ECE 583. Sensor output. Sensor output. Telescope

Transcription

1 6-1 ECE 583 Lecture 6 Radiant flux formulation with and without optical attenuation, spectral selection, detector overview 6-2 Sensor output Output of the sensor depends upon the area of the detector, detector response, bandpass, optical quality, atmospheric transmittance, and the solar irradiance PThe radiant flux through an area is =LA cos P However, we assume the sun is a point source, thus it is easier to use irradiance instead of radiance Then =EAcos A is the area of the detector in radiometer or the area of the optical collector Field of view does not impact the calculation The irradiance is from the sun P Note that a typical solar radiometer will be pointed at the sun Thus, the cosine factor will disappear However, it is still possible to measure solar irradiance without pointing at the sun In those cases, it is necessary to include the cosine factor 6-3 Telescope 6-4 Sensor output Telescope portion defines the field of view of the sensor PSimplistic view of the telescope allows for straightforward calculations of the sensor s output PAddition of lens or mirror elements will not significantly alter the methods we ll use to compute the output PNote, the field of view of the sensor will not affect the sensor s output as long as the field of view is larger than the solid angle of the sun Sun is assumed to be a point source Plane-parallel radiation P Will still be an effect due to skylight that is collected by the sensor Strictly speaking, the radiant flux through the detector will also include a spectral effect due to the finite bandpass of the sensor PWe will describe methods for making this spectral bandpass later PFor now, assume that the sensor receiver has a bandpass of R P Also, it is possible that the irradiance could change over the area of the detector PThen the radiant flux will be Φ = EdAd A Ed A Δ R Δ R R R Where A R is the area of the receiver (either telescope receiver area or detector area) Assumed that the irradiance is relatively constant over the receiver s area PThe next two questions are What is the value for E? How do we convert the radiant flux to sensor output?

2 6-5 What is the output? 6-6 Working voltage relation Assume we know the irradiance at the sensor, how do we get to a sensor output? PThe detector in the system converts the photon energy to an electric output PIgnore analog to digital conversion and work only in voltage or current P The output can be written as V = R Φ PWhere R is the system response that depends on The transmittance of any optics - T t ( ) The transmittance of any spectral filtering devices -T f ( ) The detector response - d ( ) PThen the system reponse can be written as t f d R( ) = T ( ) T ( ) δ ( ) PThe response will be valid over a finite bandpass width - at the center wavelength - Putting everything together to this point gives us our working voltage relation P This is the voltage output of a sensor viewing the sun without any attenuation Mean earth-sun distance Narrow bandpass t f d V = A T T δ E 0 R 0 = = A R E R R Φ 0 0 Δ Δ Δ P Subscript on voltage is used to indicate no attenuation of the solar irradiance and the spectral aspect of the measurement 6-7 Output 6-8 Detector selection Can predict the sensor output given the spectral response and the spectral radiant flux PThe output, V sensor can be written as V sensor = Φ R system( ) d d Output is in units of voltage or current Note that there is no wavelength subscript Output(Volts, Amperes, electrons, etc.) Is determined by the units of R If d is small and the radiant flux and response do not vary much over it, then V sensor =< ><R system ( )> PUnfortunately, we cannot predict the spectral radiant flux from a band-integrated sensor output Given enough data points and ancillary information we might be able to reconstruct the spectral radiant flux However, this problem is always underdetermined Numerous factors are considered when selecting a detector for a radiometric application P Application Commercial or experimental system Mass produced or singular system Precision or accuracy PThe application can then define the technical requirements Spectral response Speed of response Signal-to-noise ratio Linearity Dynamic range PNon-technical factors also need to be considered Cost Availability Size

3 6-9 Detector responsivity 6-10 Detector response - example Response or responsivity refers to the ability of the detector to convert incident energy into a usable output P Response is the ratio of the output from the detector to the radiant energy input R = Output Radiant input P Radiant energy input can refer to any of the energy quantities used so far Typically see radiant flux (W) or spectral radiance [W/(m 2 sr m)] Will also see photometric and photon response POutput is typically Volts or Amperes PTypically want high response Output is high for a given input radiant flux Small amount of radiant flux gives a high output Wavelength (nm) 6-11 Basic detection mechanisms Responsivity (spectral and temporal) are determined by the type of detector and material used PTwo basic detector types - thermal and quantum based Thermal detectors operate on the concept that as an object absorbs energy its temperature changes Quantum-based detectors involve a change in the characteristics of the detector when a photon is absorbed PType of detector chosen depends on Wavelength region of interest Speed of response needed Required accuracy and precision 6-12 Thermal detectors Thermal detectors operate on the concept that as an object absorbs energy its temperature changes PTemperature change is converted to an electrical signal POldest form of detectors PGeneral characteristics of thermal detectors are Slow response time compared to quantum-based detectors Extended spectral range Responsivity is constant with wavelength PBasic types of thermal detectors are Thermocouple, thermoelectric detector, thermopile Thermistor, bolometer Pyroelectric Golay cell

