Aperture Pupil (stop)
Exit Pupil
Entrance Pupil
1
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
2
F-number
D
f
dA D 2
Fraction of solid angle d  2  2
r
f
D2
1
Amount of light collected ~ 2 
f
( f /# ) 2
the f-number is defined as f /# 
f
focal length

D lens diameter
3
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
4
Aberrations:
chromatic and monochromatic
• Chromatic aberrations: n=n(w)
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.
5
Chromatic Aberration
• material usually nblue>nred (normal dispersion)
• blue reflects more than the red, blue has a
closer focus.
6
Achromatic doublet
R2
R1
R3
n1
n2
• Achromatic doublet (achormat) is often used to compensate
for the chromatic aberration
• the focuses for red and blue is the same if
1
1
1
1
(nb1  nr1 )(  )  (nb 2  nr 2 )(  )  0
R1 R2
R2 R3
7
Monochromatic Aberration
• Monochromatic aberration is due to the paraxial rays are
just an approximation to the real case.
• For paraxial approximation, we assume sin   
but actually
3
5
sin    

3!


5!

• 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
8
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
9
Coma
• Arises from off-axis object points.
• The transverse magnification is a function of ray height
• The resulting pattern is like a comet.
10
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.
11
Astigmatism
tangential
sagittal
Astigmatism often arises when focusing with a mirror
with an angle
12
Field Curvature
Object plane
Image plane
• 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
13
Distortion
With distortion
•
•
Corrected
all points in the object plane are imaged to points
in image plane
Distortion arises when he magnification of off-axis
image is a function of the distance to the lens center
14
Ray-tracing and computer-aided design
15
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
16