Point spread function: Difference between revisions

Revision as of 17:05, 31 March 2020

Revision as of 00:27, 16 April 2020

Line 54:

The figure above illustrates the truncation of the incident spherical wave by the lens. In order to measure the point spread function — or impulse response function — of the lens, a perfect point source that radiates a perfect spherical wave in all directions of space is not needed. This is because the lens has only a finite (angular) bandwidth, or finite intercept angle. Therefore, any angular bandwidth contained in the source, which extends past the edge angle of the lens (i.e., lies outside the bandwidth of the system), is essentially wasted source bandwidth because the lens can't intercept it in order to process it. As a result, a perfect point source is not required in order to measure a perfect point spread function. All we need is a light source which has at least as much angular bandwidth as the lens being tested (and of course, is uniform over that angular sector). In other words, we only require a point source which is produced by a convergent (uniform) spherical wave whose half angle is greater than the edge angle of the lens.

Due to intrinsic limited resolution of the imaging systems, measured PSFs are not free of uncertainty.<ref>{{Cite journal|last=Ahi|first=Kiarash|last2=Shahbazmohamadi|first2=Sina|last3=Asadizanjani|first3=Navid|date=July 2017|title=Quality control and authentication of packaged integrated circuits using enhanced-spatial-resolution terahertz time-___domain spectroscopy and imaging|url=https://www.researchgate.net/publication/318712771|journal=Optics and Lasers in Engineering|volume=104|pages=274–284|doi=10.1016/j.optlaseng.2017.07.007|via=|bibcode=2018OptLE.104..274A}}</ref>. In imaging, it is desired to suppress the side-lobes of the imaging beam by [[apodization]] techniques. In the case of transmission imaging systems with Gaussian beam distribution, the PSF is modeled by the following equation<ref>{{Cite journal|last=Ahi|first=K.|date=November 2017|title=Mathematical Modeling of THz Point Spread Function and Simulation of THz Imaging Systems|journal=IEEE Transactions on Terahertz Science and Technology|volume=7|issue=6|pages=747–754|doi=10.1109/tthz.2017.2750690|issn=2156-342X|bibcode=2017ITTST...7..747A}}</ref>:

<math>PSF(f,z)=I_r(0,z,f)\exp(-z\alpha(f))-\dfrac{2\rho^2}{0.36{\frac{cka}{\text{NA}f}}\sqrt{{1+\left ( \frac{2\ln 2}{c\pi}\left ( \frac{\text{NA}}{0.56k} \right )^2 fz\right )}^2}},</math>