Patent Application
20170276548
The present disclosure relates to techniques for estimating optical detector nonlinearity.
Optical detectors and associated electronic circuitry used to amplify signals output by the detector are more or less inherently nonlinear with a dependence on operating conditions, and range of fluxes to be detected. An important factor in calibration of an optical system using optical detectors is the extent to which linearity of a transfer/response function of the system, from light energy input to the system to electrical energy output by the system, can be assumed. If the output versus (vs.) input energy is nonlinear, then either error associated with that nonlinearity must be tolerated, or a correction needs to be applied to a calibration equation(s) to account for that nonlinearity. In order to provide a viable correction, nonlinearity of the system (or the relative lack thereof) needs to be measured accurately to enable the system to be calibrated accurately; otherwise, the system will be calibrated incorrectly, which may introduce even more system nonlinearity and calibration uncertainty. Conventional nonlinearity measurements estimate (often incorrectly) a value of optical flux applied to the optical detector, and fit a straight line to the detector output vs. flux, and then assume that any deviation from a straight line can be assigned to nonlinearity of the detector only, rather than to nonlinearity in test equipment used to apply the optical flux. Errors inherent in estimating the value of the input optical flux directly negatively impact accuracy in the measured nonlinearity and may result in a false indication of the presence of nonlinearity.
A method of estimating non-linearity in a response of an optical detector comprises emitting optical radiation at different intensities and, at each intensity: amplitude modulating the emitted optical radiation at a modulating frequency to produce amplitude modulated optical radiation; detecting the amplitude modulated optical radiation with the optical detector to produce a detected waveform; and generating a Fourier transform of the detected waveform that includes a fundamental frequency equal to the modulating frequency and harmonics thereof. The method further comprises estimating the non-linearity in the response of the optical detector based on a change in an amplitude of a second harmonic of the fundamental frequency relative to an amplitude of the fundamental frequency across the Fourier transforms corresponding to the different intensities.
With reference to
Amplitude modulated optical radiation 122 impinges on optical detector 110. Optical detector 110 detects amplitude modulated optical radiation 122 impinging thereon, to produce an electrical detected waveform 124 representative of the intensity of the impinging optical radiation. In a typical configuration, optical detector 110 includes (i) a photodetector 110a that converts optical radiation to an electrical signal 110b, and (ii) an electrical amplifier 110c, coupled to an output of the photodiode, thermal, or other type of detector, to amplify the electrical signal to produce an amplified electrical signal as detected waveform 124.
Digitizer 112 digitizes detected waveform 124 at a sampling rate set by sampling rate control input 114, to produce a digitized detected waveform 126, and provides the digitized waveform to analyzer 118. Analyzer 118 estimates/determines nonlinearity of the optical detector based on the digitized detected waveform, and outputs an estimated/determined nonlinearity 128. Waveforms 124 and 126 may each be referred to as the “detected waveform” output by optical detector 110.
A method of estimating nonlinearity of optical detector 110 using apparatus 100 is now described. Black body radiator 102 is controlled to emit optical radiation 120 at successively increasing known temperatures to produce optical radiation 120 at successively increasing intensities each corresponding to a corresponding one of the temperatures. For example, (i) for a first time period during which black body radiator 102 is held at a known first temperature, the black body radiator emits optical radiation at a first intensity corresponding to the first temperature, (ii) for a second time period following the first time period and during which the black body radiator 102 is held at a known second temperature greater than the first temperature, the black body radiator emits black body radiation at a second intensity greater than the first intensity corresponding to the second temperature, and so on. The range of temperatures may cause black body radiator 102 to emit black body radiation over a range of wavelengths in the light spectrum, including ultraviolet, infrared, and/or visible wavelengths.
At each temperature and corresponding intensity (i.e., “temperature/intensity”), light modulator 106 amplitude modulates optical radiation 120 at the modulating frequency to produce amplitude modulated optical radiation 122 for the corresponding temperature/intensity. In an embodiment, light modulator 106 may be a light chopper positioned between black body radiator 102 and optical detector 110 and that rotates at the modulating frequency to produce the amplitude modulated optical radiation as chopped radiation. An example light chopper is described below in connection with
Optical detector 110 detects amplitude modulated optical radiation 122 impinging on the optical detector at each intensity corresponding to each temperature of black body radiator 102, to produce detected waveform 124 for each intensity. In turn, digitizer 112 digitizes detected waveform 124 for each intensity, to produce digitized detected waveform 126 for each intensity, and provides each digitized detected waveform to analyzer 118. Thus, analyzer 118 receives successive digitized detected waveforms corresponding to successive ones of the temperatures/intensities of/from black body radiator 102. Digitizer 112 samples detected waveform 124 at an adequately high sampling frequency/rate to allow accurate analysis of a fundamental frequency of detected waveform 124 and many harmonics of the fundamental frequency. For purposes of analysis, the fundamental frequency of detected waveform 124 is the amplitude modulating frequency. In an example in which the amplitude modulating frequency (and thus the fundamental frequency) is in a range of 10-100 Hz, it is preferable to sample detected waveform 124 at a rate in a range that is at least an order or magnitude higher than the modulating frequency (e.g., 10,000 Hz to 100,000 Hz) in order to provide a large number (high density) of samples in digitized waveform 126.
