Optics III: Chromatic + Monochromatic Aberrations

Dispersion

• White light incident on a prism → Dissociates into constituent colors

• RI of the media changed based on the wavelength

Shorter or longer wavelengths bend more?

• Shorter (Blue) wavelengths bend more vs. longer wavelengths

Blue is at the bottom of the rainbow

Optics of rainbow formation

• White light dispersion through water droplets

  • Blue light bends more → At bottom of the rainbow

Cause of chromatic aberration

Chromatic aberration occurs due to the fluctuation in power based on a light ray’s wavelength

• Shorter wavelength → Greater RI → F increases → More bending

  • And vice versa for longer wavelengths

Longitudinal vs Transverse chromatic aberration (CA)

• Longitudinal/Axial → Measured along optical axis

• Transverse/Lateral → Measured perpendicular to the optical axis

Positive vs. Negative chromatic aberration

• Positive

  • Blue focuses before red (Normal)

  • Convex lenses

• Negative CA

  • Red focuses before blue

  • Concave lenses

During duochrome what would uncorrected ____ report as clearer

• Myopes

• Hyperopes

• Emmetropes

• Myopes → Red is better

• Hyperopes → Green is better

• Emmetropes → Both equal

Transverse CA

• When an off-axis object experiences chromatic aberration

• In the image, blue focuses closer to the fovea than red

  • Blue light is smaller and sharper

  • Red part of image would be larger and blurrier

Describe 1, 2, and 3

1. No chromatic aberration

2. Longitudinal CA… Production of a red halo

3. Transverse CA… Rainbow-fringed edges

Eye much more sensitive to transverse CA

3 standard wavelengths

• Purpose

• Name, wavelength, and the source

Standardize lens powers across the industry (USA)

• F → 486nm _(Blue) → Hydrogen

• d → 587.56nm _(Yellow) → Helium

• C → 656nm _(Red) → Hydrogen

Quantifying CA and Abbe number

CA = F_F - F_C

• Dioptric difference between the red and blue foci

Abbe number (v)

AKA refractive efficiency, nu value, or V-value

= F_d / (F_F - F_C)

= (n_d -1) / (n_F - n_c)

Relationship between CA and abbe #

• CA inversely related to abbe #

  • Higher Abbe, lower CA

Disadvantages of CA

• Ophthalmic lenses

  • Powers/Magnifications vary

  • Degrading image quality

• The eye

  • Transverse CA degrading image quality

  • Production of colored fringes

Advantages of CA

• Prism spectrometers

  • Dissociate white light into spectral components

• The eye

  • Longitudinal CA used for duochrome test

  • Cue for accommodation direction _{(Based on amount of CA experienced)}

How does CA affect ophthalmic lenses

• Degraded images → Reduction in acuity

  • CA causes overlapping images of different wavelengths

    • One or more wavelengths displaced due to CA

• Colored fringes

  • Red or blue band seen around borders _{(Like sheet of paper)}

How to reduce CA in ophthalmic lenses

• Use materials with higher Abbe number

  • Crown glass > Polycarbonate

Patient complaints related to CA

• Colored fringes

• Reduced off-axis VA

  • Tunnel vision/Blurry periphery

Achromatic doublet

Using a positive and negative lens of differing materials to reduce chromatic aberration

• Materials with differing Abbe numbers → Red, yellow, and blue focus at different points

• Find the right ratio of (+) or (-) power between both lenses to line up red and blue foci _{(Yellow foci still unfocused, but better than nothing)}

Chromatic aberrations vs. Monochromatic aberrations

• Chromatic

  • Variation of image properties due to dispersion

• Monochromatic

  • Variation of image properties across a lens aperture

  • Independent of wavelength

Seidel aberrations

• Monochromatic aberrations named after the dude who systemized them

First order optics approximation

Snell’s law: n₁ sin(i) = n₂ sin(r)

Approximation → n₁ * i = n₂ * r

• The sine function should look more like the image

  • The approximation is assuming sin θ ≈ θ

• Only incorporates first order aberrations

Seidel approximation

• Incorporates primary or third order aberrations

Standard order of Seidel aberrations

Image blur

1. Spherical aberration

2. Coma

3. Radial Astigmatism

Image dislocation

4. Curvature of field

5. Distortion

Spherical aberration

• Peripheral rays get refracted more than paraxial rays

• Only aberration that applies to on-axis and off-axis points

Positive vs. negative spherical aberration

• Positive when peripheral rays refract more than paraxial rays _(Image)

  • Periphery focuses first

• Negative when paraxial > peripheral

How to reduce SA

• Reduce aperture → Less peripheral rays → Less SA

• Aspheric surfaces

  • Change of curvature at periphery reduces SA

Spherical aberration relation to shape of lens

Coma aberration

• Results from off-axis rays meeting different curvatures of the lens

  • Deviation of rays is not identical, depends on ray position _(Image)

• Comet-shaped aberration

  • Bright head

  • Dim tail

Most important aberrations to control at high level microscopy

• Coma and spherical aberration

  • Coma dependent on the square of the aperture size

• Controlled by reducing aperture size

Radial astigmatism

AKA oblique or marginal astigmatism

• Occurs with toric & spherical surfaces

  • When off-axis light hits spherical lens → Acts as toric surface

• Not the same as sphero-cyl astigmatism

Two planes associated with radial astigmatism

• Sagittal plane

  • Horizontal plane

  • Forms vertical image

• Tangential plane

  • Vertical plane

  • Forms horizontal image

Astigmatic interval

• Dioptric difference between the foci of radial astigmatism

Relationship of radial astigmatism and oblique viewing

• RA generated when looking obliquely through a lens _(Image)

  • Viewing something at near → Look through bottom of lens

  • ↑ Oblique angle → ↑ Average power

• Solution: Pantoscopic tilt

Controlling radial astigmatism

• Use a lens that minimizes astigmatic interval to ≤ 0.125D

Determinants of the amount of radial astigmatism

• Viewing distance

• Oblique angle

• Back vertex power

• Vertex distance

• Refractive index

• Base curve

Standard oblique angle used in calculations to reduce RA

27 degs

Tscherning ellipse

• What is it

• X-axis

• Y-Axis

• Graph showing combinations of base curve/Rx power to reduce radial astigmatism

• X-axis → Rx power

• Y-Axis → Base curve

Ostwalt branch of tschernings ellipse

• Uses flatter base curves

  • Flatter looking lens, more aesthetic → More common

What what Rx powers is radial astigmatism incurrable

> +8D

< -25D

Curvature of field

AKA Power error

• Off-axis object → Goes through curved lens → Focuses in a curved line _{(Petzval surface)}

• Problem: Camera sensors and other things lie as a flat surface

Far point sphere

• Surface swept out by the far point of the eye as the eye moves

  • Compensated for by the lens

• FPS is more curved than the petzval surface → Aberration

Power error in myopes vs. hyperopes

• Myopia → Off-axis object blur

  • Image falls farther than far point of the eye

• Hyperopia → Less blur (Accomodation)

Minimizing curvature of field/power error in camera & lenses

• Cameras → Multi-element lenses to flatten the field

• Spectacles

  • All seidel aberrations are intermixed, compromise between them all

    • Radial astigmatism corrected first

Distortion

• Non-uniform magnification across the VF

• Caused by object distance from axis

  • Can either decrease or increase

Controlling distortion

• Affected by position of the ‘stop’ from the lens

  • NOT THE SIZE

Stop too far before the lens

Stop too far after the lens

• Stop too far before the lens

  • Barrel distortion

  • More mag in middle

• Stop too far after the lens

  • Pincushion distortion

  • More mag at edges