Linearization of mercury cadmium telluride photodetectors

Abstract

A method for linearization of a photodetector response is provided that includes establishing one or more static calibration coefficients based on a comparison of a test photodetector response to a linear reference photodetector. In some examples, a dynamic calibration coefficient is determined based on an averaged photodetector signal. In some applications such as FTIR, a single calibration coefficient is utilized to obtain a linearized ratio.

Description

[0001] This divisional application of the invention application is a divisional application of the invention patent application with the application number 202310293101.1, the application date of March 22, 2023, and the title of "Linearization of Mercury Cadmium Telluride Photodetectors". Technical Field

[0002] This disclosure relates to photodetector compensation. Background Art

[0003] Typical photodetectors used at wavelengths in the short wavelength infrared band (about 1.4 μm to 3 μm), mid wavelength infrared band (about 3 μm to 8 μm), long wavelength infrared band (8 μm to 15 μm), and far infrared band (15 μm to 1000 μm) exhibit a non-linear response to incident optical radiation. In some applications, such non-linearity does not significantly limit the usability of the detector, but in other applications, even a small deviation from a linear response can cause problems. For example, some applications require detecting optical radiation over a power range spanning 6 or more orders of magnitude. Any detector non-linearity makes the comparison of small signal values and large signal values inaccurate. In applications such as Fourier transform spectroscopy, detector non-linearity introduces or enhances frequency components in a manner independent of the nature of the sample being studied. Methods are needed to address these and other limitations. Summary of the Invention

[0004] The method includes directing a modulated light beam to a test photodetector and obtaining the modulation amplitude of the optical signal associated with the detection of the first portion of the modulated light beam by the test photodetector. Based on the modulation amplitude of the optical signal from the test photodetector, at least one first calibration coefficient operable to linearize the test photodetector is determined and stored in a memory device. In some examples, a second portion of the modulated light beam is directed to a reference photodetector to obtain the modulation amplitude of the optical signal associated with the detection of the second portion of the modulated light beam by the reference photodetector. Based on the modulation amplitudes of the optical signals from the test photodetector and the reference photodetector, at least one first calibration coefficient is determined.

[0005] A representative FTIR system includes a photodetector, a memory device, and a processor. The memory device stores at least one calibration coefficient associated with the photodetector. The processor is coupled to receive an optical signal in response to the illumination of the photodetector and linearize the optical signal based on the at least one calibration coefficient. In some examples, the at least one calibration coefficient includes one or more of the calibration coefficients a, b, c, where the linearized optical signal I MEAS associated with the measured optical signal I LINEAR is generated as I LINEAR = aexp(bI MEAS) + c. In some examples, the processor is coupled to linearize an optical signal based on a back - calculation of the received optical signal to a network node between a first amplifier and a second amplifier.

[0006] The foregoing and other features and advantages of the present technology will become more apparent from the following detailed description taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 A representative Fourier Transform Infrared Spectrometer (FTIR) including a linearized HgCdTe (MCT) photodetector is shown.

[0008] Figure 2 A system for linearizing a photodetector based on a reference photodetector is shown.

[0009] Figures 2A through 2C A photodetector calibration data that can be obtained using a system such as that shown in Figure 2 is shown.

[0010] Figure 3A A representative method for establishing static photodetector calibration coefficients and linearizing an optical signal based on the calibration coefficients is shown.

[0011] Figure 3B A representative method for linearizing an optical signal based on selected calibration coefficients is shown.

[0012] Figure 4 A representative method for establishing dynamic photodetector calibration coefficients is shown.

[0013] Figure 4A A representative beam modulation for dynamic calibration is shown.

[0014] Figure 4B and Figure 4C A data acquisition associated with dynamic linearization is shown.

[0015] Figure 4D A representative method for dynamic calibration is shown.

[0016] Figure 5 A representative spectral system including a processing system that provides a linearized optical signal is shown.

[0017] Figure 6 A representative spectral system including a processing system that provides a linearized optical signal and provides a current offset to reduce the DC component of the optical signal before coupling for additional amplification is shown.

[0018] Figure 7Schematic diagram of a representative DC-coupled amplifier suitable for providing optical signals for dynamic or static linearization.

[0019] Figure 8 Schematic diagram of an alternative representative DC-coupled amplifier suitable for providing optical signals for dynamic or static linearization.

[0020] Figure 9 Illustrates a representative method of dynamic or static photodetector calibration based on back-calculation to a reference node.

