CS6640 Computational Photography 9. Practical Photographic Optics

CS6640 Computational Photography

9. Practical photographic optics

• First-order optics: what lenses are supposed to do • In practice lenses vary substantially in quality where “quality” ≈ “behaves like the ﬁrst order approximation”

Cornell CS6640 Fall 2012 2 Important question • Why is this toy so expensive –EF 70-200mm f/2.8L IS USM –$1700

• Why is it better than this toy? –EF 70-300mm f/4-5.6 IS USM –$550 • Why is it so complicated? slidebyFrédo Durand, MIT

• What do these buzzwords and acronyms mean? Marc Levoy, Stanford MarcLevoy,

Stanford Big Dish Panasonic GF1 Marc Levoy, Stanford MarcLevoy,

Leica 90mm/2.8 Elmarit-M Stanford Big Dish prime, at f/4 Panasonic GF1 $2000 Marc Levoy, Stanford MarcLevoy,

Panasonic 45-200/4-5.6 Leica 90mm/2.8 Elmarit-M Stanford Big Dish zoom, at 200mm f/4.6 prime, at f/4 Panasonic GF1 $300 $2000 for lots more lens evaluation: Zoom vs. prime www.slrgear.com www.photozone.de www.dpreview.com

17 elements / 14 groups 7 elements / 6 groups

source: the luminous landscape

Cornell CS6640 Fall 2012 5 Sources of blur

• Diﬀraction fundamental constraint • Aberrations in design deviations in practical glass shape and properties from the ideal • Manufacturing tolerances centering and other assembly errors create aberrations

Cornell CS6640 Fall 2012 6 Fourier optics in one slide

• Thin lens in contact with transparency • In neighborhood of center of lens, sinusoidal grating of frequency ω admits plane wave traveling at angle sin θ = ±ωλ • Considering whole lens, focus is at y ≈ fωλ • Fourier: represent aperture transparency as sum of sinusoids frequency maps • Result: intensity at to position y = fωλ is proportional 1/ to FT of aperture at ω • Focus spot is FT of aperture, scaled up by fλ f

Cornell CS6640 Fall 2012 7 Diffraction limit

• Aperture of size D produces spot with size about fλ/D • This is wavelength times f-number rule of thumb: f-number in microns, for visible light camera with 5-micron pixels limited by diffraction past f/5 camera with 2-micron pixels limited by diffraction past f/2! (not quite this bad, because of color ﬁlter array) • Practical consequence 1: lenses on smaller cameras don’t go to big f-numbers ≈ 16 for an SLR, 8 for a compact, 4 for a cell phone • Practical consequence 2: there’s no point reducing aberration- induced blur much past the diﬀraction spot size

Cornell CS6640 Fall 2012 8 Diffraction spots

• The blur kernel is the FT of the aperture transparency function • Circular aperture leads to Airy disk a sinc-like radially symmetric function diglloyd.com • Apertures with straight edges produce stars every edge orientation produces a linear feature cameratechnica.com

Cornell CS6640 Fall 2012 9 Aberrations

• Chromatic aberration • Third order “Seidel” aberrations ﬁrst order effects of dispersion nonlinear terms in the expansion - longitudinal chromatic aberration to order 3 in (qx,qy,px,py) (order 2 terms all zero by rotational symmetry) - lateral color - spherical aberration - coma - astigmatism - curvature of field - geometric distortion • How to reduce them s,c,a decreased by stopping down aperture c,a,f,d,lc decreased by narrowing ﬁeld f,d do not prevent sharp focusing ca you are stuck with

Cornell CS6640 Fall 2012 10 Chromatic aberration

(wikipedia)

✦ dispersion causes focal length to vary with wavelength slide by Marc Levoy, Stanford slidebyMarcLevoy, • for convex lens, blue focal length is shorter

✦ correct using achromatic doublet • strong positive lens + weak negative lens = weak positive compound lens • by adjusting dispersions, can correct at two wavelengths 11 © Marc Levoy red and blue have Chromatic aberration the same focal length

