1

Visual Performance

• Resolution Limit• Pattern Detection• Pattern Recognition• Contrast Level• Color• Temporal Response

• 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.

Lens

10

Fourier Theory

Object PSF Image

ObjectSpectrum OTF Image

Spectrum

Convolution =

=Multiplication

FT FT FTPadding

|FT{P(x,y)exp(i2π(Wavefront Error)}|2 = PSFFT{PSF} = OTF

Effects of Refractive Surgery

No Surgery -2.75 D PRK -7.00 D PRK

11

Retinal Image Quality

• Ideally, if the optics of the eye are known, then we can determine the quality of the image falling onto the retina.

• Need to measure the aberrations of the eye.• Would like to measure wavefront error directly, but this

has only recently become feasible.• Early researchers settled for MTF (no phase information).• More recently, the PSF was measured directly.

Campbell & Green Experiment• Campbell & Green, “Optical and Retinal Factors Affecting

Visual Resolution,” J Physiology, vol 181, p.576-593 (1965).

• 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

Mitchell et al. Experiment• Mitchell, Freeman & Westheimer, J Opt Soc Am, vol. 57,

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

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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.