Approximate analytical expression of flattened Gaussian beams passing through a paraxial optical system with an annular aperture

2012 ◽  
Author(s):  
Longsheng Xiao ◽  
Yingxiong Qin ◽  
Xiahui Tang
Keyword(s):  
Optical System ◽  
Gaussian Beams ◽  
Approximate Analytical Expression ◽  
Analytical Expression ◽  
Annular Aperture

Approximate analytical expressions of Laguerre-Gaussian beams passing through a paraxial optical system with an annular aperture

Optik ◽  
2004 ◽  
Vol 115 (7) ◽  
pp. 311-316 ◽  
Author(s):  
Zhangrong Mei ◽  
Daomu Zhao ◽  
Juguang Gu ◽  
Haidan Mao
Keyword(s):  
Optical System ◽  
Gaussian Beams ◽  
Annular Aperture ◽  
Analytical Expressions

Propagation of Bessel-modulated Gaussian beams through a paraxial ABCD optical system with an annular aperture

Optik ◽  
2005 ◽  
Vol 116 (11) ◽  
pp. 521-526 ◽  
Author(s):  
Zhangrong Mei ◽  
Daomu Zhao ◽  
Xiaofeng Wei ◽  
Feng Jing ◽  
Qihua Zhu
Keyword(s):  
Optical System ◽  
Gaussian Beams ◽  
Annular Aperture ◽  
Abcd Optical System

scholarly journals Degradation of multiphoton signal and resolution when focusing through a planar interface with index mismatch: Analytical approximation and numerical investigation

2018 ◽  
Vol 11 (04) ◽  
pp. 1850020
Author(s):  
Ping Qiu ◽  
Chen He
Keyword(s):  
Spherical Aberration ◽  
Numerical Aperture ◽  
Analytical Approximation ◽  
Planar Interface ◽  
Excitation Wavelength ◽  
Physical Parameters ◽  
Approximate Analytical Expression ◽  
Excitation Light ◽  
Analytical Expression ◽  
Imaging Depth

Multiphoton microscopy (MPM) is an invaluable tool for visualizing subcellular structures in biomedical and life sciences. High-numerical-aperture (NA) immersion objective lenses are used to deliver excitation light to focus inside the biological tissue. The refractive index of tissue is commonly different from that of the immersion medium, which introduces spherical aberration, leading to signal and resolution degradation as imaging depth increases. However, the explicit dependence of this index mismatch-induced aberration on the involved physical parameters is not clear, especially its dependence on index mismatch. Here, from the vectorial equations for focusing through a planar interface between materials of mismatched refractive indices, we derive an approximate analytical expression for the spherical aberration. The analytical expression explicitly reveals the dependence of spherical aberration on index mismatch, imaging depth and excitation wavelength, from which we can expect the following qualitative behaviors: (1) Multiphoton signal and resolution degradation is less for longer excitation wavelength, (2) a longer wavelength tolerates a higher index mismatch, (3) a longer wavelength tolerates a larger imaging depth and (4) both signal and resolution degradations show the same dependence on imaging depth, regardless of NA or immersion on the condition that the integration angle is the same. Detailed numerical simulation results agree quite well with the above expectations based on the analytical approximation. These theoretical results suggest the use of long excitation wavelength to better suppress index mismatch-induced signal and resolution degradation in deep-tissue MPM.

Long Focal-Length Optical System Using Annular Aperture

2010 ◽  
Vol 30 (4) ◽  
pp. 1140-1143
Author(s):  
张蕊蕊 Zhang Ruirui ◽  
沈为民 Shen Weimin
Keyword(s):  
Optical System ◽  
Focal Length ◽  
Annular Aperture

Propagation of off-axial Hermite–cosine–Gaussian beams through an apertured and misaligned ABCD optical system

2003 ◽  
Vol 224 (1-3) ◽  
pp. 5-12 ◽  
Author(s):  
Daomu Zhao ◽  
Haidan Mao ◽  
Weichun Zhang ◽  
Shaomin Wang
Keyword(s):  
Optical System ◽  
Gaussian Beams ◽  
Abcd Optical System
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