Recap!

• Depth of field! The Art, Science and Algorithms – Parameters?! of !

Lenses ! Optics II! CSCI 4900/6900! Maria Hybinette!

1! 2!

Single-Lens Reflect (SLRs)! SLRs and Other !

Typical SLRs:! • See the scene through the lens how the • Moving mirror that enables you to see the scene sensor sees it! through the lens ! • Shorter lag! Pre SLRs:! • Customizations (how about CHDK?)! • 2 separate light paths:! – Interchangeable parts (e.g., lenses)! – Capturing: Through lens to film! • Thought: Great LCDs cannot compete with – Viewing (‘image preview’ realistic for long distances)! seeing a ‘real’ image preview.! • Above (twin-lens reflect TLR)! – Is this changing?! • to the side (rangefinder)!

3! 4!

Camera Cross Section: Optics! Pentaprism (1955)!

/+'01)2*&%3) 45+)2&+#+) • Correct light to ,"'-+'%+*).+'%) the eye piece! !"#$%&'()%#*++') • Interchangeable?! – Macro specific!

7+8+9)3&**"*)))) :;<°=) !"#1.)2.1'+) !*"'063"$'0).+'%) !&.3)"*) %>$?+*) • Mirror is a bottleneck %+'%"*) (shutter lag)! • Larger than other cameras (mirror/pentaprism)!

>?2@AA+'BC&D&2+-&1B"*(AC&D&AE&'(.+6.+'%F*+8+9F#13+*1) • Limit the ‘wideness of lens’ unless mirror lockup)! 5! 6! Focusing Screen! Lenses!

• Ground glass • Made of many different typically! lenses! • Split screen (not • Different prices! auto focus – Primes (generally better cameras)! than zoom at their • Plain (auto focus)! ‘specialized’ length)! – Zooms (more expensive)! – architectural! >?2@AA>$G21(+%B#"3A>$GAHI6J"%06492+'%&K+6 • Gridded! ,13+*16L+'%+) Markings! >?2@AACCCB#1'"'B#"3A#13+*163$%+$3A0+#>A • .F2.1'0A&'-+9B>03.)

7! >?2@AA8! +'BC&D&2+-&1B"*(AC&D&A,13+*1F.+'%)

Price and Quality?! Optical Quality? Evaluating Lenses!

• EF 70-200 mm f/2.8L IS USM ($1.7K)! • Typically price is correlated to optical quality but • EF 70-200mm f/4-5.6 IS USM ($550)! sometimes price can be misleading.! • Sharpness (resolution, acutance, diffraction limits)! What matters?! • Contrast! • Optical quality (from the middle of lens to edges)! • (out of focus areas, including highlights)! • (@ biggest, stopped down)! • : no color casts! • Focusing motor! • Chromatic aberrations (sagittal & axial)! • Zoom! • Flare & Ghosting! • Nearest focusing distance! • Light fall off (, shading)! • Built & Handling! • Distortion! 9! 10!

Sharpness (perceived)! Acutance (contrast)!

• Clarity of detail in a photo! • Acutance is about how sharply an edge – Resolution, and ! – Acutance (contrast)! transitions to the white area.! M&(>) L+%%) • Resolution: Resolve details, texture N#$01'#+) N#$01'#+) (camera bottle neck), Large prints! O""-)L+'%) P"*%+)L+'%) • Acutance (crispness): Edge transition • Sharpening! (lens), Important for Online! – In-camera! – post processing (Yay!)!

>?2@AA11! CCCB#13G*&-(+&'#"."$*B#"3A0$0"*&1.%A%>1*2'+%%B>03) 12! Resolution! Acutance to Resolving Power!

• How many lines per mm N#$01'#+):Q+C+*).&'+%)2+*)33=) 7+%".$R"'):3"*+).&'+%)2+*)33=) can be distinguished? (lines HI).2A33) SI6;I).2A33) thinner & thinner)! – smallest details a lens can resolve! – Microcontrast! • Sharpening?! – Cannot really be improved in post processing!

13! 14!

Quantitative Measure! Acutance (contrast) & Resolution!

• Modulation Transfer Function (MTF)! – Spatial measure of acutance & resolution! • Sharp images = High Acutance & High – Measure lines per millimeter ! • How much contrast is retained between the lines in the reproduced Resolution! image, compared to the original pattern, a MTF of:! – [1.00, 100%] : no difference between original patter and image.! • Camera’s with high resolution does not – [0.85, or 85%] : 85% of the original lines are retained in the image! necessarily produce images that are – [0.00, 0%] : Fine lines are indistinguishable in the image (grey)! perceived as sharp.! • Example images here:!

>?2@AACCCB#13G*&-(+&'#"."$*B#"3A0$0"*&1.%A%>1*2'+%%B>03)

>?2@AA15! CCCB*+K&%+3*&B#"3AT$+%R"'%A+T$&2FT1A3U) >?2@AACCCB'"*31'D"*+'B#"3AV$0"*&1.%AJV!03.) 16!

