Ulf Schnars · Claas Falldorf John Watson · Werner Jüptner Digital Holography and Wavefront Sensing Principles, Techniques and Applications Second Edition Digital Holography and Wavefront Sensing Ulf Schnars Claas Falldorf (cid:129) ü John Watson Werner J ptner (cid:129) Digital Holography and Wavefront Sensing Principles, Techniques and Applications Second Edition 123 Ulf Schnars JohnWatson Hagen School ofEngineering Germany Universityof Aberdeen Aberdeen Claas Falldorf Scotland,UK Bremer Institutfürangewandte Strahltechnik(BIAS) Werner Jüptner Bremen Ritterhude Germany Germany ISBN 978-3-662-44692-8 ISBN 978-3-662-44693-5 (eBook) DOI 10.1007/978-3-662-44693-5 LibraryofCongressControlNumber:2014949296 SpringerHeidelbergNewYorkDordrechtLondon ©Springer-VerlagBerlinHeidelberg2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserof thework.Duplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsofthe CopyrightLawofthePublisher’slocation,initscurrentversion,andpermissionforusemustalwaysbe obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright ClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface to the Second Edition Life always bursts the boundaries of formulas Antoine de Saint Exupéry As we sat down to consider writing a new edition of Digital Holography, we, the original authors (U. Schnars and W. Jüptner), asked ourselves if the field had advanced sufficiently with enough new and novel developments to merit a second edition.TheanswerwasanoverwhelmingYESandcamefromseeingtheprofound developments and scale of applications to which digital holography, and in the widercontext3Dimagingtechnologiesingeneral,arenowbeingroutinelyapplied. In the intervening years, the evolution of digital holography has been, both, extensive and dramatic. Someoftheareasinwhichwehaveseenconsiderableadvancesandapplication includecomputationalwavefieldsensinganddigitalholographicmicroscopy,with ahugenumberofpapersbeingpublishedintheseandrelatedfields.Toreflectthese advancesadequatelyinourbookandtobroadenitsscope,weinvitedClaasFalldorf (BIAS) and John Watson (University of Aberdeen) to join us as co-authors. Claas works actively in wave field sensing using computational methods such as phase retrieval or computational shear interferometry. John is an international expert in digital holographic microscopy and, particularly, to underwater holography of aquatic organisms and particles; and also 3DTV and related fields. Both are ideal partners to support the approach and philosophy of the new edition. Accordingly,thissecondeditionhasbeensignificantlyrevisedandenlarged.We have extended the chapter on Digital Holographic Microscopy to incorporate new sections on particle sizing, particle image velocimetry and underwater holography. A new chapter now deals comprehensively and extensively with computational wavefieldsensing.Thesetechniquesrepresentafascinatingalternativetostandard interferometryandDigitalHolography.Theyenablewavefieldsensingwithoutthe requirement of a particular reference wave, thus allowing the use of low brilliance light sources and even liquid-crystal displays (LCD) for interferometric applica- tions. We believe that, in the coming years, computational wave field sensing will prove to be an excellent complement to Digital Holography to determine the full complex amplitude of wave fields. All the authors wish to thank colleagues past and present (too numerous to mention) with whom they have worked over the years. As with the first edition, v vi PrefacetotheSecondEdition several pictures and figures in this book originate from common publications with othercolleaguesandwethankthemforpermissiontodescribetheirworkandtouse their pictures. All of our co-workers are gratefully acknowledged. Bremen, May 2014 Ulf Schnars Aberdeen Claas Falldorf John Watson Werner Jüptner Preface to the First Edition Sag’ ich zum Augenblicke verweile doch, Du bist so schön J.W.v. Goethe, “Faust” An old dream of mankind and asign ofcultureisthe conservation ofmoments by taking an image of the world around. Pictures accompany the development of mankind. However, a picture is the two-dimensional projection of the three- dimensional world. The perspective—recognized in Europe in the Middle Ages— wasafirstapproachtoovercomethedifficultiesofimagingclosetoreality.Ittook up to the twentieth century to develop a real three-dimensional imaging: Gabor invented holography in 1948. Yet