International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Since Year 2012 | Open Access | Double Blind Reviewed

ISSN: 2319-7064




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Research Paper | Physics Science | Iraq | Volume 5 Issue 3, March 2016


Study of Zernike Polynomials Properties for Oblique Elliptical Aperture at an Angle (? / 4) with X-Axis

Sanaa G. Abd [2] | Sundus Y. Hasan [2]


Abstract: In this research, some of the optical properties have been studied for oblique elliptical aperture at an angle ( / 4) with x-axis, by using Zernike polynomials. Zernike polynomials for circular aperture and Gram Schmidt orthogonalization method were adopted to find Zernike polynomials for the new aperture. And in this case the equations used are very complex, therefore, new coordinates m and n were used, that they were oblique at (/ 4) to both x and y axes respectively. The relationship between Zernike polynomials for the new aperture with first and third order aberrations was derived. And it found that aberrations of high orders were balanced with aberrations of lower orders, for example, third order coma aberration were balanced with first order tilt error, while the third order spherical and astigmatism aberrations were balanced with focus aberration of first order. The standard deviation is also found in this research for balanced and unbalanced aberrations for any value of aspect ratio.


Keywords: Zernike polynomials, stander deviation, aberrations, astigmatism


Edition: Volume 5 Issue 3, March 2016,


Pages: 1115 - 1124


How to Cite this Article?

Sanaa G. Abd, Sundus Y. Hasan, "Study of Zernike Polynomials Properties for Oblique Elliptical Aperture at an Angle (? / 4) with X-Axis", International Journal of Science and Research (IJSR), Volume 5 Issue 3, March 2016, pp. 1115-1124, https://www.ijsr.net/get_abstract.php?paper_id=NOV161358

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