Detectors nearsightedness

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           • Human Eye
              • Characteristics
              • Optical Model
           • Semiconductor detectors
           • Noise sources
           • CMOS Imagers
           • CCD Imagers
           • Diodes

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           The Eye - Anatomy

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                      The Eye – Some facts
      • Roughly a sphere of ~12 mm radius
      • Typical extreme range of vision is 380 nm to 740 nm (~83% of light available)
      • The rods are sensitive to weak light, inoperative in strong light, and have
        maximum sensitivity at about 507 nm. Rods cover the retina.
      • The cones are sensitive to strong light, insensitive to weak light, and have a
      • maximum sensitivity at 555 nm. Cones occupy only the fovea.
      • Cones and rods on retina are waveguides. Cats back these with a reflective
        tapetum to get double pass, but eyes become cat’s eye retroreflectors.
      • Pupil diameter changes from 4 to 8 mm, many times less that ~106 dynamic
        range of eye. Reason is not light reduction but aberration reduction by
        “stopping down the system”. At any one time, dynamic range of eye is ~103.
      • Spacing of rods on fovea is about equal to diffraction-limited spot size of the
        pupil at the minimum diameter. Center 0.3mm of fovea has cones only.
      • Most refraction occurs at the cornea (large index contrast) while the lens
        adjusts via change of shape to change total power.
      • Typical visual resolution is about 6 minutes of arc. 20/20 vision = ability to
        resolve 5 arc minute features at 20 feet.
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           Relative Spectral Response
                    Human Eye
                                Solid lines are the photonic
                                (daylight) response

                                Dashed lines are the
                                scotopic (dark-adapted)

                                2 curves: one relative
                                response at given λ, other
                                (integrated) fractional of
                                the response for λ shorter
                                than indicated

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  A measure of Visual Acuity (VA).
  • 20 / XX implies that a subject can identify a
  letter at 20’ what a standard observer can at
  XX feet in white light.
  • 20 / 10 GOOD
  • 20 / 40 BAD
  • The fovea can support better than 20 / 10 –
  ONLY the fovea
  • Slightly higher for yellow-green, slightly lower
  in blue or far red (chromatic aberration)

     See 8.3 Smith
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           VA vs Brightness
           20/20 VA=1 (reciprocal minutes)

                                Circles are pupil diameter
                               (should be exit pupil diameter for
                               well design system)

                               Dashed and dotted lines show
                               effect of increased and decreased
                               surrounding brightness.

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                            Defects in Eye
    •      Myopia (nearsightedness) – to much power in lens/cornea and/or
           eyeball is to long. Results in distant object focusing BEFORE the
           retina. Correct with negative lens chosen to focus its image at the
           most distant point on which the eye can focus. 2 diopters of myopia
           means a person can not see beyond 1/2m so a -2D lens is used.
    •      Hyperopia (farsightedness) – to little power in lens/cornea and/or
           eyeball is to short resulting in image behind the retina. Need positive
           lens to correct.
    •      Astigmatism – different power in different directions due to cornea
           imperfections. Typically stronger radius in vertical direction than
    •      Presbyopia – inability for eye to accommodate.
    •      Cataracts – cloudy lens. Remove lens and replace with plastic
           intraocular lens near iris (no accommodation)

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           Correction of Nearsighted Eye

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      Simple Optical Model of Eye focused at ∞

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           Eye focused at ∞

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           Most important quantity
           angular magnification – focal length

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           • Power of accommodation = 4 diopters in young, decreases with age.
           • Near point Dnp is 25 cm in young and increases with age as power of
ECE 5616   accommodation decreases
             Accommodation vs. Age

           Dashed line is time for eye to accommodate to 1.3 diopters
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           Ray Tracing the Eye as Single Lens
                    Single lens magnifier

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           Ray Tracing the Eye as Single Lens
                    Single lens magnifier

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                     Magnifier Again
                     Useful for infinite conjugates

           For a equal focal lengths, fe,
           visual magnification should be
           proportional to ratio of angles

