Image Formation Optics and Imagers Real world Optics

Image Formation: Optics and Imagers Real world Optics Sensor Acknowledgment: some figures by B. Curless, E. Hecht, W. J. Smith, B. K. P. Horn, and A. Theuwisse

Optics • Pinhole camera • Lenses • Focus, aperture, distortion

Pinhole Camera • “Camera obscura” – known since antiquity Image plane Image Object Pinhole camera

Pinhole Camera • “Camera obscura” – known since antiquity Image plane Image Object Pinhole camera • First recording in 1826 onto a pewter plate (by Joseph Nicéphore Niepce)

Pinhole Camera Limitations • Aperture too big: blurry image • Aperture too small: requires long exposure or high intensity • Aperture much too small: diffraction through pinhole blurry image

Lenses • Focus a bundle of rays from a scene point onto a single point on the imager • Result: can make aperture bigger

Ideal Lenses • Thin-lens approximation • Gaussian lens law: 1/do + 1/di = 1/f • Real lenses and systems of lenses may be approximated by thin lenses if only paraxial rays (near the optical axis) are considered

Camera Adjustments • Focus? – Changes di • Zoom? – Changes f • Iris? – Changes aperture

Focus and Depth of Field • For a given di, “perfect” focus at only one do • In practice, focus is OK for some range of depths – Circle of confusion smaller than a pixel • Better depth of field with smaller apertures – Better approximation to pinhole camera

Field of View • Q: What does field of view of camera depend on? – Focal length of lens – Size of imager – Object distance?

Computing Field of View 1/do + 1/di = 1/f tan /2 = ½ xo / do xo xi xo / do = xi / di = 2 tan-1 ½ xi (1/f 1/do) do di Since typically do >> f, 2 tan-1 ½ xi / f

Aperture • Controls amount of light • Affects depth of field • Affects distortion (since thin-lens approximation is better near center of lens)

Aperture • Aperture typically given as “f-number” (also “f-stops” or just “stops”) • What is f /4? – Aperture is ¼ the focal length

Monochromatic Aberrations • Real lenses do not follow thin lens approximation because surfaces are spherical (manufacturing constraints) • Result: thin-lens approximation only valid iff sin

Distortion • Pincushion or barrel radial distortion • Varies with placement of aperture

Distortion • Varies with placement of aperture

Distortion • Varies with placement of aperture

Distortion • Varies with placement of aperture

First-Order Radial Distortion • Goal: mathematical formula for distortion • If distortion is small, can be approximated by “first-order” formula: r’ = r (1 + r 2) r = ideal distance to center of image r’ = distorted distance to center of image • Why (1 + r 2) and not (1 + r)?

Chromatic Aberration • Due to dispersion in glass (focal length varies with the wavelength of light) • Result: color fringes near edges of image • Correct by building lens systems with multiple kinds of glass

Correcting for Aberrations • High-quality compound lenses use multiple lens elements to “cancel out” distortion and aberration • Often 5 -10 elements, more for extreme wide angle

Sensors • Film • Vidicon • CCD • CMOS

Vidicon • Best-known in family of “photoconductive video cameras” • Basically television in reverse ++++ Scanning Electron Beam Electron Gun Lens System Photoconductive Plate

MOS Capacitors • MOS = Metal Oxide Semiconductor Gate (wire) Si. O 2 (insulator) p-type silicon

MOS Capacitors • Voltage applied to gate repels positive “holes” in the semiconductor +10 V ++++++ Depletion region (electron “bucket”)

MOS Capacitors • Photon striking the material creates electron-hole pair +10 V Photon ++++++ +

Charge Transfer • Can move charge from one bucket to another by manipulating voltages

CCD Architectures • Linear arrays • 2 D arrays

Linear CCD • Accumulate photons, then clock them out • To prevent smear: first move charge to opaque region, then clock it out

Full-Frame CCD • Other arrangements to minimize smear

CMOS Imagers • Recently, can manufacture chips that combine photosensitive elements and processing elements • Benefits: – Partial readout – Signal processing – Eliminate some supporting chips low cost

Color • 3 -chip vs. 1 -chip: quality vs. cost

Video • Depending on the scene, pictures updated at 15– 70 Hz. perceived as “continuous” • Most video cameras use a shutter, so they are capturing for only part of a frame – Short shutter: less light, have to open aperture – Long shutter: more light, but motion blur • Television uses interlaced video

Interlacing These rows transmitted first These rows transmitted 1/60 sec later

Television • US: NTSC standard – Fields are 1/60 sec. – 2 fields = 1 frames are 1/30 sec. – Each frame has 525 scanlines, of which approximately 480 are visible – No discrete pixels along scanlines, but if pixels were square, there would be about 640 visible

Television • NTSC standard – Thus, an NTSC frame is about 640 480 – Color at lower resolution than intensity • PAL standard – Lower rate: fields at 50 Hz. (frames at 25 Hz. ) – Higher resolution: about 768 576