Image formation by use of continuously self-imaging gratings and diffractive axicons

When illuminated by a plane wave, continuously self-imaging gratings (CSIGs) produce a field whose intensity profile is a propagation- and wavelength-invariant biperiodic array of bright spots. In the case of an extended and incoherent source, we show that CSIGs produce multiple images of the source. The fundamental properties of these gratings will be derived. In particular, methods to assess the image quality in angle of CSIGs will be introduced. It turns out that this new type of pinhole-array camera works on the same principle as diffractive axicons, which are known to produce wavelength-invariant nondiffracting beams. The formalism developed for CSIGs will be also extended to axicons. CSIGs and axicons both produce focal lines and can be robust in field, in compensation of a trade-off with the resolution. They also offer interesting properties in terms of compactness, achromaticity and long depth of focus for imaging systems. However, compared to classical imaging systems, they produce degraded images and an image processing is necessary to restore these images. Experimental images obtained with these components in the visible and infrared spectral ranges will be presented.

[1]  Jérôme Primot,et al.  Nondiffracting array generation using an N-wave interferometer , 1999 .

[2]  J Primot,et al.  Extended hartmann test based on the pseudoguiding property of a hartmann mask completed by a phase chessboard. , 2000, Applied optics.

[3]  Hsu-hsin Chu,et al.  Efficient generation of extended plasma waveguides with the axicon ignitor-heater scheme , 2004, InternationalQuantum Electronics Conference, 2004. (IQEC)..

[4]  Zhihua Ding,et al.  High-resolution optical coherence tomography over a large depth range with an axicon lens. , 2002, Optics letters.

[5]  Z Bin,et al.  Diffraction property of an axicon in oblique illumination. , 1998, Applied optics.

[6]  R. Edgar.  The Fresnel Diffraction Images of Periodic Structures , 1969 .

[7]  G. Häusler,et al.  Light sectioning with large depth and high resolution. , 1988, Applied optics.

[8]  C. Zapata-Rodriguez,et al.  Three-dimensional field distribution in the focal region of low-Fresnel-number axicons. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  Z. Jaroszewicz,et al.  Nonparaxial design of generalized axicons. , 1992, Applied optics.

[10]  Bin Zhao,et al.  Measurement method of spatial straightness error using non-diffracting beam and moiré-fringe technology , 2004 .

[11]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[12]  K Heggarty,et al.  Generation of achromatic and propagation-invariant spot arrays by use of continuously self-imaging gratings. , 2001, Optics letters.

[13]  Ari T. Friberg,et al.  Stationary-phase analysis of generalized axicons , 1996 .

[14]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[15]  Takuo Tanaka,et al.  Comparison of aberration between axicon and lens , 2000 .

[16]  L. Soroko,et al.  II Axicons and Meso-Optical Imaging Devices , 1989 .

[17]  S. Gull,et al.  Image reconstruction from incomplete and noisy data , 1978, Nature.

[18]  Ruediger Grunwald,et al.  Angular tolerance of Shack-Hartmann wavefront sensors with microaxicons. , 2007, Optics letters.

[19]  C Saloma,et al.  Imaging properties of axicon in a scanning optical system. , 1992, Applied optics.

[20]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[21]  Kishan Dholakia,et al.  Atom guiding along Laguerre-Gaussian and Bessel light beams , 2000 .

[22]  Zbigniew Jaroszewicz,et al.  Lens axicons in oblique illumination. , 2007, Applied optics.

[23]  Zbigniew Jaroszewicz,et al.  Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons. , 2003, Applied optics.