Basic Principles of Imaging and Lenses

Light

Light Photons ElectromagneticRadiation

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 10 8 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/ Putting these equations together, we see that E = hc/

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 Visible Infrared Radio Composite

EM Spectrum Relative Sizes

The Visible Spectrum Light waves extend in wavelength from about 400 to 700 nanometers.

Transparent Materials Transparent - the term applied to materials through which light can pass in straight lines.

Opaque Materials Opaque - the term applied to materials that absorb light.

Are clouds transparent or opaque to visible light? –Answer: opaque Are clouds transparent or opaque to ultraviolet light? –Answer: almost transparent

Special Things About a Light Wave It does not need a medium through which to travel It travels with its highest velocity in a vacuum Its highest velocity is the speed of light, c, equal to 300,000 km/sec The frequency (or wavelength) of the wave determines whether we call it radio, infrared, visible, ultraviolet, X-ray or gamma-ray.

Camera Obscura, Gemma Frisius, A Brief History of Images

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". Da Vinci Slide credit: David Jacobs

Abu Ali Al-hasen Ibn Alhasen, mathematician, born in Basra, d Cairo, claimed he could control the inundations of the Nile, for which caliph Hakim ordered him to Cairo in 1015 or Realizing his abilities as civil engineer were less than his skill as a mathematician, he feigned insanity to save his head. Until Hakim died in 1021, Alhazen spent his time at the library of Alexandria, writing on geometry, optics, perspective and the camera obscura. Translated into Latin in 1270 and printed as Opticae Thesaurus Alhazani in MSS at Paris, Oxford, Leyden. An additional MS at the Vatican Library is annotated by Lorenzo Ghiberti of the Florence Baptistry doors ( ). Earlier MSS may have existed, for Roger Bacon writes a[bout] optics and the camera obscura before Alhazen is the first to show how an image is formed on the eye, using the camera obscura as an analog. Alhazen states (in the Latin translation), and with respect to the camera obscura, "Et nos non inventimus ita", we did not invent this. Source:

Lens Based Camera Obscura, A Brief History of Images

(Jack and Beverly Wilgus) Jetty at Margate England, Slide credit: David Jacobs

Still Life, Louis Jaques Mande Daguerre, A Brief History of Images

Abraham Lincoln? ? 1568 A Brief History of Images

Silicon Image Detector, A Brief History of Images

A Brief History of Images Digital Cameras

A Brief History of Images Hasselblad HD

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 (x,y) screenscene Is an image being formed on the screen? YES! But, not a “clear” one. image plane effective focal length, f’ optical axis y x z pinhole

Magnification image plane f’ optical axis y x z Pinhole planar scene A B A’ B’ d d’ From perspective projection: Magnification:

Properties of Projection Points project to points Lines project to lines Planes project to the whole or half image Angles are not preserved Degenerate cases –Line through focal point projects to a point. –Plane through focal point projects to line

Distant Objects are Smaller Note that B’ and C’ labels should be switched. Size is inversely proportional to distance.

Parallel Lines Meet Common to draw film plane in front of the focal point. Moving the film plane merely scales the image.

Vanishing Points Each set of parallel lines meets at a different point –The vanishing point for this direction Sets of parallel lines on the same plane lead to collinear vanishing points. –The line is called the horizon for that plane Good ways to spot faked images –scale and perspective don’t work –vanishing points behave badly –supermarket tabloids are a great source.

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 Example: If f’ = 50mm, = 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! i o Gaussian Lens Formula: 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! P P’ f

Focus and Defocus 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. d aperture diameter aperture Gaussian Law: Blur Circle, b Blur Circle Diameter :

Problems with Lenses Compound (Thick) Lens Vignetting Chromatic AbberationRadial and Tangential Distortion thickness principal planes nodal points B A more light from A than B ! Lens has different refractive indices for different wavelengths. image plane ideal actual ideal actual

Spherical Aberration Spherical lenses are the only easy shape to manufacture, but are not correct for perfect focus.

Two Lens System 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. image plane lens 2lens 1 object intermediate virtual image final image Magnification: 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

Insect Eye We make cameras that act “similar” to the human eye Fly Mosquito

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 Slide credit: David Jacobs

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

Human Eye vs. the Camera We make cameras that act “similar” to the human eye

CCD Cameras Slide credit: David Jacobs