Optimal Phase Masks for High Contrast Imaging Applications

Phase-only optical elements can provide a number of important functions for high-contrast imaging. This thesis presents analytical and numerical optical design methods for accomplishing specific tasks, the most significant of which is the precise suppression of light from a distant point source. Instruments designed for this purpose are known as coronagraphs. Here, advanced coronagraph designs are presented that offer improved theoretical performance in comparison to the current state-of-the-art. Applications of these systems include the direct imaging and characterization of exoplanets and circumstellar disks with high sensitivity. Several new coronagraph designs are introduced and, in some cases, experimental support is provided. In addition, two novel high-contrast imaging applications are discussed: the measurement of sub-resolution information using coronagraphic optics and the protection of sensors from laser damage. The former is based on experimental measurements of the sensitivity of a coronagraph to source displacement. The latter discussion presents the current state of ongoing theoretical work. Beyond the mentioned applications, the main outcome of this thesis is a generalized theory for the design of optical systems with one of more phase masks that provide precise control of radiation over a large dynamic range, which is relevant in various high-contrast imaging scenarios. The optimal phase masks depend on the necessary tasks, the maximum number of optics, and application specific performance measures. The challenges and future prospects of this work are discussed in detail.

[1]  L. Pueyo,et al.  HIGH-CONTRAST IMAGING WITH AN ARBITRARY APERTURE: ACTIVE COMPENSATION OF APERTURE DISCONTINUITIES , 2012, 1211.6112.

[2]  Enrico Santamato,et al.  Tunable liquid crystal q-plates with arbitrary topological charge. , 2011, Optics express.

[3]  B. Macintosh,et al.  Angular Differential Imaging: A Powerful High-Contrast Imaging Technique , 2005, astro-ph/0512335.

[4]  William H. Richardson,et al.  Bayesian-Based Iterative Method of Image Restoration , 1972 .

[5]  E Hasman,et al.  Pancharatnam--Berry phase in space-variant polarization-state manipulations with subwavelength gratings. , 2001, Optics letters.

[6]  A. Vaughan,et al.  Simplified solution of diffraction from a Lyot system. , 1988, Applied optics.

[7]  Jason J. Wang,et al.  Discovery and spectroscopy of the young jovian planet 51 Eri b with the Gemini Planet Imager , 2015, Science.

[8]  Peyman Milanfar,et al.  Statistical analysis of achievable resolution in incoherent imaging , 2004, SPIE Optics + Photonics.

[9]  Reduction of diffraction of use of a Lyot stop , 1973 .

[10]  Frans Snik,et al.  Performance characterization of a broadband vector Apodizing Phase Plate coronagraph. , 2014, Optics express.

[11]  Wayne M. Gibbons,et al.  Surface-mediated alignment of nematic liquid crystals with polarized laser light , 1991, Nature.

[12]  G. V. Uspleniev,et al.  The Phase Rotor Filter , 1992 .

[13]  Alexis Carlotti,et al.  Apodized phase mask coronagraphs for arbitrary apertures , 2013 .

[14]  D. Mawet,et al.  An image of an exoplanet separated by two diffraction beamwidths from a star , 2010, Nature.

[15]  Grover A. Swartzlander,et al.  Nodal areas in coherent beams , 2015 .

[16]  Erez Hasman,et al.  Formation of helical beams by use of Pancharatnam-Berry phase optical elements. , 2002, Optics letters.

[17]  R. Soummer Apodized Pupil Lyot Coronagraphs for Arbitrary Telescope Apertures , 2004, astro-ph/0412221.

[18]  R. Vanderbei,et al.  Optimal pupil apodizations of arbitrary apertures for high-contrast imaging. , 2011, Optics express.

[19]  Ebrahim Karimi,et al.  Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface , 2014, Light: Science & Applications.

[20]  D. Malacara-Hernández,et al.  PRINCIPLES OF OPTICS , 2011 .

