Metrology and Sensing

Transcription

1 Metrology and Sensing Lecture 3: Sensors Herbert ross Winter term

2 2 Preliminary Schedule No Date Subject Detailed Content Introduction Introduction, optical measurements, shape measurements, errors, definition of the meter, sampling theorem Wave optics (ACP) Basics, polarization, wave aberrations, PSF, OTF Sensors Introduction, basic properties, CCDs, filtering, noise Fringe projection Moire principle, illumination coding, fringe projection, deflectometry Interferometry I (ACP) Introduction, interference, types of interferometers, miscellaneous Interferometry II Examples, interferogram interpretation, fringe evaluation methods Wavefront sensors Hartmann-Shack WFS, Hartmann method, miscellaneous methods eometrical methods Tactile measurement, photogrammetry, triangulation, time of flight, Scheimpflug setup Speckle methods Spatial and temporal coherence, speckle, properties, speckle metrology Holography Introduction, holographic interferometry, applications, miscellaneous Measurement of basic system properties Bssic properties, knife edge, slit scan, MTF measurement Phase retrieval Introduction, algorithms, practical aspects, accuracy Metrology of aspheres and freeforms Aspheres, null lens tests, CH method, freeforms, metrology of freeforms OCT Principle of OCT, tissue optics, Fourier domain OCT, miscellaneous Confocal sensors Principle, resolution and PSF, microscopy, chromatical confocal method

3 3 Content Introduction Basic properties CCD Filtering Noise

4 Signal Chain Signal chain signal detection signal processing reproduction sensor electronic system computer image processing display record of image pixels digital data processing reproduction of image pixels Optical signal detection K B( x, y) T( x, y) Comb( x, y) N ( x, ) S( x, y) y T : transfer function B : signal conversion N : noise D

5 Classification of Optical Sensors optical detectors chemical detectors thermal detectors bolometer pyrometer photon detectors internal photo effect photoconductor 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 external photo effect photodiode photomultiplier phototube

6 Signal Recording Recording of a signal radiation field object O(x,y,t, ) correction Dependencies: 1. space coordinate and angle 2. time 3. wavelength radiation field image B(x,y,t, ) signal S(x,y,t, ) coded signal S e (x,y,t, ) optical system image detection sensor system signal coding OTF disturbances sensistivity discretization noise quantization noise filtering signal processing noise digital image I(x,y,t, ) processing discretization display noise information OTF

7 Discretizaion and Pixelation 2D sensor: Discrete pixel of finite size pixel column geometric sensor area Dead zones between pixels: finite effective area of signal collection row p D pixel active pixel area 2 pixel size p pixel size D pixel size of the grid element D pixel dead area

8 Pixelation and Quantization Discrete pixel area of finite size 1. integration 2. averaging 3. dead area 4. finite spatial resolution pixel x x Nyquist frequency of spatial resolution intensity profile v Ny 1 2D pixel I(x) D pixel error read out correct

9 Digitization of the Signal Combined effect of spatial discretization and digitization Averaging and rounding of signals per pixel Rounding corresponds to noise signal S discrete quantization steps input signal input signal after pixel integration input signal after pixel integration and digitizing yellow : I < 0 blue : I > 0 pixel grid position x

10 Sensitivity on Direction Acceptance angle of optical sensor Sensitivity of the response on the incidence angle Empirical description: generalized cos-law s( ) s 0 cos m Largest sensitivity for normal incidence m = 0.5 m = 1 m = 2 m = 4 m =8 m = 14 m =

11 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 B R R R R R B B B B B Sony Color Filter Array B R R B B R R B B R R B Hitachi Color Filter Array C W C W C W C W C W C W

12 CCD Sensors Spectral properties: sensitive in VIS and NIR 1 visible range 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

13 Spectral Sensitivity of a CCD Sensor Typical sensor of a SLR photo camera: Canon 5D RB sensitivity curves at daylight sensitivity thin lines: ISO norm wavelength in [nm] Ref: D. ängler

14 Detector Layout of a modern CCD camera

15 Resolution and Spot size 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 small spot : equal signal x = x 2 - x 1 not measurable x 1 large spot : different signal x = x 2 - x 1 is measurable x 1 D pixel D spot Pixel x D spot x signal S signal S x 2 x 2 pixel x x signal changes signal S signal S

16 ain of Information 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 s too large focussed s too small receiver plane a spot D spot s s'

17 ain of Information ain of information as a function of the object distance information density 10 0 ideal NA large 10-1 ideal NA small stopped down object distance s in a.u.

18 Discretization of the Signal 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 I M 2 B I S N P 6 B noise, quant db max I k 12 2 Representation of discretized black-white image as gray levels grey tone division

19 Characteristic Numbers of Sensors System model: sensor signal as function of measuring quantity ideal case: linear behavior sensitivity: slope S s a b 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 s ds( a) da a a o

20 Accuracy Accuracy of a sensor: error of signal for a given input S to be distinguished: 1. calibration 2. hysteresis 3. reproduction 4. sample scatter real transfer function specified precision interval ideal linear transfer function error S a error a error interval range of acceptance

21 Hysteresis Hysteresis: the size of the signal depends on the fact, if the inpout is increasing / decreasing S quantity decreases signal difference S ideal linear transfer function quantity grows stimulus a

