This content has been downloaded from IOPscience. Please scroll down to see the full text. Download details: IP Address: 170.106.202.8 This content was downloaded on 25/09/2021 at 11:50 Please note that terms and conditions apply. Physics of Digital Photography (Second Edition) IOP Series in Emerging Technologies in Optics and Photonics Series Editor R Barry Johnson a Senior Research Professor at Alabama A&M University, has been involved for over 50 years in lens design, optical systems design, electro-optical systems engineering, and photonics. He has been a faculty member at three academic institutions engaged in optics education and research, employed by a number of companies, and provided consulting services. Dr Johnson is an IOP Fellow, SPIE Fellow and Life Member, OSA Fellow, and was the 1987 President of SPIE. He serves on the editorial board of Infrared Physics & Technology and Advances in Optical Technologies. Dr Johnson has been awarded many patents, has published numerous papers and several books and book chapters, and was awarded the 2012 OSA/SPIE Joseph W Goodman Book Writing Award for Lens Design Fundamentals, Second Edition. He is a perennial co-chair of the annual SPIE Current Developments in Lens Design and Optical Engineering Conference. Foreword Until the 1960s, the field of optics was primarily concentrated in the classical areas of photography, cameras, binoculars, telescopes, spectrometers, colorimeters, radio- meters, etc. In the late 1960s, optics began to blossom with the advent of new types of infrared detectors, liquid crystal displays (LCD), light emitting diodes (LED), charge coupled devices (CCD), lasers, holography, fiber optics, new optical materials, advances in optical and mechanical fabrication, new optical design programs, and many more technologies. With the development of the LED, LCD, CCD and other electo-optical devices, the term ‘photonics’ came into vogue in the 1980s to describe the science of using light in development of new technologies and the performance of a myriad of applications. Today, optics and photonics are truly pervasive throughout society and new technologies are continuing to emerge. The objective of this series is to provide students, researchers, and those who enjoy self-teaching with a wide- ranging collection of books that each focus on a relevant topic in technologies and application of optics and photonics. These books will provide knowledge to prepare the reader to be better able to participate in these exciting areas now and in the future. The title of this series is Emerging Technologies in Optics and Photonics where ‘emerging’ is taken to mean ‘coming into existence,’‘coming into maturity,’ and ‘coming into prominence.’ IOP Publishing and I hope that you find this Series of significant value to you and your career. Physics of Digital Photography (Second Edition) D A Rowlands IOP Publishing, Bristol, UK ª IOP Publishing Ltd 2020 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organizations. Permission to make use of IOP Publishing content other than as set out above may be sought at [email protected]. D A Rowlands has asserted his right to be identified as the author of this work in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. ISBN 978-0-7503-2558-5 (ebook) ISBN 978-0-7503-2559-2 (print) ISBN 978-0-7503-2560-8 (myPrint) ISBN 978-0-7503-2561-5 (mobi) DOI 10.1088/978-0-7503-2558-5 Version: 20201001 IOP ebooks British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library. Published by IOP Publishing, wholly owned by The Institute of Physics, London IOP Publishing, Temple Circus, Temple Way, Bristol, BS1 6HG, UK US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia, PA 19106, USA For my parents, Ann and Gareth Contents Preface xv Author biography xvi Abbreviations xvii 1 Photographic optics 1-1 1.1 Optical image formation 1-2 1.1.1 Refraction 1-2 1.1.2 Lens design 1-3 1.1.3 Paraxial imaging 1-4 1.1.4 Gaussian optics 1-6 1.1.5 Compound lenses: ynu raytrace 1-7 1.1.6 Principal planes 1-9 1.1.7 Gaussian conjugate equation 1-11 1.1.8 Thick and thin lenses 1-12 1.1.9 Focal length 1-14 1.1.10 Magnification 1-18 1.1.11 Lens aberrations 1-19 1.2 Focusing 1-20 1.2.1 Unit focusing 1-21 1.2.2 Internal focusing 1-23 1.2.3 Single lens reflex cameras 1-24 1.2.4 Phase-detect autofocus 1-25 1.3 Framing 1-27 1.3.1 Entrance and exit pupils 1-27 1.3.2 Chief rays 1-28 1.3.3 Pupil magnification 1-30 1.3.4 Angular field of view formula 1-32 1.3.5 Focus