Read e-book online Optical Scanning Holography with MATLAB® PDF

By Ting-Chung Poon

Optical scanning holography (OSH) is an rising niche with many strength novel purposes, corresponding to three-D trend attractiveness, three-D microscopy, three-D cryptography, and 3-D optical distant sensing.

Optical Scanning Holography with MATLAB® introduces readers to the newest advances of digital (or electronic) holography and succinctly covers the required mathematical historical past and wave optics that pertain to Fourier optics and holography. The reader is guided via modeling of the idea and functions using MATLAB®. Optical scanning holography is defined in a way that allows readers to start imposing their very own setups for novel OSH purposes.

Optical Scanning Holography with MATLAB® contains tutorials (with a number of MATLAB® examples through the textual content) and study fabric, in addition to new principles and insights for graduate scholars, scientists, and engineers operating within the fields of Fourier optics, optical scanning imaging, and holography.

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B#  C# Ñ 45! exp’ “. #D #1 D 2ÐBß Cà DÑ œ expÐ  45! 3-11) If Eq. 3-11) is now used in Eq. 3-9), we obtain <: ÐBß Cà DÑ œ <:! ÐBß CÑ ‡ 2ÐBß Cà DÑ œ expÐ  45! DÑ ‚ expÖ 45! #1 D ( ( <:! ÐBw ß Cw Ñ  45! Cw . 3-12) is called the Fresnel diffraction formula and describes the Fresnel diffraction of a beam during propagation and having an arbitrary initial complex profile, <:! ÐBß CÑ. To obtain the output field distribution <: ÐBß Cà DÑ at a distance D away from the input (the location of the diffracting screen), we would simply convolve the input field distribution, <:!

X ] . 1-8) where we have used the first of the constitutive relations [Eq. 1-6a)] and assumed % to be time-independent. 1-9) in Eq. % # X ]œ. + f(f † X ). 1-10) If we also assume the permittivity, %, to be space-independent, then we can now recast the first of Maxwell’s equations [Eq. 1-11) f†X œ @ , % by using the first of the constitutive relations [Eq. 1-6a)]. Incorporating Eq. 1-11) into Eq. % # X ]" œ. 1-12) 24 Optical Scanning Holography with MATLAB which is a vector wave equation having source terms on the right-hand side.

TÑ into the 3-D scalar wave equation given by Eq. 2-4), we have Ò # <: # <: # <: Ð4=! Ñ# = <: ÐBß Cà DÑexpÐ4=! tÑ Ð4 + + Ó exp t Ñ œ ! # <: + + Ó œ  B# C # D # @# which is the Helmholtz equation [Eq. 3-2)], where we have incorporated the fact that 5! œ =! /@. Note that the Helmholtz equation contains no time variable. 3 Derivation of Eq. , YBC , of Eq. # <: × œ ! # G: 5B# #  5 Ð"   Ñ G: œ !. # C  ! D # which has the solution CÐDÑ œ C! DÑ where C! Ñ is given as the initial condition. Using this result, the solution to Eq.

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