[21]  Shane Jacobson,et al.  HiCIAO: the Subaru Telescope's new high-contrast coronographic imager for adaptive optics , 2008, Astronomical Telescopes + Instrumentation.

[22]  Robert W Boyd,et al.  Rapid generation of light beams carrying orbital angular momentum. , 2013, Optics express.

[23]  B. Lyot The study of the solar corona and prominences without eclipses (George Darwin Lecture, 1939) , 1939 .

[24]  C. Aime,et al.  Stellar coronagraphy with prolate apodized circular apertures , 2003 .

[25]  Michael F. Becker,et al.  Laser-Induced Damage To Silicon CCD Imaging Sensors , 1989, Defense, Security, and Sensing.

[26]  Zhongyi Guo,et al.  Ultra-thin optical vortex phase plate based on the metasurface and the angular momentum transformation , 2015 .

[27]  Law,et al.  Optical vortex solitons observed in Kerr nonlinear media. , 1992, Physical review letters.

[28]  Joseph P. Kirk,et al.  Phase-Only Complex-Valued Spatial Filter* , 1971 .

[29]  Robert D. Fiete,et al.  Comparison of SNR image quality metrics for remote sensing systems , 2001 .

[30]  David Mouillet,et al.  Pupil stabilization for SPHERE's extreme AO and high performance coronagraph system. , 2007, Optics express.

[31]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[32]  A. W. Lohmann,et al.  Computer-generated binary holograms , 1969 .

[33]  I. Khoo,et al.  Nonlinear-absorbing fiber array for large-dynamic-range optical limiting application against intense short laser pulses , 2004 .

[34]  Kenneth Riehl,et al.  Comparison of two common aerial reconnaissance image quality measures , 1996, Optics & Photonics.

[35]  A. Labeyrie,et al.  The Four‐Quadrant Phase‐Mask Coronagraph. I. Principle , 2000 .

[36]  Toshiaki Nose,et al.  Liquid Crystal Polarizers with Axially Symmetrical Properties , 1989 .

[37]  B. Macintosh,et al.  Direct Imaging of Multiple Planets Orbiting the Star HR 8799 , 2008, Science.

[38]  T. Pertsch,et al.  A broad-band scalar vortex coronagraph , 2013, 1307.4347.

[39]  Jeong-Ki Pack,et al.  Numerical simulation of optical wave propagation through random media , 1988 .

[40]  W. Traub,et al.  A Coronagraph with a Band-limited Mask for Finding Terrestrial Planets , 2002, astro-ph/0203455.

[41]  G. Swartzlander,et al.  Peering into darkness with a vortex spatial filter. , 2001, Optics letters.

[42]  Martin Schadt,et al.  Optical patterning of multi-domain liquid-crystal displays with wide viewing angles , 1996, Nature.

[43]  Marco W. Beijersbergen,et al.  Helical-wavefront laser beams produced with a spiral phaseplate , 1994 .

[44]  M. Berry Quantal phase factors accompanying adiabatic changes , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[45]  Steven A. Israel,et al.  Metrics to estimate image quality in compressed video sequences , 2007, SPIE Defense + Commercial Sensing.

[46]  J. P. Woerdman,et al.  Production and characterization of spiral phase plates for optical wavelengths. , 2004, Applied optics.

[47]  Gordon A. H. Walker,et al.  A Planetary Companion to γ Cephei A , 2003 .

[48]  J. Angel,et al.  First On-Sky High-Contrast Imaging with an Apodizing Phase Plate* , 2007, astro-ph/0702324.

[49]  R. Skidanov,et al.  Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[50]  R. Gerchberg A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[51]  Kerstin Vogler,et al.  Table Of Integrals Series And Products , 2016 .

[52]  Natalie M. Batalha,et al.  Exploring exoplanet populations with NASA’s Kepler Mission , 2014, Proceedings of the National Academy of Sciences.

[53]  C. Marois,et al.  A NEW ALGORITHM FOR POINT SPREAD FUNCTION SUBTRACTION IN HIGH-CONTRAST IMAGING: A DEMONSTRATION WITH ANGULAR DIFFERENTIAL IMAGING , 2007 .

