LIGHT AND THE RETINAL IMAGE: KEY POINTS
-
Upload
florence-marcus -
Category
Documents
-
view
38 -
download
1
description
Transcript of LIGHT AND THE RETINAL IMAGE: KEY POINTS
![Page 1: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/1.jpg)
LIGHT AND THE RETINAL IMAGE: KEY POINTSLight travels in (more or less) straight lines: the pinhole camera’s inverted
imageEnlarging the pinhole leads to BLURHow a lens prevents blur: refraction reunites light rays by bending themPoint-to-point projection from object to inverted imageRefraction: which way is light bent? Slowing in glass: lifeguard analogy.The eye: retina, lens and cornea; fovea, periphery and blind spotFocus errors; distant vision and near visionMyopia, hypermetropria, emmetropia, accommodation; emmetropizationVisual angle and image size: (in radians) = size/distance(in degrees) = (180/ ) * size/distance
(minutes of arc) = 60 * (180/ ) * size/distancePoint spread function: width is 1 minute in visual angle, or 5 microns (.005 mm) Sources of light spread making the image imperfect:
focus error; chromatic aberration; other aberrations; diffractionDirect observation of the image: Helmholtz’s ophthalmoscopeQuality of the image: spread is about 5 microns (1 minute of arc)Visual resolution limit: about 1 minute of arc or 30 cpd (for 20/20 vision)Can vision be perfected?? William’s magic mirror and laser surgeryAliasing through sampling by the photoreceptor mosaic: Nyquist limit (60cpd)
![Page 2: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/2.jpg)
![Page 3: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/3.jpg)
A Review of OpticsA Review of Optics
Austin Roorda, Ph.D.University of Houston College of Optometry
![Page 4: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/4.jpg)
(Most of) these slides were prepared by Austin Roorda, (UC Berkeley Optometry School) and used by permission.
![Page 5: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/5.jpg)
Geometrical Optics
Relationships between pupil size, refractive error
and blur
![Page 6: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/6.jpg)
Optics of the eye: Depth of Focus Optics of the eye: Depth of Focus
2 mm 4 mm 6 mm
![Page 7: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/7.jpg)
2 mm 4 mm 6 mm
In focus
Focused in front of retina
Focused behind retina
Optics of the eye: Depth of Focus Optics of the eye: Depth of Focus
![Page 8: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/8.jpg)
7 mm pupil
Bigger blurcircle
Courtesy of RA ApplegateCourtesy of RA Applegate
![Page 9: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/9.jpg)
Smaller blurcircle
2 mm pupil
Courtesy of RA ApplegateCourtesy of RA Applegate
![Page 10: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/10.jpg)
DemonstrationRole 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.
![Page 11: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/11.jpg)
Physical Optics
The Wavefront
![Page 12: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/12.jpg)
What is the Wavefront?What is the Wavefront?converging beam
=spherical wavefront
parallel beam=
plane wavefront
![Page 13: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/13.jpg)
What is the Wavefront?What is the Wavefront?ideal wavefrontparallel beam
=plane wavefront
defocused wavefront
![Page 14: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/14.jpg)
What is the Wavefront?What is the Wavefront?parallel beam
=plane wavefront
aberrated beam=
irregular wavefront
ideal wavefront
![Page 15: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/15.jpg)
What is the Wavefront?What is the Wavefront?aberrated beam
=irregular wavefront
diverging beam=
spherical wavefront
ideal wavefront
![Page 16: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/16.jpg)
The Wave Aberration
![Page 17: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/17.jpg)
What is the What is the Wave AberrationWave Aberration??diverging beam
=spherical wavefront wave aberration
![Page 18: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/18.jpg)
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Wavefront Aberration
mm (right-left)m
m (
supe
rior
-infe
rior)
Wave Aberration of a SurfaceWave Aberration of a Surface
![Page 19: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/19.jpg)
Diffraction
![Page 20: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/20.jpg)
DiffractionDiffraction
“Any deviation of light rays from a rectilinear path which cannot be interpreted as reflection or refraction”
Sommerfeld, ~ 1894
![Page 21: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/21.jpg)
Diffraction and InterferenceDiffraction 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
![Page 22: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/22.jpg)
rectangular aperture
square aperture
![Page 23: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/23.jpg)
Airy Disc
circular aperture
![Page 24: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/24.jpg)
The Point Spread Function
![Page 25: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/25.jpg)
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.
![Page 26: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/26.jpg)
Airy Disc
The Point Spread FunctionThe Point Spread Function
The PSF for a perfect optical system is the Airy disc, which is the Fraunhofer diffraction pattern for a circular pupil.
