A Review of Optics

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A Review of Optics

• Austin Roorda, Ph.D.
• University of Houston College of Optometry

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These slides were prepared by Austin Roorda,
except where otherwise noted. Full permission is
granted to anyone who would like to use any or
all of these slides for educational purposes.
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Geometrical Optics Relationships between pupil
size, refractive error and blur
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Optics of the eye Depth of Focus
2 mm
4 mm
6 mm
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Optics of the eye Depth of Focus
Focused behind retina
In focus
Focused in front of retina
2 mm
4 mm
6 mm
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7 mm pupil
Bigger blur circle
Courtesy of RA Applegate
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2 mm pupil
Smaller blur circle
Courtesy of RA Applegate
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Demonstration Role of Pupil Size and Defocus on
Retinal Blur
Draw a cross like this one on a page, hold it so
close that is it completely out of focus, then
squint. You should see the horizontal line become
clear. The line becomes clear because you have
made you have used your eyelids to make your
effective pupil size smaller, thereby reducing
the blur due to defocus on the retina image. Only
the horizontal line appears clear because you
have only reduced the blur in the horizontal
direction.
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Physical Optics The Wavefront
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What is the Wavefront?
parallel beam plane wavefront
converging beam spherical wavefront
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What is the Wavefront?
parallel beam plane wavefront
ideal wavefront
defocused wavefront
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What is the Wavefront?
parallel beam plane wavefront
ideal wavefront
aberrated beam irregular wavefront
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What is the Wavefront?
diverging beam spherical wavefront
aberrated beam irregular wavefront
ideal wavefront
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The Wave Aberration
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What is the Wave Aberration?
diverging beam spherical wavefront
wave aberration
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Wave Aberration of a Surface
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Diffraction
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Diffraction
Any deviation of light rays from a rectilinear
path which cannot be interpreted as reflection or
refraction Sommerfeld, 1894
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Fraunhofer Diffraction

• Also called far-field diffraction
• Occurs when the screen is held far from the
  aperture.
• Occurs at the focal point of a lens!

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Diffraction and Interference

• diffraction causes light to bend perpendicular to
  the direction of the diffracting edge
• interference due to the size of the aperture
  causes the diffracted light to have peaks and
  valleys

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rectangular aperture
square aperture
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circular aperture
Airy Disc
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The Point Spread Function
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The Point Spread Function, or PSF, is the image
that an optical system forms of a point source.
The point source is the most fundamental
object, and forms the basis for any complex
object. The PSF is analogous to the Impulse
Response Function in electronics.
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The Point Spread Function
The PSF for a perfect optical system is the Airy
disc, which is the Fraunhofer diffraction pattern
for a circular pupil.
Airy Disc
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Airy Disk
q
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As the pupil size gets larger, the Airy disc gets
smaller.
2.5
2
1.5
separatrion between Airy disk peak and 1st min
(minutes of arc 500 nm light)
1
0.5
0
1
2
3
4
5
6
7
8
pupil diameter (mm)
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Point Spread Function vs. Pupil Size
1 mm
2 mm
3 mm
4 mm
5 mm
6 mm
7 mm
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Small Pupil
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Larger pupil
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Point Spread Function vs. Pupil SizePerfect Eye
1 mm
2 mm
3 mm
4 mm
5 mm
6 mm
7 mm
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Point Spread Function vs. Pupil SizeTypical Eye
1 mm
2 mm
3 mm
4 mm
pupil images followed by psfs for changing
pupil size
5 mm
6 mm
7 mm
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Demonstration Observe Your Own Point Spread
Function
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Resolution
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Unresolved point sources
Rayleigh resolution limit
Resolved
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uncorrected
corrected
AO image of binary star k-Peg on the 3.5-m
telescope at the Starfire Optical Range
About 1000 times better than the eye!
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Keck telescope (10 m reflector) About 4500
times better than the eye!
Wainscott
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Convolution
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Convolution
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Simulated Images
20/20 letters
20/40 letters
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MTF Modulation Transfer Function
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low
medium
high
object 100 contrast
image
1
contrast
0
spatial frequency
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• The modulation transfer function (MTF) indicates
  the ability of an optical system to reproduce
  (transfer) various levels of detail (spatial
  frequencies) from the object to the image.
• Its units are the ratio of image contrast over
  the object contrast as a function of spatial
  frequency.
• It is the optical contribution to the contrast
  sensitivity function (CSF).

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MTF Cutoff Frequency
cut-off frequency
1 mm
1
2 mm
4 mm
Rule of thumb cutoff frequency increases by 30
c/d for each mm increase in pupil size
6 mm
8 mm
modulation transfer
0.5
0
0
50
100
150
200
250
300
spatial frequency (c/deg)
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Effect of Defocus on the MTF
450 nm
650 nm
Charman and Jennings, 1976
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PTF Phase Transfer Function
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low
medium
high
object
image
180
phase shift
0
-180
spatial frequency
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Relationships Between Wave Aberration, PSF and
MTF
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The PSF is the Fourier Transform (FT) of the
pupil function
The MTF is the real part of the FT of the PSF
The PTF is the imaginary part of the FT of the PSF
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Adaptive Optics Flattens the Wave Aberration
AO OFF
AO ON
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Other Metrics to Define Imagine Quality
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Strehl Ratio
diffraction-limited PSF
Hdl
actual PSF
Heye
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Retinal Sampling
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Sampling by Foveal Cones
Projected Image
Sampled Image
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Sampling by Foveal Cones
Projected Image
Sampled Image
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Nyquist Sampling Theorem
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Photoreceptor Sampling gtgt Spatial Frequency
1
I
0
1
I
0
nearly 100 transmitted
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Photoreceptor Sampling 2 x Spatial Frequency
1
I
0
1
I
0
nearly 100 transmitted
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Photoreceptor Sampling Spatial Frequency
1
I
0
1
I
0
nothing transmitted
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Nyquist theorem The maximum spatial frequency
that can be detected is equal to ½ of the
sampling frequency. foveal cone spacing 120
samples/deg maximum spatial frequency 60
cycles/deg (20/10 or 6/3 acuity)