Physics of Digital Photography Andy Rowlands IOP Publishing, Bristol, UK Contents XIII About the author xiv Acronyms XV 1 Fundamental optical formulae 1-1 1.1 Image: formation 1-2 1.1.1 Refraction 1-2 1.1.2 Gaussian optics 1-3 1.1.3 Lens refractive power 1-8 1.1.4 Magnification 1-13 1.1.5 Focal length 1-14 1.1.6 Lens focusing movement 1-17 1.2 Field of view 1-21 1.2.1 Entrance and exit pupils 1-22 1.2.2 Chief and marginal rays 1-23 1.2.3 Angular field of view 1-24 1.2.4 Field of view area 1-28 1.2.5 Focal-length multiplier 1-29 1.3 Depth of field 1-30 1.3.1 Circle of confusion 1-30 1.3.2 Depth of field equations 1-32 1.3.3 Hyperfocal distance 1-37 1.3.4 Focus and recompose limits 1-38 1.3.5 Keystone distortion 1-40 1.4 Exposure 1-42 1.4.1 Photometry 1-43 1.4.2 Flux emitted into a cone 1-44 1.4.3 Relative aperture 1-47 1.4.4 f-number 1-49 1.4.5 Working f-number 1-50 1.4.6 f-stop 1-52 1.4.7 Natural vignetting 1-52 1.4.8 Photometric exposure 1-54 Vll Physics of Digital Photography 1.4.9 Exposure value 1-56 1.4.10 f-number for aplanatic lenses 1-57 Bibliography 1-61 2 Exposure strategy 2-1 2.1 Digital output 2-2 2.1.1 Sensor response 2-2 2.1.2 Colour 2-3 2.1.3 Digital output levels 2-4 2.1.4 Dynamic range 2-5 2.1.5 Tonal range 2-7 2.1.6 Tone reproduction 2-7 2.1.7 Gamma 2-8 2.1.8 Tone curves 2-14 2.1.9 Histograms 2-16 2.2 Average photometry 2-17 2.2.1 Reflected-light metering 2-18 2.2.2 Meter calibration 2-19 2.2.3 Average scene luminance 2-22 2.3 Exposure index 2-23 2.3.1 ISO speed 2-24 2.3.2 Standard output sensitivity 2-27 2.3.3 Recommended exposure index 2-29 2.3.4 Extended highlights 2-29 2.4 Exposure modes 2-31 2.4.1 Metering modes 2-31 2.4.2 Exposure compensation 2-32 2.4.3 Aperture priority (A or Av) 2-32 2.4.4 Shutter priority (S or Tv) 2-33 2.4.5 Program mode (P) 2-34 2.4.6 Manual mode (M) 2-34 Bibliography 2-35 3 Raw data model 3-1 3.1 Linear systems theory 3-2 3.1.1 Radiometry 3 -3 3.1.2 Ideal image 3-5 vni Physics of Digital Photography 3.1.3 Point-spread function (PSF) 3-6 3.1.4 Convolution 3-7 3.1.5 Optical transfer function 3-12 3.1.6 Modulation transfer function (MTF) 3-13 3.1.7 Phase transfer function 3-15 3.1.8 Model camera system 3-16 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 Wavefront error 3-31 3.2.7 Polarisation 3-34 Sensor 3-39 3.3.1 Irradiance spatial integration 3-39 3.3.2 Detector-aperture PSF 3-40 3.3.3 Detector-aperture MTF 3-42 Optical low-pass filter 3-44 3.4.1 Sampling theorem 3-44 3.4.2 Sensor Nyquist frequency 3-48 3.4.3 Pre-filtering 3-50 3.4.4 Four-spot filter PSF 3-50 3.4.5 Four-spot filter MTF 3-51 Real image 3-52 3.5.1 System PSF 3-53 3.5.2 System MTF 3-54 Sensor signal 3-55 3.6.1 Charge collection 3-55 3.6.2 Colour filter array 3-58 3.6.3 Spectral responsivity 3-58 3.6.4 Polychromatic PSF and MTF 