![Page 27: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/27.jpg)
Airy DiskAiry Disk
1.22
a
![Page 28: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/28.jpg)
angle subtended at the nodal point
wavelength of the light
pupil diameter
1.22
a
a
0
0.5
1
1.5
2
2.5
1 2 3 4 5 6 7 8
pupil diameter (mm)sepa
ratr
ion
betw
een
Airy
dis
k pe
ak a
nd 1
st m
in
(min
utes
of a
rc 5
00 n
m li
ght)
As the pupil size gets larger, the Airy disc gets smaller.
![Page 29: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/29.jpg)
Point Spread Function vs. Pupil SizePoint Spread Function vs. Pupil Size
1 mm 2 mm 3 mm 4 mm
5 mm 6 mm 7 mm
![Page 30: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/30.jpg)
![Page 31: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/31.jpg)
Small PupilSmall PupilLittle spreading due to defocus or aberrationsLittle spreading due to defocus or aberrations
So diffraction is limitingSo diffraction is limiting
![Page 32: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/32.jpg)
Larger pupil: Larger pupil: Less diffraction (not shown)Less diffraction (not shown)
But more blur and more aberrationsBut more blur and more aberrations
![Page 33: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/33.jpg)
![Page 34: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/34.jpg)
Aberrations
![Page 35: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/35.jpg)
![Page 36: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/36.jpg)
1 mm 2 mm 3 mm 4 mm
5 mm 6 mm 7 mm
Point Spread Function vs. Pupil Size
Perfect Eye (Diffraction Limited)
![Page 37: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/37.jpg)
pupil images
followed by
psfs for changing pupil size
1 mm 2 mm 3 mm 4 mm
5 mm 6 mm 7 mm
Point Spread Function vs. Pupil Size
Typical Eye with aberrations
![Page 38: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/38.jpg)
DemonstrationObserve Your Own Point Spread Function
![Page 39: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/39.jpg)
Resolution
![Page 40: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/40.jpg)
Rayleigh resolution
limit
Unresolved point sources
Resolved
![Page 41: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/41.jpg)
Keck telescope: (10 m reflector) About 4500 times better than the eye!“Pupil” is 10M: almost no diffraction
Wainscott
![Page 42: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/42.jpg)
• Compound eye:
• Each facet must be large to fight diffraction
• Many facets (pixels) needed to capture details
![Page 43: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/43.jpg)
Convolution with the PSF
![Page 44: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/44.jpg)
( , ) ( , ) ( , )PSF x y O x y I x y
Convolution
![Page 45: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/45.jpg)
Simulated Images
20/40 letters
20/20 letters
![Page 46: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/46.jpg)
MTFModulation Transfer
Function
![Page 47: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/47.jpg)
low medium high
object:100% contrast
image
spatial frequency
cont
rast
1
0
![Page 48: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/48.jpg)
• 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).
![Page 49: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/49.jpg)
MTF: Cutoff FrequencyMTF: Cutoff Frequency
0
0.5
1
0 50 100 150 200 250 300
1 mm2 mm4 mm6 mm8 mm
mo
du
lati
on
tra
nsf
er
spatial frequency (c/deg)
cut-off frequency
57.3cutoff
af
Rule of thumb: cutoff frequency increases by ~30 c/d for each mm increase in pupil size
![Page 50: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/50.jpg)
Effect of Defocus on the MTF
Charman and Jennings, 1976
450 nm
650 nm
![Page 51: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/51.jpg)
Relationships Between Wave Aberration,
PSF and MTF
![Page 52: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/52.jpg)
Retinal Sampling
![Page 53: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/53.jpg)
Projected Image Sampled Image
5 arc minutes20/20 letter
Sampling by Foveal ConesSampling by Foveal Cones
![Page 54: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/54.jpg)
5 arc minutes20/5 letter
Projected Image Sampled Image
Sampling by Foveal ConesSampling by Foveal Cones
![Page 55: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/55.jpg)
Nyquist Sampling TheoremNyquist Sampling Theorem
![Page 56: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/56.jpg)
Photoreceptor Sampling >> Spatial Frequency
I
0
1
I
0
1
nearly 100% transmitted
![Page 57: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/57.jpg)
I
0
1
I
0
1
nearly 100% transmitted
Photoreceptor Sampling = 2 x Spatial Frequency
![Page 58: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/58.jpg)
I
0
1
I
0
1
nothing transmitted
Photoreceptor Sampling = Spatial Frequency
![Page 59: LIGHT AND THE RETINAL IMAGE: KEY POINTS](https://reader036.fdocuments.net/reader036/viewer/2022081516/568134ac550346895d9bc1af/html5/thumbnails/59.jpg)
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)