4 6-13 Bolometers 6-14 Quantum-based Detectors Temperature change in the bolometer material leads to a change in resistance PThermistors have the same property PUse either metals or semiconductors for the resistive element PTypical metals are platinum and nickel Mechanically strong Very thin ribbons minimize the heat capacity PSemiconductors have a larger temperature coefficient The resistance decreases with temperature in semiconductors This can lead to burnout when operated at large bias voltages Joule heating causes the resistance to go down Excessive power begins to be dissipated until the unit is destroyed P Langley used this type of detector in the 1880s to measure the solar constant Photons interact directly with the electronic energy levels within the detector to produce free carriers and a current PAlso known as photon-based detectors As an example, the photons can interact directly with the electronic energy levels within the detector to produce free carriers Eye and camera film are simple examples of quantum detectors PFast response PPhotoemissive detectors rely on the photo-effect the material emits an electron when a photon strikes the detector material with sufficient energy PPhotoconductive detectors change their resistance allowing the current flow to change when the photon strikes the detector PPhotovoltaic detectors have a p-n junction that causes the electronhole pairs to separate to produce a voltage that can be measured 6-15 Photoemissive detectors 6-16 Photodiodes Photoemissive detectors have very high sensitivity and are most often seen in photomultiplier tubes (PMTs) Electron released when h exceeds work function of the photocathode Process depends on material and wavelength Electron typically attracted to an anode for detection PMTs use this concept in an avalanche philosophy where the emitted electron strikes subsequent surfaces emitting further electrons and increasing output levels Solid-state detectors use the incident photons to create charge carriers P Charge carriers cross the junction of the two materials in a semiconductor Produces a voltage difference relative to an external circuit Applying a voltage to a photovoltaic detector essentially creates a photoconductive detector P Basically, the detector is designed to use absorption of a photon in a depletion region Convert the photon to an electron-hole pair The pairs give rise to a photocurrent due to the electric field in the depletion region PCrude way to view the system is that Incident photon of sufficient energy frees an electron (generation) Electron flows to fill any holes (recombination) Large size makes them less desirable for array systems

5 6-17 Photodiodes Photodiode terminology arises from the fact that the p-n junction in a semiconductor is used PDope two adjacent regions of the semiconductor One region is donor (n-type) - electron Other region is acceptor (p-type) - hole Free electrons in the n-region are attracted to the p-region Holes in the p-region drift to the n-region Result is that the n-region has a net positive charge versus negative charge in the p-region PCan consider the spectral response in terms of the quantum efficiency of converting photons to electrons i( ) ηq ηq R( ) = = = Φ ( ) hν hc is the quantum efficiency q is the electronic charge 6-18 P-N Junctions All P-N junctions are light sensitive but photodiodes have been specifically designed for light detection PLight emitting diodes, for example, can be used as detectors by altering the circuit Circuit in one direction gives off light when a current is applied Other direction allows light to generate a current PThe quantum efficiency is related to the efficiency of electron generation electron hole generation rate η Q = photon incident rate PQuantum efficiency declines due to Some light not being absorbed in the sensitive layer Surface reflections Recombination of electron-hole pairs 6-19 Quantum-based spectral response All quantum-based detectors will have a similarly-shaped spectral response based on q/h PCutoff wavelength is the long wavelength limit above which photons do not have sufficient energy to release an electron (exceed the bandgap energy) 1 P Decrease in response is due to the choice of representing 0.8 response in terms of energy units (W) 0.6 Each photon that exceeds the bandgap energy releases an 0.4 electron Electrons/W however is 0.2 larger at longer wavelengths because the radiant flux is Wavelength (micrometer) lower per photon P Low wavelength limit is due to this energy effect as well as the fact that the detector material typically becomes highly absorbing 6-20 I-V curve The detection process of a photodiode can be understood to some extent using the I-V curve P Current-voltage curve 100 A PGives the output of the system as a function of input power Each curve represents a 50 A different input power Reverse bias Difference in power between curves is constant PSystems can be operated -50 A at constant current or voltage Forward bias Strictly not true since there is also the resistance -100 A Ohm s law PLinear systems have small resistances operated in reverse bias Voltage