still one thing was missing: the phase of the objectwavecouldbereconstructedopticallybutnotbemeasureddirectly.Thelast huge step to the complete access of the object wave was Digital Holography. By Digital Holography the intensity and the phase of electromagnetic wave fields can be measured, stored, transmitted, applied to simulations and manipulated in the computer: An exciting new tool for the handling of light. WestartedourworkinthefieldofDigitalHolographyin1990.Ourmotivation mainly came from Holographic Interferometry, a method used with success for precisemeasurementofdeformationandshapeofopaquebodiesorrefractiveindex variations within transparent media. A major drawback of classical HI using pho- tographic plates was the costly process of film development. Even thermoplastic films used as recording medium did not solve the hologram development problem successfully. On the other hand the Electronic Speckle Pattern Interferometry (ESPI) and its derivate digital shearography reached a degree mature for applica- tions in industry. Yet, with these speckle techniques the recorded images are only correlatedandnotreconstructedasforHI.Characteristicfeaturesofholographylike thepossibilitytorefocusonotherobjectplanesinthereconstructionprocessarenot possible with speckle metrology. OurideawastotransferallmethodsofclassicalHIusingphotographicplatesto Digital Holography. Surprisingly, we discovered that Digital Holography offers more possibilities than classical HI: The wavefronts can be manipulated in the numerical reconstruction process, enabling operations not possible in optical holography. Especially the interference phase can be calculated directly from the holograms, without evaluation of an interference pattern. vii viii PrefacetotheFirstEdition The efficiency of Digital Holography depends strongly on the resolution of the electronictargetusedtorecordtheholograms.Whenwemadeourfirstexperiments in the 1990s of the last century, Charged Coupled Devices began to replace ana- logue sensors in cameras. The resolution of commercially available cameras was quite low, about some hundred pixels per line, and the output signal of cameras already equipped with CCDs was still analogue. In those days, digital sampling of cameraimages andrunningofroutines for numerical hologram reconstruction was only possible on special digital image processing hardware and not, as today, on ordinary PCs. The reconstruction of a hologram digitized with 512 × 512 pixels took about half an hour in 1991 on a Digital Image Processing unit developed at BIAS especially for optical metrology purposes. Nevertheless we made our first experiments with these types of cameras. Today, numerical reconstruction of holograms with 1 million pixel is possible nearly in real time on state-of-the-art PCs. Then, fully digital CCD cameras with 1 million pixels and smaller pixels than those of the previous camera generation emerged on the market. These cameras showed better performance and first applications in optical metrology became possible. Today, digital CCD cameras with 4 million pixels are standard. The tremendous development inopto-electronicsand indata processing pushed Digital Holography to new perspectives: It is applied with success in optical deformation and strain analysis, shape measurement, microscopy and for investi- gationsofflowsinliquidsandgases.Inthisbookwemakethetrialtodescribethe principlesofthismethodandtoreportonthevariousapplications.Wetookpainsto prepare the manuscript carefully and to avoid mistakes. However, we are not perfect. Comments, suggestions for improvements or corrections are therefore welcome and will be considered in potential further editions. Some pictures in this book originate from common publications with other co-authors. All of our co-workers, especially W. Osten, Th. Kreis, D. Holstein, S. Seebacher, H.-J. Hartmann and V. Kebbel are gratefully acknowledged. Contents 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Fundamental Principles of Holography . . . . . . . . . . . . . . . . . . . . . 5 2.1 Light Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Coherence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Temporal Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.3 Spatial Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.5 Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 Holography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6.1 Hologram Recording and Reconstruction . . . . . . . . . . . . 