Intelligent reduction of zero-order diffraction in Fourier optical systems

2005 ◽  
Vol 44 (10) ◽  
pp. 103602
Author(s):  
Yuexin Liu ◽  
Bo Wang ◽  
Ruyan Guo ◽  
Francis T. S. Yu
Keyword(s):  
Zero Order ◽  
Optical Systems ◽  
Order Diffraction

The imaging properties of electron beams in arbitrary static electromagnetic fields

1952 ◽  
Vol 245 (894) ◽  
pp. 155-187 ◽  
Keyword(s):  
Variational Equation ◽  
Chromatic Aberration ◽  
Relativistic Correction ◽  
Zero Order ◽  
Second Order ◽  
Optical Systems ◽  
Characteristic Functions ◽  
Tensor Calculus ◽  
Paraxial Ray ◽  
Imaging Properties

Electron-optical systems with curved axes—such as mass spectrographs and certain beta-ray spectrometers—have long been in practical use, but there has been available no complete theory of the aberrations of such systems. It is the object of the present paper to construct such a theory and to demonstrate, by an example, its application to practical problems. An appropriate co-ordinate system is set up by means of a ray-axis together with its normal and binormal. The electric and magnetic fields are then investigated with the help of tensor calculus; the variational principle of electron optics is also put into tensor form. The integrand of the variational equation may be separated into a series of polynomials, one of which determines the paraxial imaging properties of the system and the rest of which determine the aberrations. The condition is established for which, upon an appropriate transformation, either of the paraxial ray equations contains only one off-axis co-ordinate. Subsequent investigations are restricted to systems, which are termed ‘orthogonal’, for which this condition is satisfied. It is shown that, in a certain sense, no orthogonal electron-optical system can be wholly divergent. The second-order aberration and the zero-order and paraxial chromatic aberrations are then investigated by the method of perturbation characteristic functions. All formulae are given in their relativistic forms but their non-relativistic forms are indicated; formulae are therefore given for the calculation of the zero-order and paraxial relativistic correction. It is indicated to what extent one forfeits control over the second-order aberration—and hence over the paraxial chromatic aberration also—by specifying that the paraxial behaviour of rays should be Gaussian. As an example, the imaging properties of a helical beam moving in the field of a pair of coaxial cylindrical electrodes are calculated. There is also an appendix which gives formulae for the effect upon aberrations of a change in the aperture position.

scholarly journals Alternative approach to variable wavelength interferometry

2020 ◽  
Vol 12 (4) ◽  
pp. 112
Author(s):  
Dariusz Litwin ◽  
Kamil Radziak ◽  
Jacek Galas
Keyword(s):  
Classical Method ◽  
Incidence Angle ◽  
Visible Spectrum ◽  
Thickness Measurement ◽  
Optical Path Difference ◽  
Zero Order ◽  
Optical Systems ◽  
Fast Variable ◽  
Current Increase ◽  
Measurement Science

The paper presents an alternative technique of calculation the retardance of quartz waveplates. The technique utilizes continuously tuned wavelength, which identifies the zero-order fringe and simultaneously facilitates high repeatability of the optical path difference across the entire visible spectrum. Unlike in classical method, precise monitoring of the current increase or decrease of the interference order is not required. The discussion includes comparison of the standard deviation between the classical and novel approaches. Full Text: PDF ReferencesM. Pluta, Advanced Light Microscopy (Vol. 3, PWN, Elsevier, Warszawa-Amsterdam-London-New York-Tokyo, 1993). DirectLinkM. Pluta, "Object-adapted variable-wavelength interferometry. I. Theoretical basis", Journal of Opt. Soc. Am., A4(11), 2107 (1987). CrossRef M. Pluta, "Variable wavelength microinterferometry of textile fibres", J. Microscopy, 149(2), 97 (1988). CrossRef M. Pluta, "On double‐refracting microinterferometers which suffer from a variable interfringe spacing across the image plane", Journal of Microscopy, 145(2), 191 (1987). CrossRef M. Pluta, "Variable wavelength interferometry of birefringent retarders", Opt. Laser Technology, 19(3), 131 (1987). CrossRef D. Litwin, A. M. Sadik, "Computer-aided variable wavelength Fourier transform polarizing microscopy of birefringent fibers", Optica Applicata 28(2), 139 (1998). DirectLink A. Sadik, W. A. Ramadan, D. Litwin, "Variable incidence angle method combined with Pluta polarizing interference microscope for refractive index and thickness measurement of single-medium fibres", Measurement Science and Technology, IOP Publishing 14(10), 1753 (2003). CrossRef J. Galas, S. Sitarek; D. Litwin; M. Daszkiewicz, "Fringe image analysis for variable wavelength interferometry", Proc. SPIE 10445, 1044504 (2017). CrossRef D. Litwin, J. Galas, N. Błocki, "Automated variable wavelength interferometry in reflected light mode", Proc.SPIE 6188, 61880F (2006). CrossRef J. Galas, D. Litwin, M. Daszkiewicz, "New approach for identifying the zero-order fringe in variable wavelength interferometry", Proc. SPIE 10142, 101421R (2016). CrossRef D. Litwin, J. Galas, M. Daszkiewicz, T. Kryszczyński, A. Czyżewski, K. Radziak, "Dedicated optical systems of the Institute of Applied Optics", Phot. Lett. Pol., vol. 11, no. 2, pp. 29-31, (2019). CrossRef D. Litwin, K. Radziak, J. Galas "A fast variable wavelength interferometer", Proc. SPIE 11581, 115810O, (2020). CrossRef