22 Dynamic Range Every sensor has a finite range of operation for the input stimulus Limitations: - upper limit: saturation - lower limit: noise signal S S max dead area linear range saturation range S min 0 a min a max stimulus a

23 Time Response Removed input: - sensor reacts with a delay - switch-on curve with characteristic delay time S max 0.9 S max signal S Alternative description: - frequency response for periodic activation - maximum acceptance frequency stimulus a signal S signal S S max 0 t start T time t 0.9 S max 0.7 S max signal S 0 f max90 f max70 frequency f

24 Time Response Step response: - usually oscillations - damping feasible signal S damped S max optimum critical damping stimulus a supercritical damping 0 time t t start

25 Photo Diode Photoconductive sensors: inner and outer photo effect photon extracts electron out of the binding photo current measured ph J e ( ) Important: - materials - gain - geometry 1 s Siphotoresistor ephotoresistor 0.5 CdSphotoresistor aasphotocathode

26 CCD Sensor Solid state array of sensitive pixels Types: CCD, CMOS, CID Typical size: pixel length 2-20 mm signal S S max S max dark current linear range saturation range S min 0 a min a max stimulus a

27 Color Sensor Bayer mask of color sensor Possible algorithms in signal processing: Non-adaptive Nearest neighbor replication Bilinear interpolation Cubic convolution Smooth hue transition Smooth logarithmic hue transition Adaptive Edge scaling interpolation Interpolation with color correction Variable number gradient method Pattern recognition Pattern matching interpolation Ref: E. Derndinger

28 Sensor Formats Digital sensor formats Sensor (mm) Type Aspect Ratio Dia. tube Diagonal Width Height (mm) 1/3.6" 4: /3.2" 4: /3" 4: /2.7" 4: /2.5" 4: /2.3" 4: /2" 4: /1.8" 4: /1.7" 4: /3" 4: " 4: /3" 4: Cine 35mm 4: " APS-C 3: mm film 3:2 n/a Ref: D. ängler

29 CCD Sensor Architecture: 3 different types of carrier transport 1. full frame 2. interline 3. frame transfer full frame interline transfer frame transfer 1. shift to the right by one column 1. shift row-wise downwards 1. shift row-wise downwards 2. shift read out columns downwards 2. shift row-wise downwards 2. read out serially pixel by pixel 3. read out serially pixel by pixel not optically active 3. read out serially pixel by pixel

30 CCD-Sensors Typical dimensions Size [mm] Diagonal [mm] Pixel size [mm] Pixel number Optical effect of arrays: dead zone and change of acceptance angle signal / loss signal CCD CCD CCD CCD CCD CCD CCD CCD active detector areas active detector areas

31 CCD-Sensors H MTF Spatial transfer function: depends on shape and direction of illumination horizontal ( solid line ) front interline front frame back frame vertical ( dashed line ) S/N 1/(2 x) v 1000 Noise behavior thermal noise slope signal 10 read noise constant Schottky noise slope lx s

32 CMOS Sensor Element Setup of internal elements OOM L OOF 4 μm pixel Principal plane Layer Thick Height n MicroLen FOC Filter FOC Pass Pass IMD Metal na IMD Metal na IMD Metal na ILD Poly na FOX Active Area Ref: D. ängler

33 Photografic Film 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 H MTF Log s in LP/mm

34 Photo Layer Photolayer darkening Linearity in medium range of brightness Description of sensitivity with the optical density D D Log(H) Solarization at higher density D = tan solarization linear range 0.1 fog log H in Lux

35 Detector Sampling Discrete pixelized detector: sinc-transfer function H MTF Nyquistfrequency cutoff frequency /D pix

36 Signal Filtering 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 I(x) strong smoothing weak smoothing measured data x

37 Signal Filtering rectangle filter spectrum W( ) filter function W(x) linear filter function log W(x) logarithmic Hanning triangle Hamming Blackman

38 Savitzky-olay Filter Fit of polynomial with order k and N points ood conservation of gradients k = 15 k = 35 k = 61 Features with higher frequency content preserved N = 41 N = 81 N = 151 N = 251 N = 351 N = 491

39 Savitzky-olay Filtering Optimization of 1. polynomial order k 2. number of points N N limit N min Rms limit N = N ges / N renze N min renze k = N k limit k = N k

40 Noise 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 ob noise reasons: S S n N N many sin gle

41 Noise eneration of noise in photo-eletric sensors noise optional for amplification optional for digitization quantization quantum noise photo effect photoelectron. noise optional for diode arrays fixed pattern + reset noise thermal darkcurrent noise transit time noise photo current electron current signal

42 Noise Thermal white noise Flicker noise Schottky noise of runtime P R P R 4 P 1 f k B T P 2e f I0 R Flicker noise thermal noise Dominating noise depends on frequency transit time noise 1 khz 10 MHz log f

43 Quantum Noise and Lock-in Poisson statistics of photons: quantum noise for small signal strengths f(n) Width of distribution N = N N N Lock-in: imprtovement of signal to noise ratio by transform into low-noise band f(n) 1/f - noise <N> N lock-in transformation signal bevor thermal noise signal after modulation frequency f

44 Quantum Noise Poisson noise and white noise original signal 10 % Photon noise 10 % white noise

45 Noise Characteristic: Noise grows with 1. time of integration 2. size of detector area 100 A detect SNR t integral

46 Background Noise Noise reduction and subtraction of background Log w noise below 10 % original data 10-2 signals filtered data intensity