Download Optics Observations

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( ) n '

sin( ') n
Lensmaker’s Equation
1 1 1
 
d s di
f
d s  source dist
d i  image dist
f  focal length
Optical power and object distance
(From Jenkins and White, I think)
Diffraction Limits The Sharpness Of
Image With A Small Pinhole
Aperture
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
Pupil diameter (mm)
(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 (A)
aberration is
a differences Stimulus
in optical
focus that
varies with (B)
wavelength
Stimulus
-0.3
0.3
Position
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
Relative intensity
0.4
0.3
580nm
0.2
0.1
430nm
0
-1
-0.5
0
0.5
Position (deg)
1
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
Spatial position (deg)
Recent Advances In Adaptive Optics
Getting to the Diffraction Limit
HartmannShack
Wavefront
Sensor Senses
The Local
Planarity Of
The Image
Wavefront
Using a Lenslet
Array
Wavefront
Retina
Artal, Guirao, Berrio & Williams
Journal of Vision
Example H-S displacement images at
the CCD sensor
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 paper
Roorda 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.