(wikipedia)

✦ dispersion causes focal length to vary with wavelength slide by Marc Levoy, Stanford slidebyMarcLevoy, • for convex lens, blue focal length is shorter

hyperbolic lens

spherical lens (wikipedia) slide by Marc Levoy, Stanford slidebyMarcLevoy, ✦ focus varies with ray height (distance from optical axis)

✦ can reduce by stopping down the aperture

✦ can correct using an aspherical lens

✦ can correct for this and chromatic aberration

12 by combining with a concave lens of different properties © Marc Levoy Examples slide by Marc Levoy, Stanford slidebyMarcLevoy,

(Canon) sharp soft focus

13 Canon 135mm f/2.8 soft focus lens © Marc Levoy Hubble telescope slide by Marc Levoy, Stanford slidebyMarcLevoy,

before correction

14 © Marc Levoy Hubble telescope slide by Marc Levoy, Stanford slidebyMarcLevoy,

before correction after correction

14 © Marc Levoy Hubble Space Telescope Eagle Nebula (NASA) Marc Levoy, Stanford MarcLevoy, Coma

(ryokosha.com) slide by Marc Levoy, Stanford slidebyMarcLevoy,

(Hecht)

✦ magniﬁcation varies with ray height (distance from optical axis)

16 © Marc Levoy Astigmatism slide by Marc Levoy, Stanford slidebyMarcLevoy, (Pluta)

✦ tangential and sagittal rays focus at different depths

17 © Marc Levoy Astigmatism

focus of sagittal rays focus of tangential rays slide by Marc Levoy, Stanford slidebyMarcLevoy, (Pluta)

✦ tangential and sagittal rays focus at different depths

17 © Marc Levoy Two kinds of astigmatism

(Wikipedia)

(http://toothwalker.org/optics/astigmatism.html)

ophthalmic astigmatism (due to oblong eye) slide by Marc Levoy, Stanford slidebyMarcLevoy,

third-order astigmatism (even in rotationally symmetric photographic lenses)

18 © Marc Levoy Field curvature slide by Marc Levoy, Stanford slidebyMarcLevoy, (Hecht) ✦ spherical lenses focus a curved surface in object space onto a curved surface in image space

✦ so a plane in object space cannot be everywhere in focus

19 when imaged by a planar sensor © Marc Levoy Curvilinear/radial distortion

slidebyFrédo Durand, MIT http://www.dxo.com/us/photo/dxo_optics_pro/ optics_geometry_corrections/distortion

From "The Manual of Photography" Jacobson et al http://en.wikipedia.org/wiki/Distortion_(optics) Aspherical lenses slidebyFrédo Durand, MIT

source: canon red book Describing lens performance in space

• Spot diagrams • Result of tracing many rays distributed over the aperture • Results vary by distance from image center

size of diﬀraction limited spot for reference

Zemax corp. | Mars Rover panoramic camera lens (f:20)

Cornell CS6640 Fall 2012 22 Describing lens performance in frequency

Cornell CS6640 Fall 2012 23 LEICA SUMMILUX-M 35 mm f/1.4 ASPH. 3

Modulation transfer LEICAfunction SUMMILUX-M 35 mm(MTF) f/1.4 ASPH. 3

MTF graphs • Function of spatial frequency and image position lens from hw3 Aperture Stop 1.4 Aperture Stop 2.8 [%] [%] 100 100 MTF graphs LEICA SUMMILUX-M 35 mm f/1.4 ASPH. 3 80 80

Aperture Stop 1.4 Aperture Stop 2.8 60[%] 60[%] 100 100

40 40 80 80 MTF graphs 20 20 60 60

Aperture Stop 1.4 Aperture Stop 2.8 0 [%] 0[%] 40 0 1005 10 15 20 10040 0 5 10 15 20 Y'[mm] Y' [mm] 20 80 8020

