Presentation on theme: "Lens Aberrations Aberration: a departure from the paraxial limit."— Presentation transcript:
1 Lens Aberrations Aberration: a departure from the paraxial limit. Hope College, PHYS 352, Spring 2013Lens AberrationsAberration: a departure from the paraxial limit.Paraxial limit: (1) Rays are kept close to the optic axis.(2) Small angle approximation (1st Order)5th Order3rd Order1 Order3rd Order aberration theory: Keep the 3rd order terms.
2 Quantify the aberration: a(Q)=Path 2 – Path 1 Hope College, PHYS 352, Spring 2013Pages 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).n1n2QℓoPath 2ℓiPath 1sosiParaxial Approximation: Path 1 and Path 2 have the same Optical Path LengthQuantify the aberration: a(Q)=Path 2 – Path 1a(Q)=(n1ℓo+n2ℓi)-(n1so+n2si)a=0 means no aberration
3 The Five Monochromatic Seidel Aberrations Hope College, PHYS 352, Spring 2013The Five Monochromatic Seidel Aberrationsyi and yo are paraxial image and object heights.n1n2QℓiℓoryiyoDistortionCurvature of fieldAstigmatismComaSpherical aberrationSpread the image point(From Pedrotti, 3rd Ed., Section 20.2)
4 Hope College, PHYS 352, Spring 2013 1. Spherical aberrationThe only aberration that exists even for objects on the optic axis (no yi dependence).XPositive 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 20131. Spherical aberrationr2r1Minimizing spherical aberration requires using two different radii.nThe 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 20132. ComaDepends on yi. e.g. It’s an “off-axis” aberration.Not symmetrical, which is the origin of the name.screenoff-axis objectNegative 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. AstigmatismAstigmatism: rays from off-axis source do not strike the lens symmetrically (tangential rays versus saggital rays).Tangential raysSaggital raysSee 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 2013Circle of least confusion
9 Hope College, PHYS 352, Spring 2013 4. Curvature of FieldCurvature 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 raysSaggital raysTS(T left of S: Positive astigmatism)
10 Elimination of astigmatism and curvature of field aberrations Hope College, PHYS 352, Spring 2013Elimination of astigmatism and curvature of field aberrationsEngineer 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 ifn1f1=-n2f2Ultimately, the film must conform to P.TSPP is always 3x farther from T than S
11 Hope College, PHYS 352, Spring 2013 5. DistortionDistortion aberration is caused by non-uniform lateral magnification and is often minimized using aperture stops.