[0021] Figure 10 Illustrates a representative system for linearizing a photodetector using a variable optical attenuator or a variable light source. Detailed Description

[0022] As used herein, "sample photodetector" and "test photodetector" refer to the photodetector to be calibrated. In some cases, calibration of a single sample detector may be sufficient for use with other photodetectors having the same configuration or type. Alternatively, each photodetector may be provided with its own unique calibration coefficient, which may be stored in a processor-readable memory device coupled to or provided with each photodetector. In some examples, a calibrated or inherently linear photodetector is used to compare and calibrate the response to beam modulation, and such a photodetector is referred to as a "reference photodetector". The reference photodetector may be a photodetector that is inherently suitably linear, or a previously calibrated test photodetector may be used as the reference photodetector. In the following examples, for ease of illustration, calibration of a HgCdTe (MCT or mercury cadmium telluride) photodetector and the use of such a calibrated MCT photodetector are described. However, other ultraviolet, visible, or infrared photodetectors or photodetectors for other ranges may also be used. In some cases, a photodetector may operate linearly in some circuit connections and non-linearly in other circuit connections, and calibration may be performed for any or all configurations as needed.

[0023] The disclosed methods are generally shown as using a reference photodetector to generate an optical signal that will be used for linearization or other compensation of the photodetector under test. In other examples, a reference electrical signal can be provided to a light source or variable optical attenuator to generate a reference light beam. In these examples, the linearization or compensation can be based on the reference electrical signal. Although a reference detector with a linear response is convenient for calibration, any photodetector with known response characteristics can be used. In an example, the photodetector and associated electronics (e.g., an amplifier) are said to produce a DC signal component or be DC-coupled. As used herein, such a photodetector and associated electronics produce an optical signal that includes a signal contribution associated with the average value of the received optical radiation. Thus, the optical signal reflects both the average value and the spectrally induced modulation. In some examples, multiple amplifier stages are used, and in such examples, only the first stage (the stage coupled to the photodetector) must be DC-coupled so that a signal portion indicative of the DC component of the received optical radiation can be produced. If the DC component of the signal has been completely removed, the subsequent amplifier stages can be AC-coupled. However, since the DC component is typically not removed perfectly, it may be preferable to DC-couple the entire amplifier chain. With appropriate measurements and processing as discussed below, the subsequent amplifier stages do not need to be DC-coupled. In the following examples, the average optical signal value associated with the optical signal measurement indicates the power delivered to the test photodetector and is referred to as E EFF . In some examples, the test photodetector calibration coefficient is dynamic and varies as a function of E EFF or other measurements of the average power. As used herein, a static calibration coefficient refers to a value obtained without change based on E EFF or other indications of the average optical signal; a dynamic calibration coefficient refers to a value that is a function of E EFF or other indications of the average optical signal.

[0024] An exemplary application of the disclosed methods is FTIR. Although MCT detectors are commonly used in FTIR, other detectors, such as thermoelectric detectors or other photodetectors based on deuterated triglycine sulfate, lithium tantalate, InGaAs, silicon, or germanium bolometers, can be similarly compensated if desired.

[0025] In the following text, the correction or compensation of the output signal of a photodetector is discussed with reference to linearization, i.e., compensating the output signal of the photodetector or a signal based on the output signal of the photodetector to be proportional to the detected optical power. Other types of compensation can be provided such that the output signal of the photodetector has other predetermined relationships with respect to the detected optical power. In the examples discussed below, linearization is discussed, where the compensated output signal of the photodetector or other signal is proportional to the detected optical power within a range of 5%, 2%, 1%, 0.5%, 0.1%, 0.01% or less. The photodetector compensation is also referred to as calibration in the disclosed method, and calibration or compensation parameters are obtained based on a specific model (exponential), but the calibration parameters can also be based on second-order, third-order or fourth-order polynomials, Bessel curves or other functions. In some of the examples below, the calibration of HgTeCd (“MCT”) detectors is described, but other detector types can be calibrated similarly. The “output signal of the photodetector” refers to the current, voltage or a combination thereof generated by the photodetector in response to received optical radiation. The term “signal” refers to a time-varying current or voltage generated in response to the processing of the output signal of the photodetector. Such a signal can correspond to the output signal of the photodetector that has been amplified, filtered or otherwise processed (as an analog signal or a digital signal). For convenience, the output signal of the photodetector and the signal in response to the output signal of the photodetector (such as the processed output signal of the photodetector) are generally referred to as “optical signals” herein. Additionally, although the signal refers to a time-varying current or voltage, such a time variation can be obtained and stored as a digital representation corresponding to a series of signal amplitudes stored in a processor-readable memory device. These digital signals are generally defined as representing the time variation of the analog signal. For example, a series of optical signal values I(n) is also referred to as an optical signal having a time variation defined by n, where n = 0, 1, …, N−1, where N is a positive integer. As used herein, I can refer to the optical power or the optical signal in response to the detected optical power. In some examples, for convenience, the optical signal is represented as a voltage V because in many practical applications, the optical signal is processed as a voltage. However, depending on the photodetector type and circuit arrangement, the optical signal can be based on the light-induced current, voltage or resistance.

