PHY20004Modern Optics

Lecture 6

Cardinal points

PhotoTech_03_Ray_Tracing_Slides.pdf

In a remarkable result…The equation governing a thick lens is…The same as the one for a thin lens….

fss io

111

Except for a very important proviso!The distances are measured from principle planes!!!What are the principle planes?

Cardinal points

F0

Incident ray

Geometrical continuation of incident ray

Surface normal

Cardinal points

F0

Incident ray

Geometrical continuation of incident ray

Refracted ray

Cardinal points

F0

Incident ray

Geometrical continuation of incident ray

Refracted ray

Cardinal points

F0

Principal plane

Principal point H 1

vertex point V 1

2nd incident ray

Geometrical continuation of incident ray

Refracted rays

Geometrical continuation of refracted ray

Locus of intersection

Fron

t foc

al p

oint

F 0

Cardinal points

F0

Cardinal points

Principal plane

F0

Cardinal points

Principal plane

Principal point H 1

F0

Cardinal points

Primary Principal plane

Principal point H 1

vertex point V 1

F0

Cardinal points

Principal plane

Principal point H 1

vertex point V 1

Fron

t foc

al p

oint

F 0

Cardinal points

H1V1F0

Cardinal points

H1V1F0 Fi

Cardinal points

H1V1F0 Fi

Cardinal points

H1V1F0 Fi

Cardinal points

H1V1F0 Fi

Cardinal points

H1V1F0 Fi

Cardinal points

H1V1F0 Fi

Secondary Principal plane

Cardinal points

H1V1F0 Fi

Secondary Principal plane

Cardinal points

H1V1F0 Fi

Secondary Principal plane

H2

Cardinal points

H1V1F0 Fi

Secondary Principal plane

H2

Cardinal points 61. 2 focal points2. 2 principal points3. 2 nodal points

H1V1F0 Fi

Secondary Principal plane

H2 V2

Cardinal points 61. 2 focal points2. 2 principal points3. 2 nodal points

H1V1F0 Fi

Secondary Principal plane

H2 V2N1 N2C

Cardinal points 61. 2 focal points2. 2 principal points3. 2 nodal points

H1V1F0 Fi

Secondary Principal plane

H2 V2N1 N2

Coincident if lens immersed in same medium

C

Matrix methods

• Translation matrix

• Refraction matrix

n

n

n

nn

R

y1

01

0

0

1

1

10

1

yLy

Ray transfer matrices

• Translation matrix

• Refraction matrix

10

1 LT

n

n

nR

nnR01

n n

R

convexR :)(concaveR :)(

L

Ray transfer matrices

• Refraction matrix, plane interface

• Thin lens matrix

21

111

RRn

nn

f

n

n

fR 1

01

n n

n

nR 0

01

n n

1R

convexf :)(concavef :)(

2R

n

Ray transfer matrices

• Spherical mirror

n n

1

201

RR

RconvexR :)(concaveR :)(

Optic axis

y

a

n1

n2

n3

n4d1

d2

f

d3

d4

R

d5 d6 d7 a’y’

BYU Photonics - ABCD Matrix Analysis Tutorial-Ray Transfer Matrix Analysis-Transfer Matrices_phtml.mht

Calculate the system transfer

Optic axis

y

a

n1

n2

n3

n4d1

d2

f

d3

d4

R

d5 d6 d7 a’y’

y

r0

Optic axis

y

a

n1

n2

n3

n4d1

d2

f

d3

d4

R

d5 d6 d7 a’y’

y

r0 011 rTr

Optic axis

y

a

n1

n2

n3

n4d1

d2

f

d3

d4

R

d5 d6 d7 a’y’

y

r0 011 rTr

112 rRr

Optic axis

y

a

n1

n2

n3

n4d1

d2

f

d3

d4

R

d5 d6 d7 a’y’

y

r0 011 rTr

112 rRr

223 rTr

Optic axis

y

a

n1

n2

n3

n4d1

d2

f

d3

d4

R

d5 d6 d7 a’y’

