Is Aberration-Free Correction the
Best Goal
Stephen Burns , PhD, Jamie McLellan, Ph.D.,
Susana Marcos, Ph.D.
The Schepens Eye Research Institute.
Schepens
Schepens Eye
Eye Research
Research Institute,
Institute,
an
an affiliate
affiliate of
of Harvard
Harvard Medical
Medical School
School
Outline
1. Background - Vision in the real world
2. Chromatic Aberration
• The Impact of Chromatic Aberration on
image quality across the spectrum
• The relation of chromatic aberration and
depth of field
3. Calculations of how chromatic images arise
with changes in depth of fied
4. Aberrations can help
Issues for Optimizing Vision
Vision occurs in a complex world.
Polychromatic Light
Many distances.
Many analyses of the potential
for improving vision have
concentrated on limited
conditions
Take Home Message: Monochromatic wave
aberrations decrease the variability in image
quality across the visible spectrum caused by
chromatic aberration and decrease the variation
in chromatic content with distance.
Aberrations may be good for vision!
Image Quality: Modulation Transfer Function
MTF
The optics of the eye
attenuate the image
contrast at higher
spatial frequencies.
MTF
1.0
0.1
0.01
20 40 60 80
Spatial Frequency (cpd)
1
A Poor MTF
Produces
Blur
0.75
0.5
0.25
0
0
10
20
30
40
50
60
Retinal image quality.
1. Retinal image quality is an estimate of the
information which is available to the
photoreceptors.
2. This definition is NOT synonymous with
image appearance.
3. For the most part we will talk about the
modulation transfer function (MTF) of the
eye.
Diffraction Limited Optics
If the eye were a perfect
optical system, light from
a monochromatic point
source would be imaged
in a point at the retina.
Retinal Image of Point Source
1.0
>
MTF
Fourier
0.1
Transform
PSF
0.01
20 40 60 80
Spatial Frequency (cpd)
The Diffraction Limited “Model Eye”
We will use the performance of the
“diffraction limited eye” as a standard for
comparison throughout the talk. It has
perfect optical properties at one wavelength
(560nm), but the same material properties as
real eyes.
Monochromatic Wave Aberrations
Aberrations cause rays
from a monochromatic
point source entering
different parts of the
pupil to hit the retina at
different points.
MTF
1.0
PSF
0.1
0.01
20 40 60 80
Spatial Frequency (cpd)
Chromatic Aberrations
We don’t live in a monochromatic world.
Real materials (in this case, water,
proteins and lipids) exhibit chromatic
dispersion, and because of this the optical
properties of the eye vary with
wavelength.
How does this influence Retinal Image
Quality?
Longitudinal Chromatic Aberration
LCA
Variation in refractive power
with wavelength.
~ 2 Dioptres of defocus
across the visible spectrum.
White Light
MTF
1.0
PSF
0.1
0.01
20 40 60 80
Spatial Frequency (cpd)
Transverse Chromatic Aberration TCA
Angular displacement
of retinal images of
different wavelengths
caused by prismatic
dispersion.
Estimated by the
difference in position
of the PSFs for red
and blue tests.
TCA
Psychophysical Method Spatially Resolved
Refractometer (SRR)
37 pupil positions
TRANSVERSE CHROMATIC ABERRATION
with the SRR
Magenta filter
Optical
TCA
Achromatic axis
Marcos, Burns, Moreno & Navarro. Vis Res 2000
Variation in Wavefront with Wavelength
450 nm
490 nm
530 nm
570 nm
620 nm
650 nm
Marcos, Moreno-Barriuso, Navarro and Burns Vision Research (1999)
Results: Longitudinal Chromatic Aberration
1
0.5
Diopters
0
SM
-0.5
JM
-1
-1.5
400
SB
500
600
Wavelength
700
LCA is very consistent across subjects.
About 2 Diopters across spectrum.
Results:
Wave Aberrations
570 nm
JM
SB
10
0
-10
RMS
Error
(microns)
1.71
1.23
2.86
Monochromatic wavefronts
vary widely across subjects.
microns
SM
Chromatic Aberrations limit the White Light
MTF
Modulation Transfer
1
Legend
570 nm, aberrations corrected
570nm, uncorrected MTF
White Light, aberrations corrected
White Light, uncorrected MTF
0.1
0.01
0.001
0
10
20
30
40
50
60
70
80
90 100
Spatial Frequency (c/deg)
Marcos, Moreno-Barriuso, Navarro and Burns Vision Research (1999)
Results: Model Eye with LCA only
Eye focused for best
performance at 550 nm.
1.0
MTF
450 nm
500 nm
550 nm
0.1
0.01
0
600 nm
10 20 30 40 50 60
Spatial Frequency (cpd)
450 nm
550 nm
Results: Model Eye with LCA only
Eye focused for best
performance at 550 nm.
1.0
MTF
25 x
450 nm
500 nm
550 nm
0.1
600 nm
PSFs
0.01
0
10 20 30 40 50 60
Spatial Frequency (cpd)
450 nm
550 nm
Results: Real Eyes with Aberrations
Eye focused for best
performance at 550 nm.
1.0
SB
MTF
450 nm
500 nm
550 nm
0.1
600 nm
PSFs
0.01
0
10 20 30 40 50 60
Spatial Frequency (cpd)
450 nm
550 nm
Results: Real Eyes
450 nm
500 nm
550 nm
600 nm
1.0
MTF
SM
JM
0.1
0.01
0
10 20 30 40 50 60
Spatial Frequency (cpd)
0
10 20 30 40 50 60
Spatial Frequency (cpd)
Depth of Focus
How does retinal image quality vary
with distance from the plane of best
focus?
For simplicity, let’s consider a
prebyope.
Monochromatic light 560 nm
8
7
Best focus, model eye
MTF Volume
6
5
4
3
2
Best focus, real eye
1
0
0
2
4
6
8
Distance in Meters
10
12
Model Eye with white light
8
7
MTF Volume
6
5
4
3
2
1
0
0
2
4
6
8
Distance in Meters
10
12
Combing Depth of Focus with
longitudinal chromatic aberration
Computational Methods
Color rendered
retinal image
Accounting for Optics
Equal Energy
White Visual
Stimulus
Diffraction limited at 560 nm, focused at 57 cm
80 cm
Diffraction limited at 560 nm, focused at 57 cm
57 cm
Diffraction limited at 560 nm, focused at 57 cm
50 cm
Diffraction limited at 560 nm, focused at 57 cm
36 cm
Small Text 0.5 diopters in from of best focus
Small Text 1.0 diopters in from of best focus
Model Eye, Diffraction limited at 560 nm, Effect of distance
80
67
57
50
44
40
Distance in cm
composite image 3mm pupi
36
33
Model Eye,, Spherical Aberration left in
80
67
57
50
44
40
Distance in cm
36
33
Subject JSM,Effect of distance
80
67
57
50
44
40
Distance in cm
Jm, small psf,
36
33
jm p075diopt
36 cm
Results
• Monochromatic wavefront aberrations
decrease the variability in image quality across
wavelengths caused by longitudinal chromatic
aberration.
•Monochromatic aberrations can decrease the
variability in image quality over different
distances from the plane of best focus. This is
the “flip side” of the change in wavelength.
Conclusions
1. A simple approach to aberration free
optics is liable to generate problems due
to the interaction of longitudinal
chromatic aberration and depth of focus.
2. Spherical aberration can decrease this
interaction, by spreading out the range of
wavelengths in “best focus” at any given
distance
3. Longitudinal Chromatic Aberration is a
tougher problem. LCA interacts with
asymmetric aberrations, in a focus
dependent manner.