[0026] Optical radiation refers to electromagnetic radiation propagating at wavelengths between approximately 100 nm and 1 mm. In some cases, the optical radiation is referred to as propagating within a finite volume and is called a light beam. Optical power refers to the energy per unit time associated with the light beam and is thus proportional to the square of the associated electric field.

[0027] As noted above, a static calibration or compensation coefficient is a value that provides optical signal compensation (such as linearization) independent of the average value of the optical signal; a dynamic calibration or compensation coefficient is a value that provides optical signal compensation (such as linearization) based on a change in the average optical signal (typically based on determining the dependence of one or more static calibration coefficients on the average optical signal).

[0028] Example 1. Compensated detector FTIR

[0029] Referring Figure 1 , a representative FTIR system 100 includes a light source 102 that directs a light beam to a beam splitter 104 that delivers beam portions 105A, 105B to respective reflectors 106, 108 that reflect beam portions 105A, 105B back to beam splitter 104 to form a combined beam 105C. A sample 112 is located in the path of combined beam 105C incident on a detector 110 (such as an MCT detector). A platform 114 is coupled to reflector 106 to generally change the optical path length between beam portions 105A, 105B by continuous or stepwise scanning. Scanning is initiated in response to processor-executable instructions stored in a portion 118 of a processor-readable storage device provided as part of a control system 120 that also includes a CPU or other programmable or dedicated processor hardware (such as an FPGA, CPLD, or ASIC). In this example, control system 120 is coupled to photodetector 110 and receives an optical signal 111 associated with the scanning of reflector 106. In this example, optical signal 111 is digitized at an analog-to-digital converter (ADC) 122 and then the digital optical signal 123 is linearized or compensated using processor-executable instructions and calibration parameters stored in a portion 124 of the processor-readable storage device.

[0030] The digitized optical signal associated with the scan may be referred to as an interferogram or, if compensation has been applied, as a linearized or compensated interferogram. For a sample scan associated with N optical path length differences, the interferogram includes a series of N optical signal values IG for the N optical path length differences S(n), where n = 0, …, N-1. In some examples, digitization and linearization or other compensation processing can be performed before delivering the optical signal to the controller system 120. In some cases, the photodetector is part of a detection system that provides a suitable electrical bias (if needed) to the photodetector 110 and includes an ADC to provide a digital optical signal to the control system 120. The linearization parameters can be stored by the controller 120 in and retrieved from a portion 124 of the processor-readable storage device. Then, a Fourier transform is performed on the linearized optical signal 125 (interferogram) using processor-executable instructions stored in a portion 128 of the processor-readable storage device to produce a series of values FFT K (IG S ), where K is an integer, typically K = 0, …, N / 2-1, to correspond to I(G S ). In most applications, a background scan without a sample is performed, and a corresponding background optical signal (i.e., background interferogram IG B (n)) is obtained and Fourier-transformed. The ratio FFT K (IG S ) / FFT K (IG B ) of the corresponding components of the Fourier transforms of the linearized sample optical signal and the background optical signal is obtained and provided as the FTIR system spectral output.

[0031] The sample 112 can typically be removed from the path of the combined beam so that the sample 112 can be retrieved to perform a background scan. In some applications, an evacuated sample cell or a sample cell filled with a preferred material can be used. Although Figure 1 transmission FTIR is shown, in other examples, the beam is reflected from the sample surface, totally internally reflected in the sample, or interacts with the sample in some other way. Additionally, the linearization of a detector (such as an MCT detector for FTIR) is only an example of the disclosed methods, and these methods can be used with other measurement systems, detectors, and can be used in other wavelength ranges.

[0032] Example 2. Linearization using static coefficients

[0033] In some examples, photodetector compensation (such as linearization) can be provided by selecting one or more static or dynamic calibration coefficients. For example, an exponential function

[0034]

[0035] can be used to linearize an MCT photodetector,

[0036] where a cal , b cal and ccal is the static calibration coefficient, f cal is the compensated (usually linearized) output signal of the photodetector, V mct is the output signal of the photodetector without compensation. More generally, using such calibration coefficients, a series of optical signal values I n (n = 0, …, N−1) can be linearized to produce a series of linearized optical signal values where

[0037]

[0038] the optical signal I n can correspond to current, voltage, resistance, or other electrical characteristics in response to a light beam. The optical signal I n can be a processed signal associated with amplification, filtering, or other processing applied to the photodetector signal. In some examples, linearization or other processing is applied to include the effects of amplification, filtering, or other processing. By performing calibration using the amplified photodetector signal, non-linear or other response characteristics associated with amplification or other photodetector processing can be compensated along with the response characteristics of the photodetector.

