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Basic Principles of Imaging and Lenses Light Electromagnetic Radiation Photons Light These three are the same… • Light * pure energy • Electromagnetic Waves * energy-carrying waves emitted by vibrating electrons • Photons * particles of light EM Radiation Travels as a Wave c = 3 x 108 m/s EM Radiation Carries Energy • Quantum mechanics tells us that for photons E = hf where E is energy and h is Planck’s constant. • But f = c/l • Putting these equations together, we see that E = hc/l Electromagnetic Wave Velocity • The speed of light is the same for all seven forms of light. • It is 300,000,000 meters per second or 186,000 miles per second. The Electromagnetic Spectrum • • • • • • • Radio Waves - communication Microwaves - used to cook Infrared - “heat waves” Visible Light - detected by your eyes Ultraviolet - causes sunburns X-rays - penetrates tissue Gamma Rays - most energetic The Multi-Wavelength Sun X-Ray UV Composite Infrared Visible Radio EM Spectrum Relative Sizes The Visible Spectrum Light waves extend in wavelength from about 400 to 700 nanometers. A Brief History of Images Camera Obscura, Gemma Frisius, 1558 1544 Camera Obscura "When images of illuminated objects ... penetrate through a small hole into a very dark room ... you will see [on the opposite wall] these objects in their proper form and color, reduced in size ... in a reversed position, owing to the intersection of the rays". Leonardo da Vinci http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html (Russell Naughton) Slide credit: David Jacobs A Brief History of Images Lens Based Camera Obscura, 1568 1558 1568 Jetty at Margate England, 1898. http://brightbytes.com/cosite/collection2.html (Jack and Beverly Wilgus) Slide credit: David Jacobs A Brief History of Images 1558 1568 1837 Still Life, Louis Jaques Mande Daguerre, 1837 A Brief History of Images 1558 1568 1840? Abraham Lincoln? A Brief History of Images 1558 1568 1837 Silicon Image Detector, 1970 1970 A Brief History of Images 1558 1568 1837 Digital Cameras 1970 1995 A Brief History of Images 1558 1568 1837 Hasselblad HD2-39 1970 1995 2006 Geometric Optics and Image Formation Pinhole Cameras • • • Pinhole camera - box with a small hole in it Image is upside down, but not mirrored left-to-right Question: Why does a mirror reverse left-to-right but not top-to-bottom? Pinhole and the Perspective Projection Is an image being formed on the screen? (x,y) YES! But, not a “clear” one. screen scene image plane r ( x, y , z ) y optical axis effective focal length, f’ z pinhole x r ' ( x' , y ' , f ' ) r' r f' z x' x f' z y' y f' z Problems with Pinholes • Pinhole size (aperture) must be “very small” to obtain a clear image. • However, as pinhole size is made smaller, less light is received by image plane. • If pinhole is comparable to wavelength of incoming light, DIFFRACTION effects blur the image! • Sharpest image is obtained when: pinhole diameter d 2 f 'l Example: If f’ = 50mm, l = 600nm (red), d = 0.36mm The Reason for Lenses Image Formation using (Thin) Lenses • Lenses are used to avoid problems with pinholes. • Ideal Lens: Same projection as pinhole but gathers more light! o i P P’ f Gaussian Lens Formula: 1 1 1 i o f • f is the focal length of the lens – determines the lens’s ability to bend (refract) light • f different from the effective focal length f’ discussed before! Focus and Defocus aperture Blur Circle, aperture diameter b d o i i' Gaussian Law: 1 1 1 i o f o' 1 1 1 i ' o' f Blur Circle Diameter : (i'i) b f f (o o' ) (o' f ) (o f ) d (i ' i ) i' Depth of Field: Range of object distances over which image is sufficiently well focused, i.e., range for which blur circle is less than the resolution of the imaging sensor. Problems with Lenses Compound (Thick) Lens Vignetting B L3 L2 L1 principal planes A nodal points thickness Chromatic Abberation more light from A than B ! Radial and Tangential Distortion ideal FB FG FR actual ideal actual image plane Lens has different refractive indices for different wavelengths. Spherical Aberration Spherical lenses are the only easy shape to manufacture, but are not correct for perfect focus. Two Lens System d object final image f2 i2 o2 i1 f1 o1 image plane intermediate virtual image lens 2 lens 1 • Rule : Image formed by first lens is the object for the second lens. • Main Rays : Ray passing through focus emerges parallel to optical axis. Ray through optical center passes un-deviated. • Magnification: m i2 i1 o2 o1 Exercises: What is the combined focal length of the system? What is the combined focal length if d = 0? Lens systems • A good camera lens may contain 15 elements and cost a many thousand dollars • The best modern lenses may contain aspherical elements Human Eye • The eye has an iris like a