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
Lawsin( ) 'sin( ')
nn
Lensmaker’s Equation
fdd is
111
lengthfocalfdistimageddistsourced
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
Pupi
l dia
met
er (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 0.3Position
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
Wavelength (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.