y

r0 011 rTr

112 rRr

223 rTr

334 rRr

011 rTr

112 rRr

223 rTr

324 rRr

445 rTr

536 rRr

657 rTr

748 rRr

869 rTr

9710 rTr

10411 rRr

11812 rTr

solution

rd

n

nd

n

nd

f

d

Rn

nnd

n

nddr

10

10

01

10

10

01

10

11

101

10

11

01

10

10

01

10

1

10

01

10

1 1

2

12

1

234

4

415

1

467

solution

rd

n

nd

n

nd

f

d

Rn

nnd

n

nddr

10

10

01

10

10

01

10

11

101

10

11

01

10

10

01

10

1

10

01

10

1 1

2

12

1

234

4

415

1

467

Answer according to text

Tessar lensCalculate the system transfer

10

1 212

dM

111

111101

tt

t

nnR

nM

1

101

1

2

13 tt n

R

nM

10

1 436

dM

333

351101

tt

t

nnR

nM

10

1 324

dM

1

101

3

4

37 tt n

R

nM

10

1 548

dM

5

91

0

01

tnM

10

1 6510

dM

6

5

66

6511

01

t

t

t

tt

n

n

nR

nnM

6

5

66

6512

01

t

t

t

tt

n

n

nR

nnM

10

1 7613

dM

1

101

6

6

614 tt n

R

nM

Aberrations

Aberrations

• Monochromatic• Spherical• Coma• Astigmatism• Field curvature• Distortion• Chromatic• Doublets• Separated achromatic doublets

aberrations

ChromaticRefractive index n varies

with frequency

Monochromatic

Image deterioration1. Spherical aberration2. Coma3. astigmatism

Image deformation1. Petzval field curvature2. distortion

http://amazing-space.stsci.edu/resources/explorations/groundup/lesson/basics/g13/

Return to "Where you came from"   Telescopes from the Ground Up Get to the root of it   

Figure Reducing spherical aberration in lenses.htm

Spherical aberration•Spherical surfaces require paraxial region for good imaging.

•By using various system parameters such as power, shape, thickness, glass types, lens separation and stop location, these effects can be minimized

•Computer ray tracing. Can calculate the optimum configuration but not the optimum design. Quality factor is a rough guide.

monchromatic aberrationParaxial assumption sin

So that Snell’s law was written ttiittii nnnn sinsin

Now, using a series expansion ...

!7!5!3sin

753

And keeping the first two terms !3

sin3

We have a third order theory

Departures from the first order theory are described by 5 primary aberrations

Primary aberrations

5 primary aberrations1. Spherical aberration2. Coma3. Astigmatism4. Field curvature5. Distortion

Collectively known as Seidel aberrations

Philipp Ludwig von SeidelMathematicianPhilipp Ludwig von Seidel was a German mathematician. His mother was Julie Reinhold and his father was Justus Christian Felix Seidel. WikipediaBorn: October 23, 1821, Zweibrücken, GermanyDied: August 13, 1896, Munich, Germany

Spherical aberrations

0

0122

0

1 1

l

sn

l

sn

Rl

n

l

n

i

i

i

s0 si

0l il

Rh

C

R

nn

s

n

s

n

i

122

0

1

!6!4!21cos

642

Previously it was found

and using

obtained

Spherical aberrations

R

nn

s

n

s

n

i

122

0

1

Using a better approximation

2

2

2

00

12122

0

1 11

2

11

2 iii sRs

n

Rss

nh

R

nn

s

n

s

n

Measure of deviation from first order theory

Focal length depends on aperture for nonparaxial rays

Paraxial focus

h

Different focus

Circle of least confusion

h

iF

SA L

SA T

LC

Circle of least confusion

Lateral spherical aberration

Transverse spherical aberration

h

iF

SA L

SA T

LC

Circle of least confusion

Lateral spherical aberration

Transverse spherical aberration

Spherical aberration pertains only to object points that are on the optic axis

Circle of least confusion

h

iF

SA L

SA T

LC

Circle of least confusion

Lateral spherical aberration

Transverse spherical aberration

Spherical aberration pertains only to object points that are on the optic axis

If the marginal rays cross the optic axis before the focal point then the L.SA is positive

Circle of least confusion

Circle of least confusion

h

iF

SA L

SA T

LC

Circle of least confusion

Lateral spherical aberration

Transverse spherical aberration

Spherical aberration pertains only to object points that are on the optic axis

If the marginal rays cross the optic axis before the focal point then the L.SA is positive

If the marginal rays cross the optic axis after the focal point then the L.SA is negative

h

iF

SA L

SA T

LC

Circle of least confusion

Lateral spherical aberration

Transverse spherical aberration

Spherical aberration pertains only to object points that are on the optic axis

If the marginal rays cross the optic axis before the focal point then the L.SA is positive

If the marginal rays cross the optic axis after the focal point then the L.SA is negative

Circle of least confusion

h

iF

SA L

SA T

LC

Circle of least confusion

Lateral spherical aberration

Transverse spherical aberration

Spherical aberration pertains only to object points that are on the optic axis

If the marginal rays cross the optic axis before the focal point then the L.SA is positive

