This Week • Exposure (today) The Art, Science and Algorithms – Camera Basics of Photography – Simple Math • Metering Exposure & Metering • Zone System Maria Hybinette 1 2 Maria Hybinette Exposure Shutter Speed • Controls light to digital sensor (or film) • Controls how long the sensor is exposed to light • Two main controls (parameters): • Linear effect on exposure until sensor saturates – Shutter Speed • Denoted in fraction of a second: – 1/30, 1/60, 1/125, 1/250, 1/500 • Controls amount of time light ‘shines’ on the sensor – Get the pattern ? – Aperture On a normal lens, hand-hold down to 1/60 • Controls the amount of light falls on a unit area per • second – Rule of thumb: shortest exposure: 1/ focal length • 1/50 for a 50 mm lens (slower motion blur) • Exposure = Irradiance x Time • 1/500 for a 500mm lens, – so large lenses needs faster shutter speeds to avoid camera Aperture Control: Amount of light falling shake on a unit area of sensor per second. 3 Photo Credit: 4 Side-Effect of Shutter Speed Creative Shutter Speeds Photo Credit: • Motion Blur Pasant @Flickr • Halving the shutter doubles the motion blur. 3 seconds 4 seconds Bulb: 3-10 second 1/30 Panning 30 seconds 15 seconds Wikipedia Fast Shu:er Speed Slow Shu:er Speed 6 5 Photo Credit: Wikipedia, Cooriander & Pasant @flickr Effect of shutter speed Shutters • Freezing motion • Central Shutters – Rule of thumb – Mounted within lens assembly (some in-front of lens, early cameras) Walking people Running people Car Fast train – Leaf mechanism generally used for this (see next slide for a simple version) 1/125th second – Diaphragm shutter (thin blades) 1/500th second • Focal plane shutters near the focal plane and 1/125 1/250 1/500 1/1000 moves to uncover sensor • Modern are mostly electronic • Digital cameras typically use a combination of mechanical and electronic timings Photo Credit: 7 Fredo Durand 8 Shutter Shutter • Simple leaf-shutter, typically Simple Leaf Shu3er only one speed 1. Shu:er plate 2. Aperture covered – Disposable cameras 3. Aperture during exposure 4. Leaf blade • Typically long way from 5. Catch mechanism sensor plate 6. Bu:erfly spring – Slow to open & close • edges less exposure time – Doesn’t matter for DOF • Leaf-shutter, typically only one speed • Near focal plane shutters – Disposable cameras – Faster not to affect DOF – Slit action to ensure all of sensor • Typically long way from sensor plate get same amount of light – Slow to open & close = edges less exposure time 9 Diagram Credit: London, Stone Upton (2910) Diagram Credit: Wikipedia 10 Your Best Friend Aperture regulates Light per Unit Area • Light and Distance adheres to • Use a tripod – it will enhance sharpness the Inverse Square Law: – How Area A (light intensity per – Avoid camera shake unit area), changes with distance. – Light Intensity falls of within the square of the distance. • Inversely proportional to the square of the distance • Lenses regulates the lens opening by the f-number (or f-stop) of the aperture. – At a given f/stop lenses allow the same amount of light • e.g., @ f/4 all lenses allow the same Photo Credit: 11 12 amount of light ⎛ f ⎞2 f Area = π⎜ ⎟ N = ⎝ 2N⎠ Aperture D Simple Geometry • We call this Irradiance: – Light on unit area of sensor per second ) is proportional to size of the area. € – Inversely proportional to the square distance to the 2 sensor € – Proportional to the square of the diameter of the 1 opening – Inverse square distance to the sensor (~ focal length f) 1 1 • 2 x D (doubling the aperture), its area § Twice the diameter means four times the area. f (hence the light that can get through it) § Stop down à higher f-number N = increases by 4X (because area) D § Fast lens allowing a low f-number à you can • [same focal length] use lower shutter speeds in lower light situation • As the distance to the sensor is doubled, § Light captured by a lens is proportional to the area of the aperture. (circle) 2 2 the area intersecVng the cone increases ⎛ D ⎞ ⎛ f ⎞ by 4 so the light falling per unit area A€re a = π ⎜ ⎟ = π ⎜ ⎟ 13 14 decreases by 4X [changing focal length] ⎝ 2 ⎠ ⎝ 2N ⎠ Wide Open (full) Aperture Aperture f f = focal length f f = focal length D = diameter of opening D = diameter of opening D = D = # General Idea: # • Lens opening given by # f-number #∗ D = f • A relative aperture size e.g., “#”, called an f-number, f written f/#, reflects the fact that it is computed by # = To maintain the same f-number a longer lens needs a dividing the focal length by the absolute aperture (D). larger diameter to produce the same illuminance D ( lumen/m2) on focal plane (longer lenses has a • Examples: magnifying effect) – Aperture of a 100 mm lens at f/2 is a #∗ D = f • Circle of diameter 100/2 = 50mm. – Aperture of a 50 mm lens at f/2 is a [example coming too see this better] • Circle of diameter 50/2 = 25mm • At a given f/stop, e.g., @ f/4 all lenses allow the same We will continue to use amount of light. – Aperture of a 100 mm lens at f/2 is a • Greater f-number (smaller hole) • Circle of diameter 100/2 = 50mm. – And less light per unit area reaches the image plane – Aperture of a 50 mm lens at f/2 is a 2 (irradiance), watts/m lower f-number long lenses fat & expensive • Circle of diameter 50/2 = 25mm More ``glass’’ required. 