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

Transcription

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

2 The Eye - Anatomy

3 The Eye Some facts Roughly a sphere of ~1 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. 0/0 vision = ability to resolve 5 arc minute features at 0 feet.

4 Relative Spectral Response Human Eye Solid lines are the photonic (daylight) response Dashed lines are the scotopic (dark-adapted) response curves: one relative response at given λ, other (integrated) fractional of the response for λ shorter than indicated

5 0/0 A measure of Visual Acuity (VA). 0 / XX implies that a subject can identify a letter at 0 what a standard observer can at XX feet in white light. 0 / 10 GOOD 0 / 40 BAD The fovea can support better than 0 / 10 ONLY the fovea Slightly higher for yellow-green, slightly lower in blue or far red (chromatic aberration) See 8.3 Smith

6 VA vs Brightness 0/0 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.

7 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. diopters of myopia means a person can not see beyond 1/m so a -D 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 horizontal. Presbyopia inability for eye to accommodate. Cataracts cloudy lens. Remove lens and replace with plastic intraocular lens near iris (no accommodation)

8 Correction of Nearsighted Eye

9 Simple Optical Model of Eye focused at

10 Eye focused at

11 Most important quantity angular magnification focal length

12 Accommodation Power of accommodation = 4 diopters in young, decreases with age. Near point D np is 5 cm in young and increases with age as power of accommodation decreases

13 Accommodation vs. Age Dashed line is time for eye to accommodate to 1.3 diopters

14 Ray Tracing the Eye as Single Lens Single lens magnifier

15 Ray Tracing the Eye as Single Lens Single lens magnifier

16 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

17 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 ) 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.

18 Semiconductor Detectors

19 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.

20 Photo Diodes Normal, PSD, Avalanche p-n diode common photodiode, has limited linear range can saturate a photodiode with too much light. Reverse voltage mode 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 enough energy to liberate other charges within the layer. Sensitive, but noisy and slow and can be unstable in too much light. 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. Quad cells are very useful for centering beams. ηep i = + h ν pd i D GηeP i = + hν ad i D

21 R i p P Responsivity of Detector = eλ = Gη hc Gη eφ hν Φ Gη e = Gη hν λ 0 [μm] 1.4

22 D Lateral Effect Position-Sensing Detectors The D 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.

23 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 used. Efficiencies in the low 0 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.

24 ev kbt i = i s e 1 i Open circuit aka Photovoltaic Solar cells Low dark current Slow response 3 Modes of Operation p Short circuit Reversed biased Drift field incr speed Lower capacitance Larger sensitive area > R gives > sensitivity, < range, < BW

25 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. k λ λ e p( k, λ) = k! 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 The shot noise scales with the square root of average intensity (or number of photons in a given time) for coherent light. Wikipedia SNR = Where k is # of occurrences, λ is average expected during interval N N But. σ I = qiδf

26 Noise Sources Shot Noise in the circuit n n SNR Detected SNROptical = = = σ n nn n n Because P Electrical = i R However, must consider quantum efficiency of detection so the SNR for photoelectrons is actually: SNR pe = ηn = ηp / hνb = ηφ / B = m P optical power/hv results in number of photons/s (φ) B is bandwidth of signal. η is quantum efficiency of detector Wikipedia

27 Equivalent Noise Source Due to Shot Noise Photocurrent give by rate of photoelectrons times intrinsic gain, G G e G e i = m = η n = egη Φ T T G e σ i = σ m T σ i = G e T σ m = G e T η n = G e i T = Mean photocurrent Standard deviation of photocurrent BGei Where B=1/T SNR i = σ i = i BGe η Φ = B = m as expected. i RMS Noise = σ i = BGei RMS noise current. Equivalent current source.