[54]  T. Mazeh,et al.  The unseen companion of HD114762: a probable brown dwarf , 1989, Nature.

[55]  Miles J. Padgett,et al.  Observation of chromatic effects near a white-light vortex , 2003 .

[56]  Francesco Maria Grimaldi Physico-mathesis de lumine, coloribus, et iride, aliisque adnexis libri duo, in quorum primo afferuntur nova experimenta, & rationes ab ijs deductae pro substantialitate luminis , 1981 .

[57]  J. Maxwell VIII. A dynamical theory of the electromagnetic field , 1865, Philosophical Transactions of the Royal Society of London.

[58]  Xiang Zhu,et al.  Removing Atmospheric Turbulence via Space-Invariant Deconvolution , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[59]  Auguste Fresnel Memoire sur la diffraction de la lumiere , 1819 .

[60]  Enrico Santamato,et al.  Liquid crystal spatial-mode converters for the orbital angular momentum of light , 2012, 1209.4534.

[61]  Erez Hasman,et al.  Polychromatic vectorial vortex formed by geometric phase elements. , 2007, Optics letters.

[62]  Mikhail V. Vasnetsov,et al.  Screw Dislocations in Light Wavefronts , 1992 .

[63]  Lisa Poyneer,et al.  The Gemini Planet Imager , 2006, SPIE Astronomical Telescopes + Instrumentation.

[64]  Junchang Li,et al.  Algorithm study of Collins formula and inverse Collins formula. , 2008, Applied optics.

[65]  J C Leachtenauer,et al.  General Image-Quality Equation: GIQE. , 1997, Applied optics.

[66]  M. Quintanilla,et al.  Holographic optical element to generate achromatic vortices. , 2013, Optics express.

[67]  Z. Sacks,et al.  Holographic formation of optical-vortex filaments , 1998 .

[68]  R. Vanderbei,et al.  Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs , 2003 .

[69]  M F Becker,et al.  Mechanisms for laser-induced functional damage to silicon charge-coupled imaging sensors. , 1993, Applied optics.

[70]  W H Lee,et al.  Binary computer-generated holograms. , 1979, Applied optics.

[71]  Frantz Martinache,et al.  The Subaru Coronagraphic Extreme AO project , 2009 .

[72]  G. Nordin,et al.  Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region. , 1999, Optics express.

[73]  David Mouillet,et al.  Apodized Lyot coronagraph for VLT-SPHERE: laboratory tests and performances of a first prototype in the visible , 2008, Astronomical Telescopes + Instrumentation.

[74]  B. Eberle,et al.  Research on laser protection: an overview of 20 years of activities at Fraunhofer IOSB , 2013, Optics/Photonics in Security and Defence.

[75]  Ravi K. Komanduri,et al.  Multi-twist retarders: broadband retardation control using self-aligning reactive liquid crystal layers. , 2013, Optics express.

[76]  Dimitri Mawet,et al.  Optimized focal and pupil plane masks for vortex coronagraphs on telescopes with obstructed apertures , 2015, SPIE Optical Engineering + Applications.

[77]  D. Mawet,et al.  RING-APODIZED VORTEX CORONAGRAPHS FOR OBSCURED TELESCOPES. I. TRANSMISSIVE RING APODIZERS , 2013, 1309.3328.

[78]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[79]  O. Guyon Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging , 2003, astro-ph/0301190.

[80]  C. Jenkins Optical vortex coronagraphs on ground-based telescopes , 2007, 0709.0153.

[81]  D. Mawet,et al.  Laboratory demonstration of a mid-infrared AGPM vector vortex coronagraph , 2013, 1304.1180.

[82]  C. Fabron,et al.  SPHERE: a planet finder instrument for the VLT , 2006, Astronomical Telescopes + Instrumentation.

[83]  J. Goodman,et al.  Spectrum shaping with parity sequences. , 1972, Applied optics.

