Lens Aberrations Aberration: a departure from the paraxial limit.

Slides:



Advertisements
Similar presentations
Reflection at a Spherical Surface
Advertisements

Consider Refraction at Spherical Surfaces:
Mirror and Lens Properties. Image Properties/Characteristics Image Type: Real or Virtual Image Orientation: Erect or Inverted Image Size: Smaller, Larger,
Chapter 31: Images and Optical Instruments
Modern Optics Lab Experiment 2: REFLECTION AND REFRACTION AT SPHERICAL INTERFACES  Measuring: Radii of mirrors and lenses Focal points of mirrors, spherical.
3.7. Magnification by plane mirrors A plane mirror generates a virtual image that occurs as far into the mirror as the object is placed in front of the.
Chapter 23:Mirrors and Lenses Flat Mirrors Homework assignment : 20,24,42,45,51  Image of a point source P P’ The reflected rays entering eyes look as.
Flat Mirrors Consider an object placed in front of a flat mirror
Chapter 31 Images.
Chapter 36 Image Formation.
Chapter 23 Mirrors and Lenses.
Light: Geometric Optics
Ch. 18 Mirrors and Lenses Milbank High School. Sec Mirrors Objectives –Explain how concave, convex, and plane mirrors form images. –Locate images.
Chapter 36 Image Formation. Summary: mirrors Sign conventions: + on the left - on the right Convex and plane mirrors: only virtual images (for real objects)
Aperture Pupil (stop) Exit Pupil Entrance Pupil.
Optical Theory II ABERRATIONS Copyright Ellen Stoner, MALS, ABOM, NCLC.
Geometric Optics of thick lenses and Matrix methods
Optics 1----by Dr.H.Huang, Department of Applied Physics
Small f/number, “fast” system, little depth of focus, tight tolerances on placement of components Large f/number, “slow” system, easier tolerances,
Fig Reflection of an object (y) from a plane mirror. Lateral magnification m = y ’ / y © 2003 J. F. Becker San Jose State University Physics 52 Heat.
Chapter 36 Serway & Jewett 6 th Ed.. Fig Q36-26, p.1167 Mirrors and Lenses.
Lenses We will only consider “thin” lenses where the thickness of the lens is small compared to the object and image distances. Eugene Hecht, Optics, Addison-Wesley,
Optical Center Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Fig Spherical aberration for a lens
Fiber Optics Defining Characteristics: Numerical Aperture Spectral Transmission Diameter.
C F V Light In Side S > 0 Real Object Light Out Side S ’ > 0 Real Image C This Side, R > 0 S < 0 Virtual Object S ’ < 0 Virtual Image C This Side, R
Chapter 23 Mirrors and Lenses.
Concave/Convex Mirror Image Formation Rules 1.Parallel Rays - Light rays parallel to the principal axis are reflected through the focus of the mirror.
Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Mirrors and Lenses.
Chapter 34. Images What is Physics? Two Types of Image
Physics 1C Lecture 26A.
Physics C Chapter 36 From serway book Prepared by Anas A. Alkanoa M.Sc.( master degree) in Theoretical Physics, Electromagnetic Waves (Optical Science),
Lenses and Mirrors. How does light interact with pinholes? How does light interact with lenses? –___________ How does light interact with mirrors? –___________.
Chapter 23 Mirrors and Lenses.
Fundamental of Optical Engineering Lecture 3.  Aberration happens when the rays do not converge to a point where it should be. We may distinguish the.
Chapter 18-1 Mirrors. Plane Mirror a flat, smooth surface light is reflected by regular reflection rather than by diffuse reflection Light rays are reflected.
Mirrors & prisms MIT 2.71/ /12/01 wk2-b-1 Last time: optical elements, – Pinhole camera – Lenses Basic properties of spherical surfaces Ray tracing.