           Via similar triangles

                via lens power equation

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             Semiconductor Detectors
      The basic device is a p-n junction operated under reverse bias. When
      photons are absorbed in the diode, the depleted region’s electric field
      serves to separate the photo-generated electron-hole pairs, and an
      electric current is produced that is proportional to the optical flux.
      For high frequency operation, the depletion region must be kept thin to
      reduce transit time, but must still be sufficiently thick to absorb a large
      fraction of the light. Absorption is the key criteria for QE and is very
      wavelength dependant.
      The long λ cutoff is determined by the material’s bandgap and the short
      λ cutoff is typically due to too large an absorption coefficient (the light is
      absorbed near the surface where recombination is a serious problem).
      Frequency of operation is limited by 3 factors
               1) diffusion of carriers
               2) drift time in the depletion region
               3) capacitance of the depletion region
      Good detector has thin (to minimize drift, but not too thin or capacitance
      kills you) depletion region close to surface.
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           Semiconductor Detectors

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           QE of Various Materials vs. λ

                              η= QE = (1-R)S(1-e-αd)
           R is reflectance, S is the fraction of e & holes that contribute to the
           current, α is the absorption coefficient and d is the depth.

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                              Photo Diodes
                             Normal, PSD, Avalanche
           p-n diode common photodiode, has limited linear range – can            ηeP
                                                                           i pd =     + iD
           saturate a photodiode with too much light. Reverse voltage mode         hν
           p-i-n is common structure because thickness can be tailored to
           reduce C (faster) and better capture photons.
           Metal-semiconductor (Schottky-barrier) photodiodes are used in
           visible with very thin transparent AR coated metal contact.
           Heterojunction structures are common in IR to optimize where
           the absorption occurs. Top layer larger band gap…
           Avalanche Photodiodes is PD operated under a reverse-bias
           voltage large enough to enable multiplicative gain by impact
           ionization. The reverse electric field gives the mobile charge    iad =        + iD
           enough energy to liberate other charges within the layer.
           Sensitive, but noisy and slow and can be unstable in too much
           Position sensitive diodes are useful to measure point and point
           stability of beams. Output is proportional to beam centriod’s
           location on sensor. This includes discrete sensors like quad cells.
ECE 5616   Quad cells are very useful for centering beams.
                Responsivity of Detector
            Gη e Φ
           ip             e
    R≡ =            =G η
        P    hν Φ        hν
         eλ      λ0 [μm]
    = Gη    ≈ Gη
         hc        1.24

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           2D Lateral Effect Position-Sensing Detectors
      •     The 2D lateral effect sensors provide an accurate way to measure displacement -
            movements, distances, or angles – as well as feedback for alignment systems
            such as mirror control, microscope focusing, and fiber launch systems.

      •     On a laminar semiconductor, a so-called PIN diode is exposed to a spot of light.
            This exposure causes a change in local resistance and thus electron flow in four
            electrodes. These sensor work by proportionally distributing photocurrent using
            resistive elements to determine position. Position is calculated as below.

           Where x and y are the distances from the center of the sensor. Lx
           and Ly are the resistance lengths of the active sensor region.
           Resolution of ~5 microns is typical.
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                                 Solar Cells
     •     p-n junction and heterojunction solar cells are commonly used in
           open circuit mode. The light generates electrons and holes which
           frees e’s in the n side of the layer recombine with the holes on the p
           side and vice versa. This increases the electric field which produces
           a photo-voltage across the diode that increases with photon flux.
     •     Silicon is the most common but other material can effectively be
            – Efficiencies in the low 20’s % are being produced.
            – Electrical circuit parameters are important (load resistance, etc) to
              maximize output power.
            – Coatings are critical for both AR and protection.
     •     Concentrators such as mirrors, lenses, and diffractive optics are
           increasingly being investigated.