[84]  E. Cady,et al.  HIGH PERFORMANCE LYOT AND PIAA CORONAGRAPHY FOR ARBITRARILY SHAPED TELESCOPE APERTURES , 2013, 1305.6686.

[85]  S. Pancharatnam,et al.  Generalized theory of interference, and its applications , 1956 .

[86]  David M. Shemo,et al.  Optical Vectorial Vortex Coronagraphs using Liquid Crystal Polymers: theory, manufacturing and laboratory demonstration. , 2009, Optics express.

[87]  Andrew G. White,et al.  Generation of optical phase singularities by computer-generated holograms. , 1992, Optics letters.

[88]  Frantz Martinache,et al.  On-sky demonstration of low-order wavefront sensing and control with focal plane phase mask coronagraphs , 2015 .

[89]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[90]  Cornelis Uiterwaal,et al.  Creation of optical vortices in femtosecond pulses. , 2005, Optics express.

[91]  M. J. Miller,et al.  General optical limiting requirements , 1998, Optics + Photonics.

[92]  Grover A. Swartzlander,et al.  Lyot-plane phase masks for improved high-contrast imaging with a vortex coronagraph , 2015, 1509.05750.

[93]  Bertrand Mennesson,et al.  FUNDAMENTAL LIMITATIONS OF HIGH CONTRAST IMAGING SET BY SMALL SAMPLE STATISTICS , 2014, 1407.2247.

[94]  C. Aime,et al.  Achromatic dual-zone phase mask stellar coronagraph , 2003 .

[95]  M. Escuti,et al.  Direct-writing of complex liquid crystal patterns. , 2014, Optics express.

[96]  Jeffrey A. Davis,et al.  Encoding amplitude information onto phase-only filters. , 1999, Applied optics.

[97]  R. Soummer,et al.  DETECTION AND CHARACTERIZATION OF EXOPLANETS AND DISKS USING PROJECTIONS ON KARHUNEN–LOÈVE EIGENIMAGES , 2012, 1207.4197.

[98]  D. Mawet,et al.  Subwavelength surface-relief gratings for stellar coronagraphy. , 2005, Applied optics.

[99]  M. Tamura,et al.  Design and laboratory demonstration of an achromatic vector vortex coronagraph. , 2013, Optics express.

[100]  Prachyathit Kanburapa White-Light Optical Vortex Coronagraph , 2012 .

[101]  T. Fusco,et al.  Final performance and lesson-learned of SAXO, the VLT-SPHERE extreme AO: from early design to on-sky results , 2014, Astronomical Telescopes and Instrumentation.

[102]  John E. Krist,et al.  The Vector Vortex Coronagraph: sensitivity to central obscuration, low-order aberrations, chromaticism, and polarization , 2010, Astronomical Telescopes + Instrumentation.

[103]  S. Barnett,et al.  Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body , 2014 .

[104]  Otto Struve,et al.  Proposal for a project of high-precision stellar radial velocity work , 1952 .

[105]  J. Goodman Introduction to Fourier optics , 1969 .

[106]  D. Frail,et al.  A planetary system around the millisecond pulsar PSR1257 + 12 , 1992, Nature.

[107]  L. Marrucci,et al.  Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. , 2006, Physical review letters.

[108]  R. Lane,et al.  Simulation of a Kolmogorov phase screen , 1992 .

[109]  K. D. GROUND-BASED CORONAGRAPHY WITH HIGH-ORDER ADAPTIVE OPTICS , 2001 .

[110]  M. Berry The Adiabatic Phase and Pancharatnam's Phase for Polarized Light , 1987 .

[111]  J. Yu High Dynamic Range Imaging Using a Deformable Mirror for Space Coronography , 1995 .

[112]  K. Ulaczyk,et al.  One or more bound planets per Milky Way star from microlensing observations , 2012, Nature.

[113]  Grover A. Swartzlander,et al.  Vortex-phase filtering technique for extracting spatial information from unresolved sources. , 2014, Applied optics.