6 6-21 Linearity 6-22 Photoconductive detectors It is typically desired to have a detector that is linear with input radiant energy PThat is, the response versus input (not wavelength) is linear P Then, doubling the input energy causes the output to double PLinearity of a detector depends on Detector approach and circuitry Detector material Input energy P The main advantage to a linear system is that it is more easily characterized Two measurments, in theory, are all that are required Detectors are well enough understood that it is usually apparent when a system is non-linear Electronics can cause a system to be non-linear in unanticipated ways Photoconductive detectors rely on the semiconductor property that they contain free electrons and holes PIncident photons provide the energy required to alter the resistance of the semiconductor material by producing free electrons Applying an external voltage allows the resistance change to be measured as changes in current (Ohm s Law) Running in constant current gives a changing voltage P Detector used in a circuit with a bias voltage & load resistor in series The change in electrical conductivity leads to an increase in the current flowing in the circuit Gives measurable change in voltage drop across the load resistor PTypically require cooling (most often liquid nitrogen or TE cooling) for use at longer wavelengths PPhotoconductive detectors can be used at longer wavelengths into the TIR 6-23 Phototvoltaic detectors 6-24 Photovoltaic responsivities Photovoltaic detector relies on a photodiode detector in a different circuit PPV detector creates a potential barrier at the junction between the two regions while maintaining charge neutrality of the entire system PPotential barrier is similar in concept to the work function of the photoemissive detector Depends on temperature (higher temperature smaller barrier) Depends on material type PAn external bias across the junction changes the barrier height Forward bias reduces the barrier height (positive terminal of the power source to the p-junction) Reverse bias increases the barrier height PImprovements in controlling the electron-hole pairs can be obtained by adding an intrinsic region between the p-n junction Results in the p-i-n diode Behavior of p-i-n diode similar to that of the p-n junction, thus it is not covered in detail here Graph here is similar to previous one except now shows mostly photovoltaic detectors One can see how it might be difficult to chose a specific detector Materials here show different responsivities for different temperatures Impossible to cover a wide range of the spectrum with a single detector Have not even discussed cost, availability, and size yet

7 Photovoltaic circuit Typical op-amp circuit gives a voltage ouput that is more linear with input POperational amplifier (op-amp) is a collection of transistors and resistors in a single chip PInclusion of the op-amp produces a feedback between the input and output of the op-amp Loss in gain in the process Response time is longer Signal conditioning is Detector improved including a more linear response PTypical circuit appears as shown (this is a short-circuit current mode) - + Output Photovoltaic circuit Alternate schematic of photovoltaic circuit can be used to show the relation between irradiance and output PI p = R where is the photodiode current responsivity PV= d ( ) R = R f R where d ( ) is the photodiode/op amp voltage responsivity R f PMade use of Ohm s Law - V= R f I P Irradiance Photodiode Detector I P - + Output 6-25 Silicon detectors Silicon detectors have wide use in radiometry and other applications PPrimarily due to the low cost of silicon wafers (outcome of the computer industry PVideo cameras and digital cameras use silicon detectors PGood response and thermal effects are limited to high and low wavelengths 6-26 Silicon detectors Silicon detectors, and others, will have strong temperature dependencies PPlot here shows that the quantum efficiency improves at long wavelengths as temperature increases PThis is a change in response PWill see later that there is also a dark current that depends on temperature PResponse changes cannot be determined by taking a dark reading

