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Visual Performance Theoretical Limit of Resolution

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Visual Performance Theoretical Limit of Resolution Visual Performance Aspects Conditions • Resolution Limit • Illumination • Pattern Detection • Monocular vs. Binocular • Pattern Recognition • Distance • Contrast Level • On-axis vs. Off-axis • Color • Single or multiple targets • Temporal Response • Literacy & Verbal ability Theoretical Limit of Resolution θ Rayleigh Criterion 1.22λ θ = radians D For λ = 587.6 nm D ranges from 2 – 8 mm 0.090 ≤θ≤0.358 mrad 0.3 ≤θ≤1.23 minutes of arc 1 Rayleigh Criteria 1 1.6 mm Pupil 0.75 Contrast 14% Airy #1 0.5 Airy #2 Sum Relative Irradiance 0.25 Photorecptor Photorecptor Photorecptor 0 -15 -10 -5 0 5 10 15 20 25 Position (microns) Visual Acuity Visual Acuity is a measure of the smallest detail that can be resolved by 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 2 Visual Acuity Grating Acuity – Sinusoidal or Square wave gratings are used to determine the smallest separation between peaks that can be resolved. Typically 2 arcmin. θ Visual Acuity Letter Acuity – Different Letters or Symbols need to be recognized Typically 5 arcmin. E θ F P T O Z L P E D ETDRS Landolt C Tumbling Es Lea 3 Visual Acuity & Pupil Size Visual Acuity Charts 5’ N Visual Acuity Charts are designed so the 20/20 line subtends 5 arcmin. 20/40 subtends 10 arcmin 20/10 subtends 2.5 arcmin 4 Stereo Acuity Given one object slightly closer than the other, find the smallest separation that is resolvable. Typically - 5 seconds of arc θ Modulation Transfer Function (MTF) The MTF measures the loss in contrast in the image of a sinusoidal target. It is the ratio of the object contrast and the image contrast. m=100% m=55% Lens 055. MTF ==055. 100. 5 Contrast Intensity I − I Contrast C = max min Imax Imax + Imin Contrast Sensitivity CS is the reciprocal of the Imin minimum value of C that is detectable. 1 CS = Cmin Contrast Sensitivity m=98% m=85% m=70% m=55% m=40% m=25% m=10% 6 Spatial Frequency 7.5 cycles Lens 1o Spatial frequency is the number of cycles (1 black bar plus 1 white bar equals 1 cycle) subtending 1 degree. Arden Grating 7 Spatial Frequency 20/20 Letter 1 cycle ⎛1000 μm ⎞ cycles ⎜ ⎟ =100 (on retina) 5 arcmin10 μm ⎝ 1 mm ⎠ mm or 1 cycle ⎛ 60 arcmin ⎞ cycles 25 μm ⎜ ⎟ = 30 2 arcmin ⎝ 1 deg ⎠ deg Aberrations & Contrast Sensitivity m=98% m=85% m=70% m=55% m=40% m=25% m=10% 8 Point Spread Function The Point Spread Function (PSF) is the image of a point source of light formed on 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 contrast in 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 9 Fourier Theory Convolution = Object PSF Image Padding FT FT FT Object Multiplication = OTF Image Spectrum Spectrum |FT{P(x,y)exp(i2π(Wavefront Error)}|2 = PSF FT{PSF} = OTF Effects of Refractive Surgery No Surgery -2.75 D PRK -7.00 D PRK 10 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 Incoherent Coherent 11 Campbell and Green Experiment 1000 100 Retinal CSF External CSF 10 Contrast Sensitivity Contrast 1 0204060 Spatial Frequency (cyc/deg) MTF & Contrast Sensitivity Cext Cret Lens C C MTF = ret ⇒ ret min Cext Cext min 1 CSext CS = MTF = ext C ext min CSret 1 Define CSret = Cret min 12 Campbell and Green Experiment 1 0.9 0.8 0.7 0.6 0.5 0.4 Modulation 0.3 0.2 0.1 0 0 1020304050 Spatial Frequency (cyc/deg) Improving Vision CS MTF = ext CSret ΔMTF = [Cret min ]ΔCSext Changes to Visual Performance Changes to Modulation Threshold Optical System Under a given illumination, this is fixed by the retina & brain 13 Van Nes & Bouman Experiment • Van Nes & Bouman, J Opt Soc Am, vol. 57, p. 401-406 (1967). • Measured Modulation Threshold for different illumination levels. 100 900 td Troland 90 td 2 10 td = 0.0035 lm/m 9 td 0.9 td 0.09 td 1 0.009 td 0.0009 td 0.1 0.1 1 10 100 Higher contrast objects are needed for darker conditions High 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 easier than these gratings to see… 14 Grating Acuity 1 0.9 0.8 Increased 0.7 0.6 Aberrations MTF 0.5 0.4 Modulation Threshold Modulation 0.3 0.2 0.1 0 0204060 Decreased Illumination Grating Acuity Spatial Frequency (cyc/deg) Square Wave Gratings 4.5 4 Sine Wave 3.5 3 1st & 3rd Harmonics 2.5 2 1st, 3rd, 5th 1.5 Harmonics 1 Square Wave 0.5 0 02468 4a ⎡ 1 1 ⎤ a o + ⎢sin x + sin 3x + sin 5x +K⎥ π ⎣ 3 5 ⎦ 15 Square Wave Response Square 4a ⎡ 1 1 ⎤ Wave a o + ⎢sin x + sin 3x + sin 5x +K⎥ π ⎣ 3 5 ⎦ If a square wave pattern is used for Sine Wave contrast sensitivity testing in place of a sine wave, the sensitivity is higher. For spatial frequencies higher than 1 cyc/deg, the fundamental frequency is detected. For lower spatial frequencies, the harmonics are seen. 16.
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