Fourier Optics Analysis of Phase and Amplitude Grating with Uniform Beam

2020 ◽  
pp. 91-95
Author(s):  
Prashant Povel Dwivedi
Keyword(s):  
Fourier Optics ◽  
Uniform Beam

scholarly journals Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

2018 ◽  
Vol 5 (2) ◽  
pp. 171717 ◽  
Author(s):  
Srivatsa Bhat K ◽  
Ranjan Ganguli
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Beam Equation ◽  
The Finite Element Method ◽  
Rayleigh Beam ◽  
Uniform Beam ◽  
Governing Differential Equation ◽  
The Given

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

Introduction to Fourier Optics, Second Edition

1996 ◽  
Vol 35 (5) ◽  
pp. 1513 ◽  
Author(s):  
Joseph W. Goodman
Keyword(s):  
Fourier Optics

Effect of Hub Radius on the Vibrations of a Uniform Bar

1956 ◽  
Vol 23 (2) ◽  
pp. 287-290
Author(s):  
W. E. Boyce
Keyword(s):  
Lower Bounds ◽  
Constant Speed ◽  
Upper And Lower Bounds ◽  
Beam Length ◽  
Uniform Beam

Abstract Methods are discussed for obtaining upper and lower bounds on the frequencies of a uniform beam, rotating at a constant speed about an axis at one end, and vibrating transversely to the plane of rotation. Previous results are extended to include the case of a nonzero hub radius. Bounds on the first two frequencies are given for several ratios of hub radius to beam length. These show that the frequencies depend almost linearly on the hub radius for various rotational speeds.

The New Physical Optics Notebook: Tutorials in Fourier Optics

1990 ◽  
Vol 37 (5) ◽  
pp. 1005-1005 ◽  
Author(s):  
Christopher Dainty
Keyword(s):  
Fourier Optics ◽  
Physical Optics
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