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                       3 Modes of Operation
         ⎛ − keVT    ⎞
  i = is ⎜ e   B
                  − 1⎟ − i p
         ⎜           ⎟
         ⎝           ⎠
          Open circuit
          •aka “Photovoltaic”
          •Solar cells
          •Low dark current
          •Slow response

            Short circuit

           Reversed biased
           • Drift field incr speed
           • Lower capacitance “ “
           • Larger sensitive area

      > R gives > sensitivity, < range,
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                               Noise Sources
                                          Shot Noise
           Shot noise is a type of noise that occurs when the finite
           number of particles that carry energy, (electrons or photons), is
           small enough to give rise to detectable statistical fluctuations in
           a measurement. The distribution is a Poisson Distribution.
                       λk e − λ
           p(k , λ ) =          Where k is # of occurrences, λ is average expected during interval
           The magnitude of this noise increases with the average
           magnitude of the current or intensity of the light. However,
           since the mag of the average signal increases faster than that
           of the shot noise (its relative strength decreases with increasing
           signal), shot noise is often only a problem with small currents
           or light intensities. SD in current is given by
                                                                        σ I = 2qIΔf
           The shot noise scales with the square root of average intensity
           (or number of photons in a given time) for coherent light.
                        SNR =                            But….
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Curtis     Wikipedia
                               Noise Sources
                                Shot Noise in the circuit

                                                       n2          n2
                         SNRDetected ≡ SNR
                                                   =           =        = nn
                                                       σ   2
                                                           n       nn          Because PElectrical = i2 R

            However, must consider quantum efficiency of detection so the
            SNR for photoelectrons is actually:

                   SNR pe = η n = ηP / 2hνB = ηφ / 2 B = m

           P optical power/hv results in number of photons/s (φ)
           B is bandwidth of signal.
           η is quantum efficiency of detector

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Curtis       Wikipedia
     Equivalent Noise Source Due to Shot Noise

            Photocurrent give by rate of photoelectrons times intrinsic gain, G

                Ge     Ge
            i=      m=    η n = e Gη Φ                                Mean photocurrent
                 T     T
            σi =    σm                                  Standard deviation of photocurrent
                           2          2
                   ⎛Ge⎞ 2 ⎛Ge⎞           Ge
            σ i2 = ⎜   ⎟ σm = ⎜   ⎟ ηn =    i = 2 BG ei                    Where 2B=1/T
                   ⎝ T ⎠      ⎝ T ⎠      T
                    i2            i   ηΦ
            SNR =          =        =    =m                                    as expected.
                    σ i2       2 BGe 2 B

           iRMS − Noise = σ i = 2 BGei               RMS noise current. Equivalent current source.

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                             Random gain noise
                   Typical of APDs and photomultipliers
           i = eGη Φ                                     Mean photocurrent due to mean gain

                  ⎛     σG ⎞
           σ = 2 B⎜ G +
                  ⎜        ⎟ei = 2 BG F ei
                        G ⎟
            i                                              Standard deviation of photocurrent
                  ⎝        ⎠
           F ≡ 1+        2
                                   “Excess noise factor” = additional noise from random gain
                    i2      i      ηΦ m
           SNR =         =       =   =                              SNR lower by factor of F
                 σ i2 2 BG Fe 2 BF F
                            ⎛    1⎞
           F = hG + (1 − h )⎜ 2 − ⎟                                               for an APD
                            ⎝    G⎠
                 Feedback          Random locations of ionization
                                   F~2 for h=0, large gain
            1≤ F < 2          for photomultiplier tubes with no feedback and discrete gain locations

                                    Variance of gain                                                   []
                             G      Mean gain                                                          []
                             F      Excess noise factor                                                []
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Curtis                       h      Ionization ratio of APD = αh/αe (=0 for Si)                        []
                         Dark current noise
                   Thermal excitation of photocarriers
  Typical dark current for Si photodiode

           id vs temperature at VR = 10 V   id vs bias at 25 oC

                                                              Sharp PD412PI
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                         Dark current noise
                  Thermal excitation of photocarriers
       • Assume that average dark current is calibrated and subtracted so no signal error.
       • Dark current then adds shot noise (only) due to greater number of carriers in circuit.
       • Since shot noise variance is mean of photocarriers, variances of two sources add.