The splitting mechanism of zero order diffraction pattern by roof prisms

2013 ◽  
Vol 42 (4) ◽  
pp. 367-375
Author(s):  
Lu Jinjun ◽  
Sun Xueping ◽  
Zhu Weibing
Keyword(s):  
Diffraction Pattern ◽  
Zero Order ◽  
Order Diffraction

Effect of Phase-Shifting Error on Deformation Evaluation Using Phase-Shifting Digital Holography

2006 ◽  
Vol 326-328 ◽  
pp. 27-30
Author(s):  
Xin Kang ◽  
Xiao Yuan He ◽  
Cho Jui Tay ◽  
C. Quan
Keyword(s):  
Computer Simulation ◽  
Digital Holography ◽  
Zero Order ◽  
Phase Shifting ◽  
Phase Shifting Technique ◽  
Order Diffraction

Phase-shifting technique is an effect way to suppress the zero order diffraction and the conjugate term in digital holography. However the phase-shifting error will influence inevitably the evaluation precision in practice operation. In this paper, the deformation evaluation errors by means of two kinds of four-step phase-shifting algorithms, which are in common use in digital holography, are analyzed and compared by computer simulation. In addition, the phase-shifting errors may cumulate or not according to different phase-shifting techniques, and both cases are considered in this paper. The results based on the digital in-line holography show that the two four-step phase-shifting algorithms possess different sensitivity to the phase-shifting errors, and the preferable one, which is more immune to the phase-shifting errors, is educed in conclusion.

Fast mask CD uniformity measurement using zero order diffraction from memory array pattern

2009 ◽  
Author(s):  
Jinseok Heo ◽  
Jinhong Park ◽  
Jeongho Yeo ◽  
Seongwoon Choi ◽  
Woosung Han
Keyword(s):  
Zero Order ◽  
Memory Array ◽  
Array Pattern ◽  
Order Diffraction

scholarly journals The study of color digital holography free from the zero-order diffraction interruption

2011 ◽  
Vol 60 (3) ◽  
pp. 034204
Author(s):  
Fan Ze-Bin ◽  
Song Qing-He ◽  
Li Jun-Chang ◽  
Tankam Patrice ◽  
Picart Pascal
Keyword(s):  
Digital Holography ◽  
Zero Order ◽  
Order Diffraction

Heat reflecting optical filter based on zero-order diffraction

2008 ◽  
Vol 516 (14) ◽  
pp. 4656-4658 ◽  
Author(s):  
Harald Walter ◽  
Alexander Stuck
Keyword(s):  
Optical Filter ◽  
Zero Order ◽  
Order Diffraction

Restoration and Enhancement of Digitally Reconstructed Holographic Images

2011 ◽  
pp. 105-120
Author(s):  
Rajeev Srivastava
Keyword(s):  
Image Quality ◽  
Image Data ◽  
Speckle Noise ◽  
Zero Order ◽  
Speckle Reduction ◽  
Average Intensity ◽  
Robust Algorithms ◽  
Order Diffraction ◽  
High Pass

Holograms can be reconstructed optically or digitally with the use of computers and other related devices. During the reconstruction phase of a hologram by optical or digital methods, some errors may also be introduced that may degrade the quality of obtained hologram, and may lead to a misinterpretation of the holographic image data, which may not be useful for particular application. The basic common errors are zero-order diffraction and speckle noise. These errors have more undesirable effects in digital than in optical holography because the systems of recording and visualization used in the digital holography are extremely sensitive to them or inclusively increase them. The zero-order diffraction can be removed by using high pass filters with low cut-off frequencies and by subtracting the average intensity of all pixels of the hologram image from the original hologram image. Further, the speckle noise introduced during the formation of digital holographic images, which is multiplicative in nature, reduces the image quality, which may not be suitable for specific applications. As the range of applications get broader, demands toward better image quality increases. Hence, the suppression of noise, higher resolution of the reconstructed images, precise parameter adjustment, and faster, more robust algorithms are the essential issues. In this chapter, the various methods available in literature for enhancement and speckle reduction of digital holographic images have been discussed, and a comparative study of results has been presented.

Elimination of zero-order diffraction in digital off-axis holography

2004 ◽  
Vol 240 (4-6) ◽  
pp. 261-267 ◽  
Author(s):  
Yimo Zhang ◽  
Qieni Lü ◽  
Baozhen Ge
Keyword(s):  
Zero Order ◽  
Order Diffraction
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