[0039] Figure 2 FIG. shows a representative system 200 for the linearization of an MCT photodetector 202. The system 200 includes a controller 204 coupled to a variable light source 206 that generates a light beam 208 incident on a beam splitter 210. The beam splitter 210 directs corresponding portions of the light beam 208 to the MCT detector 202 and a reference detector 212 that generates a reference optical signal proportional to the optical power detected at the reference detector 212. The reference detector 212 can be a photodiode or other detector that produces a suitable proportional output, or a detector that is combined with a calibration circuit to produce a proportional output. The optical signals generated by the MCT 202 and the reference detector 212 are coupled to corresponding amplifiers 214, 216, or other amplification, buffering, or filtering circuits, and the corresponding optical signals are delivered to the controller 204.

[0040] The controller 204 is operable to vary the power of the light beam 208 and receive the corresponding varying optical signals associated with the MCT detector 202 and the reference detector 212. In some examples, the power of the light beam generated by the variable light source 206 is periodically modulated (such as sinusoidal modulation) such that the light beam 208 is associated with a range of optical powers. The controller 204 can include an analog-to-digital converter and a processor-readable storage device such that the input optical signals are digitized and stored as the reference optical signal amplitude I REF and the MCT optical signal amplitude I MCT , such as at Figure 2A and Figure 2Bas shown in Figure 2A shows the basic sinusoidal response of reference detector 212 to the sinusoidal modulation of beam 208, while Figure 2B shows the corresponding response of the MCT detector to the same sinusoidal modulation, which response exhibits distortion. Figure 2C is I ref and I MCT is a graph plotted relative to each other, which shows that the optical signal generated by MCT detector 208 deviates from the linear response of reference detector 212. For a linear response, the plot of I REF and I MCT would be a straight line. MCT detector linearization can be provided by curve fitting the values of I MCT to the linear response values of I REF as discussed in detail below.

[0041] The beam power of beam 208 can be varied stepwise, with other periodic or aperiodic modulations including sawtooth modulation and triangular modulation, and / or with variable or fixed DC offset.

[0042] Example 3. Linearization using static calibration coefficients

[0043] Referring to Figure 3A , a representative method 300 for linearizing an optical signal to be proportional to the detected optical power includes obtaining compensation data at 301, such as I REF , I MCT discussed above. Although it is convenient that I REF is a linear function of the detector optical signal, other known responses can be used. At 302, a linearization function f is selected, such as an exponential, polynomial, Bessel curve or function. A particular analysis format (such as a continuous function) is convenient so that compensation for any optical signal can be obtained for all values, but some or all of the selected data pairs (I ref , I MCT ) can be used to provide linearization for the selected values of I MCT and other values determined by interpolation for example. At 304, any coefficients defining the compensation function are determined by curve fitting to f or otherwise processing the compensation data. For example, if the compensation function

[0044]

[0045] is selected (where I L (I MCT ) is the linearized optical signal value associated with I MCT ), the static calibration coefficients a cal , b cal and c calDetermined by curve fitting, such as using a least squares fitting process to minimize Then, f(I MCT ) = I L ((I MCT ) is the linearized optical signal obtained from the uncompensated optical signal I MCT . At 306, one or more of the constant calibration coefficients a cal , b cal and c cal are stored in the memory device.

[0046] As Figure 3A further shown in, the constant calibration coefficients a cal , b cal and c cal can be used. Representative method 307 of linearization includes receiving one or more optical signals of interest at 308, and at 310, processing these optical signals using the compensation function f through calculation using the calibration coefficients a cal , b cal and c cal or a look-up table corresponding to the calibration function and an interpolation process retrieved from the processor-readable storage device. At 312, the linearized value I L (I MCT ) is output.

[0047] Example 4. Linearization using a reduced set of calibration coefficients

[0048] In some applications, the average optical signal value is not of interest, or is removed by filtering out the DC component. In these applications, the linearized optical signal I L can be generated as , because the contribution related to c cal is either removed by filtering or is not of interest. For these applications, only a cal and b cal can be used, and only these values are stored and / or retrieved.

[0049] In systems using ratio-based measurements, further simplification is possible. In such systems, optical signals associated with the sample and reference under study are obtained, i.e., a series of optical signal values associated with the sample and a series of optical signal values associated with the reference are obtained Linearizing the sample and reference optical signal values includes the value a as a factor such that in the ratio cal effectively removes any application of the value a in the linearization, where cal and and They are linearized optical signal values associated with the sample and the reference, respectively.

[0050] In some applications, the sample and reference optical signal values are processed in a manner different from being just a simple ratio. For example, in an FTIR spectrometer, the optical signals associated with both the sample and the reference are Fourier transformed, and the sample spectrum of interest is obtained as the ratio of the corresponding components of the respective FFTs. In these applications, the calibration constant a cal is also effectively removed by the FFT ratio and thus does not need to be applied to the linearization and does not need to be stored for such use.

