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Detectors

• 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 ResponseHuman Eye

Solid lines are the photonic (daylight) response

Dashed lines are the scotopic (dark-adapted) response

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

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20/20A 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 Brightness20/20 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 horizontal.

• 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 quantityangular 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 ofaccommodation decreases

Accommodation

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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 LensSingle lens magnifier

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Ray Tracing the Eye as Single LensSingle lens magnifier

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Magnifier Again Useful for infinite conjugates

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

Via similar triangles

via lens power equation

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Semiconductor DetectorsThe 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 carriers2) drift time in the depletion region3) 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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p-n diode common photodiode, has limited linear range – can saturate a photodiode with too much light. Reverse voltage modep-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’slocation on sensor. This includes discrete sensors like quad cells. Quad cells are very useful for centering beams.

Photo DiodesNormal, PSD, Avalanche

Dpd ihePi +=ν

η

Dad ih

ePGi +=νη

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Responsivity of Detector

24.1]μm[0ληλη

νη

νη

GhceG

heG

heG

Pip

≈=

=ΦΦ

=≡R

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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 beused.– 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

Open circuit•aka “Photovoltaic”•Solar cells•Low dark current•Slow response

Short circuit

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

pTk

eV

s ieii B −⎟⎟⎠

⎞⎜⎜⎝

⎛−=

−

1

> R gives > sensitivity, < range, < BW

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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.

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.

Noise SourcesShot Noise

!),(

kekp

k λλλ−

=

NNSNR =

fqII Δ= 2σ

Wikipedia

Where k is # of occurrences, λ is average expected during interval

But….

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Noise SourcesShot Noise in the circuit

n

nnOpticalDetected n

nnnSNRSNR ===≡

2

2

22

σ

Wikipedia

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

mBBhPnSNRpe ==== 2/2/ ηφνηη

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

Because PElectrical = i2 R

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Equivalent Noise Source Due to Shot Noise

Photocurrent give by rate of photoelectrons times intrinsic gain, G

Φ=== ηη GenT

eGmT

eGi Mean photocurrent

ieGBiT

eGnT

eGT

eGT

eG

mi

mi

22

22

2 ==⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

=

ησσ

σσ Standard deviation of photocurrent

Where 2B=1/T

mBBGe

iiSNRi

=Φ

===222

2 ησ

as expected.

iBGei iNoiseRMS 2==− σRMS noise current. Equivalent current source.

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Random gain noiseTypical of APDs and photomultipliers

Φ= ηGei Mean photocurrent due to mean gain

ieFGBieG

GB Gi 22

22 =⎟⎟

⎠

⎞⎜⎜⎝

⎛+=σσ Standard deviation of photocurrent

“Excess noise factor” = additional noise from random gain

Fm

BFFeGBiiSNR

i

=Φ

===222

2 ησ

SNR lower by factor of F

Variance of gain []Mean gain []

F Excess noise factor []h Ionization ratio of APD = αh/αe (=0 for Si) []

2Gσ

G

2

2

1G

F Gσ+≡

( ) ⎟⎠⎞

⎜⎝⎛ −−+=

GhGhF 121 for an APD

Random locations of ionizationF~2 for h=0, large gain

Feedback

21 <≤ F for photomultiplier tubes with no feedback and discrete gain locations

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Dark current noiseThermal excitation of photocarriers

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

Typical dark current for Si photodiode

Sharp PD412PI

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Dark current noiseThermal 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.

( )di iieFGB += 22σ

( )⎟⎠⎞

⎜⎝⎛ +

=+

==

mmF

miiFeGB

iiSNRddi 12

2

2

2

σ

Result is new excess noise factor due to dark current.

Variances add

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Circuit Noise SourcesFor diodes (Johnson-Nyquest Noise)

RBTk eBi /42 =σ Thermal noise current variance in a resister R

The amplifier contribution can also be written as “noise figure” FT

RBTFkBi /4 02 =σ

K2901 o

eT

TF +≡where

Amplifier can also be characterized as shot noise due to amplifier leakage current and noise voltage

( )222NoiseRMSTNoiseRMSi vCi −− += ωσ

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

290 oK is standard chosen for definiteness

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Circuit Noise SourcesFor diodes (Johnson-Nyquist Noise)

Becircuiti

q 2−=

σσ

( ) ( )( ) 22

22

ersphotocarriin variancenoiseersphotocarriin signal

qdmnFGnGSNR

σηη

++=≡

∑

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

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

Std. dev. of amplifier noise electrons in time T.

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

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How to choose PD or APD?Look at SNR

100 500 1000 5000 10000 50000 1000m�

0

10

20

30

40

50

RNSBd

( )( ) ( ) 2

2

22

2

PDqPDdAPDqAPDd

PDAPD

mmm

mmFGmG

SNRSNR

−−−− ++≥

++

≥

σσ

At what average photon count does the APD SNR exceed a PD?m

Solve for photon flux:

1000,1000,2,100 ==== −− APDqAPDdmFG σ100,10 == −− APDqPDdm σ

APD:

PD:

Conclusion: APDs can outperform PDs+Ampfor low signals by overcoming amplifier noise

( ) ( )1

222

−

−+−≤ −−−−

FGmFm

m APDqPDqAPDdPDd σσ

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Detector figures-of-meritNoise equivalent power & specific detectivity

RRR∑==≡ −

2σσ iNoiseRMSiNEP

Noise equivalent power is incident optical signal required to generatea photocurrent equal to the RMS noise current:

Variances add

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

[W]

RRR∑==≡ −

B

BBiNEP iNoiseRMS

B

/2σσ⎥⎦

⎤⎢⎣

⎡HzW

NEPBA

D ≡∗

Since NEP is proportional to the square root of BW (B) and area (A), itis common to define a figure-of-merit, the specific detectivity:

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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 multipleanalog-to digital converters. CMOS sensors can support camera on a chip architectures.