3-60 Analog-to-digital conversion 3-61 3.7.1 Charge detection 3-61 3.7.2 ISO gain 3-62 3.7.3 Digital numbers 3-63 3.7.4 Conversion factor 3-63 3.7.5 Bias offset 3-65 IX Physics of Digital Photography 3.8 Noise 3-65 3.8.1 Temporal noise 3-66 3.8.2 Fixed pattern noise 3-67 3.8.3 Noise measurement 3-68 3.8.4 Noise models 3-70 Bibliography 3-74 4 Raw conversion 4-1 4.1 Reference colour spaces 4-2 4.1.1 Physics of colour 4-2 4.1.2 Standard colourimetric observer 4-3 4.1.3 CIE RGB colour space 4-7 4.1.4 Chromaticity diagram (rg) 4-8 4.1.5 CIE XYZ colour space 4-9 4.1.6 Chromaticity diagram (xy) 4-11 4.1.7 Absolute colourimetry 4-13 4.1.8 Relative colourimetry 4-14 4.1.9 Reference white 4-14 4.2 Illumination 4-15 4.2.1 Colour temperature 4-15 4.2.2 Correlated colour temperature 4-15 4.2.3 White point 4-17 4.2.4 Standard illuminants 4-17 4.3 Camera raw space 4-18 4.3.1 Eye response functions 4-18 4.3.2 Camera response functions 4-20 4.3.3 Luther-Ives condition 4-22 4.3.4 Demosaicing methods 4-23 4.3.5 Camera colour characterisation 4-24 4.4 sRGB colour space 4-27 4.4.1 sRGB gamut 4-27 4.4.2 sRGB gamma 4-29 4.4.3 sRGB dynamic range 4-31 4.4.4 sRGB colour cube 4-31 4.5 White balance 4-32 4.5.1 Adopted white 4-34 4.5.2 Chromatic adaptation transforms 4-36 x Physics of Digital Photography 4.5.3 White balance strategies 4-39 4.6 Example 1: Adobe® DNG (raw to XYZ D50) 4-42 4.6.1 Method 1 (transformation matrix + CAT) 4-43 4.6.2 Method 2 (raw WB multipliers + forward matrix) 4-47 4.7 Example 2: der aw (raw to sRGB D65) 4-52 4.8 Image editing 4-59 4.8.1 Colour management 4-59 4.8.2 Adobe® Photoshop® colour settings 4-61 4.8.3 Image resizing 4-65 Bibliography 4-67 5 Image quality 5-1 5.1 Perceived resolution 5-3 5.1.1 Observer resolving power 5 -3 5.1.2 Circle of confusion specification 5-4 5.2 Cross-format comparisons 5-9 5.2.1 Equivalence ratio 5-10 5.2.2 Equivalence at infinity focus 5-11 5.2.3 Equivalence at arbitrary focus 5-15 5.2.4 Summary of equivalence 5-23 5.3 Lens MTF 5-25 5.3.1 Aberrations 5-25 5.3.2 Lens MTF plots 5-26 5.3.3 Lens MTF and sensor format 5-30 5.3.4 Lens resolving power 5-31 5.4 System MTF 5-34 5.4.1 System MTF and sensor format 5-34 5.4.2 System resolving power 5-35 5.5 Sharpness 5-36 5.5.1 Sharpness metrics 5-38 5.5.2 Image resampling 5-41 5.5.3 Diffraction softening 5-46 5.6 Signal-to-noise ratio 5-49 5.6.1 SNR and ISO setting 5-51 5.6.2 Shadow improvement 5-55 5.6.3 ISO invariance 5-56 5.6.4 SNR and pixel count 5-57 xi Physics of Digital Photography 5.6.5 SNR and sensor format 5-59 5.7 Dynamic range 5-59 5.7.1 Engineering dynamic range 5-59 5.7.2 Photographic dynamic range 5-61 5.8 Practical strategies 5-63 5.8.1 Object resolution 5-64 5.8.2 Non-destructive noise reduction 5-66 5.8.3 Exposing to the right 5-68 Bibliography 5-72 XH .