Abstract

In our previous paper [Appl. Opt. 51, 8490 (2012)] we considered the Zernike polynomials for a unit annular ellipse aperture. In that paper many equations were used and were solved by MATLAB language and by hand, and many times these rewritten equations had some written mistakes. In the Diaz and Mahajan comment [Appl. Opt. 52, 5962 (2013)] on the work, some remarks were true and others were not. In this reply, we will discuss their comment in detail.

© 2013 Optical Society of America

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References

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  1. S. Y. Hasan and A. S. Shaker, “Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration,” Appl. Opt. 51, 8490–8497 (2012).
    [CrossRef]
  2. J. A. Diaz and V. N. Mahajan, “Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration: comment,” Appl. Opt. 52, 5962–5964 (2013).
  3. E. Suli and D. F. Mayers, An Introduction to Numerical Analysis (Cambridge, 2003).
  4. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. 11, pp. 1–53.

2013

2012

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. 11, pp. 1–53.

Diaz, J. A.

Hasan, S. Y.

Mahajan, V. N.

Mayers, D. F.

E. Suli and D. F. Mayers, An Introduction to Numerical Analysis (Cambridge, 2003).

Shaker, A. S.

Suli, E.

E. Suli and D. F. Mayers, An Introduction to Numerical Analysis (Cambridge, 2003).

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. 11, pp. 1–53.

Appl. Opt.

Other

E. Suli and D. F. Mayers, An Introduction to Numerical Analysis (Cambridge, 2003).

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. 11, pp. 1–53.

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Equations (3)

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Z2(x,y)=Z2(x,y)11b1x2b1x2Z1(x,y)Z2(x,y)dydxkkbkx2bkx2Z1(x,y)Z2(x,y)dydx11b1x2b1x2Z12(x,y)dydxkkbkx2bkx2Z12(x,y)dydx*Z1(x,y).
g=[1,x,y,2*(x2+y2)1,x2y2,2*x*y,3*x*(x2+y2)2*x,3*y*(x2+y2)2*y,6*(x2+y2)26*(x2+y2)+1,x33*x*y2,3*x2*yy3,4*x3*y4*x*y3,8*x*y*(x2+y2)6*x*y,4*x43*x24*y4+3*y2,x46*x2*y2+y4]
C4=12(k2b2(3b2k212k28)+3k4+3b4+32b2).

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