SMLM

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Fourier theorem – Fourier series
The mathematical basis of SIM
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A periodic function, which is reasonably continuous, may be expressed as the sum
of a series of sine or cosine terms, each of which has specific amplitude and phase
coefficients known as Fourier coefficients.
A) A step function representing an
arbitrary signal. B) This complex
shape can still be approximated by
a sum of sine functions. C) To
approximate the original signal
faithfully, a large number of
sinusoidal signals (blue) need to
be summed (red).

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A) Simple time domain sinusoidal signal can
be fully defined in terms of its amplitude (0.8)
and frequency (50 Hz). A-right) Fourier
transform of the sinusoidal signal. The average
amplitude can be found at the 0 Hz (or DC)
point.
Fourier spectrum – Fourier transform
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The Fourier transform (FT) decomposes a
function into the frequencies that make it up.
B) The Fourier transform of a 120 Hz signal.
C) The sum of signal A and B and its
corresponding Fourier transform.

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Fourier transform of images – Spatial domain
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FT principles can be extended to two
dimensional images, in this case we will
work on the spatial domain.
In the 2D Fourier spectrum (or image) the
distance from the center encodes
frequency whereas brightness encodes
amplitude. Directionality of the features is
encoded in the orientation of the line
extending between the center and the
frequency component.
A) 2D sine wave (left) is Fourier transformed (right), the center spot is again the DC point.
C) The sum of A and B and its corresponding Fourier transform.
B) 2D sine signals of higher frequency and different directions will generate patterns where the points are
farther from the center and the orientation of the points will always be on the line representing the x-axis of
the sine function.

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A lens works as a Fourier Transform!
Fourier optics
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A lens performs a Fourier transform. This is the result of constructive and destructive
interference.
Image space Frequency space

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Diffraction limit in terms of Fourier optics
Optical Transfer Function
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𝐷
2𝑓
PSF
Object PSF Image
=⊗
Convolution
Fourier
Spectrum
Optical
Transfer
Function
Image
F. Spec.
∙ =
Dot
Product
Higher frequencies = thinner structures; Larger the disk in the OTF = Larger the resolution
Task: what is the difference between the
object and image Fourier Spectrum

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Diffraction limit in terms of Fourier optics
Optical Transfer Function
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OTF
OTF PSF Spoke target image
Abbe
frequency
limit
Higher frequencies = thinner structures; Larger the disk in the OTF = Larger the resolution
𝐷
2𝑓
While in super resolution microscopy we evaluate the response
of microscopes via the PSF, most lens companies evaluate their
lenses (microscopy or camera) via the OTF. In this test the
image of a resolution test chart is analyzed. However, remember
the OTF is just the Fourier transform of the PSF.

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Moiré pattern
Interference patterns
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Large-scale (low frequency) interference patterns that are produced when
imaging super imposed periodic features.
By introducing a well defined, periodic
illumination pattern, Moiré patterns
appear.
As these patterns are of lower
frequency they can be resolved by
the microscope.
As we know the illumination pattern
and measure the Moiré image, then
we can reconstruct the high
frequency details that created the
pattern – Sample!

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SIM
Experimental demonstration showing the reconstruction of the high frequency components of the sample in
reciprocal, i.e. Fourier, space. Gustafsson M G L 2000 Surpassing the lateral resolution limit by a factor of
two using structured illumination microscopy J. Microsc. 198 82–7
Frequencies that can be
transferred – resolution limit
Components of a sinusoidal
illumination pattern
Frequency domain we can
observe via Moiré pattern
Repeating for differently
oriented illumination pattern
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Task: Can you guess
from this figure what is
the resolution
improvement of SIM?
https://memegenerator.net/

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Ok but how does it look
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Actin fibers in HeLa cells as seen by
wide field (A) and SIM (B).
C), D) Comparing a close up shows that
previously unresolvable fibers can now
be visually separated.
Gustafsson M G L 2000 Surpassing the lateral
resolution limit by a factor of two using structured
illumination microscopy J. Microsc. 198 82–7

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Be aware of reconstruction artifacts
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Typical artifacts caused by suboptimal parameter choice:
• Grainy background noise
too heavily emphasized high frequencies amplify noise
• Ringing
recombination of poorly weighted components
• Decreased resolution
combination of incorrectly chosen parameters
Slide from Hendrik Deschout, former Scientific Officer at CCI
Optics Communications, 436 (2018), 69–75.

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SIM available at the CCI
Elyra PS1
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Inverted confocal microscope (780 head) coupled with two techniques
of super resolution SIM and SMLM.