Chapter 34 Lecture Eight: Images: II. Image Formed by a Thin Lens A thin lens is one whose thickness is small compared to the radii of curvature For a.
Last Word on Chapter 22 Geometric Optics Images in a Plane Mirror.
Chapter 36 Image Formation (Lens and Mirrors) Using the ray approximation of geometric optics, we can now study how images are formed with mirrors and.
Unit 11: Part 2 Mirrors and Lenses. Outline Plane Mirrors Spherical Mirrors Lenses The Lens Maker’s Equation Lens Aberrations.
3/4/ PHYS 1442 – Section 004 Lecture #18 Monday March 31, 2014 Dr. Andrew Brandt Chapter 23 Optics The Ray Model of Light Reflection; Image Formed.
1 Chapter 5 Geometrical optics January 21,23 Lenses 5.1 Introductory remarks Image: If a cone of rays emitted from a point source S arrives at a certain.
Geometric Optics. An object inside the focus casts a virtual image that is only focused by the eye.
Geometrical Optics Chapter 24 + Other Tidbits 1. On and on and on …  This is a short week.  Schedule follows  So far, no room available for problem.
Chapter 34 Lecture Seven: Images: I HW 3 (problems): 34.40, 34.43, 34.68, 35.2, 35.9, 35.16, 35.26, 35.40, Due Friday, Sept. 25.
1 32 Optical Images image formation reflection & refraction mirror & lens equations Human eye Spherical aberration Chromatic aberration.
Lenses and imaging MIT 2.71/ /10/01 wk2-a-1 Huygens principle and why we need imaging instruments A simple imaging instrument: the pinhole camera.
Thin-lens equation: 1/f = 1/d 0 + 1/d i. Magnification equation: h i /h o = d i /d o.
3.30. Image location by ray tracing Consider a real object that is placed in front of a convex lens. The location of the image can be found by considering.
Physics 203/204 4: Geometric Optics Images formed by refraction Lens Makers Equation Thin lenses Combination of thin lenses Aberration Optical Instruments.
ABERRATIONS Lecturer in PHYSICS Silver Jubilee Govt.,College(A),
Chapter 36 Image Formation 1: 1. Flat mirror 2. Spherical mirrors.
Image Formation. Flat Mirrors  p is called the object distance  q is called the image distance  θ 1 = θ 2 Virtual Image: formed when light rays do.
Matrix methods, aberrations & optical systems
Image Formation III Chapter 1 (Forsyth&Ponce) Cameras “Lenses” Guido Gerig CS-GY 6643, Spring 2016 (slides modified from Marc Pollefeys, UNC Chapel Hill/
GEOMETRICAL OPTICS. Laws of Reflection Laws of Refraction.
Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors. Draw ray diagrams to find the image distance.
Lenses, mirrors and refractive surfaces
Chapter 18 Mirrors and Lenses. Curved Mirrors Concave shaped mirrors cause parallel light rays to converge. Convex shaped mirrors cause parallel light.
Today’s agenda: Plane Mirrors. You must be able to draw ray diagrams for plane mirrors, and be able to calculate image and object heights, distances, and.
Geometric Optics: Mirrors and Lenses. Mirrors with convex and concave spherical surfaces. Note that θ r = θ i for each ray.
Basics Reflection Mirrors Plane mirrors Spherical mirrors Concave mirrors Convex mirrors Refraction Lenses Concave lenses Convex lenses.
Spherical Aberration. Rays emanating from an object point that are incident on a spherical mirror or lens at different distances from the optical axis,
RAY DIAGRAMS Steps for drawing a plane mirror ray diagram: 1. A ray that strikes perpendicular to the mirror surface, reflects perpendicular to the mirror.
Ray Diagrams for Lenses
HW #4, Due Sep. 21 Ch. 2: P28, PH8, PH16 Ch. 3: P3, P5.
SPHERICAL MIRROR EQUATIONS
Mirrors, Plane and Spherical Spherical Refracting Surfaces
SPHERICAL MIRROR EQUATIONS
Presentation transcript:

Lens Aberrations Aberration: a departure from the paraxial limit. Hope College, PHYS 352, Spring 2013 Lens Aberrations Aberration: a departure from the paraxial limit. Paraxial limit: (1) Rays are kept close to the optic axis. (2) Small angle approximation (1st Order) 5th Order 3rd Order 1 Order 3rd Order aberration theory: Keep the 3rd order terms.

Quantify the aberration: a(Q)=Path 2 – Path 1 Hope College, PHYS 352, Spring 2013 Pages 153-159 of Hecht, 4th ed., treats refraction in the paraxial (1st Order) limit. If the 3rd order terms are kept in ℓo and ℓi (p. 154) we find that extended images don’t land on exactly the same focal surface (See Fig. 6.14, p, 254). n1 n2 Q ℓo Path 2 ℓi Path 1 so si Paraxial Approximation: Path 1 and Path 2 have the same Optical Path Length Quantify the aberration: a(Q)=Path 2 – Path 1 a(Q)=(n1ℓo+n2ℓi)-(n1so+n2si) a=0 means no aberration

The Five Monochromatic Seidel Aberrations Hope College, PHYS 352, Spring 2013 The Five Monochromatic Seidel Aberrations yi and yo are paraxial image and object heights. n1 n2 Q ℓi  ℓo r yi yo Distortion Curvature of field Astigmatism Coma Spherical aberration Spread the image point (From Pedrotti, 3rd Ed., Section 20.2)

Hope College, PHYS 352, Spring 2013 1. Spherical aberration The only aberration that exists even for objects on the optic axis (no yi dependence). X Positive SA: The marginal rays converge left of the paraxial image (positive lens) Negative SA: The marginal rays converge right of the paraxial image (negative lens) Homework: Analyze this for a concave mirror.

n r2 r1 1. Spherical aberration Hope College, PHYS 352, Spring 2013 1. Spherical aberration r2 r1 Minimizing spherical aberration requires using two different radii. n The Coddington shape factor: Spherical aberration is minimized when (Shown in Jenkins & White, Sections 9.4-9.5) Homework: For what value of n does a planar convex lens produce a minimum spherical aberration for an object located at infinity? Which side of the lens should the light enter?

2. Coma Depends on yi. e.g. It’s an “off-axis” aberration. Hope College, PHYS 352, Spring 2013 2. Coma Depends on yi. e.g. It’s an “off-axis” aberration. Not symmetrical, which is the origin of the name. screen off-axis object www.telescope-optics.net Negative coma: Marginal rays focus closer to the optic axis. Positive coma: …farther from.. Figure 6.22a (Hecht, page 260) shows the formation of a comatic image from a series of comatic circles. The same lens designs minimize coma & spherical aberration. www.ryokosha.com

Hope College, PHYS 352, Spring 2013 3. Astigmatism Astigmatism: rays from off-axis source do not strike the lens symmetrically (tangential rays versus saggital rays). Tangential rays Saggital rays See Fig. 6.27 (page 263): tangential and saggital rays will fan out and form line images of the point source at two different image surfaces.

Circle of least confusion Hope College, PHYS 352, Spring 2013 Circle of least confusion http://www.olympus-ims.com/en/microscope/terms/classification/

Hope College, PHYS 352, Spring 2013 4. Curvature of Field Curvature of field: Tangential and saggital rays do not form images on the same surface. Very similar to astigmatism, but symmetric about the optic axis. Tangential rays Saggital rays T S (T left of S: Positive astigmatism)

Elimination of astigmatism and curvature of field aberrations Hope College, PHYS 352, Spring 2013 Elimination of astigmatism and curvature of field aberrations Engineer the lens curvatures or spacing so that tangential and saggital surfaces coincide. A focal surface that eliminates astigmatism to 3rd order is called a Petzval surface. Flat P surface – eliminates both astigmatism and curvature of field aberrations. Two lenses will have a flat P surface if n1f1=-n2f2 Ultimately, the film must conform to P. T S P P is always 3x farther from T than S

Hope College, PHYS 352, Spring 2013 5. Distortion http://www.olympus-ims.com/en/microscope/terms/classification/ Distortion aberration is caused by non-uniform lateral magnification and is often minimized using aperture stops.