           σ = 2 BG F e(i + id )
                                                                 Variances add

                    i2    i2                         m
           SNR = 2 =                 =
                σ i 2 BG Fe(i + id )              ⎛ m ⎞
                                                F ⎜1 + d ⎟
                                                  ⎝   m ⎠

                   Result is new excess noise factor due to dark current.

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                        Circuit Noise Sources
                          For diodes (Johnson-Nyquest Noise)

            Thermal motion of electronics in load resistor R give rise to zero mean noise.

             σ i2 = 4k BTe B / R      Thermal noise current variance in a resister R

            The amplifier contribution can also be written as “noise figure” FT
             σ i2 = 4k B F T0 B / R

                         Te                   290 oK is standard chosen for definiteness
              FT ≡ 1 +
                       290 o K
           Amplifier can also be characterized as shot noise due to amplifier
           leakage current and noise voltage

           σ =i
               2      2
                      RMS − Noise        (
                                      + ω CT vRMS − Noise             )2

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                         Circuit Noise Sources
                            For diodes (Johnson-Nyquist Noise)

           or as a dimensionless circuit noise parameter (Saleh 17.5-27)

                   σ i −circuit
           σq =                       Std. dev. of amplifier noise electrons in time T.
                      2 Be

           Including amplifier noise via the last definition, the total SNR would be:

             SNR ≡
                           (signal in photocarriers )2    =
                                                                     (G η n )

                     ∑ noise variance in photocarriers        G 2 F (η n + md ) + σ q

                kB      Boltzman’s constant = 1.380622 10-23             [J/ o K]

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                      How to choose PD or APD?
                                                                Look at SNR
 At what average photon count m does the APD SNR exceed a PD?
                                   SNR APD ≥ SNRPD
                   (G m )   2

  G 2 F (m + md − APD ) + σ q − APD
                                                    (m + md − PD ) + σ q2− PD
Solve for photon flux:

                                                                                 APD: G = 100, F = 2, md − APD = 1000, σ q − APD = 1000
     (md − PD − F md − APD ) + (σ q2− PD − σ q2− APD   G2   )         40
                                                                                  PD: md − PD = 10, σ q − APD = 100
                             F −1


Conclusion: APDs can outperform PDs+Amp
for low signals by overcoming amplifier noise
                                                                           100            500   1000           5000   10000       50000 1000
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                    Detector figures-of-merit
                 Noise equivalent power & specific detectivity
           Noise equivalent power is incident optical signal required to generate
           a photocurrent equal to the RMS noise current:

           NEP ≡
                   iRMS − Noise σ i
                               =    =
                                        ∑ σ2
                                                   [W]           Variances add
                      R          R      R

           Since both shot noise and Johnson noise variances are proportional to
           bandwidth, some sources define NEP/Sqrt[B] :

           NEP B
                   ≡ RMS − Noise =
                                            ∑σ     2
                                                       /B   ⎡ W ⎤
                                                            ⎢ Hz ⎥
                      R B          R B         R            ⎣    ⎦
           Since NEP is proportional to the square root of BW (B) and area (A), it
           is common to define a figure-of-merit, the specific detectivity:

                        ∗  AB
                      D ≡
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                          Image Sensors
    • Two types of images sensors, CCD and CMOS. Both
      are pixilated metal oxide semiconductors that
      accumulate charge in each pixel proportional to the
      incident optical flux. Neither is superior, though their
      different properties may have advantages depending on
      the application.
           – CCD (charge coupled device) sensors are analog sensors that
             transfer the accumulated pixel charges sequentially to a
             common output circuit where they are converted to a voltage,
             buffered, amplified, and converted to a digital signal.
           – CMOS (complimentary metal oxide semiconductor) imagers
             convert the accumulated pixel charge to a voltage and also
             amplify the signal in the pixel structure. They also typically have
             parallel processing in the column structures, including multiple
             analog-to digital converters. CMOS sensors can support camera
             on a chip architectures.