[114]  Russell A Chipman,et al.  Creating vortex retarders using photoaligned liquid crystal polymers. , 2008, Optics letters.

[115]  F. Roddier,et al.  STELLAR CORONOGRAPH WITH PHASE MASK , 1997 .

[116]  Gordon A. H. Walker,et al.  A search for substellar companions to solar-type stars , 1988 .

[117]  Ronald G. Driggers,et al.  Surveillance and Reconnaissance Imaging Systems: Modeling and Performance Prediction , 2001 .

[118]  Federico Capasso,et al.  Ultra-thin plasmonic optical vortex plate based on phase discontinuities , 2012 .

[119]  D. Mouillet,et al.  A giant planet candidate near a young brown dwarf - Direct VLT/NACO observations using IR wavefront sensing , 2004 .

[120]  L. Lucy An iterative technique for the rectification of observed distributions , 1974 .

[121]  G. F. Brand Phase Singularities in Beams , 1999 .

[122]  S. Ridgway,et al.  Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle , 2004, astro-ph/0412179.

[123]  Grover A. Swartzlander,et al.  Reducing the risk of laser damage in a focal plane array using linear pupil-plane phase elements. , 2015, Applied optics.

[124]  José R. Salgueiro,et al.  Making optical vortices with computer-generated holograms , 2008 .

[125]  R. Galicher,et al.  Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph III. Hybrid Approach: Optical Design and Diffraction Analysis , 2005 .

[126]  Marcel Carbillet,et al.  Apodized Lyot coronagraph for SPHERE/VLT: II. Laboratory tests and performance , 2011 .

[127]  S. A. Collins Lens-System Diffraction Integral Written in Terms of Matrix Optics , 1970 .

[128]  Hoi Sing Kwok,et al.  Photoalignment of Liquid Crystalline Materials: Physics and Applications , 2008 .

[129]  T. F. Boggess,et al.  A review of optical limiting mechanisms and devices using organics, fullerenes, semiconductors and other materials , 1993 .

[130]  Laird M Close,et al.  Astronomical demonstration of an optical vortex coronagraph. , 2008, Optics express.

[131]  Dimitri Mawet,et al.  Improving vector vortex waveplates for high-contrast coronagraphy. , 2013, Optics express.

[132]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[133]  David Lafreniere,et al.  Direct Imaging and Spectroscopy of a Planetary-Mass Candidate Companion to a Young Solar Analog , 2008, 0809.1424.

[134]  M. Vasnetsov,et al.  Laser beams with screw dislocations in their wavefronts , 2003 .

[135]  John R. Schott,et al.  Remote Sensing: The Image Chain Approach , 1996 .

[136]  Fionn Murtagh,et al.  Deconvolution in Astronomy: A Review , 2002 .

[137]  David M. Shemo,et al.  THE VECTOR VORTEX CORONAGRAPH: LABORATORY RESULTS AND FIRST LIGHT AT PALOMAR OBSERVATORY , 2009, 0912.2287.

[138]  James R Fienup,et al.  Application of the general image-quality equation to aberrated imagery. , 2010, Applied optics.

[139]  Robert D. Fiete,et al.  Image quality of sparse-aperture designs for remote sensing , 2002 .

[140]  T. Brown,et al.  Detection of Planetary Transits Across a Sun-like Star , 1999, The Astrophysical journal.

[141]  Joseph V. Hajnal,et al.  Singularities in the transverse fields of electromagnetic waves. I. Theory , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[142]  M. Berry,et al.  Dislocations in wave trains , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[143]  Erez Hasman,et al.  Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings. , 2002, Optics letters.

[144]  Frantz Martinache,et al.  Lyot-based Low Order Wavefront Sensor for Phase-mask Coronagraphs: Principle, Simulations and Laboratory Experiments , 2014, 1404.7201.

[145]  Claude Aime,et al.  Phase mask coronagraphy using a Mach-Zehnder interferometer , 2009 .