If the marginal rays cross the optic axis after the focal point then the L.SA is negative

The height above or below the optic axis the rays intersect a screen is the lateral or transverse SA

Spherical aberration caustic

caustic

Reducing SA1. Stopping down the aperture

Reducing SA1. Stopping down the aperture2. Placing the screen at the circle of least confusion

http://www.olympusmicro.com/primer/java/aberrations/spherical/index.html

Calculate the system transfer

http://toothwalker.org/optics/spherical.html

Circle of least confusion

http://toothwalker.org/optics/spherical.html

Moving towards the lens

Moving away from the lens

http://www.telescope-optics.net/spherical1.htm

Spherical aberration with mirrors

http://www.telescope-optics.net/spherical1.htm

Reducing SA1. Stopping down the aperture2. Placing the screen at the circle of least confusion3. Turning the lens around

1. Stopping down the aperture2. Placing the screen at the circle of least confusion3. Turning the lens around

Reducing SA

1. Stopping down the aperture2. Placing the screen at the circle of least confusion3. Turning the lens around4. Symmetrical lens if object distance = image distance

Reducing SA

1. Stopping down the aperture2. Placing the screen at the circle of least confusion3. Turning the lens around4. Symmetrical lens if object distance = image distance5. Achromatic doublet

Reducing SA

http://photographylife.com/what-is-spherical-aberration

Real examples

Camera lensHubble telescope

Contact lenses

http://www.momentcorp.com/review/nikon_noct-nikkor_58mm.html

Nikon Noct-Nikkor 58mm f/1.2 AI-S

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S

f/1.4

f/1.2

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S

f/1.4

f/1.2

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S

f/1.4

f/1.2

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S Nikkor 50mm f/1.4SC AI' d

f/1.4

f/1.2

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S Nikkor 50mm f/1.4SC AI' d

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S Nikkor 50mm f/1.4SC AI' d

f/2

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S Nikkor 50mm f/1.4SC AI' d

f/2

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S Nikkor 50mm f/1.4SC AI' d

f/2

Nikon Noct-Nikkor 58mm f/1.2 AI-S Nikon Nikkor 50mm f/1.2 AI-S Nikkor 50mm f/1.4SC AI' d

f/2

f/2.8

Historical Example: Hubble Space TelescopeSoon after the Hubble Space Telescope (HST) was put in orbit (1990), it was discovered that it could not be put into good focus (at the circle of least confusion, the images were still very ugly). The Airy diffraction limit desired was being reached (0.1 arcsec), but only 12% of energy there compared to expected 70%. Too much of the light from stars was put into the Airy rings and in a diffuse light halo, and the point-spread-function. has a Strehl ratio of only ~ 15-20%. The telescope was showing classical signs of spherical aberration.

Image from the HST Wide Field/Planetary Camera 1 (WF/PC1). The "tendrils" are from diffraction off the secondary support struts.

It was later determined that HST primary was polished to exquisite precision, but to an incorrect shape! The mirror was too flat at the margins by ~ λ / 2. The error was a result of a 1.3-mm error in the placement of the device used to measure the shape of the primary when being made by Perkin-Elmer. The result was a 38-mm longitudinal spherical aberration: From Hecht, Optics, Fourth Edition.

The response of NASA was a dramatic servicing mission with the Space Shuttle to insert "corrective eyewear" -- the Corrective Optics Space Telescope Axial Replacement (COSTAR) -- into the HST instrument bay. COSTAR restored >70% of the energy in the central disk, increasing its magnitude limit by several magnitudes and much cleaner images.

http://www.astro.virginia.edu/class/majewski/astr313/lectures/telescopes/telescopes_schmidt.html

http://www.astro.virginia.edu/class/majewski/astr313/lectures/telescopes/telescopes_schmidt.html

Real example

Contact lensesNote the spelling in the website!

                                                                                                                                                                                    

Aspherical http://www.colourvue.net.au/airsoft.html

The Asperical design is meant to minimize optical aberration which gives better visual acuity in the meanwhile, resulting in better comfort and statisfaction.

Human eyes have roughly +0.10D spherical aberration on average, with the minimum level at around 19, when the aberration is 0.0 microns. The situation worsens with age accompanied with blurring, descreasing contrast sensitivity and the rest functional vision. A spherically surfaced contact lens will introduce spherical aberration in proportion to its sphere power, that is in a negative lens power generates negative spherical aberration, whilst an aspheric contact lens, with appropriate aspheric design such as Airsoft, will correct and ease the situation.