•Design of ideal imaging syst ems with geometrical optics ...ecee.colorado.edu/~mcleod/pdfs/OESD/lecturenotes/ParaxialRay... · ECE 5616 OE System Design Robert McLeod Reflective

ECE 5616 OE System Design

Robert McLeod 69

The telescopeKeplerian

Shown in the afocal geometry (d=f1+f2). Relaxed eye focuses at ~1m, thus telescope are usually not afocal. Analysis simpler, however.

Afocal: system has no power: ray || to OA

does not intersect OA in image space

f1 f2

M

f

f

M

fh

fh

12

1

1

2

Definition of angular magnification

Via similar triangles

f1 f2

h1 -h’2

1

2

1

2

f

f

h

hM

•Design of ideal imaging systems with geometrical optics–Single and compound lens systems

d

This is both important and fundamental.

h


Robert McLeod 70

The telescopeGalilean

f1 -f2

h1 h2’

f1 -f2

d

M

f

f

M

fh

fh

12

1

1

2

More compact, upright image. Same afocal

condition: d=f1+f2


Note that formula is identical to Keplerian. This is the advantage

of the sign convention.

1

2

1

2

f

f

h

hM

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


Robert McLeod

Reflective telescopes

71


Gregorian

Cassegrain

Newtonian

Replace first lens with combo of two positive mirrors

Replace first lens with combo of positive & negative mirrors. Shorter throw.

Replace first lens with mirror, use intermediate fold to direct light out of tube. Common hobbyist design, inexpensive.

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

Schmidt-Cassegrain

Add refractive plate at entrance to correct aberrations, support secondary mirror without struts.


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

= DNP


Robert McLeod

Anatomy of a modern microscope

73


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


Robert McLeod

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

74


Huygens

Ramsden

Kellner

Flat toward eye, cheap but bad eye relief.

Common. Better eye relieve that Huygens.

Achromatic version of Ramsden. Wider field.


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 than orthoscopic.

Most common wide field eye piece.


Robert McLeod

Microscope conjugate planes and illumination

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



Robert McLeod 77

Microscope analysisFinite conjugate objective


Focal system. Form image at infinity for

simplicity of analysis.

fobj feyepiece

tube length

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

Standard tube length is 160 mm.

eyepiece

np

obj

tube

eyepiecevobjmicroscopev

f

D

f

l

MMM

Mobj fobj [mm] Typical NA

4 30 0.10

10 16 0.25

20 8 0.40

60 3 0.85

100 1.8 1.3

Note eq.s are approximateltube >> fobj, Dnp >> feyepice

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


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 image distances, and

achromatic. Design can be simplified by illumination system.

Screen is white, diffuse reflector to

send light into large angle

Mirror flips parity so speaker and viewers

see same image


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 lens 2: Reflex mirror at 45°3: Focal plane shutter 4: Film or sensor 5: Focusing screen6: Condenser lens 7: Pentaprism8: Eyepiece

Typical camera lens, Nikon AF Micro-Nikkor 105 mm, f/2.8


Robert McLeod 80

ABCD matrices Matrix formulation of paraxial ray-tracing

•Design of ideal imaging systems with geometrical optics–Paraxial ray-tracing

k

kk

k

kk

k

k

u

y

u

yd

u

yT

10

1

1

1

k

kk

k

k

kk

k

u

y

u

y

u

yR

1

01

Transfer equation

Refraction equation

1

1

1

11111 u

y

u

y

u

yKKK

K

K MRTRTR System matrix

0

0

0

1011

1

1

u

y

u

y

u

y

K

K NTRT Conjugate matrix

1 k

K

y0 0u y11u

-yK+1

1u

1Ku

M

N

Kd

0d

kkkk duyy 1

kkkk yuu


Robert McLeod 81

Properties of M, N

1 NMTR

1 BCADDC

BAM Determinant = 1

If planes 0 and K+1 are conjugates, final ray height does not depend on initial ray angle:

0120111 uyyK NN

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 uyuK NN

022 N Object at front focal plane

If the system is afocal, the direction of the image-space ray depends 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-space ray height depends only on the entrance angle:

011 N Image at rear focal plane



Robert McLeod 82

Use of matrices M, NFind image plane given object

CdDC

CdA

CdDC

CdAdDdBCdA

d

DC

BAd

K

KKK

K

K

1

1

1

1

01

0

)(

10

1

10

1

MTTN

gives the image location 012 NDCd

BAddK

1

1

Conjugate condition


1 k

K

y0 0u y11u

-yK+1

1u

1Ku

M

Kd

1d

11

1 11

1

01

ddd

dd

KK

E.g. single lens


Robert McLeod 83

Form of NAnd EFL, first thick-lens concept

CdAy

yM K

K 11

0

1 N If thenis the magnification

012 N11N

M

122 N Determinant = 1

1Ku00 u

0220211 uyuK NN

1

01

Ku

yF Effective focal length & system power

0

21N

M

M

1

0N


tt

tt

tt

t

ttt

0

1

1 11

011 TRTN 0

E.g. single lens

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•Design of ideal imaging syst ems with geometrical optics ...ecee.colorado.edu/~mcleod/pdfs/OESD/lecturenotes/ParaxialRay... · ECE 5616 OE System Design Robert McLeod Reflective