Analyzer 118 processes successive digitized waveforms 126 corresponding to the successive temperatures/intensities, and estimates optical detector nonlinearity or relative lack thereof based on results of the processing. First, analyzer 118 generates a Fourier transform of digitized waveform 126 for each intensity, to produce Fourier transforms each corresponding to a respective one of the successive intensities/temperatures. In an example, analyzer 126 computes the Fourier transforms as Fast Fourier transforms (FFTs). Each Fourier transform includes a fundamental frequency (the modulating frequency) and harmonics thereof. Analyzer 118 estimates nonlinearity of optical detector 110 based on a change in an amplitude primarily of the second harmonic of the fundamental frequency relative to an amplitude of the fundamental frequency across the Fourier transforms corresponding to the different intensities. In one example, normalized amplitudes of the second harmonics (i.e., normalized with respect to the amplitude of the fundamental frequency in the same Fourier transform) are plotted against their corresponding temperatures. In another example, the normalized amplitudes are plotted against rough estimates of their corresponding intensities. The nonlinearity of optical detector 110 is proportional to an increase in the normalized amplitudes with an increase in intensity; thus, if the normalized amplitudes remain relatively flat as intensity increases, then the optical detector is relatively linear. The above described techniques are described in further detail below.
With reference to
A theoretical basis for the method of estimating nonlinearity presented herein is described below under the Sections Theory 1, Theory 2, and Theory 3. Then, two examples of estimating nonlinearity are described. The descriptions assume, by way of example only, an arrangement of apparatus 100 that includes black body radiator 102 followed by a light chopper as optical modulator 106. In this arrangement, the combination of black body radiator 102 followed by the light chopper is referred to as a “chopped black body,” and modulated optical radiation 122 produced by the chopped black body is referred to as a “chopped black body waveform.” Also, the terms “intensity” and “flux” are used synonymously and interchangeably.
Theory 1
When a linear optical system is stimulated with a modulated input waveform, an output signal of the linear optical system is expected to be a faithful representation of the modulated waveform albeit amplified by some factor (system gain), shifted in phase, or possibly offset by a fixed direct current (d.c.) level. For a linear optical system, the output will be a perfect sinusoid if the input is a perfect sinusoid.
In a case of an imperfectly modulated input waveform (as will generally be true in all practical/realizable applications), a linear system/detector with a bandwidth much higher than a fundamental frequency (i.e., amplitude modulating frequency) will faithfully reproduce the input waveform with the same distortions inherently present in the input waveform; however, if the system/detector is nonlinear, distortion will be made worse by the nonlinearity. If the system/detector has a finite-bandwidth, amplitudes of a fundamental frequency and harmonics thereof will be reduced in amplitude.
As discussed above, a chopped black body may be used to provide input flux to optical detector 110 for measurements of responsivity and nonlinearity of the optical detector. If (i) the temperature of black body radiator 102 of the chopped black body is known accurately, and (ii) the transmissive characteristics of space and any objects between optical detector 110 and the black body radiator are known accurately, then the flux (i.e., intensity) emitted by the black body radiator onto the detector is calculable using Planck's law. The light chopper of the chopped black body alternately obscures and opens a view of the black body aperture to a view of optical detector 110, thus providing a chopped black body waveform (e.g., amplitude modulated optical radiation 122) to the optical detector. If a defining boundary between each opening and adjacent opaque area of the chopper is essentially a straight line, and the black body aperture is circular and of the same size as the opening, the chopped black body waveform is nearly a sinusoid as shown in
After the chopped black body waveform has been detected and passed through a linear system, such a linear optical detector with a finite bandwidth, the detected waveform (e.g., detected waveform 124) produced by the linear system is closer to sinusoidal than the original input waveform (e.g., the input chopped black body waveform) because of a reduction in higher frequency (harmonic) content. In contrast, systems with a higher frequency response reproduce the original shape of the input waveform more faithfully. Advantageously, the method of estimating nonlinearity presented herein does not depend on maintaining the higher frequency harmonic content (i.e., frequency components) of the chopped black body waveform input to optical detector 110, nor does the method require a perfect sinusoidal shape for the chopped black body waveform. This is because the method estimates nonlinearity based on a change of normalized harmonic content in detected waveform 124 corresponding to a change in input flux of the chopped black body waveform. The method normalizes the harmonic content to the fundamental frequency of detected waveform 124, as represented in a Fourier transform of the detected waveform, as described below.