8 Figures of merit Figures of merit help to decide which detector is the best suited for a given application PMultiple figures are used with each having its own specific usefulness P Care must be used to ensure that the appropriate figure of merit is applied to the given application PFurther care must be used to ensure that comparisons of different detector packages are made on the same scale Apples to apples not apples to oranges Responsivity may be sufficient for selection What about noise? What about areal size? Ever present cost decision? Signal-to-noise ratio Most straightforward figure of merit is signal-to-noise ratio (SNR) which is the ratio of the signal to the noise P Typical method for SNR is to take the average ouput as your signal and the standard deviation of the measurements as the noise P Using a case of Gaussian noise with mean of zero and standard deviatiion of 0.05 and a signal level of unity Average signal is1.00 The SNR is 1.00/0.05=20 P The difficulty is determining each of the pieces that are needed to determine the SNR P Easiest way to improve SNR is to operate at a higher signal Noise usually increases less slowly than signal Means that the SNR metric will depend upon the signal level POther way to improve SNR is to decrease noise Noise Equivalent Power This is the incident radiant flux needed to yield an SNR of unity PRecall that we have the following for responsivity photocurrent Signal output S R det ector ( ) = = = optical input radiant flux optical input radiant flux Φ PAnd SNR is SNR S = N PSolve the responsivity equation for radiant flux and substitute the signal for the noise since SNR=1 and S N NEP = Φ ( S = N ) = = R R NEP depends on responsivity and the noise Physically, the NEP is the smallest radiant flux that we can measure with any confidence and discern it from the noise Detectivity and D* Would prefer a figure of merit that gets larger as the detector gets better PDetectivity is the inverse of NEP Larger values imply better detector Occurs by either having a large responsivity (good detector) or having low noise P Can also get good responsivity by simply using a larger collecting area and altering the electronic behavior of the detector PSpectral specific detectivity (D* or D-star) attempts to put all of the detectors on a level playing field by accounting for these effects D = D A Δf * det A det is the detector area and f is the bandwidth frequency of the detector Units are (cm Hz 1/2 )/W

9 6-27 Spectral band The output from the detector will also depend on width of the spectral filtering system we are using P Width does not refer to the physical width, but the span of wavelengths that we allow through the system Wider band allows more energy through detector and higher output Narrow band blocks energy from reaching the detector but refines our knowledge of the spectral nature of the object/source/media 1.2 PFor example, consider 1 the atmospheric transmittance plot 0.8 shown at right 0.6 PMeasuring the spectral 0.4 nature of transmittance 0.2 requires a spectral 0 selection that is both narrow in width and is Wavenumber (1/cm) sampled at a large number of wavelengths Spectral response The total system response is simply the product of all of the component spectral responses PDefine R system ( ) as the overall system response as a function of wavelength and it can be written as R ( ) = R det ( ) τ ( ) τ ( ) system ector optics filter R detector ( ) is the response of the detector as a function of wavelength optics is the transmittance of any optics in the system filter is the transmittance of any spectral filtering device in the system PBased on earlier discussions, can tell that typical units of responsivity will be A/W or V/W Spectral response often given with these units as well Can create confusion when attempting to predict sensor output based on a given spectral input 6-29 Spectral selection 6-30 Spectral selection - basic terms Need spectral selection to limit the wavelength region over which the detector will respond PSpectral selection allows us to further refine the wavelength region that we are measuring PEach method has advantages and disadvantages in terms of Spectral resolution Spectral sampling Stability Robustness PThe basic approaches are Dispersion systems such as prisms and gratings Transmissive filters Absorption filters Interference filters Fourier transform spectrometry Peak transmittance, peak wavelength, bandwidth and center wavelength PPeak transmittance is the largest transmittance for the system T PPeak wavelength is the peak wavelength at which the peak transmittance occurs PBandwidth is the interval between wavelengths ½T peak measured at half-peak transmittance Bandpass Halfwidth Half-power bandwidth PCenter wavelength is the wavelength at the center of the bandpass peak Bandwidth Wavelength (micrometers)

10 6-31 Spectral selection - more terms 6-32 Absorption filters Cuton and cutoff points give an idea of the out-of-band blocking P Cuton point is the short wavelength point related to the 5% transmittance point T peak PCutoff point is the same but at the long wavelength side PDifference between the two is the passband PBandpass is the full-width half maximum ½T peak Bandpass 0.05T peak Passband Cuton Cutoff Wavelength (micrometers) Absorption filters simply absorb all energy except for that portion of the spectrum which is of interest PColored glass is used in which the glass is produced in three ways The base glass will have some absorption Metal ions are introduced into the base glass in solution Metal ions are suspended in the glass POrganic dyes are mixed with gelatin PTypical camera filters and inexpensive astronomical filters are absorption filters Kodak Wratten gelatin filters #70 #21 #47 Kodak Wratten examples 6-33 Absorption filters 6-34 Fabry-Perot All of the methods described here will have advantages and disadvantages to their uses PAdvantages to absorption filters are Simple, inexpensive, compact, rugged No dependency on spectral selection on incident angle of the radiation Stable with temperature Better out-of-band rejection than other methods P Disadvantages Typically lower transmittance Fixed wavelength Limited spectral choices Filters for visible part of spectrum often transmit in the IR Difficult to get small bandpass Fabry-Perot filters rely on interference effects caused by path length differences between two mirrors PThe phase difference (which must be 180 degrees for destructive interference and 0 degrees for constructive) is 2d Δ= 2dtanθsinθ = 2dcosθ cosθ PAppropriate selection of angle, Adjustable distance distance between the mirrors, and wavelength can lead to d constructive or destructive T interference PIssues with higher order effects 2 1

