Powerpoint: Aberrations

1

Aperture Pupil (stop)

Entrance Pupil

Exit Pupil

2

Telescope

• The entrance pupil often is the entrance lens diameter (most expensive/difficult-to-fabricate element)• Magnifying the angle of the incident light• The Exit pupil should match the field of view of eye• Light collection capability depends on the size of entrance pupil

3

F-number

f

D

Fraction of solid angle 2

2

2 fD

rdAd

Amount of light collected 22

2

)/#(1~ff

D

the f-number is defined as diameter lens

length focal/# Dff

4

Airy Disk

• The actual spot size is not a dot, as described by ray optics• The ring of airy disk is due to diffraction (wave property)• The diameter of airy disk cannot be smaller than the wavelength of light

5

• Chromatic aberrations: n=n() rays corresponding to different wavelengths travel different paths

• Monochromatic aberrations: image is blurred or deformed due to the approximation error in the paraxial approximation to the exact solution.

Aberrations: chromatic and monochromatic

6

Chromatic Aberration

• material usually nblue>nred (normal dispersion)• blue reflects more than the red, blue has a closer focus.

7

n1

n2

R1R2

R3

• Achromatic doublet (achormat) is often used to compensate for the chromatic aberration• the focuses for red and blue is the same if

0)11)(()11)((32

2221

11 RR

nnRR

nn rbrb

Achromatic doublet

8

Monochromatic Aberration• Monochromatic aberration is due to the paraxial rays are just an approximation to the real case.• For paraxial approximation, we assume but actually

• The second term are called the third-order correction to the first order theory (or first-order corrections to the paraxial theory) • The third order corrections are

• Spherical aberration• coma• astigmatism• field curvature• distortion

sin

!5!3

sin53

9

Spherical Aberration

• Spherical aberration comes from the spherical surface of a lens• The further away the rays from the lens center, the bigger the error is.• The image is improved if the image plane move closer to the lens to find optimal spot size

10

Coma

• Arises from off-axis object points.• The transverse magnification is a function of ray height• The resulting pattern is like a comet.

11

Astigmatism

• In optical design, the vertical plane is general called the “tangential plane”• The “sagittal plane” is the plane at right angle to the trangential plane and containing the principle ray.• Astigmatism results in different focusing power to the tangential and sagittal plane.

12

Astigmatism

tangential

sagittal

Astigmatism often arises when focusing with a mirror with an angle

13

Field Curvature

• a thin lens image a spherical surface onto a spherical surface• therefore, image is distorted in the image plane• important in lens design for close objects

Object plane Image plane

14

Distortion

With distortion Corrected

• all points in the object plane are imaged to pointsin image plane

• Distortion arises when he magnification of off-axis image is a function of the distance to the lens center

15

Ray-tracing and computer-aided design

16

Books and software

• Software– Zemax (http://www.zemax.com)– Code V by Optical Research Associates (

http://www.opticalres.com/)

• Book– The Art and Science of Optical Design,

R. R. Shannon, Cambridge 1997