Image Formation Fundamentals
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1 03/04/2017 Image Formation Fundamentals Optical Engineering Prof. Elias N. Glytsis School of Electrical & Computer Engineering National Technical University of Athens
2 Imaging Conjugate Points Imaging Limitations Scattering Aberrations Diffraction F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2 nd Ed., Prentice Hall,
3 Perfect Imaging Using Reflective Surfaces Ellipsoid Hyperboloid Paraboloid F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2 nd Ed., Prentice Hall,
4 Perfect Imaging Using Refractive Surfaces Perfect imager 1. Each ray will travel in least time (Fermat). 2. All rays will take the same time (Isochronous). 3. Equal time implies equal nx (optical path length) Cartesian Ovoid y n o P(x,y) n i O I x s o s i 4
5 Perfect Imaging Using Refractive Surfaces Cartesian Ovoids 5
6 Reflection at a Spherical Mirror Sign Conventions (light propagation from left to right) F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 3 rd Ed., Pearson-Prentice Hall,
7 Image Formation by Spherical Mirrors Convex Concave 7
8 Real images in a concave mirror A mirror can produce a real image, provided that it is a concave mirror. In this experiment, we use an incandescent lamp as the object, whose image we project onto a vertical white screen. There is a horizontal baffle between the lamp and the screen so that light from the lamp doesn't fall directly on the screen. As we'll show below in the section on Aberration, this cheap mirror is not a good approximation to a parabola, so using its whole area would produce a very distorted image. For that reason, we use a stop (a sheet of black paper) with a small hole to reduce the mirror area. The photo at top left shows a side view, and a schematic lies below. The middle photo was taken from above the mirror, looking towards the lamp and screen. A larger version of this photo is shown at right. In this version, the top half of the photo have been brightened, while the bottom half has been darkened, to show better the details of the lamp and to make it more obvious that the image is inverted. Note that rays of light really do meet at the position of this image, which is why we call it a real image. An incandescent lamp is the object. Its (real) image is projected on a screen via a concave mirror. 8
9 Spherical Mirrors Convex Concave 9
10 Convex Spherical Mirrors Applications 10
11 Refraction at a Spherical Interface Sign Conventions (light propagation from left to right) 11
12 Thin Lens Equation Conventional Converging Lens Conventional Diverging Lens Surrounding medium of the same index n 1 Surrounding medium of the varying index n 1 (left) and n 3 (right) 12
13 Lenses Types Converging Lenses Diverging Lenses 13
14 Thin Lenses Converging Lens Diverging Lens 1: Parallel Ray 2: Chief Ray 3: Focal Ray 14
15 Positive Thin Lens Inverted Object Image s > 2f Reduced Real Object Image 2f > s > f Inverted Enlarged Real Upright Image Object f > s > 0 Enlarged Virtual 15
16 Negative Thin Lens Object F 1 F 2 Image Image is always virtual, upright, and reduced. 16
17 Negative Thin Lens 17
18 Example Imaging with Convex Lenses Image by a convex lens for object placed at different distance from it 18
19 Example Imaging with Convex Lenses Virtual image formed by the convex lens Magnifying Glass 19
20 Example Imaging with Concave Lenses 20
21 Near-Sighted Eye (Myopia) - Correction Too far for near-sighted eye to focus Near-sighted eye can focus on this! 21
22 Far-Sighted Eye (Hyperopia/Presbyopia) - Correction Too close for far-sighted eye to focus Far-sighted eye can focus on this! 22
23 Astigmatic Eye - Correction
24 Elementary ABCD Matrices 0 F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 3 rd Ed., Pearson-Prentice Hall,
25 Elementary ABCD Matrices F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 3 rd Ed., Pearson-Prentice Hall,
26 Significance of A, B, C, and D Elements D = 0 (First Focal Plane) A = 0 (Second Focal Plane) B = 0 (Imaging System) C = 0 (Telescopic System) F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 3 rd Ed., Pearson-Prentice Hall,
27 Principal Planes and Cardinal Points of an Optical System F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 3 rd Ed., Pearson-Prentice Hall,
28 Principal Planes of a Converging Lens System Principal Planes of a Thin Lens, a Thick Lens and a Complex Lens 28
29 Principal Planes and Cardinal Points h F 1 F 2 H 1 H 2 ƒ ƒ h s s PP 1 PP 2 29
30 Principal Planes of a Telephoto Lens Nikon 300mm f/4 ED-IF AF Nikkor Distances are in millimeters ED: Extra Low Dispersion Glass (reduce chromatic aberration) IF: Internal Focusing (movement of group of elements with respect to other groups, allows focusing on closer objects AF: Automatic Focusing (Rotating drive shaft through lens mounts moves lens with respect to camera) 30
31 Nikkor 135mm f/2.0 Ais. 31
32 Optical system of a real photographic lens (50mm f/1.8) 32
33 Nikkor 135mm f/2.8 Ais. 33
34 Nikkor 135mm f/2.8 Ais. 34
35 Micro-Nikkor 55mm f/2.8 Ais and AF Micro-Nikkor 55mm f/
36 Micro-Nikkor 55mm f/2.8 Ais and AF Micro-Nikkor 55mm f/
37 General Purpose Imaging Lens System Nikon 50mm (51.6mm) Nikkor-H f/2 Auto lens Distances are in millimeters 37
38 Two Thin-Lenses Example f 1 = 50mm f 2 = 25mm h 1 F 12 F 22 F 11 V 1 F 21 V 2 s 1 = 75mm L = 40mm 38
39 Two Thin-Lenses Example Method of ABCD Matrices Object Plane f 1 = 50mm f 2 = 25mm Image Plane h 1 V 1 V 2 s 1 = 75mm L = 40mm x Optical system of 2 thin lenses 39
40 Two Thin-Lenses Example Method of Cascaded Thin Lenses f 1 = 50mm f 2 = 25mm F 12 F 22 F 11 V 1 F 21 V 2 = = 75mm L = 40mm = 20.37mm = 150mm 40
41 Two Thin-Lenses Example Method of Cardinal Points Object Plane f 1 = 50mm f 2 = 25mm Image Plane r f 2 h 1 H 2 F 1 F 2 H 1 f 1 s 1 = 75mm s L = 40mm Optical system of 2 thin lenses 41
42 Two Thin-Lenses Example Method of Cardinal Points s i = mm Object Plane Image Plane r f 2 h 1 H 1 h 1 H 2 F 1 F 2 f 1 s s o = mm Optical system of 2 thin lenses 42
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