Acutance (contrast) & Resolution!

L+%%)*+%".$R"')

/+*Q+#0)#"'0*1%0) O""-)#"'0*1%0)X) L+%%)#"'0*1%0)X) Y1-)#"'0*1%0)X) X)*+%".$R"') .+%%)*+%".$R"') G+?+*)*+%".$R"') G1-*+%".$R"') • High resolution & high contrast! • Low resolution & high contrast! • Green 10 lp/mm (acutance)! • High resolution & bad contrast! • Magenta 30 lp / mm (resolution)! • Conclusion: High contrast visually more important! >?2@AA17! CCCB2>"0"W"'+B-+A3U) 18! Example MTF Charts! MTF & Bokeh!

O""-) *+%".$R"'Z) O""-) ,"'0*1%0)

L+\)&%)0>+)]I6;II)^7)10);II33):_HB`a=B)b')0>+)*&(>0)&%)0>+);II33)QAcB])^7)):_HIa=)) ["0)%")(""-) *+%".$R"'Z) ["0)%")(""-) • If the dotted (M10) and solid lines (M30) are close ,"'0*1%0) together! – the out-of-focus areas of the lens will be smooth and pleasing (good ‘bokeh’), while if they are far apart the out-of- focus areas tend to be distorted and less pleasing (bad ‘bokeh’). ! 19! 20!

Example: Low Frequency to High b*&(&'1.)/1?+*')/*"g.+) Quantitative Measure of Sharpness! V+%0)/1?+*') Frequency Details (simplified)! f31(+)"Q)/1?+*') f31(+)/1?+*')/*"g.+) • Modulation Transfer function (MTF) (now)! P>&0+) • Spatial Frequency Response (audio, hertz)! – Lens manufacturer posts these! Y.1#D) • It is the contrast at a given spatial frequency (cycles or lines per mm (lp/mm) ~ Hertz) relative to low frequencies. [cycles/]! – Cycles! – line pairs (white/black) ! H;I)

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>?2@AACCCB.+'%*+'01.%B#"3A'+C%AcIIdBIeBHSA>1K+65"$6%++'63561#$01'#+21! ) 22! >?2@AACCCBG"G10D&'%B#"3A2>"0"(*12>5A0+#>'.A3UA3UHB>03.)

Modulation Transfer Function (MTF) " & Resolving Power! ReCap!

• Simplified MTF Definition:! – MTF = (maximum intensity - minimum intensity)/ (maximum intensity + minimum intensity) ! • Imagine lines get finer and finer (as in figure)! – 255-0/255+0 = 1.0 [first part of plot]! – 140-15/140+15= 125/155 = 0.8 [second part]! – 0.5! – 0.1 * this lens! – .! – MTF = 0 uniform grey patch - no variation [127] -> 128-126/254 => 2/254 = 0.007! • This is the resolving power of the lens! >?2@AACCCB+-3$'-"2R#%B#"3A0+#>'.6 23! %$22"*0A&31(&'(A$'-+*%01'-&'(63U60+%R'(A24! ) Finally: What is MTF Really?! Test Charts & Caveats!

• The MTF is calculated by performing a Fourier transform of the line • Ideally: Test pattern is a “sine wave” pattern not bars:! spread function, and the line spread function is calculated by • Problem: Difficult to produce smooth transitions! differentiating the edge response function, which is what we measure on • Solution: Use bar patterns:! an image.! – Bar patterns unites are lines per mm! – Sinusoidal patterns unites are cycles per mm! Edge Response Function (ERF) (measured) ....differentiate:! → Line Spread Function (LSF) ....Fourier transform:! • Caveats: MTF depends on (but the variation is small)! → Modulation Transfer Function (MTF).! – Wavelength of light used:! • Blue has a higher MTF than red’s MTF ! • Normally white light is used! • The ERF is dead simple. It's just a plot of the image intensity across the edge of an angled block in an image. The differentiation of this ERF – : ! shape is obvious (or should be, to a physicist!). Why a Fourier transform • Tungsten lower than daylight (blue)! is the thing to do to then get MTF vs ν, should also be obvious to you – Tungsten has longer wavelength components! if you have looked at Fourier transforms.! – Detector! h"'i0)'++-)0")D'"C)Q"*) • Sensors more sensitive to blue light than red light! 0+%0) – Will have a higher MTF than with a detector more sensitive to red light! 25! >?2@AACCCB*+K&%+3*&B#"3AT$+%R"'%A+T$&2FT1A3+1%$*&'(F3U) 26!

Aperture: The Sweet spot! Aperture & Quality!

• Typically 2 stops down! • f/2.8 on an f/1.4 lens (f/1.4, f/2.0,f/2.8)! • f/11 on an f/5.6 one. (f/5.6, f/8,f/11)! • Better lenses peak earlier. !