28 i Random gain noise Typical of APDs and photomultipliers = egη Φ σ G σ i = B G + ei = BGFei G σ G F 1+ G i i η Φ m SNR = = = = σ i BGFe BF F 1 F = hg + ( h) G Mean photocurrent due to mean gain Standard deviation of photocurrent Excess noise factor = additional noise from random gain SNR lower by factor of F 1 for an APD Feedback 1 F < Random locations of ionization F~ for h=0, large gain for photomultiplier tubes with no feedback and discrete gain locations σ G Variance of gain [] Mean gain [] G F Excess noise factor [] h Ionization ratio of APD = α h /α e (=0 for Si) []

29 Dark current noise Thermal excitation of photocarriers Typical dark current for Si photodiode i d vs temperature at V R = 10 V i d vs bias at 5 o C Sharp PD41PI

30 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 ( i ) = B GFe + i i d Variances add SNR = i σ = i BGFe ( i + i ) = m m F + m i d 1 d Result is new excess noise factor due to dark current.

31 Circuit Noise Sources For diodes (Johnson-Nyquest Noise) Thermal motion of electronics in load resistor R give rise to zero mean noise. σ i = 4kBTe B / R Thermal noise current variance in a resister R The amplifier contribution can also be written as noise figure F T σ i = 4k B FT0 B / R where T F T + 90 e 1 o K 90 o K is standard chosen for definiteness Amplifier can also be characterized as shot noise due to amplifier leakage current and noise voltage σ i = i ω RMS Noise + ( C v ) T RMS Noise

32 Circuit Noise Sources For diodes (Johnson-Nyquist Noise) or as a dimensionless circuit noise parameter (Saleh ) σ q i = σ Be circuit Std. dev. of amplifier noise electrons in time T. Including amplifier noise via the last definition, the total SNR would be: SNR ( signal in photocarriers) ( Gηn ) = noise variance in photocarriers G F ( ηn + ) + σ m d q k B Boltzman s constant = [J/ o K]

33 G F How to choose PD or APD? Look at SNR At what average photon count does the APD SNR exceed a PD? m ( G m ) SNR APD SNR ( m + m ) + σ ( m + m ) σ PD m d APD q APD d PD + q PD Solve for photon flux: 50 m ( m F m ) + ( σ σ G ) d PD d APD F 1 q PD q APD APD: PD: G md = PD = q APD 100, F =, m d APD = 1000, σ q APD = , σ = 100 S NR d B 0 Conclusion: APDs can outperform PDs+Amp for low signals by overcoming amplifier noise m

34 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 i RMS Noise R = σ i R = R σ [W] Variances add Since both shot noise and Johnson noise variances are proportional to bandwidth, some sources define NEP/Sqrt[B] : NEP B i RMS Noise R B = σ i R B = σ 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: R / B W Hz D A B NEP

35 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.

36 Image Sensor Properties CCD vs. CMOS Property Responsivity SNR / Dynamic Range Shuttering Frame Rate Uniformity Windowing Reliability Cost Advantage CMOS has slight advantage because high gain amplifiers are included in the pixel structure. 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 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 camera functions can be integrated into a chip). CCD has clear advantage with its common output channel and simple pixel structure. This property is unique to CMOS sensors. The ability to only gather the signal 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 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 circuitry needed to integrate sensor chip. CCDs are better for high volume applications like cell phone cameras.

37 Imager Noise Sources Two Types: Random Noise Temporally random changes from frame to frame. Several Components Shot Noise Thermal Noise (Reset / ktc) Thermal Noise (Johnson-Nyquist) Flicker (Connection / 1/f) Noise Quantization Noise Random noise can be reduced by averaging multiple frames (averaging reduces the noise by the square root of the number of measurements). Pattern Noise Does not change from Frame to Frame Two components: FPN Fixed Pattern Noise PRNU Photo-Response Non- Uniformity Pattern Noise can be compensated with processing (Doing so does not increase the dynamic range of an individual measurement). Pattern noise is a much bigger problem for CMOS sensors.

38 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 Q n = k B TC Where k is Boltzmann s constant, T is temperature in Kelvin and C is capacitance. 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.

