Editing Microscopy (section)

==== Deconvolution ====
Fluorescence microscopy is a powerful technique to show specifically labeled structures within a complex environment and to provide three-dimensional information of biological structures. However, this information is blurred by the fact that, upon illumination, all fluorescently labeled structures emit light, irrespective of whether they are in focus or not. So an image of a certain structure is always blurred by the contribution of light from structures that are out of focus. This phenomenon results in a loss of contrast especially when using objectives with a high resolving power, typically oil immersion objectives with a high numerical aperture.
[[File:THZPSF.jpg|thumb|247x247px|Mathematically modeled Point Spread Function of a pulsed THz laser imaging system.<ref>{{Cite book |last1=Ahi |first1=Kiarash |first2=Mehdi |last2=Anwar |title=Terahertz Physics, Devices, and Systems X: Advanced Applications in Industry and Defense |editor3-first=Tariq |editor3-last=Manzur |editor2-first=Thomas W |editor2-last=Crowe |editor1-first=Mehdi F |editor1-last=Anwar |date=2016-05-26 |chapter=Modeling of terahertz images based on x-ray images: a novel approach for verification of terahertz images and identification of objects with fine details beyond terahertz resolution |chapter-url=https://www.researchgate.net/publication/303563365  |volume=9856 |pages=985610 |doi=10.1117/12.2228685|series=Proceedings of SPIE |bibcode=2016SPIE.9856E..10A |s2cid=124315172 }}</ref>]]
However, blurring is not caused by random processes, such as light scattering, but can be well defined by the optical properties of the image formation in the microscope imaging system. If one considers a small fluorescent light source (essentially a bright spot), light coming from this spot spreads out further from our perspective as the spot becomes more out of focus. Under ideal conditions, this produces an "hourglass" shape of this [[point source]] in the third (axial) dimension. This shape is called the [[point spread function]] (PSF) of the microscope imaging system. Since any fluorescence image is made up of a large number of such small fluorescent light sources, the image is said to be "convolved by the point spread function". The mathematically modeled PSF of a terahertz laser pulsed imaging system is shown on the right.

The output of an imaging system can be described using the equation:

<math>s(x,y) = PSF(x,y) * o(x,y) + n</math>

Where {{math|<var>n</var>}} is the additive noise.<ref>{{Cite book|title=Fundamentals of Digital Image Processing|last=Solomon|first=Chris|publisher=John Wiley & Sons, Ltd|year=2010|isbn=978-0-470-84473-1}}</ref> Knowing this point spread function<ref>{{cite journal |author1=Nasse M. J. |author2=Woehl J. C. |title=Realistic modeling of the illumination point spread function in confocal scanning optical microscopy |journal=J. Opt. Soc. Am. A |volume=27 |issue=2 |pages=295–302 |year=2010 |doi=10.1364/JOSAA.27.000295 |pmid=20126241|bibcode=2010JOSAA..27..295N }}</ref> means that it is possible to reverse this process to a certain extent by computer-based methods commonly known as [[deconvolution]] microscopy.<ref>{{cite journal |vauthors=Wallace W, Schaefer LH, Swedlow JR |title=A workingperson's guide to deconvolution in light microscopy |journal=BioTechniques |volume=31 |issue=5 |pages=1076–8, 1080, 1082 passim |year=2001 |pmid=11730015 |doi=10.2144/01315bi01|doi-access=free }}</ref> There are various algorithms available for 2D or 3D deconvolution. They can be roughly classified in ''nonrestorative'' and ''restorative'' methods. While the nonrestorative methods can improve contrast by removing out-of-focus light from focal planes, only the restorative methods can actually reassign light to its proper place of origin. Processing fluorescent images in this manner can be an advantage over directly acquiring images without out-of-focus light, such as images from [[confocal microscopy]], because light signals otherwise eliminated become useful information. For 3D deconvolution, one typically provides a series of images taken from different focal planes (called a Z-stack) plus the knowledge of the PSF, which can be derived either experimentally or theoretically from knowing all contributing parameters of the microscope.