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Aberration Theory

Geunyoung Yoon, Ph.D.
Assistant Professor Department of Ophthalmology Center for Visual Science University of Rochester

Optics
Quantum Optics Coherent Optics Diffractive Optics (Fourier Optics) Geometrical Optics (Aberration theory) Paraxial Optics (First Order Optics) (Gaussian Optics)

Outline
What Is Wavefront?
Huygens’s principle, Snell’s law, Fermat’sprinciple Paraxial (first order) approximation

What Kind Of Wavefront Aberrations Are There?
Monochromatic aberration (Seidel and wave aberrations) Chromatic aberration (Longitudinal, Transverse)

Why Are These Aberrations Important?
Relationship between aberrations and image quality (Pupil function, PSF, MTF, Image convolution…)

How Can We Measure These Aberrations Of The Eye?
Different typesof wavefront sensors

Outline
What Is Wavefront?
Huygens’s principle, Snell’s law, Fermat’s principle Paraxial (first order) approximation

What Kind Of Wavefront Aberrations Are There?
Monochromatic aberration (Seidel and wave aberrations) Chromatic aberration (Longitudinal, Transverse)

Why Are These Aberrations Important?
Relationship between aberrations and image quality (Pupilfunction, PSF, MTF, Image convolution…)

How Can We Measure These Aberrations Of The Eye?
Different types of wavefront sensors

Outline
What Is Wavefront?
Huygens’s principle, Snell’s law, Fermat’s principle Paraxial (first order) approximation

What Kind Of Wavefront Aberrations Are There?
Monochromatic aberration (Seidel and wave aberrations) Chromatic aberration (Longitudinal,Transverse)

Why Are These Aberrations Important?
Relationship between aberrations and image quality (Pupil function, PSF, MTF, Image convolution…)

How Can We Measure These Aberrations Of The Eye?
Different types of wavefront sensors

Outline
What Is Wavefront?
Huygens’s principle, Snell’s law, Fermat’s principle Paraxial (first order) approximation

What Kind Of Wavefront Aberrations AreThere?
Monochromatic aberration (Seidel and wave aberrations) Chromatic aberration (Longitudinal, Transverse)

Why Are These Aberrations Important?
Relationship between aberrations and image quality (Pupil function, PSF, MTF, Image convolution…)

How Can We Measure These Aberrations Of The Eye?
Different types of wavefront sensors

What Is Wavefront?
Huygens’s principle Snell’s law Fermat’sprinciple Paraxial (first order) approximation

Wavefront vs Ray
“A wavefront is a surface over which an optical disturbance has a constant phase.” Harmonic wave function

ψ ( x, t ) = A sin(kx − ωt )
Phase

Plane wavefront x

Spherical wavefront x

x t=0 t

x

Wavefront vs Ray
“Rays are lines normal to the wavefronts at every point of intersection.”

Plane wavefrontSpherical wavefront

Ray

Huygens’s Principle
“Every point on a primary wavefront serves as the source of spherical secondary wavelets, such that the primary wavefront at some later time is the envelope of these wavelets.” Secondary spherical wavefront Primary spherical wavefront

Snell’s law
normal Fast medium (smaller refractive index, ni)

θi

θr

θt

Slow medium (larger refractiveindex, nt)

ni sin(θ t ) = nt sin(θ i )
Reflection: Refraction: θi = θr θi > θt when ni < nt

Fermat’s Principle
“The path actually taken by light in going from some point S to a point P is the shortest optical path length (OPL).” S
h
OPL = ni ⋅ SO + nt ⋅ OP
= ni ⋅ h 2 + x 2 + nt ⋅ b 2 + (a − x) 2

P θi θr ni O nt θt
OPL = ni ⋅ SO + nt ⋅ OP

dOPL = 0 to minimize OPL dx
ni ⋅ x h +x2 2

b

+ nt ⋅

− (a − x) b + (a − x)
2 2

=0

P

x a

a-x

ni sin(θ t ) = nt sin(θ i )

Paraxial Optics (First order optics)
po S so n1 n2 si R pi θ P

n1 R( so + R) sin θ n2 R( si − R) sin θ = po pi
Approximation

sin θ ≈ θ

θ3 θ5 θ7 sin θ = θ − + − + ⋅⋅⋅ 3! 5! 7!

n1 n2 n2 − n1 + = so si R

Lens maker’s formula

Paraxial Optics (First order optics)
“The...
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