20 2.6.2 The Imaging Equations . . . . . . . . . . . . . . . . . . . . . . . . 23 2.7 Holographic Interferometry. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.7.1 Generation of Holographic Interferograms . . . . . . . . . . . 25 2.7.2 Displacement Measurement by HI. . . . . . . . . . . . . . . . . 28 2.7.3 Holographic Contouring. . . . . . . . . . . . . . . . . . . . . . . . 30 2.7.4 Refractive Index Measurement by HI. . . . . . . . . . . . . . . 34 2.7.5 Phase Shifting HI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.7.6 Phase Unwrapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 Digital Holography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1 General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Numerical Reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Reconstruction by the Fresnel Approximation. . . . . . . . . 42 3.2.2 Reconstruction by the Convolution Approach. . . . . . . . . 49 3.2.3 Digital Fourier Holography. . . . . . . . . . . . . . . . . . . . . . 52 3.3 Shift and Suppression of DC-Term and Conjugate Image . . . . . . 53 3.3.1 Suppression of the DC Term . . . . . . . . . . . . . . . . . . . . 53 3.3.2 Tilted Reference Wave. . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.3 Phase Shifting Digital Holography. . . . . . . . . . . . . . . . . 56 ix x Contents 3.4 Recording of Digital Holograms . . . . . . . . . . . . . . . . . . . . . . . 58 3.4.1 Image Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.4.2 Spatial Frequency Requirements . . . . . . . . . . . . . . . . . . 62 3.4.3 Cameras for Digital Hologram Recording. . . . . . . . . . . . 63 3.4.4 Recording Set-ups. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4.5 Stability Requirements. . . . . . . . . . . . . . . . . . . . . . . . . 66 3.4.6 Light Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4 Digital Holographic Interferometry (DHI). . . . . . . . . . . . . . . . . . . 69 4.1 General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.2 Deformation Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.2.1 Quantitative Displacement Measurement. . . . . . . . . . . . . 70 4.2.2 Mechanical Materials Properties . . . . . . . . . . . . . . . . . . 74 4.2.3 Thermal Materials Properties . . . . . . . . . . . . . . . . . . . . 78 4.2.4 Non-destructive Testing. . . . . . . . . . . . . . . . . . . . . . . . 81 4.3 Shape Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3.1 Two-Illumination-Point Method. . . . . . . . . . . . . . . . . . . 85 4.3.2 Two- and Multi-wavelength Method . . . . . . . . . . . . . . . 86 4.3.3 Hierarchical Phase Unwrapping. . . . . . . . . . . . . . . . . . . 89 4.4 Measurement of Refractive Index Variations. . . . . . . . . . . . . . . 92 5 Digital Holographic Particle Sizing and Microscopy. . . . . . . . . . . . 95 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.2 Recording and Replay Conditions . . . . . . . . . . . . . . . . . . . . . . 96 5.2.1 In-line Recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.2.2 Off-axis Recording . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2.3 Image Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2.4 Holographic Depth-of-Field and Depth-of-Focus. . . . . . . 102 5.2.5 Optical Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3 Data Processing and Autofocusing of Holographic Images . . . . . 104 5.4 Some Applications in Imaging and Particle Sizing. . . . . . . . . . . 105 5.4.1 Particle Sizing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.4.2 Digital Holographic Microscopy (DHM) . . . . . . . . . . . . 107 5.4.3 Holographic Tomography. . . . . . . . . . . . . . . . . . . . . . . 110 5.4.4 Phase Shifting DHM . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.5 Particle Image Velocimetry (PIV) . . . . . . . . . . . . . . . . . 114 5.4.6 Underwater Digital Holography. . . . . . . . . . . . . . . . . . . 115 6 Special Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.1 Applications Using Short Coherence Length Light. . . . . . . . . . . 121 6.1.1 Light-in-Flight Measurements. . . . . . . . . . . . . . . . . . . . 121 6.1.2 Short-Coherence Tomography. . . . . . . . . . . . . . . . . . . . 126 6.2 Endoscopic Digital Holography. . . . . . . . . . . . . . . . . . . . . . . . 127 6.3 Optical Reconstruction of Digital Holograms. . . . . . . . . . . . . . . 129