Theory 2
The method of estimating nonlinearity is based on Fourier transforms (e.g., FFTs) of detected waveform 124/126 corresponding to the different fluxes (i.e., intensities) of the chopped black body waveform applied to optical detector 110. With reference to
As stated above, if optical detector 110 is linear, then detected waveform 124/126 has similar relative frequency content to the chopped black body waveform, albeit possibly modified by a frequency dependent gain and phase shift, as shown in
Theory 3
In apparatus 100, optical components positioned between black body radiator 102 and optical detector 110 may be nonlinear, and the optical detector itself may be nonlinear. As mentioned already, a nonlinear system distorts the shape of a waveform from an input of the system to an output of the system, as shown in
With reference to
Appearance of even harmonics is necessary for asymmetrically nonlinear systems; however, in apparatus 100, the mere appearance of even harmonics in a Fourier transform of detected waveform 124/126 does not necessarily mean that nonlinearity is present only in optical detector 110, because nonlinearity may also exist in the chopped black body that produces the chopped black body waveform applied to the optical detector. For example, original asymmetric distortion may be “built-into” the chopped black body waveform (possibly geometric or other fixed cause), in which case the even harmonic content will remain constant as a function of flux (i.e., will not change with a change in flux) because the chopped black body arrangement is fixed in a given apparatus and thus does not change with a change in the flux. That is, the chopped black body waveform is determined by the relationship between the light chopper and the black body aperture, and is independent of the temperature and flux. While the contribution to the even harmonic content from a nonlinearly chopped black body will not change with a change in flux, the contribution to the even harmonic content will change with a change in flux if optical detector 110 is also asymmetrically nonlinear. In other words, in the aforementioned situation, a change in the even harmonic content corresponding to a change in flux is indicative of nonlinearity of optical detector 110, only. Thus, estimating nonlinearity based on a change in the even harmonic content effectively subtracts-out the effect of nonlinearity in the test arrangement used in the estimating, and thus focuses instead on exposing nonlinearity of the unit under test, i.e., of optical detector 110.
Described below are two examples uses of the method of estimating linearity/nonlinearity of optical detector 110, including a first example in which optical detector 110 has a nonlinear response, and a second example in which the optical detector has a linear response. In each example, generally: The chopped black body emits successively increasing optical radiation intensities at successively increasing temperatures of the black body radiator; optical detector 110 detects the chopped black body radiation resulting from the successive temperatures/intensities, to produce detected waveform 124/126 at each of the successive temperatures/intensities; for each successive temperature/intensity, analyzer 118 generates a Fourier transform of the corresponding detected waveform, to produce successive Fourier transforms for the successive black body temperatures/intensities; and the analyzer estimates nonlinearity/linearity based on the Fourier transforms. Analyzer 118 plots and displays results of the estimating.
In the first example, optical detector 110 includes an infrared (IR) photoconductive detector that has an expected nonlinear response to flux levels in the infrared applied to the detector by the chopped black body at different temperatures of black body radiator 102. The detector includes a 1.3 millimeter2 (mm2) light detector area, and operates with a bias current of 1 mA at a quiescent temperature of 99K. The chopped black body waveform applied to the detector has a chopped frequency (i.e., an amplitude modulating/fundamental frequency) of 100 Hz.
Illustrations of results produced and used by the method of estimating nonlinearity in example 1 are shown in
Each Fourier transform depicted in
As shown in
The plots of
In the second example, optical detector 110 includes a 1.5 mm2 thermopile detector that has an expected linear response to flux levels in the infrared applied to the detector by the chopped black body at different temperatures of black body radiator 102. The black body chopped waveform applied to the detector has a chopped frequency of 10 Hz.
Illustrations of results produced and used by the method of estimating nonlinearity (or relative lack thereof) in example 2 are shown in
High-Level Method Flowchart
With reference to
At 1005, black body radiator 102 emits optical radiation at different intensities. In other embodiments, an optical emitter other than a black body radiator may be used.