[0051] For example, as shown by method 350 in Figure 3B , at 352, a calibration process is selected based on one, two, or three calibration coefficients. At 354, the selected calibration coefficients are retrieved from a processor-readable storage device, and at 356 the selected calibration coefficients are used to linearize one or more input optical signals. At 358, the linearized signals are output.

[0052] Example 5. Dynamic calibration

[0053] The above constant (or static) calibration method can significantly reduce optical signal and / or photodetector non-linearity, but does not compensate for heating or other variations in the optical signal or photodetector in response to the input light beam. For example, a change in the photodetector temperature can be associated with an offset in the calibration coefficient value. In some applications, such an offset is acceptably small and the static calibration coefficient value is sufficient. To address the offset in the calibration coefficient value in response to the input, the calibration coefficient value can be refined based on the total optical signal. The total optical signal can be considered to be associated with the total thermal load applied to the photodetector and referred to as the effective energy E eff which can be obtained as the sum or average of N optical signal values I k , as:

[0054]

[0055] Other methods for estimating E eff can be used, such as using optical signal values obtained from previous measurements. This method is particularly applicable to FTIR using continuous scans, where the signal values do not change rapidly between scans. Alternatively, in an FTIR system, the optical signal associated with the optical delay away from the 0 path difference can be used as an approximation of the average value. However, to obtain E eff , the DC optical signal value must be obtained and the optical signal must include a DC component at at least one location in the processing, such that E effis available. As discussed above, the compensation can include effects attributable to the optoelectronic detection electronics (such as amplifiers and filters), rather than just the effects of the photodetector. The optical signal values used to establish E eff are obtained at appropriate intervals to correspond to the current photodetector temperature or other photodetector or processing circuit effects associated with the measurement of interest.

[0056] As discussed above, when using an exponential function, the linearization can be based on one, two, or three calibration coefficients. In one example discussed above, only the calibration coefficient b cal is used. This method is particularly suitable for applications where the DC or average value is not of interest and the ratio to a reference measurement value is used. For calibration using only the calibration coefficient b cal , a DC value is required to determine E eff for dynamic compensation, but these DC values are not otherwise required. In this example, the calibration coefficient b cal can be dynamically compensated as:

[0057] b cal (E eff ) = a dbCal E eff + b dbCal ,

[0058] where a dbCal and b dbCal are the dynamic calibration coefficients for the dynamic compensation of the calibration coefficient b cal , and do not correspond to the a cal and b cal used above. To determine b cal (E eff ), the values of these additional calibration coefficients must be estimated. In one method, a light beam with DC and modulation components can be directed to the detector under test. Varying the DC component allows for the variation of E eff , and the modulated component allows for the determination of the calibration coefficients a eff , b cal , and c cal at multiple values of E cal . Curve fitting such as that discussed above can be used.

[0059] Referring to Figure 4 , a representative method 400 for determining one or more dynamic calibration coefficients includes selecting a beam modulation amplitude and frequency at 402. These are typically selected to be in or near the range in which the detector will be used. At 404, the average beam power P AVE is selected, and at 406, a beam with the selected modulation and average beam power is applied to a sample detector and a reference detector. Typical beam modulation is at Figure 4Aas shown in Figure 4A shows the average (or DC) value P at modulation components 450 and 452 AVE . At 408, multiple t j measure the optical signals IS(t j ), I REF (t j ) associated with the sample detector and the reference detector respectively. At 410, one or more calibration coefficients are determined using I S (t j ) and I REF (t j ) together with the average optical signal value corresponding to E EFF as discussed above. At 414, the calibration coefficients and the associated E EFF are stored. At 416, it is determined whether calibration data at an additional value of the beam power is required. If so, the method returns to 404 to select the beam power. If not, dynamic calibration can be utilized at 418 to provide the selected calibration coefficients.

[0060] By varying the average optical power, a data set can be obtained for varying E EFF values, as Figure 4B shown Figure 4B shows the E EFF values of data sets 461 - 465 obtained using different average optical powers. Each data set provides a set of one or more calibration coefficients (i.e., one or more of a EFF , b cal , and c cal ) for the associated E cal . Figure 4C shows the variation of b EFF as a function of E EFF for various values of E cal associated with data sets 461 - 465, along with the linear fit 470 that defines the dynamic calibration coefficients a dCal and b dCal stored at 420.

[0061] In other examples, two calibration coefficients are varied dynamically. In addition to b cal as shown above, a cal can be obtained dynamically as

[0062] a cal (E eff ) = a daCal E eff + b daCal ,

[0063] where a daCal and bdaCal is a dynamic calibration coefficient for using the same calibration data I discussed above S (t j ) and I REF (t j ) to dynamically compensate the calibration coefficient b cal .

