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.)

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Overview: thin lens and object/image at infinityobject at infinity image at infinity

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Overview: composite optical elements

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FFP

1st PP

BFP

2nd PP

FFL BFL

EFL EFL

ray from infinity bends at

2nd PP

then goes through the BFP

ray from the FFP

bends at 1st PP

FFP

1st PP

BFP

2nd PP

then goes on to infinity

object FFP

BFP image

1st PP 2nd PP

EFL EFL

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Overview: real and virtual images

BFP

object

image

FFP BFP

object

image

FFP

+ +

image: real & inverted; MT<0 image: virtual & erect; MT>1

image image– – objectobject

FFP BFP FFPBFP

image: virtual & erect; 0<MT<1 image: virtual & erect; 0<MT<1

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Overview: apertures, stops, pupils, windows

Field Stop

2nd FP

1st FP

Exit pupil

(virtual)

Aperture Stop

& Entrance Pupil

M.R. from on-axis object

C.R. from object at field edge

NA

FoV

Entrance & Exit Window Window

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Today

• Ray optics of mirrors • [[ Some terminology:

– catoptric ≡ utilizing mirrorsκάτοπτρον (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)

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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 direction

(after reflection)

positive ray elevation

positive ray angle

positive ray angle

positive direction (before positive

reflection) curvature

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Object/image at infinity with spherical mirror

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⇒Focal length

object at ∞

image

Object at infinity

image at ∞

object

Image at infinity 8

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Catoptric imaging formulae

object imageimage/ object at ∞

object/ image

Object/image at infinity Object, image at finite distances

Imaging conditionFocal length

Ray transfer Magnificationmatrix

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The single lens magnifier

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object at near point (25cm) ➙maximum unaided magnification eye

lens

real image

at retina

virtual image (erect and magnified)

real image

at retina

(magnified)

magnifier lens

Magnifying power

Near point

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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

–

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center the exit pupil (eye point) where the observer’s eye is placed at 10mm (eye relief) from the instrument

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Fig. 5.93 in Hecht, Eugene. Optics. Reading, MA: Addison-Wesley, 2001.ISBN: 9780805385663. (c) Addison-Wesley. All rights reserved. This content is excludedfrom our CreativeCommons license. For more information, see http://ocw.mit.edu/fairuse.

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Field Stop

Eyepiece

Entrance Pupil

Exit Pupil

Aperture Stop

Microscope

• Purpose: to “magnify” thereby providing additional detail on a small, nearby object

• Objective lens followed by an eyepiece – 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

(unaccommodated) eye ➡ compound magnifying power is the product of the

magnifications of the two elements, i.e.

• 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.)

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Fig. 5.99 in Hecht, Eugene. Optics. Reading, MA: Addison-Wesley, 2001.ISBN: 9780805385663. (c) Addison-Wesley. All rights reserved. This content is excludedfrom our CreativeCommons license. For more information, see http://ocw.mit.edu/fairuse.

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