At each intensity:
At 1025, analyzer 118 estimates the non-linearity in the response of optical detector 110 based on a change in the amplitudes of the second (and to lesser extent the higher even-numbered harmonics) harmonics of the fundamental frequency relative to the amplitudes of the fundamental frequency across the Fourier transforms corresponding to the different intensities. For example, analyzer 118 may estimate the non-linearity based on a change in the normalized amplitudes of the second harmonics across the different Fourier transforms for purposes of performing a quadratic nonlinearity correction for the optical detector during calibration
In one embodiment, at 1025, analyzer 118 estimates each intensity based on the temperature of black body radiator 102 that caused the black body radiator to emit the radiation corresponding to that intensity, and Planck's law; and plots the normalized amplitudes of the second harmonics against the corresponding estimated intensities, to produce a plot of the normalized second harmonic amplitudes having a slope representative of the non-linearity, as shown in
In another embodiment, at 1025, analyzer 118 plots the normalized amplitudes of the second harmonics against the corresponding temperatures, to produce a plot of the normalized second harmonic amplitudes having a slope representative of the non-linearity.
Analyzer 118 may display as screen shots the detected waveforms, plots of the Fourier transforms, and a plot of the normalized amplitude vs. temperature or intensity, and may display a determined slope value from the plots indicative of nonlinearity.
Analyzer
With reference to
The memory 1156 may comprise read only memory (ROM), random access memory (RAM), magnetic disk storage media devices, optical storage media devices, flash memory devices, electrical, optical, or other physical/tangible (non-transitory) memory storage devices. The processor 1154 is, for example, a microprocessor or a microcontroller that executes instructions stored in memory. Thus, in general, the memory 1156 may comprise one or more tangible computer readable storage media (e.g., a memory device) encoded with software comprising computer executable instructions and when the software is executed (by the processor 1154) it is operable to perform the operations described herein. Memory 1156 stores control logic 1170 to perform the methods described herein, including estimating nonlinearity of an optical device based on detected waveforms and Fourier transforms, and plotting results of the estimating, as described above. The memory may also store data 1180 used and generated by control logic 1170 as described herein, such as Plank's law equations, temperatures, estimated intensities, digitized detected waveforms, Fourier transforms, and various other information for plotting and displaying results.
If an output of an optical detector is nonlinearly related to increasing flux applied to an input of the optical detector, 2nd harmonic content relative to a fundamental component in an alternating current (a.c.) output by the optical detector (i.e., a detected output), responsive to a chopped waveform of light incident on the optical detector, will increase as the flux/intensity of the chopped waveform of light increases. Methods described herein measure an increase in the 2nd harmonic content with an increase in flux, and thus estimate the extent to which the optical detector response is nonlinear. Typically response nonlinearity is relatively small over the range of fluxes characteristic for many applications, so with conventional nonlinearity measurements techniques, estimating an accurate estimate of nonlinearity suffers from error in determination of the flux applied to the detector. In the methods described herein, by measuring the increase (or lack thereof) of the 2nd harmonic relative to the fundamental, the nonlinearity may be characterized advantageously with less than a perfect knowledge of the flux applied to the detector. The methods describe herein provide for an accurate estimation of nonlinearity of an optically responsive element (e.g., an optical detector) while greatly reducing a need for accurately estimating light fluxes applied to the optical detector. The methods also obviate the need to for applying a “perfect” sine-modulated optical source of flux to the optical detector. In the methods, nonlinearity as a function of optical detector operating frequency may be measured.
For the methods described herein, applied flux is only reasonably well-known; however the impact of input flux error on the estimation of the nonlinearity is almost completely mitigated, compared to conventional techniques. Flux error is less important in the methods because the nonlinearity is measured using growth in distortion of the optical detector (response) output relative to the original energy waveform applied to the detector, to produce the output signal as the input signal is increased.
In summary, in one form, a method is provided as described above in the Overview section.
In summary, in another form, an apparatus is provided comprising: an optical emitter to emit optical radiation at different intensities; an amplitude modulator to amplitude modulate the optical radiation at each intensity at a modulating frequency to produce amplitude modulated optical radiation for each intensity; an optical detector to detect the amplitude modulated optical radiation at each intensity to produce a detected waveform for each intensity; and an analyzer to: generate a Fourier transform of the detected waveform for each intensity that includes a fundamental frequency equal to the modulating frequency and harmonics thereof, to produce Fourier transforms each corresponding to a respective one of the intensities; and estimate the non-linearity in the response of the optical detector based on a change in an amplitude of a second harmonic of the fundamental frequency relative to an amplitude of the fundamental frequency across the Fourier transforms corresponding to the different intensities.
In summary, in yet another form, a processor readable medium is provided. The processor readable medium stores instructions that, when executed by a processor, cause the processor to perform the methods described above.
The above description is intended by way of example only. Various modifications and structural changes may be made therein without departing from the scope of the concepts described herein and within the scope and range of equivalents of the claims.