[0064] Figure 4D Illustrates a representative method of dynamic linearization 480. At 482, one or more optical signals of interest are received, and at 484, an average optical signal value (corresponding to E EFF ) is obtained based on the received optical signal, the optical signal from a previous similar measurement, and the electrical offset provided to one or more optical signal amplifier circuits based on the average optical signal amplitude, or the average optical signal value is obtained in other ways. At 486, one, two, or more calibration coefficients can be retrieved from a look-up table in a processor-readable storage device, or one, two, or more calibration coefficients can be calculated by interpolation or otherwise from the retrieved values. One or more of a cal , b cal and c cal can be adjusted based on the average optical signal value. At 488, at least one dynamic calibration coefficient associated with the average of the received optical signals is used to linearize the received optical signals.

[0065] Example 6. Representative FTIR measurement

[0066] In FTIR, an optical signal associated with a sample and an optical signal associated with a background are obtained such that the measured spectrum reflects the sample rather than any extraneous effects included in the background. In FTIR, linearization can be performed without the full set of calibration coefficients. For example, a background interferogram vector b = b 0 , …, b N-1 and a sample interferogram vector s = s 0 , …, s N-1 are obtained, where each is a series of N optical signal values. As discussed above, calibration coefficients can be used to correct the background interferogram and the sample interferogram. The symbol “^” is used to denote the corrected (i.e., linearized) values such that the nth element of the linearized background interferogram vector and the sample interferogram vector is:

[0067]

[0068] and

[0069]

[0070] The average value can be removed by subtraction; the resulting vectors and elements are denoted with the symbol “~” such that

[0071] And

[0072]

[0073] These are simplified to:

[0074] where

[0075]

[0076] and

[0077] where

[0078]

[0079] Using capital letters to represent the Fourier transform, i.e., as vectors B and S, the k-th component of the Fourier transform of the linearized zero-mean background interferogram and the linearized zero-mean sample interferogram is:

[0080]

[0081] and

[0082]

[0083] In FTIR, the ratio T k = S k / B k is the quantity of interest, and clearly the common factor a cal cancels. Thus, in FTIR, the linearization of the background interferogram and the sample interferogram with the mean removed can be performed as: where i k is the k-th component of the interferogram or its Fourier transform.

[0084] Example 7. Representative spectrometer

[0085] Referring to Figure 5 , the compensated spectrometer system 500 includes a spectrometer 502 that couples a portion of the light beam associated with the spectral component to a detector 504 (such as an MCT detector). The detector provides an optical signal to a DC-coupled amplifier 506, which provides the amplified and / or filtered optical signal to a processing system 508 that may include an ADC (not shown), a processing device, and a processor-readable storage device that includes instructions for linearization, determining E EFF, parts 510, 512, 514 that store constant and / or dynamic calibration to provide a linearized output using dynamic or constant calibration with one, two, or three calibration coefficients.

[0086] Figure 6 The compensated spectrometer system 600 is shown, which includes a spectrometer 602 similar to the Figure 5 spectrometer and a first amplifier (DC-coupled amplifier) 606 coupled to a photodetector 604 (such as an MCT photodetector). The amplifier 606 is coupled to a second amplifier 608 to direct the optical signal to a processor system 610. In this example, the processor system 610 is coupled to establish a fixed output of the photodetector when the photodetector 604 is not exposed to any light beam, thereby reducing the apparent signal contribution attributed to the dark current. If desired, the processor system 610 also provides one or more control signals to the amplifier 606 via a digital-to-analog converter (DAC) 614 to select the amplifier gain and offset using processor-executable instructions stored in a memory device. By adjusting the offset and gain, the amplifier range can be used for the AC part of the optical signal, and the associated digital optical signal can use the full range. The optical signal from the DC-coupled amplifier 606 and any offset provided by the ADC 614 can be used to establish an E for dynamic calibration EFF . The processing system 610 can store calibration coefficients and processor-executable instructions for linearization, determining E EFF , dynamic calibration, and selecting one, two, or three calibration coefficients.

[0087] Example 8. Representative optoelectronic signal amplifier

[0088] Referring Figure 7 , a representative amplifier 700 used with a photodetector 702 includes a first operational amplifier 706 and a resistor 708 that is arranged as a transimpedance amplifier based on the photocurrent received from the photodetector 702. The resistance of the resistor 708 can be selected to provide a suitable voltage output for any detected optical signal. The first operational amplifier 706 provides the optical signal to a second operational amplifier 710, which provides an optical signal voltage output V OUT . The first operational amplifier 706 is also coupled to a peak detector 712, which provides an indication of the peak optical signal amplitude from the first operational amplifier 706 as a digital signal to a processor 714. The processor 714 is coupled to a DAC 716 and a digital potentiometer 718, which establishes the offset and gain provided by the operational amplifier 710 via a digital controller resistor R POT ; the DAC output is coupled to a buffer amplifier 720 and to the digital potentiometer 718 via a resistor 722; the gain is based on the ratio RPOT / R 2 (For purposes of explanation, the dashed lines indicate digital signal paths). The offset can be set to have a small magnitude, and the gain is set such that the optical signal magnitude matches the available digital and / or analog voltage range, including the range associated with any downstream ADC, but additional gain stages can be used if desired.

