www.iap.uni-jena.de

Metrology and Sensing

Lecture 3: Sensors

2019-10-29

Herbert Gross

Winter term 2019

2

Schedule Optical Metrology and Sensing 2019

No Dat Subject L Detailed Content

1 15.10. Introduction HGIntroduction, optical measurements, shape measurements, errors,

definition of the meter, sampling theorem

2 22.10. Wave optics IS Basics, polarization, wave aberrations, PSF, OTF

3 29.10. Sensors HG Introduction, basic properties, CCDs, filtering, noise

4 05.11. Fringe projection IS Moire principle, illumination coding, fringe projection, deflectometry

5 12.11. Interferometry I IS Introduction, interference, types of interferometers, miscellaneous

6 19.11. Interferometry II IS Examples, interferogram interpretation, fringe evaluation methods

7 26.11. Wavefront sensors HG Hartmann-Shack WFS, Hartmann method, miscellaneous methods

8 03.12. Geometrical methods ISTactile measurement, photogrammetry, triangulation, time of flight,

Scheimpflug setup

9 10.12. Speckle methods IS Spatial / temporal coherence, speckle, properties, speckle metrology

10 17.12. Holography IS Introduction, holographic interferometry, applications, miscellaneous

11 07.01.Measurement of basic

system propertiesHG Basic properties, knife edge, slit scan, MTF measurement

12 14.01. Phase retrieval HG Introduction, algorithms, practical aspects, accuracy

13 21.01.Metrology of aspheres

and freeformsHG Aspheres, null lens tests, CGH method, metrology of freeforms

14 28.01. OCT HG Principle of OCT, tissue optics, Fourier domain OCT, miscellaneous

15 04.02 Confocal sensors HG Principle, resolution and PSF, chromatical confocal method

3

Content

Introduction

Basic properties

CCD

Filtering

Noise

Signal chain

Optical signal detection

T : transfer function

B : signal conversion

N : noise

Signal Chain

),(),(),(),(),( yxNyxCombyxTyxBKyxS D

record of

image pixels

sensorelectronic

systemcomputer

digital data

processing

image

processingdisplay

reproduction

of image pixels

signal detection signal processing reproduction

Classification of sensors

according to physical principle

1. absorption and growing temperature

2. change of conductivity

3. chemical reaction

4. generation of electrical current

Different properties of

1. spectral sensitivity

2. time behavior

3. dependence on temperature

4. sensitivity of signal power

Classification of Optical Sensors

chemical

detectors

bolometer

pyrometer

internal

photo effectphotoconductor

external

photo effect

photodiode

photomultiplier

phototube

optical

detectors

thermal

detectors

photon

detectors

Recording of a signal

Dependencies:

1. space coordinate and angle

2. time

3. wavelength

Signal Recording

radiation field

image B(x,y,t,)

image detection

sensor system

sensistivity

discretization

noisesignal

S(x,y,t,)

signal

coding

quantization

noisecoded signal

Se(x,y,t,)

signal

processing

filtering

noise

processingdigital image

I(x,y,t,)

display

discretization

noise

OTF

radiation field

object O(x,y,t,)

optical system

correction

OTF

disturbances

information

2D sensor:

Discrete pixel of finite size

Dead zones between pixels:

finite effective area of signal collection

Discretizaion and Pixelation

2

pixelD

p

geometric

sensor area

row

columnpixel

pixel

size

Dpixelactive pixel

area

pixel size

p

size of

the grid

element

Dpixel

dead area

Discrete pixel area of finite size

1. integration

2. averaging

3. dead area

4. finite spatial resolution

Nyquist frequency of spatial

resolution

Pixelation and Quantization

pixel

NyD

v2

1

x

I(x)

error

read out

correct

pixel

intensity

profile

x

Dpixel

Combined effect of spatial discretization and digitization

Averaging and rounding of signals per pixel

Rounding corresponds to noise

Digitization of the Signal

signal S

position

x

discrete quantization steps

pixel grid

input signal

input signal after

pixel integration

input signal after

pixel integration

and digitizing

yellow : I < 0

blue : I > 0

Acceptance angle of optical sensor

Sensitivity of the response on the incidence angle

Empirical description:

generalized cos-law

Largest sensitivity for normal incidence

Sensitivity on Direction

mss cos)( 0

m = 0.5

m = 1

m = 2

m = 4

m =8

m = 14

m = 50

30

60

90-90

-60

-30

0

Wavelength sensitive detection with CCD:

- array structures with different spectral sensitivity

- reduced spatial resolution

Alternatives:

- depth resolved layers

- time multiplexing

- spatial separation by filter

Detection of Color

Bayer Color Filter Array

R

G B

G

G

G

G G

G

G

G

G

G

GR

R

R

RR

B B

B B

B

Sony Color Filter Array

G B

G

G

G R

R

B

G B

G

G

G R

R

B

G B

G

G

G R

R

B

Hitachi Color Filter Array

G

G

C

G

G

W

C W

G

G

C

G

G

W

C W

G

G

C

G

G

W

C W

Spectral properties:

sensitive in VIS and NIR

Degrading effects:

1. diffusion of electrons, blooming

2. dead zones, reduced efficiency

3. noise of reading process

4. dark current

5. quantum efficiency, 80%

6. time delay, hysteresis

CCD Sensors

200 400 600 800 1000 1200

0

0.2

0.4

0.6

0.8

1

visible

range

Spectral Sensitivity of a CCD Sensor

Typical sensor of a SLR photo camera:

Canon 5D

RGB sensitivity curves at daylight

Ref: D. Gängler

sensitivity

wavelength

in [nm]

thin lines:

ISO norm

Detector

Layout of a modern CCD camera

The spot position is more accurate,

if its size is larger than the pixel width

The signal is changed in many pixels,

this is more accurate

Spot inside one pixel:

exact position cannot be distinguished

Resolution and Spot size

signal S

x

x1

Pixel

signal S

x

x2

pixel

small spot :

equal signal

x = x2 - x

1 not measurable

Dspot

Dpixel

signal S

x

x1

signal S

x

x2

large spot :

different signal

x = x2 - x

1 is measurable

Dspot

signal changes

Optical system with fixed camera position

Change of object distance:

- s too small: broadening of spot

- focussed: optimal signal transfer

- s too large: broadening of spot, saturation for extreme distances

Gain of Information

a

s's

focussed

receiver

planes too large s too small

spot Dspot

Gain of information as a function of the object distance

Gain of Information

10-2

10-1

100

information

density

ideal

NA large

ideal

NA small

stopped

down

10-2 100 10+2 10+4 10+6object

distance

s in a.u.

Quantization of signal in intervals of finite size I

Typical powers of 2 are used

8 bit corresponds to 256 value of the signal

Rounding of real numbers is equivalent to signal noise

Noise equivalent power

Representation of discretized black-white image as gray levels

Discretization of the Signal

I

IM B

max2

12

2

,

IkP quantnoise

dBBN

S 6

grey tone division

0 25612864 192

System model: sensor signal as function of measuring quantity

ideal case: linear behavior

sensitivity: slope

Characteristic numbers of a sensor:

1. sensitivity

2. stability

3. accuracy

4. speed of response

5. hysteresis

6. life time

7. cost

8. size and weight

9. spatial resolution

10. linearity

11. range of acceptance, dynamic range

12. selectivity

13. size of dead zones

Characteristic Numbers of Sensors

basS

oaada

adSs

)(

Accuracy of a sensor:

error of signal for a given input

to be distinguished:

1. calibration

2. hysteresis

3. reproduction

4. sample scatter

Accuracy

S

a

range of acceptance

specified

precision

intervalideal linear

transfer

functionreal transfer

function

error interval

error a

error

S

Hysteresis:

the size of the signal depends on the fact, if the input is increasing / decreasing

Hysteresis

S

a

ideal linear

transfer function

stimulus

signal

difference

S

quantity

decreases

quantity grows

Every sensor has a finite range of operation for the input stimulus

Limitations:

- upper limit: saturation

- lower limit: noise

Dynamic Range

signal S

0

stimulus a

dead

arealinear

range

saturation

range

amin

amax

Smax

Smin

Removed input:

- sensor reacts with a delay

- switch-on curve with characteristic

delay time

Alternative description:

- frequency response for periodic activation

- maximum acceptance frequency

Time Response

signal S

0time t

stimulus a

tstart

T

Smax

0.9 Smax

signal S

signal S

0

frequency ffmax90

Smax

0.9 Smax

signal S0.7 Smax

fmax70

Step response:

- usually oscillations

- damping feasible

Time Response

signal S

0time t

stimulus a

tstart

Smax

supercritical

damping

optimum

critical

damping

damped

Photoconductive sensors:

inner and outer photo effect

photon extracts electron out of the binding

photo current measured

Important:

- materials

- gain

- geometry

Photo Diode

)(

e

Jph

s

1

0.5

0

400 600 800 1000 1200 1400

GaAs-

photocathode

CdS-

photoresistor

Si-

photoresistor

Ge-

photoresistor

Solid state array of sensitive pixels

Types:

CCD, CMOS, CID

Typical size:

pixel length 2-20 mm

CCD Sensor

signal S

0

stimulus a

dark

current

linear

range

saturation

range

amin

amax

Smax

Smin

Smax

Color Sensor

Bayer mask of color sensor

Possible algorithms in signal processing:

Non-adaptive Adaptive

Nearest neighbor replication Edge scaling interpolation

Bilinear interpolation Interpolation with color

correction

Cubic convolution Variable number gradient

method

Smooth hue transition Pattern recognition

Smooth logarithmic hue

transition

Pattern matching interpolation

Ref: E. Derndinger

Sensor Formats

Digital sensor formats

Sensor (mm)

Type Aspect Ratio Dia. tube

(mm)

Diagonal Width Height

1/3.6" 4:3 7.056 5.000 4.000 3.000

1/3.2" 4:3 7.938 5.680 4.536 3.416

1/3" 4:3 8.467 6.000 4.800 3.600

1/2.7" 4:3 9.407 6.721 5.371 4.035

1/2.5" 4:3 10.160 7.182 5.760 4.290

1/2.3" 4:3 11.044 7.70 6.16 4.62

1/2" 4:3 12.700 8.000 6.400 4.800

1/1.8" 4:3 14.111 8.933 7.176 5.319

1/1.7" 4:3 14.941 9.500 7.600 5.700

2/3" 4:3 16.933 11.000 8.800 6.600

1" 4:3 25.400 16.000 12.800 9.600

4/3" 4:3 33.867 22.500 18.000 13.500

Cine 35mm 4:3 31.15 24.9 18.7

1.8" APS-C 3:2 45.720 28.400 23.700 15.700

35 mm film 3:2 n/a 43.300 36.000 24.000

Ref: D. Gängler

Architecture:

3 different types of carrier transport

1. full frame

2. interline

3. frame transfer

CCD Sensor

full frame interline transfer

2. read out serially

pixel by pixel

frame transfer

1. shift row-wise

downwards

1. shift to the right

by one column

2. shift read out

columns

downwards

not optically

active

1. shift row-wise

downwards

2. shift row-wise

downwards

3. read out serially

pixel by pixel

3. read out serially

pixel by pixel

Typical dimensions

Optical effect of arrays:

dead zone and change of acceptance angle

CCD-Sensors

Size

[mm]

Diagonal

[mm]

Pixel size

[mm]

Pixel number

12.8 9.6 16 16.7 20 768 480

8.8 6.6 11 11.4 13.8 768 480

6.4 4.8 8 8.33 10 768 480

4.8 3.6 6 6.25 7.5 768 480

3.2 2.4 4 4.17 5 768 480

active detector areas

CCD CCD CCD CCD

signal / loss

CCD CCD CCD CCD

signal

active detector areas

Spatial transfer function:

depends on shape and direction

of illumination

Noise behavior

CCD-Sensors

HMTF

v1/(2x)

front interline

front frame

back frame

horizontal

( solid line )

vertical

( dashed line )

10-6 10-4 10-2 100 10+2 10+4lx s1

S/N

10

100

1000

read noise

constant

Schottky noise

slope 0.5

thermal noise

slope 1

signal

CMOS Sensor Element

Setup of internal elements

Layer Thick Height n

MicroLen 0.75 7.61 1.58

FOC 0.55 6.86 1.51

Filter 1 6.31 1.54

FOC 0.45 5.31 1.51

Pass2 0.2 4.86 2

Pass1 1.16 4.66 1.46

IMD3 0.88 3.5 1.46

Metal 3 0.43 3.05 na

IMD2 0.82 2.62 1.46

Metal 2 0.43 2.23 na

IMD1 0.82 1.8 1.46

Metal 1 0.43 1.41 na

ILD 0.6 0.98 1.46

Poly 0.2 0.58 na

FOX 0.38 0 1.46

Active Area

OOM

L

OOF

Principal plane

0

2

4

6

8

4 μm

pixel

Ref: D. Gängler

Chemical detector

Photons change silver salt atom

Size of grains defines spatial resolution

MTF depends on spectrum

Typical:

50% contrast at 100 Lp/mm

Contrast for limiting frequency

1000 Lp/mm

Photographic Film

HMTF

1

0.5

010 20 50 100 200

Log s in LP/mm

0.75

Photolayer darkening

Linearity in medium range of brightness

Description of sensitivity with the optical density D

Solarization at higher density

Photo Layer

)(HLog

D

D

log H

in Lux

fog

linear

range

solarization

= tan

0.1

Discrete pixelized detector:

sinc-transfer function

Detector Sampling

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.20

0.2

0.4

0.6

0.8

1

HMTF

cutoff

frequency

Nyquist-

frequency

1/Dpix

0

0.64

Low-pass filtering:

suppression of high-frequency signals

Numerical realization:

- Fourier spectrum limited

- smooth truncations filters to avoid

oszillations

Typical effects:

- side lobes

- reduced gradients

- higher frequencies damped

Well known filter solutions:

- rectangle

- Hanning

- Hamming

- Blackman

- Bartlett, Dreieck

Signal Filtering

I(x)

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

x

measured

data

weak

smoothing

strong

smoothing

Signal Filtering

filter spectrum W() filter function W(x) linearfilter function log W(x)

logarithmic1

10-2

10-4

10-6

1

10-2

10-4

10-6

1

10-2

10-4

10-6

1

10-2

10-4

10-6

1

10-2

10-4

10-6

rectangle

Hanning

triangle

Hamming

Blackman

Fit of polynomial with order k and N points

Good conservation

of gradients

Features with higher

frequency content

preserved

Savitzky-Golay Filter

k = 15 k = 35 k = 61

N = 41

N = 81

N = 151

N = 251

N = 351

N = 491

Optimization of

1. polynomial order k

2. number of points N

Savitzky-Golay Filtering

N

5 10 15 20 25 30 35 40 45 50

20

40

60

80

100

120

140

160

180

200

220

240

k

limit

Nmin

limit

k = N

limit

N = Nges/4

k

N

Rms

Grenze

k = NGrenze

Nmin

Types of noise in photo-electric sensors:

photons noise

Flicker noise due to elektrons

fix-pattern noise

Reset noise

Dark current, Schrot, thermal noise

Excess noise of gain

Quantization noise

Superposition of noise reasons:

Noise

sinmany gle

S Sn

N N

Generation of noise in photo-electric sensors

Noise

signal

quantum

noise

photo current

photo

effect

photoelectron.

noise

fixed pattern +

reset noise

electron

current

optional for

diode arrays

optional for

amplification

noise

thermal dark-

current noise

quantization

optional for

digitization

transit time

noise

Thermal white noise

Flicker noise

Schottky noise of runtime

Dominating noise depends on

frequency

Noise

TkP BR 4

fP

1

RIfeP 02

log f

PR

Flicker

noisethermal noise

transit time

noise

1 kHz 10 MHz

Poisson statistics of photons:

quantum noise for small signal strengths

Width of distribution

Lock-in:

imprtovement of signal to noise ratio

by transform into low-noise band

Quantum Noise and Lock-in

NN N

f(N)

<N>

N = N

f

f(N)

1/f - noise

thermal noisesignal

bevor

signal

after

modulation

frequency

lock-in

transformation

Poisson noise

and white noise

Quantum Noise

10 % white

noise

10 % Photon

noise

original

signal

Characteristic:

Noise grows with

1. time of integration

2. size of detector area

Noise

1 10 100

1

10

100

Adetect

tintegral

SNR

Noise reduction and subtraction

of background

Background Noise

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

10-4

10-3

10-2

10-1

100

10-4

10-3

10-2

10-1

100

filtered

data

original

data

intensity

Log w

signals

noise below

10 %