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Image Sensor PropertiesCCD vs. CMOS

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.

Cost

Advantage

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.Reliability

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.Windowing

CCD has clear advantage with its common output channel and simple pixel structure.Uniformity

CMOS has a clear advantage with parallel processing and small circuit size (all camera functions can be integrated into a chip).Frame Rate

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.

Shuttering

CCD has a slight advantage due to the complexity of the CMOS circuitry and its higher noise levels (FPN and PRNU).

SNR / Dynamic Range

CMOS has slight advantage because high gain amplifiers are included in the pixel structure.Responsivity

Property

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Imager Noise SourcesTwo 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 NoiseDoes 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.

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Noise SourcesThermal (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

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.

TCkQ Bn =Where k is Boltzmann’s constant, T is temperature in Kelvin and C is capacitance.

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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.

-6 -4 -2 0 2 4 6-1

0

1Original and Digitized Signal

-6 -4 -2 0 2 4 6-0.2

0

0.2Quantization Error

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Typical Imager Noise Diagram

Reset Noise (kTC)FPN

Photon Capture / Conversion

Dark Current & Dark ShotPhoton Shot Noise

PRNU

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

FPNPRNU

In Pixel Amplification

Column Buffer/Amplification A/D Conversion

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

FPN

To off-chip Electronics (and other noise sources)

Pixel Reset

Blue indicates CMOS Sensor Only

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Example SNR Calculation8 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:

In bits of Resolution:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

−=

2210log20darkbright

darkbrightdBSNR

σσ

μμ

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

−=

222logdarkbright

darkbrightbitsSNR

σσ

μμ

Imager SNR = 27.4 dB (4.6 bits of usable resolution)

0 50 100 150 200 2500

0.5

1

1.5

2

x 104

Counts

# of

Pix

els

HROM Camera Simulation - No Correction

Mean Dark Value (μ0) = 24.5796

Mean Bright Value (μ1) = 223.4649Dark Image σ0 = 5.0965

Bright Image σ1 = 6.7853Detector SNR = 24.4744 dB (4.0651 Bits)

Dark ImageBright Image

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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 = 27.4 dB (4.6 bits)

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

SNR w/ FPN & PRNU correction = 39.5 dB (6.6 bits)

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

x 105

Counts

# of

Pix

els

HROM Camera Simulation - Dark Noise (FPN) Correction

Mean Dark Value (μ0) = 1.0985

Mean Bright Value (μ1) = 199.9839Dark Image σ0 = 0.36525Bright Image σ1 = 4.488

Detector SNR = 32.2513 dB (5.3568 Bits)

Dark ImageBright Image

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

x 105

Counts

# of

Pix

els

HROM Camera Simulation - FPN and PRNU Correction

Mean Dark Value (μ0) = 1.0985

Mean Bright Value (μ1) = 199.9814Dark Image σ0 = 0.36525Bright Image σ1 = 2.071

Detector SNR = 38.2375 dB (6.3511 Bits)

Dark ImageBright Image

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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 SensorsA 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 SensorsCorrelated 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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Specifications

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QE of Silicon CCDtypical for both CCD and CMOS

Response in blue is very sensitive to processing details of particular fab

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Comparison

Feature CCD CMOSSignal out of pixel Electron packet VoltageSignal out of chip Voltage (analog) Bits (digital)Fill factor High Moderate (μlens)Amplifier mismatch N/A ModerateSystem Noise Low Moderate System Complexity High LowSensor Complexity Low ModerateCamera 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 blue, 1 red). Bayer Filter

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Coherent detectionHeterodyning and homodyning

Signal

Local oscillator( ) ( )

( ) ( )[ ]LSLSLSLS

tjL

tjS

LS

t

ee

EEILLSS

φφωω

φωφω

−+−++=

+=

+=++

cos222

2

Optical intensity due to interference on detector assuming perfect spatial mode-matching. Degradation from perfect matching (tilt) decreases interference term.

( ) ( )[ ]LSLSLSLS tiiiii φφωω −+−++= cos2

Average detected current

small for strong LO (typical case)

Homodyne detection when frequencies matched:

( )[ ]LSLSL iiii φφ −+≈ cos2

Note that phase difference must be minimized or no signal is detected.

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SNR of coherent detectionGain provided by heterodyne amplification dominates circuit noise and dark current

L

i

ieBieBnm

22

2

≈=

== ησ Shot noise variance is = number of photocarriers

⎩⎨⎧

×=Homodyne1Heterodyne

2 21

LS iii

Dominated by strong local oscillator

RMS amplitude of signal

⎩⎨⎧

×==Homodyne4Heterodyne2

22

2

BeiiSNR S

iσ

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

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Reading

W. Smith “Modern Optical Engineering”

Chapter 8 (Human Eye)