[0089] Processor 614 is also coupled to provide a digital offset signal to DAC 726, which provides an analog offset signal to buffer amplifier 728. This digital offset signal is associated with the photodetector signal in the absence of an input optical signal and is used to at least partially remove the dark current from the optical signal received at the first operational amplifier 706. The photodetector 702 is coupled to the supply voltage V s , and the resulting associated bias current 730 can be offset with a suitable digitally controlled offset voltage.

[0090] As disclosed above, the output signal V OUT is typically digitized and linearized. In some examples, the transimpedance amplifier formed by operational amplifier 706 and resistor 708 is typically sufficiently linear such that any non-linearity at the reference node 732 is due to the photodetector 702. The gain between the photodetector and the reference node is fixed; the calibration factor can be measured relative to the reference node 732. The output V OUT is a function of the digital gain and offset signals applied to digital potentiometer 718 and DAC 716, respectively, such that the output signal V OUT can be back-calculated to provide the optical signal value at the reference node 732 for linearization. The linearization can be based on this node, where the calibration data is associated with this node.

[0091] As Figure 7 shown, the output voltage V OUT is given by V OUT = V OS G OS + V RN G SIG where V OS is the offset voltage (i.e., the voltage provided by DAC716), G OS is the offset gain (i.e., the gain from DAC 716 to the output of operational amplifier 710), V RN is the voltage at the reference node 732, and G SIG is the signal gain from the reference node 732 to the output of operational amplifier 710. It can be seen that G OS and G SIG are given by and respectively. The resistor RPOT is a function of the digital control signal N POT such that G OS and G SIG are both variable. The reference node voltage V RN for the reverse calculation is then:

[0092]

[0093] Apply the linearization as discussed above to V RN .

[0094] The DAC 716 receives a control signal (such as the control word N DAC ), and the digital potentiometer 718 receives a control signal from the processor 714 (such as the control word N POT ) to establish V OS and R POT respectively. In one example, the control word establishes V OS and R POT as and where R MAX is the maximum available resistance, m is the bit resolution of the digital potentiometer 718, V REF is the reference voltage of the DAC, and k is the bit resolution of the DAC 716. Using these digital signals, the reverse calibration can be completed. Additionally, V OS and R POT can be set to reduce the DC component in V OUT and set the gain provided by the second operational amplifier 710.

[0095] The linearization can be done by the processor 714 or another processor, and if the gain and offset are to be calculated elsewhere, then V OUT , N POT and N DAC are provided along with other parameters as needed.

[0096] Example 9. Representative optoelectronic signal amplifier with current injection

[0097] In many examples, for linear correction, a DC-coupled amplifier is required because the DC component of the modulated optical signal incident on the photodetector is large. However, in FTIR measurements, spectroscopists have little analytical interest in the DC component. Thus, in an alternative amplifier configuration, in addition to the offset V OSIn addition, a DC component opposite in amplitude to the DC optical signal component is introduced in the signal chain. This introduced DC component can ensure that amplifier stages (such as the first stage) do not saturate. The first-stage amplifier is typically a transimpedance amplifier because of its excellent linearity, but such amplifiers typically have limited current driving capabilities, which limits how small the transimpedance amplifier feedback resistor (e.g., Figure 7 the R in 1 ) can be. This in turn means that there is a minimum practical gain for the first stage. In combination with a large DC optical signal component with a small superimposed interference pattern, amplifier saturation is possible, especially for hot samples where an additional DC component is generated.

[0098] Figure 8 The amplifier system 800 shown in Figure 7 can address possible transimpedance amplifier saturation. The amplifier system 800 is similar to the Figure 7 amplifier system but includes a current source 802 that injects a current I SET along with the photodetector current into the operational amplifier 706 under the control of the DAC 816. If this current offset is not needed to be introduced into the photodetector current, the current injection can be disabled. The current I SET cancels the DC portion of the photocurrent and is added as a product R 1 I SET to the voltage V RN (i.e., V OUT referenced back to the reference node 732). In this configuration, V OS can typically be set to 0. The amplifier system 800 is shown as providing a linearized output from the processor, but the linearization can be provided at a remote processing system that receives V OUT as well as N DAC , N POT , V REF and I SET or other parameters required to back-calculate to the reference node 732.