breathing 1-35 1.3.6 Focal length multiplier 1-36 1.3.7 Perspective 1-37 1.3.8 Keystone distortion 1-39 1.4 Depth of field 1-40 1.4.1 Circle of confusion 1-40 1.4.2 Depth of field formulae 1-42 vii Physics of Digital Photography (Second Edition) 1.4.3 Depth of field control 1-44 1.4.4 Hyperfocal distance 1-44 1.4.5 Focus and recompose limits 1-46 1.4.6 Bokeh 1-48 1.5 Photometric exposure 1-51 1.5.1 Photometry 1-51 1.5.2 Flux emitted into a cone 1-53 1.5.3 Relative aperture 1-56 1.5.4 f-number 1-58 1.5.5 Working f-number 1-59 1.5.6 f-stop 1-61 1.5.7 Natural vignetting 1-62 1.5.8 Camera equation 1-64 1.5.9 Shutters 1-65 1.5.10 f-number for aplanatic lenses 1-68 References 1-71 2 Digital output and exposure strategy 2-1 2.1 Raw data 2-2 2.1.1 Sensor response 2-2 2.1.2 Colour 2-3 2.1.3 Dynamic range transfer 2-5 2.2 Digital output levels 2-6 2.2.1 Bit depth reduction 2-7 2.2.2 Posterisation 2-8 2.2.3 Lightness 2-9 2.2.4 Gamma encoding 2-9 2.2.5 Gamma decoding 2-11 2.3 Image dynamic range 2-13 2.3.1 Gamma curves 2-14 2.3.2 Tone curves 2-15 2.3.3 Raw headroom 2-17 2.3.4 Shadow and highlight dynamic range 2-17 2.4 Histograms 2-18 2.4.1 Luminance histograms 2-19 2.4.2 Image histograms 2-19 viii Physics of Digital Photography (Second Edition) 2.5 Average photometry 2-20 2.5.1 Reflected light meter equation 2-21 2.5.2 Proportionality constant 2-22 2.5.3 Photographic constant 2-23 2.5.4 Hand-held meter calibration constant 2-24 2.5.5 Average scene luminance 2-24 2.5.6 Exposure value 2-25 2.6 Exposure index 2-26 2.6.1 ISO speed 2-27 2.6.2 Standard output sensitivity 2-30 2.6.3 Recommended exposure index 2-32 2.6.4 Extended highlights 2-32 2.7 Advanced metering 2-34 2.7.1 Exposure compensation 2-35 2.7.2 In-camera metering modes 2-35 2.7.3 Incident light metering 2-35 2.8 Exposure modes 2-36 2.8.1 Aperture priority 2-36 2.8.2 Shutter priority 2-37 2.8.3 Program mode 2-37 2.8.4 Manual mode 2-38 2.9 Photographic lighting 2-38 2.9.1 Sunrise and sunset 2-40 2.10 Neutral density filters 2-41 2.10.1 Graduated neutral density filters 2-42 2.11 Polarizing filters 2-44 2.11.1 Malus’ law 2-45 2.11.2 Surface reflections 2-46 2.11.3 Blue skies 2-47 2.11.4 Circular polarizing filters 2-48 2.12 High dynamic range 2-49 2.12.1 High dynamic range imaging 2-50 2.12.2 Tone mapping 2-52 2.13 Image display 2-54 2.13.1 Luma 2-54 2.13.2 Display luminance 2-55 2.13.3 Display dynamic range 2-56 References 2-57 ix Physics of Digital Photography (Second Edition) 3 Raw data model 3-1 3.1 Linear systems theory 3-2 3.1.1 Radiometry 3-3 3.1.2 Ideal optical image 3-5 3.1.3 Point spread function (PSF) 3-5 3.1.4 Linear shift invariance 3-6 3.1.5 Convolution: derivation 3-7 3.1.6 Convolution: examples 3-9 3.1.7 Optical transfer function 3-11 3.1.8 Modulation transfer function (MTF) 3-13 3.1.9 Phase transfer function 3-15 3.1.10 Model camera system 3-15 3.2 Optics 3-17 3.2.1 Wave optics 3-17 3.2.2 Huygens–Fresnel principle 3-20 3.2.3 Aperture diffraction PSF 3-21 3.2.4 Circular aperture: airy disk 3-27 3.2.5 Aperture diffraction MTF 3-29 3.2.6 Aberrations: wavefront error 3-31 3.3 Sensor 3-33 3.3.1 Spatial averaging 3-34 3.3.2 Detector-aperture PSF 3-35 3.3.3 Sampling 3-36 3.3.4 Detector-aperture MTF 3-37 3.4 Optical low-pass filter 3-39 3.4.1 Function sampling 3-39 3.4.2 Replicated spectra 3-40 3.4.3 Reconstruction 3-41 3.4.4 Aliasing 3-42 3.4.5 Sensor Nyquist frequency 3-43 3.4.6 Pre-filtering 3-44 3.4.7 Four-spot filter PSF 3-45 3.4.8 Four-spot filter MTF 3-46 3.5 Sampled convolved image 3-47 3.5.1 Model camera system PSF 3-48 3.5.2 Model camera system MTF 3-49 x Physics of Digital Photography (Second Edition) 3.6 Charge signal 3-50 3.6.1 Sampled spectral exposure 3-50 3.6.2 Photoelements 3-51 3.6.3 Colour filter array 3-52 3.6.4 Camera response functions 3-53 3.6.5 Polychromatic PSF and MTF 3-56 3.6.6 Charge detection 3-57 3.7 Analog-to-digital conversion 3-58 3.7.1 Programmable ISO gain 3-58 3.7.2 Digital numbers 3-59 3.7.3 Conversion factor 3-60 3.7.4 Bias offset 3-61 3.8 Noise 3-61 3.8.1 Photon shot noise 3-62 3.8.2 Read noise 3-62 3.8.3 Dark current shot noise 3-63 3.8.4 Noise power 3-64 3.8.5 Fixed pattern noise 3-64 3.9 Noise measurement 3-65 3.9.1 Conversion factor measurement 3-65 3.9.2 Read noise measurement 3-67 3.9.3 Noise models 3-68 References 3-71 4 Raw conversion 4-1 4.1 Reference colour spaces 4-2 4.1.1 Theory of colour 4-3 4.1.2 Eye cone response functions 4-4 4.1.3 Colour-matching functions 4-5 4.1.4 Units 4-7 4.1.5 Standard luminosity function 4-8 4.1.6