Optics Observations

• Pinholes, apertures and diffraction

• Lenses, lensmaker and depth of focus

• Two-dimensions and asymmetries

• Chromatic aberration of the human eye

• Adaptive optics, H-S

• Encoding

Pinhole optics

Lens Design: Snell’s

Law

sin( ) '

sin( ')

n

n

Lensmaker’s Equation

fdd is

111

lengthfocalf

distimaged

distsourced

i

s

Optical power and object distance

Diffraction Limits The Sharpness Of Image With A Small Pinhole

Aperture

(From Jenkins and White, I think)

The Diffraction Pattern Of A Disk Has A Formula Based on Bessel

Functions That Can Be Calculated From First Principles

Airy

Some Animals Have Non-Circular Pupils: Cat Eye

Pupil Size Changes With Mean Luminance, Influencing Acuity

Pup

il d

iam

eter

(m

m)

(From Wyszecki and Stiles, 1982)

Log luminance (Trolands)

The Pointspread Function Is The Generalization of the Linespread

Astigmatism Measures The Orientation of the Pointspread

Function

Chromatic aberration is

a differences in optical focus that varies with wavelength

(A)

(B)

-0.3 0.3

Position

Stimulus

Stimulus

Chromatic Aberration

Can Be Summarized

By The Optical

Power At Various

Wavelengths; Very

Constant Across People

Short wavelength linespread functions are much broader than middle

wavelength

-1 -0.5 0 0.5 10

0.1

0.2

0.3

0.4

Position (deg)

Rel

ativ

e in

tens

ity

430nm

580nm

Chromatic aberration also can be summarized in terms of the MTF at

each wavelength

Chromatic and spherical aberration: MTF

Chromatic aberration can also be summarized by its effect on the

linespread Function

Wav

elength (n

m)

Spatial position (deg)

Recent Advances In Adaptive OpticsGetting to the Diffraction Limit

Hartmann-Shack

Wavefront Sensor Senses

The Local Planarity Of The Image Wavefront

Using a Lenslet Array

Retina

Wavefront

Example H-S displacement images at the CCD sensor

Artal, Guirao, Berrio & WilliamsJournal of Vision

Adaptive optics corrects for the optical distortions using deformable

mirror devices

Wavefront phase

corrector priniciple

Deformable mirror arrays Compensate For the Measured

Aberrations

Deform the mirror to compensate for the wavefront curvature

Real deformable mirror arrays

Hartmann-Shack wave-front sensors

Point source

Adaptive Optics

compensate for

aberrations in the optical

path, the MTF approaches

the diffraction limit

The MTF approaches the diffraction limit

Adaptive optics should permit visualization of the retina at high

spatial resolution – Not Yet Routine

(Liang and Williams)

End

Reading for next Tuesday

Liang and Williams paperRoorda and Williams paper

Who wants to lead the discussion?Anyone have other papers to discuss?

Application: Seeing The Arrangement of Cone Classes in the

Human Eye( Roorda and Williams)

mm

Zernicke Polynomials (Not Harmonics) Are Used To Model Transmission Through The Lens

The Zernike polynomials are a set of functions that are orthogonal over the unit circle. They are useful for describing the shape of an aberrated wavefront in the pupil of an optical system.

Project idea: Implement a set of Matlab functions for these polynomials. Explain their use in optics characterization. Review the human literature pertaining to measurements of wavefront aberrations in the human eye.