Editing Point spread function (section)

==Introduction==
By virtue of the linearity property of optical ''non-coherent'' imaging systems, i.e.,

: ''Image''(''Object''<sub>1</sub> + ''Object''<sub>2</sub>) = ''Image''(''Object''<sub>1</sub>) + ''Image''(''Object''<sub>2</sub>)

the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as a weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the ''images'' of these impulse functions. This is known as the ''superposition principle'', valid for [[linear systems]]. The images of the individual object-plane impulse functions are called point spread functions (PSF), reflecting the fact that a mathematical ''point'' of light in the object plane is ''spread'' out to form a finite area in the image plane. (In some branches of mathematics and physics, these might be referred to as [[Green's functions]] or [[impulse response]] functions. PSFs are considered impulse response functions for imaging systems.
[[File:PSF Deconvolution V.png|thumb|265x265px|Application of PSF: Deconvolution of the mathematically modeled PSF and the low-resolution image enhances the resolution.<ref name=Kiarash1>{{Cite journal |last1=Ahi |first1=Kiarash |first2=Mehdi |last2=Anwar |editor3-first=Tariq |editor3-last=Manzur |editor2-first=Thomas W |editor2-last=Crowe |editor1-first=Mehdi F |editor1-last=Anwar |date=May 26, 2016 |title=Developing terahertz imaging equation and enhancement of the resolution of terahertz images using deconvolution |url=https://www.researchgate.net/publication/303563271 |journal=Proc. SPIE 9856, Terahertz Physics, Devices, and Systems X: Advanced Applications in Industry and Defense, 98560N |volume=9856 |pages=98560N |doi=10.1117/12.2228680|series=Terahertz Physics, Devices, and Systems X: Advanced Applications in Industry and Defense |bibcode=2016SPIE.9856E..0NA |s2cid=114994724 }}</ref>]]
When the object is divided into discrete point objects of varying intensity, the image is computed as a sum of the PSF of each point.  As the PSF is typically determined entirely by the imaging system (that is, microscope or telescope), the entire image can be described by knowing the optical properties of the system. This imaging process is usually formulated by a [[convolution]] equation. In [[microscope image processing]] and [[astronomy]], knowing the PSF of the measuring device is very important for restoring the (original) object with [[deconvolution]]. For the case of laser beams, the PSF can be mathematically modeled using the concepts of [[Gaussian beam]]s.<ref name=Kiarash2>{{Cite journal |last1=Ahi |first1=Kiarash |first2=Mehdi |last2=Anwar  |editor3-first=Tariq |editor3-last=Manzur |editor2-first=Thomas W |editor2-last=Crowe |editor1-first=Mehdi F |editor1-last=Anwar |date=May 26, 2016 |title=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 |url=https://www.researchgate.net/publication/303563365 |journal=Proc. SPIE 9856, Terahertz Physics, Devices, and Systems X: Advanced Applications in Industry and Defense, 98560N |volume=9856 |page=985610 |doi=10.1117/12.2228685|series=Terahertz Physics, Devices, and Systems X: Advanced Applications in Industry and Defense |bibcode=2016SPIE.9856E..10A |s2cid=124315172 }}</ref> For instance, deconvolution of the mathematically modeled PSF and the image, improves visibility of features and removes imaging noise.<ref name=Kiarash1/>