Lens Design Flashcards
Most two important material properties for lens design?
Refractive index and chromatic dispersion (more specifically, what n is at different wavelengths)
What is the Abbe number meaning and formula?
The Abbe number is a ratio of the “refractivity” and “principal dispersion”, and measures the degree of chromatic dispersion of the material (at least in the visible range). High Abbe numbers mean low chromatic dispersion and vice versa. Formula is (n_D - 1)/(n_F - n_C), where n_D is the refractive index of the material at the Fraunhofer D line (orange), n_C is n at the Fraunhofer C line (red), and n_F is n at the Fraunhofer F line (blue).
What is the principal dispersion?
The principal dispersion is a crude measure of chromatic dispersion in the visible region, defined as the difference of refractive indices of the material at the F line of hydrogen (blue) and the C line (red).
Describe the meaning of the different terms in the modern chromatic dispersion formula
It is a Taylor expansion of the wavenumber as a function of angular frequency, made about some center angular frequency. Zero order term describes a common phase shift k_0. First order term (dk/dw) contains the inverse group velocity and describes an overall time delay that does not affect the shape of the pulse. Second order term contains the group delay dispersion (second-order dispersion). Third and higher orders are considered “high order dispersion”.
k(w) = k_0 + (dk/dw)(w - w_0) + (1/2)(dk/dw)^2(w-w_0)^2 + (1/6)(dk/dw)^3(w-w_0)^3 + …
What is the difference between normal and anomalous dispersion?
Normal dispersion, group velocity decreases with increasing optical frequency (k’’ > 0), and anomalous dispersion is the opposite (k’’ < 0). Anomalous dispersion usually occurs at longer wavelengths
What is a Gires-Tournois interferometer?
It is a resonator very similar to a Fabry Perot interferometer, but operating in reflection. With no resonator losses, power reflectance is unity at all wavelengths, but the phase is frequency dependent due to the resonance effect, which can be used to intentionally induce chromatic dispersion.
What are typical Abbe number values?
25 to 70
How much does refractive index vary with temperature?
dn/dT is usually positive and fluctuates quite a bit over a narrow range. Typical value might be 0.00011 over 50 degrees.
What are caustics?
Caustics are envelopes of light rays reflected by a curved surface or object, tangent to those reflected rays. They appear because as light from various angles reflect off of a curved surface, there are naturally areas where light is especially reflective. Examples are the shiny thin lines you see in reflected water or the nephroid-shaped reflection of sunlight off of a glass of water
Two types of chromatic aberrations?
Axial chromatic (the “standard” chromatic aberration), which is chromatic aberration of the marginal ray. It is variation of power with wavelength.
Lateral color, which is chromatic aberration of the chief ray. It is the variation of magnification with wavelength.
What are “odd” aberrations?
Odd aberrations are those where the field orders are odd (function of an odd exponent of the chief ray height). They can be corrected with symmetry about the stop. Examples are coma and distortion.
General guidelines for aberration correction
(1) Avoid the occurrence of the aberration, using things like aplanatic surfaces (spherical aberrations or coma) or mirrors (chromatic aberration).
(2) Counteract the aberration from another part of the system: symmetry (distortion, coma, chromatic aberration), aspherical surfaces (spherical aberration), positive and negative lenses (longitudinal chromatic aberration or spherical aberration), etc
Common causes of aberrations
(1) Large incident angle to surface (unless asphere or aplanatic)
(2) Surface power (how much curvature and refractive index mismatch there is)
What is bending (aberration correction)?
Bending changes the incident angles of the lens surface. Focal length will stay the same but the principal plane locations can change.
What is power splitting (aberration correction)?
Lenses with large power (curvature/refractive index) cause aberrations, so splitting lenses to decrease the power and consequently incident angles can help reduce aberrations