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                  Image Sensor Properties
                                   CCD vs. CMOS
      Property                                      Advantage
                    CMOS has slight advantage because high gain amplifiers are included in the
    Responsivity    pixel structure.
    SNR / Dynamic   CCD has a slight advantage due to the complexity of the CMOS circuitry and its
                    higher noise levels (FPN and PRNU).
                    Neither has an advantage, though with CMOS uniform shuttering has traded off
    Shuttering      with fill factor (requiring microlens arrays to compensate). Older CMOS sensors
                    had rolling shutters.
                    CMOS has a clear advantage with parallel processing and small circuit size (all
    Frame Rate      camera functions can be integrated into a chip).
                    CCD has clear advantage with its common output channel and simple pixel
    Uniformity      structure.
                    This property is unique to CMOS sensors. The ability to only gather the signal
    Windowing       from a region of interest can have a large effect on frame rate.
                    Neither has an advantage, though CMOS sensors tend to be better in rugged
    Reliability     environments as less off chip circuitry leads to fewer soldered connections to fail.
                    CMOS sensors have an advantage with low volume due to sensor packaging and
    Cost            circuitry needed to integrate sensor chip. CCDs are better for high volume
                    applications like cell phone cameras.
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                  Imager Noise Sources
                                  Two Types:

            Random Noise                          Pattern Noise
    Temporally random – changes from     Does not change from Frame to
      frame to frame.                      Frame

    Several Components                   Two components:
    • Shot Noise                         • FPN – Fixed Pattern Noise
    • Thermal Noise (Reset / kTC)        • PRNU – Photo-Response Non-
    • Thermal Noise (Johnson-Nyquist)      Uniformity
    • Flicker (Connection / 1/f) Noise
    • Quantization Noise                 Pattern Noise can be compensated
                                            with processing (Doing so does
                                            not increase the dynamic range of
    Random noise can be reduced by          an individual measurement).
      averaging multiple frames             Pattern noise is a much bigger
      (averaging reduces the noise by       problem for CMOS sensors.
      the square root of the number of

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                             Noise Sources
                    Thermal (kTC) noise, imaging sensors
       The noise is not caused by the capacitor itself, but by the
       thermodynamic equilibrium of the amount of charge on the capacitor.
       For imaging sensors the reset noise (the resulting charge left on the
       capacitor) is the dominant thermal noise source
           The RMS reset charge noise is given by

              Qn = k BTC                  Where k is Boltzmann’s constant,
                                          T is temperature in Kelvin and C is

       You do not want saturation of the storage node or accumulation node in
       diode or pixel; however, you do not want to make the capacity
       unnecessarily large due to this thermal noise.

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           Pattern & Quantization Noise
    •      FPN (fixed pattern noise): noise measured in the absence of illumination.
           Due to variations in:
            –   Doping concentrations
            –   Contamination
            –   Threshold Voltages (VT), etc…
            –   FPN typically increases proportionally with the exposure length.
    •      PRNU (photo response non-uniformity): noise due to non-uniformity in pixel
           responsivity. Caused by variations in:
            –   Pixel dimensions
            –   Doping Concentrations
            –   Pixel gain
            –   Passivation layer thickness and composition, etc..
    •      Quantization Noise: noise due to rounding errors during the analog to digital
           conversion.                     Original and Digitized Signal


                                            -6   -4   -2       0        2   4   6
                                                       Quantization Error


ECE 5616                                    -6   -4   -2       0       2    4   6
            Typical Imager Noise Diagram
                                                                                            Thermal (Johnson-Nyquist)
                                                     Dark Current & Dark Shot                   Flicker Noise (1/f)
                    Reset Noise (kTC)                   Photon Shot Noise                              FPN
                          FPN                                 PRNU                                    PRNU

                                        Photon Capture /
     Pixel Reset                                                          In Pixel Amplification

                                                                                              To off-chip Electronics
       Column Buffer/Amplification                  A/D Conversion
                                                                                             (and other noise sources)