39 Pattern & Quantization Noise FPN (fixed pattern noise): noise measured in the absence of illumination. Due to variations in: Doping concentrations Contamination Threshold Voltages (V T ), 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. 1 0 Original and Digitized Signal Quantization Error

40 Typical Imager Noise Diagram Reset Noise (ktc) FPN Dark Current & Dark Shot Photon Shot Noise PRNU Thermal (Johnson-Nyquist) Flicker Noise (1/f) FPN PRNU Pixel Reset Photon Capture / Conversion In Pixel Amplification Column Buffer/Amplification A/D Conversion To off-chip Electronics (and other noise sources) Thermal (Johnson-Nyquist) Flicker Noise (1/f) FPN Quantization Noise Blue indicates CMOS Sensor Only

41 Example SNR Calculation 8 bit CMOS sensor Dark image response (blue). Pixel response broadened by: FPN, ktc and Dark current Bright Image (just saturated, red). Slightly broader due to PRNU Photon Shot Noise Standard SNR calculations In db: μ SNR db = 0 log 10 σ In bits of Resolution: SNR bits bright bright μ dark + σ dark = log μ σ bright # of Pixels bright Counts μ x 10 4 dark + σ Imager SNR = 7.4 db (4.6 bits of usable resolution) dark Dark Image Bright Image HROM Camera Simulation - No Correction Mean Dark Value (μ 0 ) = Mean Bright Value (μ 1 ) = Dark Image σ 0 = Bright Image σ 1 = Detector SNR = db ( Bits)

42 Example SNR Calculation 8 bit CMOS sensor with FPN and PRNU correction After FPN subtraction (does not vary from frame to frame), spreading due to: ktc (Dark and Bright Image) Dark shot (Dark and Bright images) Photon Shot (Bright Image) PRNU (Bright Image) After PRNU removal (divide by scaled average bright image), spreading due to: ktc (Dark and Bright Image) Dark shot (Dark and Bright images) Photon Shot (Bright Image) SNR w/o correction = 7.4 db (4.6 bits) SNR w/ FPN correction = 3.9 db (5.4 bits) SNR w/ FPN & PRNU correction = 39.5 db (6.6 bits) # of Pixels # of Pixels x 10 5 Dark Image Bright Image HROM Camera Simulation - Dark Noise (FPN) Correction Mean Dark Value (μ 0 ) = Mean Bright Value (μ 1 ) = Dark Image σ 0 = Bright Image σ 1 = Detector SNR = db ( Bits) Counts x 10 5 Dark Image Bright Image HROM Camera Simulation - FPN and PRNU Correction Mean Dark Value (μ 0 ) = Mean Bright Value (μ ) = Dark Image σ 0 = Bright Image σ 1 =.071 Detector SNR = db ( Bits) Counts

43 Example Specifications - CMOS

44 Example Floor Plan - CMOS

45 See Spreadsheet

46 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.

47 Charge Transfer

48 Clocking schemes

49 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.

50 Types of CCD Sensors

51 Example: Dalsa FT50

52 Specifications

53 QE of Silicon CCD typical for both CCD and CMOS Response in blue is very sensitive to processing details of particular fab

54 Comparison 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 ( green, 1 blue, 1 red). Bayer Filter

55 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. Local oscillator I = = = E S e S S + E j L ( ω t + φ ) j( ω t + φ ) + S S L + e L + S L L L cos [( ω ω ) t + ( φ φ )] S L S L Average detected current i = i + i + i i cos S L S small for strong LO (typical case) Homodyne detection when frequencies matched: i i L + i S i L L cos [( ω ω ) t + ( φ φ )] S L [( φ φ )] S L S L Note that phase difference must be minimized or no signal is detected.

56 SNR of coherent detection Gain provided by heterodyne amplification dominates circuit noise and dark current σ i = m = ηn = B ei B ei Shot noise variance is = number of photocarriers L Dominated by strong local oscillator i = 1 i S i L 1 Heterodyne Homodyne RMS amplitude of signal SNR = i σ i = i S Be 4 Heterodyne Homodyne Multiplier represents SNR gain over direct detection in addition to overwhelming of dark current and circuit noise. Disadvantage is significantly increased system complexity.

57 Reading W. Smith Modern Optical Engineering Chapter 8 (Human Eye)