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Applications - Resources
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Applications – General comments
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SIM typically imposes little to no requirements in terms of sample
preparation. Most samples suitable for confocal microscopy can be
readily imaged by SIM as well.
Multiple microscope manufacturers offer SIM instrumentation, complete
with easy-to-use image reconstruction software.
SIM is perhaps one of the most accessible super-resolution techniques.
SIM requires prolonged exposure of the sample to relatively high
illumination intensities – phototoxicity might be a concern.
In thick samples, the illumination pattern increasingly deteriorates when
traveling through the sample.
3D-SIM requires recording a z-stack, which can lead to motion artifacts
in live cell imaging

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Applications
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SR-SIM
Wide Field
2 µm
SR-SIM image of Brp protein complexes in a neuromuscular junction (Drosophila larva).
Authors: Hermann Aberle and Christian Klämbt, University of Münster, Germany.
2 µm
Widefield microscopy SR-SIM
Slide from Hendrik Deschout, former Scientific Officer at CCI

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Applications
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Simultaneous imaging of DNA, nuclear
lamina, and Nuclear Pore Complex
epitopes by 3D-SIM. C2C12 cells are
immunostained (A) Central cross
sections. (B) Projections of four apical
sections (corresponding to a thickness of
0.5 µm). Boxed regions are shown
below at 4× magnification; scale bars
indicate 5 µm and 1 µm, respectively. (A)
confocal imaging (CLSM) and
deconvolution still show partially
overlapping signals. In contrast, with 3D-
SIM the spatial separation of NPC,
lamina, and chromatin and chromatin-
free channels underneath nuclear pores
are clearly visible
https://www.ncbi.nlm.nih.gov/pmc/article
s/PMC2916659/
Schermelleh et al. Science 2008, 320: 1332-
1336

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Can you go beyond 2X resolution improvement
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(A) The nonlinear fluorescence response upon increase of the
excitation power. (B) With increasing power, the SIM
illumination pattern gets distorted due to the nonlinear
fluorescence response. (C) The non-sinosoidal illumination
patterns are composed of a near infinite series of harmonics.
(D) In SSIM the observable region of the frequency space is
increased due to the presence of additional harmonics in the
illumination pattern. Methods Appl. Fluoresc. 6(2018), 022003.
Non-linear SIM of actin structures in
Chinese hamster ovary (CHO) cells. (A,
right) Actin structures inside CHO cells
were visualized by NL-SIM after labeling
them with LifeAct-Dronpa. Compared to
the wide-field image (left side of A, B), or
the normal SIM image (C) the NL-SIM
image (A), (D) gives a superior resolution
of approximately 50 nm. Methods Appl.
Fluoresc. 6(2018), 022003. Proc. Natl Acad. Sci. 109
(2012), E135–43.
Yes, but you have to go non-linear

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Airyscan
Special implementation of the SIM concepts
Great method to deal with low-light conditions, and thick samples.
Based on the Line scanning SIM by Heintzmann (Opt. Express 2012 20
24167) and the use of a imaging sensor demonstrated by Müller and
Enderlein (Phys. Rev. Lett. 2010 104 1).
The sample is scanned as in confocal, emitted light is captured by a sensor.
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Airyscan available at the CCI
Inverted confocal microscope (880 head) coupled with AIRYSCAN
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Image attribution
Slide Info Link
3, 14 Numerical Aperture https://commons.wikimedia.org/wiki/File:Numerical_aperture_for_a_lens.svg
4 Res. Limit https://iopscience.iop.org/article/10.1088/2050-6120/aaae0c
Hereinafter referred to as MAF Review
5 Aliasing https://commons.wikimedia.org/wiki/File:CPT-sound-nyquist-thereom-
1.5percycle.svg
5 Res. Limit MAF Review
6 Curr. Opin. Struct. Biol. 9
627–34
https://www.sciencedirect.com/science/article/pii/S0959440X99000160
8 M. Gustafsson https://www.nature.com/articles/nmeth.1612
9, 16 Moiré pattern https://giphy.com/gifs/animated-gif-processing-creative-coding-
10DhrOkl4VnHfq
9 Homer’s donut https://giphy.com/gifs/doughnut-N04Fkkzhf9slO
9 SMLM – Eiffel tower https://www.youtube.com/watch?v=RE70GuMCzww
10 Fourier picture https://commons.wikimedia.org/wiki/File:Fourier2.jpg
10 Fourier series MAF Review
11 Fourier transform 2D MAF Review
12 Fourier transform 3D MAF Review
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Image attribution
Slide Info Link
13 Lens = Fourier transform MAF Review
13 Mind blown https://knowyourmeme.com/memes/mind-blown
15 OTF https://commons.wikimedia.org/wiki/File:Illustration_of_the_optical_transfer
_function_and_its_relation_to_image_quality_v2.svg
15 USAF-1951 chart https://commons.wikimedia.org/wiki/File:USAF-1951.svg
16 Moiré pattern MAF Review
17 SIM in Fourier space MAF Review
17 SIM in Fourier space
bottom
https://onlinelibrary.wiley.com/doi/full/10.1046/j.1365-2818.2000.00710.x
18 SIM HeLa MAF Review
https://onlinelibrary.wiley.com/doi/full/10.1046/j.1365-2818.2000.00710.x
19 SIM reconstruction
artifacts
Hendrik Deschout, former Scientific Officer at CCI
https://www.sciencedirect.com/science/article/pii/S003040181831054X?via%
3Dihub
24 NPC application https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2916659/
25 Non-linear SIM MAF Review
https://www.pnas.org/content/109/3/E135.long
20, 27 Pictures from CCI https://cf.gu.se/english/centre_for_cellular_imaging
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Structured Illumination Microscopy - Fundamentals and Applications

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