                             Thermal (Johnson-Nyquist)               Quantization Noise
                                 Flicker Noise (1/f)

                                 Blue indicates CMOS Sensor Only
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                           Example SNR Calculation
                                                8 bit CMOS sensor

    •      Dark image response (blue). Pixel
                                                                                      x 10                   HROM Camera Simulation - No Correction
                                                                                                                                               Mean Dark Value (μ0) = 24.5796

           response broadened by:
                                                                                              Dark Image
                                                                                              Bright Image                                   Mean Bright Value (μ1) = 223.4649
                                                                                                                                                       Dark Image σ 0 = 5.0965

            – FPN,                                                               2                                                                 Bright Image σ 1 = 6.7853
                                                                                                                                     Detector SNR = 24.4744 dB (4.0651 Bits)

            – kTC and
            – Dark current

                                                                  # of Pixels
    •      Bright Image (just saturated, red).                                   1

           Slightly broader due to
            – PRNU                                                              0.5

            – Photon Shot Noise
    •      Standard SNR calculations                                             0
                                                                                      0             50               100
                                                                                                                                       150                200              250

                                      ⎛ μ                    ⎞                               Imager SNR = 27.4 dB
                                          bright − μ dark
            In dB:   SNRdB = 20 log10 ⎜                      ⎟
                                      ⎜ σ 2 +σ 2             ⎟                            (4.6 bits of usable resolution)
                                      ⎝    bright     dark   ⎠
                                                        ⎛ μ                                    ⎞
                                                            bright − μ dark
                                                = log 2 ⎜                                      ⎟
            In bits of Resolution:
                                      SNRbits           ⎜ σ 2 +σ 2                             ⎟
                                                        ⎝    bright     dark                   ⎠

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                         Example SNR Calculation –
                      8 bit CMOS sensor with FPN and PRNU correction
                                                                                         5          HROM Camera Simulation - Dark Noise (FPN) Correction
                                                                                  x 10

    •      After FPN subtraction (does not vary from frame                  2.5              Dark Image
                                                                                             Bright Image
                                                                                                                                              Mean Dark Value (μ0) = 1.0985
                                                                                                                                           Mean Bright Value (μ1) = 199.9839

           to frame), spreading due to:                                                                                                             Dark Image σ 0 = 0.36525
                                                                                                                                                     Bright Image σ 1 = 4.488

            –   kTC (Dark and Bright Image)                                   2                                                    Detector SNR = 32.2513 dB (5.3568 Bits)

            –   Dark shot (Dark and Bright images)

                                                              # of Pixels

            –   Photon Shot (Bright Image)
            –   PRNU (Bright Image)                                           1

    •      After PRNU removal (divide by scaled average                     0.5

           bright image), spreading due to:
            –   kTC (Dark and Bright Image)                                   0
                                                                                  0                50              100
                                                                                                                                     150                200               250

            –   Dark shot (Dark and Bright images)                                x 10
                                                                                      5             HROM Camera Simulation - FPN and PRNU Correction

            –   Photon Shot (Bright Image)                                  2.5              Dark Image
                                                                                                                                              Mean Dark Value (μ0) = 1.0985
                                                                                                                                           Mean Bright Value (μ ) = 199.9814
                                                                                             Bright Image                                                      1
                                                                                                                                                   Dark Image σ 0 = 0.36525
                                                                                                                                                     Bright Image σ1 = 2.071

    SNR w/o correction = 27.4 dB (4.6 bits)
                                                                             2                                                     Detector SNR = 38.2375 dB (6.3511 Bits)

                                                             # of Pixels

    SNR w/ FPN correction = 32.9 dB (5.4 bits)                               1

    SNR w/ FPN & PRNU correction = 39.5 dB (6.6 bits)
                                                                                  0                50              100               150                200               250

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    Example Specifications - CMOS

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           Example Floor Plan - CMOS

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           See Spreadsheet

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                            CCD Sensors
       A charge-coupled device (CCD) is an analog shift register that
       enables the transportation of analog signals (electric charges) through
       successive stages (capacitors), controlled by a clock signal.

