Aberrations
Where the simple equations for
the spherical optical elements
break down
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
1
Aberrations:
chromatic and monochromatic
Aberration: A deviation from the proper or expected course
Chromatic aberrations: n=n(w)
Rays corresponding to different wavelengths travel different
paths
Monochromatic aberrations:
The image is blurred or deformed due to the approximation
error in the paraxial approximation to the exact solution.
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 2
Chromatic Aberration
• material usually nblue>nred (normal dispersion)
• blue reflects more than the red, blue has a
closer focus.
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 3
Achromatic doublet
R2
R1
R3
n1
n2
Achromatic doublet (achromat) is often used to compensate
for the chromatic aberration.
How is this done?
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 4
Achromatic doublet
R1
R2
R3
n1
First lens:
n2
Second lens:
(n1R  1)  1
1
1 




f 1R
1
 R1 R2 
(n2 R  1)  1
1
1 




f 2R
1
 R2 R3 
1
(n1B  1)  1
1 
 


f1B
1
 R1 R2 
1
(n2 B  1)  1
1 




f2B
1
 R2 R3 
How do we add the lenses?
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 5
Adding Thin Lenses
R1
R3
First lens:
n1
1
1
1


so1 si1
f1
Then: so 2  si1  d
Second lens:
1
1
1


so 2 si 2
f2
n2
d
 si1  so 2  d
1
1
1


So:
so1  so 2  d
f1
If: d  0
R2
1
1
1


And:
 so 2 si 2 f 2
1
1
1
1
1

 

so1 si 2
f1 f 2
f
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 6
Adding Thin Lenses
R1
R2
R3
Red:
1
1
1


fR
f1R f 2 R
n1
Blue:
n2
d
1
1
1


fB
f 1B
f 2B
Red:
1
(n1R  1)  1
1  (n2 R  1)  1
1 


 
 


fR
1
1
 R1 R2 
 R2 R3 
Blue:
1
(n1B  1)  1
1  (n2 B  1)  1
1 


 
 


fB
1
1
 R1 R2 
 R2 R3 
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 7
Achromatic doublet
Want:
fR  fB

Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
1
1

fR
fB
ROINN NA FISICE
Department of Physics
PY3101
Slide 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
3
5
sin    
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland

3!


5!
ROINN NA FISICE
Department of Physics
sin   

PY3101
Slide 9
Monochromatic Aberration
The second term is 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
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 10
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 moves closer to
the lens to find the optimal spot size
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 11
Coma
• Arises from off-axis object points.
• The transverse magnification is a function of ray height
• The resulting pattern is like a comet.
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 12
Astigmatism
• In optical design, the vertical plane is general called the
“tangential plane”
• The “sagittal plane” is the plane at right angle to the
tangential plane and containing the principle ray.
• Astigmatism results in different focusing power to the
tangential and sagittal plane.
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 13
Field Curvature
Object plane
Image plane
• a thin lens images a spherical surface onto a spherical surface
• therefore, image is distorted in the image plane
• important in lens design for close objects
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 14
Distortion
•
•
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
Coláiste na hOllscoile Corcaigh, Éire
University College Cork, Ireland
ROINN NA FISICE
Department of Physics
PY3101
Slide 15