camera • Focusing is done by changing shape of lens • Retina contains cones (mostly used) and rods (for low light) • The fovea is small region of high resolution containing mostly cones • Optic nerve: 1 million flexible fibers http://www.cas.vanderbilt.edu/bsci111b/eye/human-eye.jpg Slide credit: David Jacobs The Eye • The human eye is a camera! – Iris - colored annulus with radial muscles – Pupil - the hole (aperture) whose size is controlled by the iris – What’s the “film”? • photoreceptor cells (rods and cones) in the retina Human Eye vs. the Camera • We make cameras that act “similar” to the human eye Image Formation Digital Camera Film The Eye Insect Eye We make cameras that act “similar” to the human eye Fly Mosquito The Retina Cross-section of eye Cross section of retina Pigmented epithelium Ganglion axons Ganglion cell layer Bipolar cell layer Receptor layer Retina up-close Light Two types of light-sensitive receptors Cones cone-shaped less sensitive operate in high light color vision Rods rod-shaped highly sensitive operate at night gray-scale vision © Stephen E. Palmer, 2002 Rod / Cone sensitivity The famous sock-matching problem… Human Eye • Rods – Intensity only – Essentially night vision and peripheral vision only – Since we are trying to fool the center of field of view of human eye (under well lit conditions) we ignore rods Human Eye • Cones – Three types perceive different portions of the visible light spectrum Human Eye • Because there are only 3 types of cones in human eyes, we only need 3 stimulus values to fool the human eye – Note: Chickens have 4 types of cones Distribution of Rods and Cones # Receptors/mm2 . Fovea 150,000 Rods Blind Spot Rods 100,000 50,000 0 Cones Cones 80 60 40 20 0 20 40 60 80 Visual Angle (degrees from fovea) Night Sky: why are there more stars off-center? © Stephen E. Palmer, 2002 The Physics of Light Some examples of the spectra of light sources . B. Gallium Phosphide Crystal # Photons # Photons A. Ruby Laser 400 500 600 700 400 500 Wavelength (nm.) 700 Wavelength (nm.) D. Normal Daylight # Photons C. Tungsten Lightbulb # Photons 600 400 500 600 700 400 500 600 700 © Stephen E. Palmer, 2002 More Spectra metamers The Physics of Light % Photons Reflected Some examples of the reflectance spectra of surfaces Red 400 Yellow 700 400 Blue 700 400 Wavelength (nm) Purple 700 400 700 © Stephen E. Palmer, 2002 The Psychophysical Correspondence There is no simple functional description for the perceived color of all lights under all viewing conditions, but …... A helpful constraint: Consider only physical spectra with normal distributions mean area # Photons 400 500 variance 600 700 Wavelength (nm.) © Stephen E. Palmer, 2002 The Psychophysical Correspondence # Photons Mean blue Hue green yellow Wavelength © Stephen E. Palmer, 2002 The Psychophysical Correspondence # Photons Variance Saturation hi. high med. medium low low Wavelength © Stephen E. Palmer, 2002 The Psychophysical Correspondence Area Brightness # Photons B. Area Lightness bright dark Wavelength © Stephen E. Palmer, 2002 Digital camera • A digital camera replaces retina with a sensor array – Each cell in the array is light-sensitive diode that converts photons to electrons – Two common types • Charge Coupled Device (CCD) • CMOS – http://electronics.howstuffworks.com/digital-camera.htm CCD Cameras http://huizen.ddsw.nl/bewoners/maan/imaging/camera/ccd1.gif Slide credit: David Jacobs Sensor Array CMOS sensor Sampling and Quantization Interlace vs. progressive scan http://www.axis.com/products/video/camera/progressive_scan.htm Progressive scan http://www.axis.com/products/video/camera/progressive_scan.htm Interlace http://www.axis.com/products/video/camera/progressive_scan.htm Color Sensing in Camera (RGB) • 3-chip vs. 1-chip: quality vs. cost • Why more green? Why 3 colors? http://www.cooldictionary.com/words/Bayer-filter.wikipedia Practical Color Sensing: Bayer Grid • Estimate RGB at ‘G’ cels from neighboring values http://www.cooldictionary.com/ words/Bayer-filter.wikipedia Image Formation f(x,y) = reflectance(x,y) * illumination(x,y) Reflectance in [0,1], illumination in [0,inf] White Balance White World / Gray World assumptions Problem: Dynamic Range The real world has High dynamic range 1 1500 25,000 400,000 2,000,000,000 Is Camera a photometer? Image pixel (312, 284) = 42 42 photos? Long Exposure 10-6 Real world High dynamic range 10-6 106 106 Picture 0 to 255 Short Exposure 10-6 Real world High dynamic range 10-6 106 106 Picture 0 to 255 Image Acquisition Pipeline Lens scene radiance Shutter sensor irradiance 2 (W/sr/m ) sensor exposure Dt CCD ADC analog voltages Remapping digital values Camera is NOT a photometer! pixel values Varying Exposure What does the eye sees? The eye has a huge dynamic range Do we see a true radiance map?