        An image is projected onto the capacitor array (the photoactive region),
       causing each capacitor to accumulate an electric charge proportional to
       the light intensity at that location. Once the array has been exposed to
       the image, a control circuit causes each capacitor to transfer its
       contents to its neighbor (operating as a shift register). The last capacitor
       in the array dumps its charge into a charge amplifier, which converts the
       charge into a voltage. By repeating this process, the controlling circuit
       converts the entire semiconductor contents of the array to a sequence
       of voltages, which it samples and digitizes.

       CCD advantage is that is can be made very low noise due to CDS.
       They have very high FF and therefore quantum efficiency.

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           Charge Transfer

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           Clocking schemes

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                            CCD Sensors
                         Correlated Double Sampling
    Correlated Double Sampling (CDS) is a technique for measuring electrical
    values such as voltages or currents that allows for removal of an undesired
    offset. The output of the pixel is measured twice: once in a known condition
    and once in an unknown condition. The value measured from the known
    condition is then subtracted from the unknown condition to generate a value
    with a known relation to the physical quantity being measured.
    Before the charge of each pixel is
    transferred to the output node of the
    CCD, the output node is reset to a
    reference value. The pixel charge is
    then transferred to the output node.
    The final value of charge assigned to
    this pixel is the difference between
    the reference value and the
    transferred charge. From an
    electronics standpoint, there are
    different methods for accomplishing
    this, such as digital, analog sample
    and hold, integration, and dual slope.
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           Types of CCD Sensors

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           Example: Dalsa FT50

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                      QE of Silicon CCD
                     typical for both CCD and CMOS

     Response in blue is very sensitive to processing details of particular fab
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    Feature                  CCD                         CMOS
    Signal out of pixel      Electron packet            Voltage
    Signal out of chip       Voltage (analog)           Bits (digital)
    Fill factor              High                       Moderate (μlens)
    Amplifier mismatch       N/A                        Moderate
    System Noise             Low                        Moderate
    System Complexity        High                       Low
    Sensor Complexity        Low                        Moderate
    Camera components Sensor +                          Sensor + lens
                    multiple support chips + lens

           For both types of sensors color is achieved by using color
           filters – typically four sub-pixels per colored pixel (2 green, 1
ECE 5616
           blue, 1 red). Bayer Filter
                             Coherent detection
                            Heterodyning and homodyning
Signal                             Optical intensity due to interference on detector assuming perfect spatial
                                   mode-matching. Degradation from perfect matching (tilt) decreases
                                   interference term.
                                  I = ES + E L
         Local oscillator
                                    =     S   e j (ωS t +φS ) +      L   e j (ωLt +φL )

                                                                                     cos[(ωS − ω L )t + (φS − φL )]
                                               2            2
                                    =     S        +    L       +2         S     L

   Average detected current

            i = iS + iL + 2 iS iL cos[(ωS − ω L )t + (φS − φL )]
                 small for strong LO (typical case)

 Homodyne detection when frequencies matched:

                i ≈ iL + 2 iS iL cos[(φS − φL )]

                 Note that phase difference must be minimized or no signal is detected.
ECE 5616
               SNR of coherent detection
            Gain provided by heterodyne amplification dominates circuit noise and dark current

      σ i2 = m = η n                  Shot noise variance is = number of photocarriers

              = 2 B e i ≈ 2 B e iL           Dominated by strong local oscillator

                           ⎧ 12   Heterodyne             RMS amplitude of signal
            i = 2 iS i L × ⎨
                           ⎩1      Homodyne

                     iS ⎧2 Heterodyne
           SNR = 2 =    ×⎨
                σ i 2 Be ⎩4 Homodyne

           • Multiplier represents SNR gain over direct detection in addition to
           overwhelming of dark current and circuit noise.
           • Disadvantage is significantly increased system complexity.

ECE 5616

           W. Smith “Modern Optical Engineering”

           Chapter 8 (Human Eye)

ECE 5616

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