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• Illumination• Monocular vs. Binocular• Distance• On-axis vs. Off-axis• Single or multiple targets• Literacy & Verbal ability
Aspects Conditions
Theoretical Limit of Resolution
θ
radians D22.1 λ
=θ
For λ = 587.6 nmD ranges from 2 – 8 mm0.090 ≤ θ ≤ 0.358 mrad0.3 ≤ θ ≤ 1.23 minutes of arc
Rayleigh Criterion
2
Rayleigh Criteria
0
0.25
0.5
0.75
1
-15 -10 -5 0 5 10 15 20 25
Position (microns)
Rel
ativ
e Ir
radi
ance
Airy #1Airy #2Sum
1.6 mm Pupil
Phot
orec
ptor
Phot
orec
ptor
Phot
orec
ptor
Contrast 14%
Visual AcuityVisual Acuity is a measure of the smallest detail that can be resolvedby the visual system. There are different types of acuity measures.
Point Acuity – “Binary Star” test – typically 1 arcmin resolution
Vernier Acuity – Two lines slightly offset from each other. Finds smallest detectable offset – typically 10 seconds of arc
θ
3
Visual AcuityGrating Acuity – Sinusoidal or Square wave gratings are used to determine the smallest separation between peaks that can be resolved.Typically 2 arcmin.
θ
Visual AcuityLetter Acuity – Different Letters or Symbols need to be recognizedTypically 5 arcmin.
θE
F PT O ZL P E D
ETDRS Landolt C Tumbling Es Lea
4
Visual Acuity & Pupil Size
Visual Acuity Charts
N
5’
Visual Acuity Charts are designed so the 20/20 line subtends 5 arcmin.20/40 subtends 10 arcmin20/10 subtends 2.5 arcmin
5
Stereo AcuityGiven one object slightly closer than the other, find the smallest separation that is resolvable.Typically - 5 seconds of arc
θ
Modulation Transfer Function (MTF)
Lens
The MTF measures the loss in contrast in the image of a sinusoidal target. It is the ratio of the object contrastand the image contrast.
m=100% m=55%
MTF = =0 551 00
0 55..
.
6
Contrast
Imin
Imax
Intensity
minmax
minmax
IIIIC Contrast
+−
=
Contrast Sensitivity CSis the reciprocal of theminimum value of C that is detectable.
minC1CS =
Contrast Sensitivity
m=98% m=85% m=70% m=55% m=40%
m=25% m=10%
7
Spatial Frequency
Spatial frequency is the number of cycles (1 black bar plus 1white bar equals 1 cycle) subtending 1 degree.
1o
Lens7.5 cycles
Arden Grating
8
Spatial Frequency
20/20 Letter
5 arcminor
25 μm degcycles 30
deg 1arcmin 60
arcmin 2cycle 1
)retina on(mm
cycles 100mm 1
m 1000m 10
cycle 1
=⎟⎟⎠
⎞⎜⎜⎝
⎛
=⎟⎠⎞
⎜⎝⎛ μ
μ
Aberrations & Contrast Sensitivity
m=98% m=85% m=70% m=55% m=40%
m=25% m=10%
9
Point Spread Function
The Point Spread Function (PSF) is the image of a point source of light formedon the retina. It has a finite size due to aberrations and diffraction.
Optical Transfer Function (OTF)The OTF is a complex function that measures the loss in contrastin the image of a sinusoidal target, as well as any phase shifts. The MTF is the amplitude (i.e. MTF = |OTF|) and the Phase Transfer Function (PTF) is the phase portion of the OTF.
• First, perform contrast sensitivity• Second, perform contrast sensitivity when bypassing the
optics of the eye.
Coherent
Coherent
Incoherent
12
Campbell and Green Experiment
1
10
100
1000
0 20 40 60
Spatial Frequency (cyc/deg)
Con
trast
Sen
sitiv
ity
Retinal CSFExternal CSF
MTF & Contrast Sensitivity
Lens
Cext Cret
min ext
min ret
ext
ret
CC
CCMTF ⇒=
min extext C
1CS =
min retret C
1CS Define =
ret
ext
CSCSMTF =
13
Campbell and Green Experiment
00.10.20.30.40.50.60.70.80.9
1
0 10 20 30 40 50
Spatial Frequency (cyc/deg)
Mod
ulat
ion
Improving Vision
ret
ext
CSCSMTF =
[ ] extmin ret CSCMTF Δ=Δ
Changes toOptical System
Modulation ThresholdUnder a given
illumination, thisis fixed by theretina & brain
Changes toVisual Performance
14
Van Nes & Bouman Experiment• Van Nes & Bouman, J Opt Soc Am, vol. 57, p. 401-406 (1967).• Measured Modulation Threshold for different illumination levels.
0.1
1
10
100
0.1 1 10 100
900 td
90 td
9 td
0.9 td
0.09 td
0.009 td
0.0009 td
Trolandtd = 0.0035 lm/m2
Higher contrast objects are needed for darker conditionsHigh spatial frequencies cannot be seen under dark conditions
p. 246-249 (1966).• Found modulation threshold is lowest for horizontal and
vertical gratings and highest for gratings at ±45°
These gratings are easierto see…
than these gratings
15
Grating Acuity
00.10.20.30.40.50.60.70.80.9
1
0 20 40 60
Spatial Frequency (cyc/deg)
Mod
ulat
ion
MTFModulation Threshold
Increased Aberrations
Decreased Illumination Grating Acuity
Square Wave Gratings
00.5
11.5
22.5
33.5
44.5
0 2 4 6 8
Sine Wave
1st & 3rd Harmonics
1st, 3rd, 5thHarmonicsSquare Wave
⎥⎦⎤
⎢⎣⎡ +++
π+ Kx5sin
51x3sin
31xsina4ao
16
Square Wave Response
⎥⎦⎤
⎢⎣⎡ +++
π+ Kx5sin
51x3sin
31xsina4ao
SquareWave
SineWave
If a square wave pattern is used forcontrast sensitivity testing in place ofa sine wave, the sensitivity is higher.For spatial frequencies higher than1 cyc/deg, the fundamental frequency is detected. For lower spatial frequencies, the harmonics are seen.