With the advent of modern-day computational imagers, the phase of the optical transfer function may no longer be summarily ignored. This study discusses some important properties of the phase transfer function (PTF) of digital incoherent imaging systems and their implications on the performance and characterization of these systems. The effects of aliasing and sub-pixel image shifts on the phase of the complex frequency response of these sampled systems are described, including an examination of the specific case of moderate aliasing. Key properties of this function in aliased imaging systems are derived and their potential treatment to a range of diverse applications encompassing traditional and computational imaging systems is discussed.

© 2011 OSA

1. H. H. Hopkins, “Image shift, phase distortion and the optical transfer function,” Opt. Acta (Lond.)31(3), 345–368 (1984). [CrossRef]
2. K.-J. Rosenbruch and R. Gerschler, “The Meaning of the Phase Transfer Function and the Modular Transfer Function in Using OTF as a Criterion for Image Quality,” Optik (Stuttg.)55(2), 173–182 (1980) (In German).
3. C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, 1988), pp. 207–208.
4. J. Mait, R. Athale, and J. van der Gracht, “Evolutionary paths in imaging and recent trends,” Opt. Express11(18), 2093–2101 (2003). [CrossRef] [PubMed]
5. E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt.34(11), 1859–1866 (1995). [CrossRef] [PubMed]
6. W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems, Volume 2, Physical Image Formation, 1st ed. (Wiley-VCH, November 7, 2005). pp. 446.
7. M. Somayaji and M. P. Christensen, “Enhancing form factor and light collection of multiplex imaging systems by using a cubic phase mask,” Appl. Opt.45(13), 2911–2923 (2006). [CrossRef] [PubMed]
8. M. Demenikov and A. R. Harvey, “Image artifacts in hybrid imaging systems with a cubic phase mask,” Opt. Express18(8), 8207–8212 (2010). [CrossRef] [PubMed]
9. J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), pp. 60–62.
10. R. Barakat and A. Houston, “Transfer Function of an Optical System in the Presence of Off-Axis Aberrations,” J. Opt. Soc. Am.55(9), 1142–1148 (1965). [CrossRef]
11. R. E. Hufnagel, “Significance of the Phase of Optical Transfer Functions,” J. Opt. Soc. Am.58(11), 1505–1506 (1968). [CrossRef]
12. W. Wittenstein, J. C. Fontanella, A. R. Newbery, and J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Act.29(1), 41–50 (1982). [CrossRef]
13. R. H. Vollmerhausen, D. A. Reago, and R. G. Driggers, Analysis and Evaluation of Sampled Imaging Systems (SPIE Press, 2010), Ch-3, PP 68.
14. R. D. Fiete, “Image quality and λFN/p for remote sensing systems,” Opt. Eng.38(7), 1229–1240 (1999). [CrossRef]
15. B. Tatian, “Method for obtaining the transfer function from the edge response function,” J. Opt. Soc. Am.55(8), 1014–1019 (1965).
16. D. Williams and P. Burns, “Low-frequency MTF estimation for digital imaging devices using slanted-edge analysis,” Proc. SPIE5294, 93–101 (2003). [CrossRef]
17. V. R. Bhakta, M. Somayaji, and M. P. Christensen, “Phase Transfer Function of Sampled Imaging Systems,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CTuB1.
18. H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centering errors and their influence on optical image quality,” Br. J. Appl. Phys.17(1), 33–54 (1966). [CrossRef]
19. V. R. Bhakta, M. Somayaji, and M. P. Christensen, “Image-Based Measurement of Phase Transfer Function,” in Digital Image Processing and Analysis, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DMD1.

Appl. Opt.

• E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt.34(11), 1859–1866 (1995). [CrossRef] [PubMed]
• M. Somayaji and M. P. Christensen, “Enhancing form factor and light collection of multiplex imaging systems by using a cubic phase mask,” Appl. Opt.45(13), 2911–2923 (2006). [CrossRef] [PubMed]

Br. J. Appl. Phys.

• H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centering errors and their influence on optical image quality,” Br. J. Appl. Phys.17(1), 33–54 (1966). [CrossRef]

J. Opt. Soc. Am.

• B. Tatian, “Method for obtaining the transfer function from the edge response function,” J. Opt. Soc. Am.55(8), 1014–1019 (1965).
• R. Barakat and A. Houston, “Transfer Function of an Optical System in the Presence of Off-Axis Aberrations,” J. Opt. Soc. Am.55(9), 1142–1148 (1965). [CrossRef]
• R. E. Hufnagel, “Significance of the Phase of Optical Transfer Functions,” J. Opt. Soc. Am.58(11), 1505–1506 (1968). [CrossRef]

Opt. Act.

• W. Wittenstein, J. C. Fontanella, A. R. Newbery, and J. Baars, “The Definition of the OTF and the Measurement of Aliasing for Sampled Imaging Systems,” Opt. Act.29(1), 41–50 (1982). [CrossRef]

Opt. Acta (Lond.)

• H. H. Hopkins, “Image shift, phase distortion and the optical transfer function,” Opt. Acta (Lond.)31(3), 345–368 (1984). [CrossRef]

Opt. Eng.

• R. D. Fiete, “Image quality and λFN/p for remote sensing systems,” Opt. Eng.38(7), 1229–1240 (1999). [CrossRef]

Opt. Express

• J. Mait, R. Athale, and J. van der Gracht, “Evolutionary paths in imaging and recent trends,” Opt. Express11(18), 2093–2101 (2003). [CrossRef] [PubMed]
• M. Demenikov and A. R. Harvey, “Image artifacts in hybrid imaging systems with a cubic phase mask,” Opt. Express18(8), 8207–8212 (2010). [CrossRef] [PubMed]

Optik (Stuttg.)

• K.-J. Rosenbruch and R. Gerschler, “The Meaning of the Phase Transfer Function and the Modular Transfer Function in Using OTF as a Criterion for Image Quality,” Optik (Stuttg.)55(2), 173–182 (1980) (In German).

Proc. SPIE

• D. Williams and P. Burns, “Low-frequency MTF estimation for digital imaging devices using slanted-edge analysis,” Proc. SPIE5294, 93–101 (2003). [CrossRef]

Other

• V. R. Bhakta, M. Somayaji, and M. P. Christensen, “Phase Transfer Function of Sampled Imaging Systems,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CTuB1.
• V. R. Bhakta, M. Somayaji, and M. P. Christensen, “Image-Based Measurement of Phase Transfer Function,” in Digital Image Processing and Analysis, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DMD1.
• J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), pp. 60–62.
• C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, 1988), pp. 207–208.
• W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems, Volume 2, Physical Image Formation, 1st ed. (Wiley-VCH, November 7, 2005). pp. 446.
• R. H. Vollmerhausen, D. A. Reago, and R. G. Driggers, Analysis and Evaluation of Sampled Imaging Systems (SPIE Press, 2010), Ch-3, PP 68.

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