15 h:ps://en.wikipedia.org/wiki/F-number 16 f N = f-number = (f/#) N = f = focal length Allowing Light with Aperture D Aperture D = diameter opening • f/2 on a 50 mm lens (N=2) 2 = 50/D (D=25 mm) • f/2 on a 50 mm lens (N=2) 2 = 50/D (D=25 mm) • f/2 on a 100 mm lens (N=2) 2 = 100/D (D=50 mm) • f/2 on a 100 mm lens (N=2) 2 = 100/D (D=50 mm) € 2x 1x Doubling both the absolute aperture diameter (D) and the focal f N = f-number = (f/#) length(f) cancel (b/c reciprocity); leaving the same relative aperture size N = f = focal length (N). In this example, both lenses are f/2. D = diameter opening 17 D 18[ 50 * (X) / (25 * (X) ] € f f N = D = Aperture D N Side-Effect of Aperture • Doubling D, increases the area by 4X. – light falling per unit area decreases by 4X • Doubling N (two f/stops) doubles depth of field • Doubling N reduces D by 2x€ , light is – Reduced by 4x – Example: going from f/2.0 to f/4.0 (2 stops) 2 2 • Cuts the light by 4x ⎛ D ⎞ ⎛ f ⎞ Area = π ⎜ ⎟ = π ⎜ ⎟ ⎝ 2 ⎠ ⎝ 2N ⎠ • Cut the light (2x) instead of (4x) what should the factor of N be? (has to be smaller than 2, since 2 will cut it by 4 x the light) – (1 < N < 2) – √2 = 1.41 ( 1 stop) 19 Photo Credit: London, Stone Upton 20 Depth of Field (recall) Exposure (H) : = Irradiance * Time • A point in the scene is focused Determined by : Aperture & Shutter Speed at a point on the sensor • Reciprocity • Moving the sensor in z – Equivalence of Relationship of shutter and aperture. • the depth where this happens is called the depth of focus • Irradiance (I) – (light per unit area) Aperture (by sensor) Controlled • this corresponds in the scene – Controlled by aperture to a depth of field (scene) – Aperture also affect DOF • Halving the aperture diameter (smaller) doubles the depth of • Time (T) field – controlled by the shutter – doubling exposure time doubles motion blur • Exposure Stays Constant by (more next) Diagram Credit: London, Stone Upton 21 22 • Lowering one f/stop (cramp, close) AND doubles Time Stops: Reciprocity Tool Aperture and Shutter Stops • Increase exposure by 1 stop means capturing twice as much light as the previous stop. • Example: • Apertures 1 stops differ by a 1.41 factor (sqrt(2)) • f/1, f/1.4, f/2 (sqrt(2)*sqrt(2), …. 23 h:ps://www.flickr.com/photos/hamed/2476599906/ 24 Reciprocity Trading off motion for DOF • Assume we know how much light we need • We have infinite choices of shutter speed/aperture pairs • What will guide our choice of a shutter speed? – Freeze motion vs. motion blur, camera shake • What will guide our choice of an aperture? – Depth of field, diffraction limit • Often we must compromise – Open more to enable faster speed (but shallow DoF) 25 h:p://petapixel.com/2012/06/11/whats-the-f-number-of-the-human-eye/ 26 Sensitivity (ISO) • Third variable for exposure • Linear effect (200 ISO needs half the light as 100 ISO) • film: trade sensitivity for grain • digital: trade sensitivity for noise – multiply signal before analog-to-digital conversion – linear effect (200 ISO needs half the light as 100 ISO) Diagram Credit: 27 Dpreview next 28 Demo Summary Exposure • Aperture (f number) (depth of field control) • Trade-offs – Ratio between focal length &aperture diameter: # !diameter = f / <f number>! affecting – Small f number means large aperture (factors of " 2)! • Examples: f/2.0, f/2.8, f/4.0, f/5.6, f/8.0, f/11, f/16! brightness – A good standard lens has max aperture f/1.8 (less expensive f/3.5)! • Shutter speed (motion blur control) • Flash Demo – In fraction of a second! (from • Examples: 1/30, 1/60, 1/125, 1/250, 1/500 (factor of 2)! – Rule of thumb:! Stanford) • Hand-hold up to 1/f seconds, where f is focal length without camera shake! • Sensitivity (sensor noise control)! – Gain applied to sensor! – In ISO, bigger number, more sensitive (50, 100, 200, 400, 800, 1600)! Reciprocity between these three numbers, for a given exposure:# two degrees of freedom (2 things you can change)! 29h:p://graphics.stanford.edu/courses/cs178- 10/applets/exposure.html Quiz 2! Question 1! • Short or long lens?! • Fast (small f#) aperture? (f/4, f/5.6, f/2.8, …) ! • Large (large f#) aperture (f/8, f/16, …)! • Slow shutter? (1/30, 1/15, 1/8,1/4, $ 1, … )! • High ISO? (1,600 or higher)! • Short/Long Lens, Small/Large f/#?, Fast/Slow shutter, High ISO?! • 50mm lens, f/1.4,