60 60 0 0 0 540 10 15 20 40 0 5 10 15 20 Y'[mm] Y' [mm] 20 20

0 Aperture Stop 5.6 0 [%] 0 5 10 15 20 0 5 10 15 20 100 The MTF is indicated at full aperture, at f/2.8 and at Y'[mm] Y' [mm] f/5.6 at long taking distances (infinity). Shown is 80 the contrast in percentage for 5, 10, 20 and 40 lp/mm accross the height of the 35 mm film format, for tangential (dotted line) and sagittal Aperture Stop 5.6 60[%] (solid line) structures, in white light. The 5 and 100 The10 lp/mm MTF is willindicated give an at indication full aperture, regarding at f/2.8 the and at f/5.6contrast at longratio taking for large distances object structures.The(infinity). Shown is Aperture Stop 5.6 40 [%] the contrast in percentage for 5, 10, 20 and 40 80 100 20 and 40 lp/mm records the resolution of finer Thelp/mm MTF is accross indicated theat full height aperture, of atthe f/2.8 35 and mm at film f/5.6and atfinest long takingobject distances structures. (infinity). Shown is format, for tangential (dotted line) and sagittal 20 80 the contrast in percentage for 5, 10, 20 and 40 60 lp/mm(solid accrossline) structures, the height of inthe white 35 mm light. film The 5 and format,10 lp/mm for tangential will give (dottedsagittal an indicationline) structures and sagittal regarding the 60 (solid_ _ line)_ _ _structures, _ _ _ in white light. The 5 and 0 10contrast lp/mm will ratio give for an indicationtangentiallarge object regarding structures structures.The the 40 0 5 10 15 20 contrast20 and ratio 40 forlp/mm large object records structures.The the resolution of finer source: canon red book 40 20and and finest 40 lp/mm object records structures. the resolution of finer Y'[mm] and finest object structures. 20 20 Cornell CS6640 Fall 2012 sagittalsagittal structures structures 24 ______0 0 tangentialtangential structures structures 0 5 0 105 1015 15 20 20 Y'[mm] Y'[mm] Fighting aberrations

• Add more elements • Use aspherical surfaces introduces more DOFs without adding more surfaces • Stop when aberrations are smaller than Airy disk then the lens is “diffraction limited” lenses become diffraction limited when you stop them down far enough

Cornell CS6640 Fall 2012 25 Stray light

• Reflections from optical surfaces (lens flare) classic “lens flare” with images of aperture planar filters cause annoying reflections of objects • Diffuse reflections from other parts (lens flare and camera flare) leads to general loss of contrast • Reduced by use of lens hoods goal: exclude bright sources outside the image useless when the source is in the image

Cornell CS6640 Fall 2012 26 Reducing stray light

• Paint everything black inside of lens barrel, edges of lenses, inside of camera, … • Use of knife-edge baﬄes use geometry to eliminate single-bounce diffuse paths • Anti-reﬂection coatings on optical surfaces fancy and highly developed technology old: 1/4 wave coating current: optimized multilayer coatings newest: nanostructured coatings

Cornell CS6640 Fall 2012 27 Other issues

• Vignetting • Shading

Cornell CS6640 Fall 2012 28 Vignetting • Occlusion by lens elements • The periphery does not get as much light slidebyFrédo Durand, MIT

source: canon red book Vignetting correction (ACR) slidebyFrédo Durand, MIT

Before After Characteristics of lenses

• Basic: focal length, min f number • Zoom range • Minimum focus distance if very close, it’s a “macro” lens requires extra optimization to work at all distances • Principal planes • Entrance and exit pupils • Geometric distortion • Actuation aperture autofocus image stabilization

Cornell CS6640 Fall 2012 31 Quality of lenses

• Center sharpness (IMO over-emphasized) how well it resolves small features only of interest relative to the size of pixels all modern lenses are very sharp in the center affected by some aberrations but not others • Corner sharpness affected by all aberrations generally noticeably worse than center sharpness • Contrast (IMO under-appreciated) • Lateral color

Cornell CS6640 Fall 2012 32