Overview: ray transfer matrices
optical axis
Propagation through uniform space: Refraction at spherical interface: distance d, index of refraction nleft radius R, indices nleft, nright By using these elemental matrices, we may ray trace through an arbitrarily long cascade of optical elements (provided the paraxial approximation remains valid throughout.)
MIT 2.71/2.710 02/25/09 wk4-b- 1 1 Overview: thin lens and object/image at infinity object at infinity image at infinity
MIT 2.71/2.710 02/25/09 wk4-b- 2 2 Overview: composite optical elements
ray from infinity bends at 2nd PP
ray from then goes FFP BFP the FFP through the BFP
FFL BFL FFP BFP bends at then goes EFL EFL 1st PP on to infinity
1st PP 2nd PP 1st PP 2nd PP
1st PP 2nd PP
BFP image object FFP
EFL EFL
MIT 2.71/2.710 02/25/09 wk4-b- 3 3 Overview: real and virtual images
object + image +
object image
FFP BFP FFP BFP
image: real & inverted; MT<0 image: virtual & erect; MT>1
image image – object – object
BFP FFP BFP FFP
image: virtual & erect; 0 MIT 2.71/2.710 02/25/09 wk4-b- 4 4 Overview: apertures, stops, pupils, windows C.R. from object at field edge FoV nd M.R. from on-axis object 2 FP NA 1st FP Aperture Exit Stop pupil & Entrance (virtual) Pupil Field Stop Entrance & Exit Window Window MIT 2.71/2.710 02/25/09 wk4-b- 5 5 Today • Ray optics of mirrors • [[ Some terminology: – catoptric ≡ utilizing mirrors κάτοπτρον (kátoptron) = mirror – dioptric ≡ utilizing refractive lenses δίοπτρον (díoptron) = lens – catadioptric ≡ utilizing both mirrors and refractive lenses]] • The basic optical imaging systems – magnifier lens – eyepiece – microscope – telescope • refractive: Keppler (dioptric) • reflective: Cassegrain (catoptric) • Schmidt (catadioptric) MIT 2.71/2.710 02/25/09 wk4-b- 6 6 Sign conventions for catoptric optics • Light travels from left to right before reflection and from right to left after reflection • A radius of curvature is positive if the surface is convex towards the left • Longitudinal distances before reflection are positive if pointing to the right; longitudinal distances after reflection are positive if pointing to the left • Longitudinal distances are positive if pointing up • Ray angles are positive if the ray direction is obtained by rotating the +z axis counterclockwise through an acute angle positive positive direction ray angle (after reflection) positive positive ray angle ray elevation positive direction (before positive reflection) curvature MIT 2.71/2.710 02/25/09 wk4-b- 7 7 Object/image at infinity with spherical mirror image object at ∞ Object at infinity object image at ∞ ⇒Focal length Image at infinity MIT 2.71/2.710 02/25/09 wk4-b- 8 8 Catoptric imaging formulae object/ image/ image image object object at ∞ Object/image at infinity Object, image at finite distances Focal length Imaging condition Ray transfer Magnification matrix MIT 2.71/2.710 02/25/09 wk4-b- 9 9 The single lens magnifier object at near point (25cm) ➙maximum unaided magnification eye Magnifying power lens real image at retina Near point virtual image (erect and magnified) magnifier lens real (magnified) image at retina MIT 2.71/2.710 02/25/09 wk4-b-10 10 Eyepiece • also known as “ocular” • Magnifier meant to look at the intermediate image formed by the preceding optical instrument: – eye looks into eyepiece – eyepiece “looks” into optical system (microscope, telescope, etc.) • Ideally should – produce a virtual image at infinity (⇒ MP=doP) • the final image is viewed with relaxed (unaccommodated) eye – center the exit pupil (eye point) where the observer’s eye is placed at 10mm (eye relief) from the instrument MIT 2.71/2.710 Fig. 5.93 in Hecht, Eugene. Optics. Reading, MA: Addison-Wesley, 2001. 02/25/09 wk4-b-11 ISBN: 9780805385663. (c) Addison-Wesley. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/fairuse. 11 Microscope • Purpose: to “magnify” thereby providing additional detail on a small, nearby object • Objective lens followed by an eyepiece Exit Pupil – Objective: forms real, magnified image of the object at the plane where the instrument’s field stop is located – Eyepiece: its object plane is the objective’s image plane and forms a virtual image at infinity ➡ magnified image can be viewed with relaxed Eyepiece (unaccommodated) eye ➡ compound magnifying power is the product of the magnifications of the two elements, i.e. Field Stop • The distance from the BFP of the objective to the FFP of the eyepiece is known as tube length and is standardized at 160mm. • The near point used as do is standardized at 254mm (10 inches.) Aperture Entrance Stop Pupil MIT 2.71/2.710 Fig. 5.99 in Hecht, Eugene. Optics. Reading, MA: Addison-Wesley, 2001. 02/25/09 wk4-b-12 ISBN: 9780805385663. (c) Addison-Wesley. All rights reserved. This content is excluded from our CreativeCommons license. For more information, see http://ocw.mit.edu/fairuse. 12 MIT OpenCourseWare http://ocw.mit.edu 2.71 / 2.710 Optics Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.