This paper presents a technique for reconstructing two interfering wavefronts by analyzing their 3D interference field pattern. The method is based on the numerical inverse problem and will present a robust algorithm for reconstructing of wavefronts. Several simulations are done to validate the proposed method.

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1. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).
2. D. Malacara, Optical Shop Testing (John Wiley & Sons, 1998).
3. R. Tyson, Principles of Adaptive Optics (CRC Press, 2010).
4. J. M. Geary, Introduction to Wavefront Sensors (SPIE Press, 1995).
5. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).
6. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73(11), 1434–1441 (1983). [CrossRef]
7. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984). [CrossRef]
8. J. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Opt. 43(2), 289–293 (1996). [CrossRef]
9. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
10. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21(12), 842–844 (1996). [CrossRef] [PubMed]
11. K. R. Freischlad, “Absolute interferometric testing based on reconstruction of rotational shear,” Appl. Opt. 40(10), 1637–1648 (2001). [CrossRef] [PubMed]
12. R. Kowarschik, L. Wenke, T. Baade, M. Esselbach, A. Kiessling, G. Notni, and K. Uhlendorf, “Optical measurements with phase-conjugate mirrors,” Appl. Phys. B 69(5-6), 435–443 (1999). [CrossRef]
13. C. Ai and J. C. Wyant, “Absolute testing of flats by using even and odd functions,” Appl. Opt. 32(25), 4698–4705 (1993). [CrossRef] [PubMed]
14. U. Griesmann, “Three-flat test solutions based on simple mirror symmetry,” Appl. Opt. 45(23), 5856–5865 (2006). [CrossRef] [PubMed]
15. R. de la Fuente and E. López Lago, “Mach-Zehnder diffracted beam interferometer,” Opt. Express 15(7), 3876–3887 (2007). [CrossRef] [PubMed]
16. M. T. Tavassoly and A. Darudi, “Reconstruction of interfering wavefronts by analyzing their interference pattern in three dimensions,” Opt. Commun. 175(1-3), 43–50 (2000). [CrossRef]
17. A. Darudi and M. T. Tavassoly, “Interferometric specification of lens (single and doublet) parameters,” Opt. Lasers Eng. 35(2), 79–90 (2001). [CrossRef]
18. A. Darudi, “Interferometry without reference wave,” (PhD Thesis, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran, 2001).
19. M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 2003).
20. F. Shen and A. Wang, “Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula,” Appl. Opt. 45(6), 1102–1110 (2006). [CrossRef] [PubMed]
21. D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999). [CrossRef]
22. M. Bass, Handbook of Optics (McGraw-Hill, 1995), Vol. I.
23. http://www.zemax.com

Appl. Opt.

• K. R. Freischlad, “Absolute interferometric testing based on reconstruction of rotational shear,” Appl. Opt. 40(10), 1637–1648 (2001). [CrossRef] [PubMed]
• C. Ai and J. C. Wyant, “Absolute testing of flats by using even and odd functions,” Appl. Opt. 32(25), 4698–4705 (1993). [CrossRef] [PubMed]
• U. Griesmann, “Three-flat test solutions based on simple mirror symmetry,” Appl. Opt. 45(23), 5856–5865 (2006). [CrossRef] [PubMed]
• F. Shen and A. Wang, “Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula,” Appl. Opt. 45(6), 1102–1110 (2006). [CrossRef] [PubMed]

Appl. Phys. B

• R. Kowarschik, L. Wenke, T. Baade, M. Esselbach, A. Kiessling, G. Notni, and K. Uhlendorf, “Optical measurements with phase-conjugate mirrors,” Appl. Phys. B 69(5-6), 435–443 (1999). [CrossRef]

J. Mod. Opt.

• J. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Opt. 43(2), 289–293 (1996). [CrossRef]

J. Opt. Soc. Am.

• R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

J. Opt. Soc. Am. A

• M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73(11), 1434–1441 (1983). [CrossRef]

Opt. Commun.

• N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984). [CrossRef]
• M. T. Tavassoly and A. Darudi, “Reconstruction of interfering wavefronts by analyzing their interference pattern in three dimensions,” Opt. Commun. 175(1-3), 43–50 (2000). [CrossRef]
• D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164(4-6), 233–245 (1999). [CrossRef]

Opt. Express

• R. de la Fuente and E. López Lago, “Mach-Zehnder diffracted beam interferometer,” Opt. Express 15(7), 3876–3887 (2007). [CrossRef] [PubMed]

Opt. Lasers Eng.

• A. Darudi and M. T. Tavassoly, “Interferometric specification of lens (single and doublet) parameters,” Opt. Lasers Eng. 35(2), 79–90 (2001). [CrossRef]

Opt. Lett.

• Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21(12), 842–844 (1996). [CrossRef] [PubMed]

Optik

• R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Other

• D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).
• D. Malacara, Optical Shop Testing (John Wiley & Sons, 1998).
• R. Tyson, Principles of Adaptive Optics (CRC Press, 2010).
• J. M. Geary, Introduction to Wavefront Sensors (SPIE Press, 1995).
• A. Darudi, “Interferometry without reference wave,” (PhD Thesis, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran, 2001).
• M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 2003).
• M. Bass, Handbook of Optics (McGraw-Hill, 1995), Vol. I.
• http://www.zemax.com

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