1. Lens Aberrations Aberration: a departure from the paraxial limit.
Hope College, PHYS 352, Spring 2013
Lens Aberrations
Aberration: a departure from the paraxial limit.
Paraxial limit: (1) Rays are kept close to the optic axis.
(2) Small angle approximation (1st Order)
5th Order
3rd Order
1 Order
3rd Order aberration theory: Keep the 3rd order terms.

2. Quantify the aberration: a(Q)=Path 2 – Path 1
Hope College, PHYS 352, Spring 2013
Pages of Hecht, 4th ed., treats refraction in the paraxial (1st Order) limit.
If the 3rd order terms are kept in ℓo and ℓi (p. 154) we find that extended images don’t land on exactly the same focal surface (See Fig. 6.14, p, 254). n1 n2 Q ℓo
Path 2 ℓi
Path 1 so si
Paraxial Approximation: Path 1 and Path 2 have the same Optical Path Length
Quantify the aberration: a(Q)=Path 2 – Path 1
a(Q)=(n1ℓo+n2ℓi)-(n1so+n2si)
a=0 means no aberration

3. The Five Monochromatic Seidel Aberrations
Hope College, PHYS 352, Spring 2013
The Five Monochromatic Seidel Aberrations
yi and yo are paraxial image and object heights. n1 n2 Q ℓi  ℓo r yi yo
Distortion
Curvature of field
Astigmatism
Coma
Spherical aberration
Spread the image point
(From Pedrotti, 3rd Ed., Section 20.2)

4. Hope College, PHYS 352, Spring 2013
1. Spherical aberration
The only aberration that exists even for objects on the optic axis (no yi dependence). X
Positive SA: The marginal rays converge left of the paraxial image (positive lens)
Negative SA: The marginal rays converge right of the paraxial image (negative lens)
Homework: Analyze this for a concave mirror.

5. n r2 r1 1. Spherical aberration
Hope College, PHYS 352, Spring 2013
1. Spherical aberration r2 r1
Minimizing spherical aberration requires using two different radii. n
The Coddington shape factor:
Spherical aberration is minimized when
(Shown in Jenkins & White, Sections )
Homework: For what value of n does a planar convex lens produce a minimum spherical aberration for an object located at infinity? Which side of the lens should the light enter?

6. 2. Coma Depends on yi. e.g. It’s an “off-axis” aberration.
Hope College, PHYS 352, Spring 2013
2. Coma
Depends on yi. e.g. It’s an “off-axis” aberration.
Not symmetrical, which is the origin of the name.
screen
off-axis object
Negative coma: Marginal rays focus closer to the optic axis.
Positive coma: …farther from..
Figure 6.22a (Hecht, page 260) shows the formation of a comatic image from a series of comatic circles.
The same lens designs minimize coma & spherical aberration.

7. Hope College, PHYS 352, Spring 2013
3. Astigmatism
Astigmatism: rays from off-axis source do not strike the lens symmetrically (tangential rays versus saggital rays).
Tangential rays
Saggital rays
See Fig (page 263): tangential and saggital rays will fan out and form line images of the point source at two different image surfaces.

8. Circle of least confusion
Hope College, PHYS 352, Spring 2013
Circle of least confusion

9. Hope College, PHYS 352, Spring 2013
4. Curvature of Field
Curvature of field: Tangential and saggital rays do not form images on the same surface.
Very similar to astigmatism, but symmetric about the optic axis.
Tangential rays
Saggital rays T S
(T left of S: Positive astigmatism)

10. Elimination of astigmatism and curvature of field aberrations
Hope College, PHYS 352, Spring 2013
Elimination of astigmatism and curvature of field aberrations
Engineer the lens curvatures or spacing so that tangential and saggital surfaces coincide.
A focal surface that eliminates astigmatism to 3rd order is called a Petzval surface.
Flat P surface – eliminates both astigmatism and curvature of field aberrations.
Two lenses will have a flat P surface if
n1f1=-n2f2
Ultimately, the film must conform to P. T S P
P is always 3x farther from T than S

11. Hope College, PHYS 352, Spring 2013
5. Distortion
Distortion aberration is caused by non-uniform lateral magnification and is often minimized using aperture stops.