Design of axially super-resolving phase filters using the method of generalized projections

The design of pupil phase filters that super-resolve the axial intensity distribution with controlled side-lobe peak intensity under high numerical aperture conditions can be accomplished by incorporating the theory of electromagnetic diffraction in the method of generalized projections (MGP). The MGP results are however strongly dependent on the starting conditions and the applied constraints. In this report we study this dependence by investigating different starting pupil functions and introducing modifications to the applied constraints. Methods are described and implemented to generate a systematic set of starting conditions that enable a more thorough search of the solutions space. This approach generated results for which 95% have a super-resolved central-lobe, yet only a subset of those solutions offer a satisfactory compromise between super-resolution of the central-lobe and increased intensity of the axial side-lobes. These solutions are presented and discussed in the context of specific applications.

[1]  J Rosen.  Synthesis of nondiffracting beams in free space. , 1994, Optics letters.

[2]  Colin J R Sheppard,et al.  Annular pupils, radial polarization, and superresolution. , 2004, Applied optics.

[3]  Toufic G. Jabbour,et al.  Vector diffraction analysis of high numerical aperture focused beams modified by two- and three-zone annular multi-phase plates. , 2006, Optics express.

[4]  Colin J. R. Sheppard,et al.  Axial behavior of pupil-plane filters , 1988 .

[5]  Aharon Levi,et al.  Image restoration by the method of generalized projections with application to restoration from magnitude , 1984 .

[6]  Toufic G. Jabbour,et al.  Axial field shaping under high-numerical-aperture focusing. , 2007, Optics letters.

[7]  Stephen M. Kuebler.  NONLINEAR OPTICS, APPLICATIONS | Three-Dimensional Microfabrication , 2005 .

[8]  Silvania F. Pereira,et al.  Superresolution by means of polarisation, phase and amplitude pupil masks , 2004 .

[9]  M. Cagigal,et al.  Analytical design of superresolving phase filters , 2004 .

[10]  Joseph Shamir,et al.  Synthesis of three-dimensional light fields and applications , 2002, Proc. IEEE.

[11]  Mario Bertero,et al.  Superresolving masks for incoherent high-numerical-aperture scanning microscopy in three dimensions , 1998 .

[12]  Bernard C. Kress.  Digital diffractive optics , 2000 .

[13]  Liren Liu,et al.  Three-dimensional superresolution by three-zone complex pupil filters. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  Vidal F. Canales,et al.  Three-dimensional control of the focal light intensity distribution by analytically designed phase masks , 2005 .

[15]  Satoshi Kawata,et al.  Scaling laws of voxels in two-photon photopolymerization nanofabrication , 2003 .

[16]  H. Ando,et al.  Optical Head With Annular Phase-shifting Apodizer , 1993 .

[17]  Stefan Hell,et al.  Axial superresolution with ultrahigh aperture lenses. , 2002, Optics express.

[18]  G. Saavedra,et al.  Quasi‐spherical focal spot in two‐photon scanning microscopy by three‐ring apodization , 2005, Microscopy research and technique.

[19]  J Rosen,et al.  Synthesis of an arbitrary axial field profile by computer-generated holograms. , 1994, Optics letters.

[20]  E. Wolf,et al.  Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[21]  Rishi Kant,et al.  Superresolution and increased depth of focus: An inverse problem of vector diffraction , 2000 .

[22]  Robert D. Guenther,et al.  Encyclopedia of modern optics , 2005 .

[23]  Frank Wyrowski,et al.  Diffraction efficiency of analog and quantized digital amplitude holograms: analysis and manipulation , 1990 .

[24]  J Shamir,et al.  Control of wave-front propagation with diffractive elements. , 1994, Optics letters.

[25]  G. Michael Morris,et al.  Axial superresolution with phase-only pupil filters , 1998 .

[26]  Vidal F. Canales,et al.  Focusing properties of annular binary phase filters , 2004 .

[27]  Frank Wyrowski,et al.  Diffractive optical elements: iterative calculation of quantized, blazed phase structures , 1990 .

[28]  E. Wolf,et al.  Electromagnetic diffraction in optical systems - I. An integral representation of the image field , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[29]  Genaro Saavedra,et al.  Reduction of focus size in tightly focused linearly polarized beams , 2004 .

[30]  Genaro Saavedra,et al.  Quasi-isotropic 3-D resolution in two-photon scanning microscopy. , 2005, Optics express.

[31]  Pedro Andrés,et al.  Three-dimensional superresolution by annular binary filters , 1999 .

[32]  Pedro Andrés,et al.  Tunable axial superresolution by annular binary filters. Application to confocal microscopy , 1995 .

[33]  Phase-only diffractive optical element for improving the beam quality of a vertical-cavity surface-emitting laser array , 2004 .

[34]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[35]  Jim Swoger,et al.  Tailoring the axial shape of the point spread function using the Toraldo concept. , 2002, Optics express.

[36]  Yingbai Yan,et al.  Design of three-dimensional superresolution filters and limits of axial optical superresolution. , 2003, Applied optics.

[37]  Tony Wilson,et al.  Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes , 1999 .