11 6-35 Interference filters 6-36 Interference filters Interference filters are effectively Fabry-Perot systems and figure below illustrates the layout for an interference filter PThe blocking filter is used to improve the out-of-band rejection of the multiple orders of the system PThe filter itself is the portion denoted as the multi-cavity bandpass filter POther parts are used to protect the actual filter or for mechanical mounting PPhysical size of filter can vary tremendously Larger sizes cause problems with spatial heterogeneity Smaller sizes can be more difficult to work with and characterize Newer approaches are combining the filter with the detector Figure below focuses on the dielectric layers composing the bandpass filter in previous diagram PThis shows a single cavity case PThe cavity simulates the space between the mirrors in the etalon system PThe other layers are analogous to the mirrors PThe materials that compose the layers helps determine the spectral selection 6-37 Interference filters 6-38 Example filter spectra Addition of more cavities improves the out-of-band rejection PAlso increases cost and complexity to manufacture PCombining multiple cavities of different types can alter the spectral selection of the filter as well

12 6-39 Dispersive systems 6-40 Grating systems Dispersive systems spread the light out into its component wavelengths PPlacing a detector in the appropriate place allows the wavelength region of interest to be studied PInterference approaches (gratings) and refractive (prism) Prism Grating White light Detector array Gratings are similar to interference filters in that they rely on differing path lengths to develop constructive and destructive intereference PAdvantages to gratings Can have high efficiency for blazed gratings (those design to have spectral reflection of zeroth order light into one of the other orders Dispersion is linear in wavelength High resolving power P Disadvantages Given grating is only optimum for a single order and wavelength region Overlapping orders First order output at 400 nm may overlap with the second order output at 800 nm Requires blocking filters or predispersing system to remove higher orders Blue light (400 nm) and NIR (800 nm) can overlap completely 6-41 In-band versus out-of-band 6-42 Out-of-band example Out-of-band response is a difficult problem to assess but can play a key role in destroying radiometric accuracy PAnalagous to out-of-field response Field of view of an optical system may not be as well defined as hoped Light leaks in from outside the field of view adding to the output signal PSimilarly, out-of-band light can be passed by the filter This will add to the output if the detector is responsive to these wavelengths May not be a problem if it is known to exist PMust keep in mind that a small leak over a wide spectral range can be significant PBiggest problems occur when the detector response, source s spectral shape, and out-of-band leak combine in a pathological fashion Consider a lamp source, a filter centered at 500 nm, and a silicon photodiode detector PSimplify things by assuming the filter has 100% transmittance between 495 and 505 nm with a rectangular shape PFurther assume that the filter has a 0.01% transmittance at all wavelengths longer than 505 nm P Out of band causes a 23% increase in detector output PIn the solar case, the increase is only 6% WRC-Based FEL-lamp based Wavelength (micrometer)

13 6-44 Cascading filters Cascade filter example Often use multiple filters to improve wavelength selection of the system PCascading the filters is accomplished by multiplying all of the independent spectral filters PIdentical to the concept shown during the discussion of spectral response Spectral transmittance of a filter is part of the spectral response This is the advantage of using spectral transmittance to describe the effect of the filters P Example of how this works would be One filter used to define the in-band spectral bandpass A high pass filter that blocks UV light to reduce UV degradation A low pass filter to compensate for an out-of-band leak This approach could be cheaper than buying a filter with better out-ofband blocking A three-band solar radiometer designed for retrieval of atmospheric water vapor PVariety of filters are used for Spectral selection Protection of interference filters from solar bleaching Use of detector response to limit spectral response of sensor PCascade is product of parts Cascade filter example Solar irradiance plays a role in the output and thus SNR of the radiometer PStill a temperature dependency for the longer wavelength band PCutoff of the silicon response prevents water vapor feature at longer wavelengths from playing a role Total system response

14 Solar Infrared Photometer for Aerosol Sensing (Spinhirne et al., 1985)