• f/4-f/11 sweetspot!

27! 28!

Ideal Lens! Considerations (in MTF terms)!

• Diffraction Limited! • Example: – off-centered, corner sharpness becomes more important.! – Lesson: Combinations of aperture, , and subject placement do you find yourself at most of the time? !

>?2@AAQ"0"(+'+R#B-+1*&'(g.3B#"3A>"CF0"F#>""%+F1F.+'%B>03.) 29! 30! Landscapes (General rule of thumb)! Portraits!

• Wide-Angle ! • Subjects close to center (unless you're doing • Aperture stopped down to get the most environmental portraits)! depth-of-field (DOF) and sharpness. ! • Moderate . ! • Recommendation: ! • Aperture is often fully open or almost fully – Focal length of 36mm or less that is evenly open to blur the background. ! sharp throughout the frame when the aperture • Recommendation:! is stopped down (f/8 or smaller).! – (70mm-150mm) that is sharp in the center at its widest aperture (f/4 or larger).!

31! 32!

Street & Candids! Action / Sports!

• 35-100mm! • Same as candids but longer! • Sharp throughout the frame when it is – 200-600mm! stopped down to f/8! • Sharp wide open? Or ?! – Candids often include filling the frame with the subject(s) [both in terms of depth and frame !

33! 34!

Nature! Distortions!

• Extremely long lenses 300mm or more! • Wide aperture f/4 or larger to isolate the subject!

• Need wide aperture and is sharp wide open.! 2&'#$%>&"') C1K+) G1**+.) – Most expensive!! • Zoom (barrel at wide end)! • Zoom (no distortion, in-between)! • Zoom (pincushion at the long end)! • Wave – ugly, but uncommon!

35! >?2@AA36! CCCBCCCB2>"0"W"'+B-+A.+'%60+*3&'"."(5) Wide Angle & Fish Eye (extreme barrel distortions)! Vignetting!

• Darker Illumination towards corners! • Tilted upwards! • Most obvious wide open especially for wide • Tilted downwards! angle lenses! • Fisheye! – Minimize by stopping down! 37! 38!

Color/’Tinted’ Lenses! Flare!

• Cheap glass, tend to transmit on the warm site! • Contrast deterioration (haze)! • Portrait lenses may be warmer… warmer skin • Ghosting ! tend to look healthier, no need for a tanning – aperture shaped blobs due to inner reflections! bed! – Multiple images of strong light sources! – Warming filters (1A or 1B)! 39! 40!

Blur! Bokeh!

• Spherical aberration not focused at the same point (later)! • Gaussian blur !

• Controlled by aperture!

41! 42! Can be appealing:! Bad Bokeh!

• Not the same as unfocused.! • Bokeh ! – Size (amount of blur)! – Shape! – Light distribution of disk (aberration)!

43! 44!

Good Bokeh! !

• Light of different color doesn’t converge (focus) at the same point (more later)! – Lenses have different refractive index for different wavelengths of light! – The refractive index decreases with increasing wavelength.! • Fringes of color along boundaries that separate dark and bright part of the image!

45! >?2@AACCCB2*&3+6j$'01B'+0A2"'0AM"CF0"A>1FV+%R'(F.+'%+%A1FM"CF0"F0+%0F1F.+'%B>03.46! )

Chromattic Aberration: Examples! Spherical aberration!

E1(&?1.),N@)7+-)"*)(*++')k(>"%0i)1*"$'-) 0>+)+-(+)"Q)0>+)Q*13+Z)$'1l+#0+-)G5) 12+*0$*+)6))1)2*"G.+3)C&0>)m.0*1)P&-+%B)

N9&1.),N@))/$*2.+)>1W+)"*)(."C)10)C&-+) >?2@AA+'BC&D&2+-&1B"*(AC&D&AE2>+*.F1G+**1R"') "2+')12+*0$*+B))

47! 48! Shape!

• Shape of aperture ! – Round, Hexagon!

49! 50!

Gaussian lens formula! Resources!

• http://www.prime-junta.net/pont/How_to/ha_Testing_lenses/ a_How_to_test_a_lens.html! • http://www.slrgear.com/reviews/index.php! – http://www.slrgear.com/reviews/zarticles/intros/howwetest.html! • http://www.bythom.com/rationallenses.htm! • http://www.bobatkins.com/photography/technical/ testing_lenses.html! • http://en.wikipedia.org/wiki/Critical_sharpness! • http://en.wikipedia.org/wiki/Aperture! • http://en.wikipedia.org/wiki/Acutance#Sharpness! • http://luminous-landscape.com/tutorials/resolution.shtml! • http://www.imatest.com/docs/blur_mtf.html! • http://photo.net/learn/optics/mtf/!

51! 52!