paraxialraytracingandsimpleinstruments.pdf

8/18/2019 ParaxialRayTracingAndSimpleInstruments.pdf

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ECE 5616 OE System Design

Robert McLeod 69

The telescopeKeplerian

Shown in the afocal geometry (d=f 1+f 2). Relaxed eye focuses at~1m, thus telescope are usually not afocal. Analysis simpler,however.

Afocal : system has no

power: ray || to OAdoes not intersect OA

in image space

f 1 f 2

f

f

M

f h

f h

1

2

1

1

2

Definition of angular magnification

Via similar triangles

f 1 f 2

h1 -h’2

1

2

1

2

f

f

h

h M

•Design of ideal imaging systems with geometrical optics

–Single and compound lens systems

d

This is both important and fundamental.

h


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Robert McLeod 70

The telescopeGalilean

f 1 -f 2

h1 h2’

f 1 -f 2

d

f

f

M

f h

f h

1

2

1

1

2

More compact, upright

image. Same afocalcondition: d=f 1+f 2



Note that formula isidentical to Keplerian.This is the advantage

of the sign convention.

1

2

1

2

f

f

h

h M

Really, this is just the Keplerian with the second focal lengthnegative. Lenses are still separated by the sum of the focal lengths, but one is now negative.


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Robert McLeod

Reflective telescopes

71



Gregorian

Cassegrain

Newtonian

Replace first lens withcombo of two positivemirrors

Replace first lens withcombo of positive &negative mirrors.Shorter throw.

Replace first lens withmirror, useintermediate fold todirect light out oftube. Common

hobbyist design,inexpensive.

All replace the first lens of a Keplerian telescope with mirrors.

Schmidt-Cassegrain

Add refractive plate atentrance to correctaberrations, supportsecondary mirrorwithout struts.


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Robert McLeod

The compound microscope

72

1. “Compound” = two cascaded single-lens imaging systems.• Objective produces magnified real “intermediate” image• Eyepiece produces magnified virtual image

2. Two types of objectives• Older “finite conjugate”, z´ = 160 mm “tube length”• Modern “infinite conjugate” objective + ~160 mm “tube lens”

http://www.microscopyu.com/articles/optics/components.html



Finite conjugate

Infinite conjugate

= D NP


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Robert McLeod

Anatomy of a modern

microscope

73



http://www.microscopyu.com/articles/optics/components.html


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Robert McLeod

Eye pieces (1/2)Used in microscopes and telescopes

74



Huygens

Ramsden

Kellner

Flat toward eye,cheap but bad eyerelief.

Common. Better eye

relieve that Huygens.

Achromatic version

of Ramsden. Widerfield.


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Robert McLeod

Eye pieces (2/2)Used in microscopes and telescopes

75



Orthoscopic

Plossl

Erfle

Better image quality,±20° field.

Better image quality

over large field.Distortion worse thanorthoscopic.

Most common wide

field eye piece.


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Robert McLeod

Microscope conjugate

planes and illumination

76http://microscopy.berkeley.edu/courses/tlm/cmpd/cmpd.html




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Robert McLeod 77

Microscope analysisFinite conjugate objective



Focal system. Formimage at infinity for

simplicity of analysis.

f obj f eyepiece

tube length

Visual magnification of instrument is product of linearmagnification of objective and visual magnification of eyepiece:

Standard tube length is 160 mm.

eyepiece

np

obj

tube

eyepiecevobjmicroscopev

f

D

f l

M M M

Mobj f obj [mm] Typical NA

4 30 0.10

10 16 0.25

20 8 0.4060 3 0.85

100 1.8 1.3

Note eq.s are approximate

ltube >> f obj, Dnp >> f eyepice

Analysis the same for infinite conjugate objective, but replaceobjective with two-lens system with magnification Mobj


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Robert McLeod 78

Overhead projector



Illumination systemgives uniform, directed,white illumination

Condenser lens

Fresnel lens

Platen

Projection lens must be flat field, work

over a range of imagedistances, andachromatic. Designcan be simplified byillumination system.

Screen is white,

diffuse reflector tosend light into large

angle

Mirror flips parity sospeaker and viewers

see same image


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Robert McLeod

Camera

79



35mm Camera• Single lens reflex• Wide range of lenses

available cheaply• 46.5mm from mount to

film plane• Image size:24 mm×36 mm.

http://en.wikipedia.org/wiki/Single-lens_reflex_camera

Optical layout1: Front-mount lens2: Reflex mirror at 45°3: Focal plane shutter4: Film or sensor5: Focusing screen6: Condenser lens7: Pentaprism8: Eyepiece

Typicalcameralens, NikonAF Micro- Nikkor 105mm, f/2.8


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Robert McLeod 80

ABCD matricesMatrix formulation of paraxial ray-tracing


–Paraxial ray-tracing

k

k

k

k

k k

k

k

u

y

u

yd

u

yT

10

1

1

1

k

k

k

k

k

k k

k

u

y

u

y

u

yR

1

01

Transfer equation

Refraction equation

1

1

1

1

1111 u

y

u

y

u

y

K K K K

K M R T R T R System

matrix

0

0

0

1

011

1

1

u

y

u

y

u

y

K

K N T R T Conjugate

matrix

1 k

K y0 0

u y11u

-yK+1

1u

1K u

M

N

K d

0d

k k k k d u y y 1

k k k k yuu


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Robert McLeod 81

Properties of M, N

1 N M T R

1 BC AD DC

B AM Determinant = 1

If planes 0 and K+1 are conjugates, final ray height does notdepend on initial ray angle:

0120111 u y yK N N

012 N Conjugate condition

If plane 0 is the object space focal plane, the slope at the exit plane depends only on the object height:

0220211 u yuK N N

022 N Object at front focal plane

If the system is afocal, the direction of the image-space raydepends only on the direction of the object-space ray:

021 N Afocal condition

Write out the matrix equation for N:

If plane K+1 is the image space focal plane, the image-spaceray height depends only on the entrance angle:

011 N Image at rear focal plane




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Robert McLeod 82

Use of matrices M, N Find image plane given object

C d DC

C d A

C d DC

C d Ad Dd BC d A

d

DC

B Ad

K

K K K

K

K

1

1

1

1

01

0

)(10

1

10

1

MT T N

gives the image location012 N DC d

B Ad d K

1

1

Conjugate condition



1 k

K

y00u y

1

1u-y

K+1

1u

1K u

M

K d

1d

11

1 11

1

01

d d d

d d

K

K

E.g. single lens


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Robert McLeod 83

Form of N And EFL, first thick-lens concept

C d A y

y M K

K 110

1N If then

is the magnification012 N

11N

M 122 N Determinant = 1

1K u00 u

0220211 u yuK N N

1

01

K u

yF Effective focal length & system power

0

21N

M

M

1

0N



t t

t t

t t

t

t t t

0

1

1 11011 T R T N 0

E.g. single lens

paraxialraytracingandsimpleinstruments.pdf

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