[146]  M. Kenworthy,et al.  FOCAL PLANE WAVEFRONT SENSING USING RESIDUAL ADAPTIVE OPTICS SPECKLES , 2013, 1303.0527.

[147]  L. Milne‐Thomson A Treatise on the Theory of Bessel Functions , 1945, Nature.

[148]  Grover A. Swartzlander,et al.  Zernike amplitude pupil apodization for vortex coronagraphy with obscured apertures , 2014, 1412.8731.

[149]  John M. Irvine,et al.  National imagery interpretability rating scales (NIIRS): overview and methodology , 1997, Optics & Photonics.

[150]  S. Khonina,et al.  Diffraction of a plane, finite-radius wave by a spiral phase plate. , 2006, Optics letters.

[151]  M. Mayor,et al.  A Jupiter-mass companion to a solar-type star , 1995, Nature.

[152]  Dimitri Mawet,et al.  Development of a subwavelength grating vortex coronagraph of topological charge 4 (SGVC4) , 2014, Astronomical Telescopes and Instrumentation.

[153]  David M. Shemo,et al.  Vortex retarders produced from photo-aligned liquid crystal polymers. , 2008, Optics express.

[154]  Jason E. Riggs,et al.  Organic and inorganic optical limiting materials. From fullerenes to nanoparticles , 1999 .

[155]  Jiaxuan Han Imaging Unresolved Object using Vortex Mode Detection , 2012 .

[156]  Alexander A. Manenkov,et al.  Fundamental mechanisms of laser-induced damage in optical materials: today’s state of understanding and problems , 2014 .

[157]  G. Biener,et al.  Spiral phase elements obtained by use of discrete space-variant subwavelength gratings , 2005 .

[158]  Johanan L. Codona,et al.  Imaging extrasolar planets by stellar halo suppression in separately corrected color bands , 2004 .

[159]  J. Hajnal Singularities in the transverse fields of electromagnetic waves. II. Observations on the electric field , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[160]  Fr'ed'eric Bouchard,et al.  Achromatic orbital angular momentum generator , 2014, 1407.0065.

[161]  Pierre Baudoz,et al.  The four-quadrant phase-mask coronagraph : white light laboratory results with an achromatic device , 2006 .

[162]  Pierre Baudoz,et al.  Post-coronagraphic tip-tilt sensing for vortex phase masks: The QACITS technique , 2015, 1509.06158.

[163]  Julien H. Girard,et al.  Searching for companions down to 2 AU from β Pictoris using the L′-band AGPM coronagraph on VLT/NACO , 2013, 1311.4298.

[164]  Grover A. Swartzlander,et al.  Optical vortex coronagraphy with an elliptical aperture. , 2013, Applied optics.

[165]  Obtaining spatial information from an extremely unresolved source. , 2011, Optics letters.

[166]  W. Traub,et al.  A laboratory demonstration of the capability to image an Earth-like extrasolar planet , 2007, Nature.

[167]  D. Mawet,et al.  Annular Groove Phase Mask Coronagraph , 2005 .

[168]  G. Swartzlander,et al.  Optical vortex coronagraph. , 2005, Optics letters.

[169]  Thomas Young,et al.  I. The Bakerian Lecture. Experiments and calculations relative to physical optics , 1804, Philosophical Transactions of the Royal Society of London.

[170]  Joseph P. Ellul,et al.  A Buttable 2048 X 96 Element TDI Imaging Array , 1984, Optics & Photonics.

[171]  Nelson Tabiryan,et al.  Fabrication of liquid crystal polymer axial waveplates for UV-IR wavelengths. , 2009, Optics express.

[172]  A. Campillo,et al.  CHARACTERISTICS OF A LOW F-NUMBER BROADBAND VISIBLE THERMAL OPTICAL LIMITER , 1993 .

[173]  L. Abe,et al.  Apodized Lyot coronagraph for SPHERE/VLT , 2011 .

[174]  H. Kikuta,et al.  Achromatic quarter-wave plates using the dispersion of form birefringence. , 1997, Applied optics.