[0099] Example 10. Representative linearization method with back calculation

[0100] Refer to Figure 9, method 900 includes measuring an output optical signal at 902 and back-calculating the optical signal amplitude to a reference node at 904. This back-calculation can be based on a gain and / or offset applied to the photodetector signal. At 906, a linearization method and corresponding linearization coefficients are selected, such as those associated with single-parameter or multi-parameter static or dynamic compensation. At 908, calibration coefficients are retrieved, and at 910, the back-calculated optical signal is linearized, and at 912, the linearized back-calculated optical signal is stored. In an FTIR measurement, the FFT of the back-calculated optical signal is calculated and stored or displayed.

[0101] Example 11. Calibration using a variable light source or optical attenuator

[0102] Reference Figure 10 , a representative photodetector calibration system 1000 includes a variable light source 1006 and / or a variable optical attenuator 1008 coupled to a processor system 1010, the processor system being operable to vary the optical power in the light beam 1010 using respective control signals (such as control voltages V LS , V ATTN ). The light beam 1010 is directed to a test photodetector 1012, which generates an optical signal that is directed to an amplifier 1014, and the corresponding amplified optical signal is coupled to the processor 1014, typically coupled to an ADC, to provide a digital optical signal having a value that can be stored in a memory device processor 1024 together with a related value of V LS or V ATTN , and the related value can be used in any of the calibration processes disclosed above.

[0103] Representative embodiment

[0104] Example 1 is a method that includes: directing a modulated light beam to a test photodetector; obtaining a modulation amplitude of an optical signal associated with detection of a first portion of the modulated light beam by the test photodetector; determining at least one first calibration coefficient operable to linearize the test photodetector based on the modulation amplitude of the optical signal from the test photodetector; and storing the at least one first calibration coefficient in a memory device.

[0105] Example 2 includes the subject matter of Example 1 and further includes: directing a second portion of the modulated light beam to a reference photodetector; obtaining a modulation amplitude of an optical signal associated with detection of the second portion of the modulated light beam by the reference photodetector; and determining the at least one first calibration coefficient based on the modulation amplitudes of the optical signals from the test photodetector and the reference photodetector.

[0106] Example 3 includes the subject matter according to any one of Examples 1-2, and further specifies establishing the modulation of the light beam based on variable activation of the light source generating the light beam or a variable attenuator placed in the path of the light beam from the light source, and determining the at least one calibration coefficient based on the modulation amplitude of the light signal from the test photodetector and the variable activation or variable attenuation of the light source.

[0107] Example 4 includes the subject matter according to any one of Examples 1-3, and further specifies that the light signal is a photodetector signal.

[0108] Example 5 includes the subject matter according to any one of Examples 1-4, and further specifies that the at least one first calibration coefficient includes only one first calibration coefficient.

[0109] Example 6 includes the subject matter according to any one of Examples 1-5, and further specifies that the at least one first calibration coefficient includes three first calibration coefficients associated with linearization based on an exponential function with an offset.

[0110] Example 7 includes the subject matter according to any one of Examples 1-6, and further specifies that the at least one first calibration coefficient includes calibration coefficients a, b, c, where the linearized light signal is generated as I LINEAR = a exp(bI MEAS ) + c, where I LINEAR is the linearized light signal associated with the measured light signal I MEAS .

[0111] Example 8 includes the subject matter according to any one of Examples 1-7, and further specifies that the at least one first calibration coefficient includes a first calibration coefficient b, where the linearized light signal is generated as I LINEAR = exp(bI MEAS ), where I LINEAR is the linearized light signal associated with the measured light signal I MEAS .

[0112] Example 9 includes the subject matter according to any one of Examples 1-8, and further specifies that the first calibration coefficients a, b, c are constants.

[0113] Example 10 includes the subject matter according to any one of Examples 1-9, and further includes: changing an average power of the modulated light beam directed to the test photodetector; determining at least one second calibration coefficient based on the changed average power of the modulated light beam, wherein the second calibration coefficient is at least one dynamic calibration coefficient associated with an average power dependence of a selected one of the first calibration coefficients; and storing the at least one second calibration coefficient in the memory device.

[0114] Example 11 includes the subject matter according to any one of Examples 1-10, and further specifies that the at least one second calibration coefficient is associated with the calibration coefficient b.

[0115] Example 12 includes the subject matter according to any one of Examples 1-11, and further specifies that the at least one dynamic calibration coefficient includes two calibration coefficients A and B such that the calibration coefficient b = A(E eff ) + B, where E eff is associated with the average power of the modulated light beam.

[0116] Example 13 includes the subject matter according to any one of Examples 1-12, and further includes linearizing a measured optical signal to I LINEAR = exp(bI MEAS ), where I LINEAR is the linearized optical signal associated with the measured optical signal I MEAS .

[0117] Example 14 is an FTIR system that includes: a photodetector; a memory device that stores at least one calibration coefficient associated with the photodetector; and a processor that is coupled to receive an optical signal in response to illumination of the photodetector and linearize the optical signal based on the at least one calibration coefficient.

[0118] Example 15 includes the subject matter according to Example 14, and further specifies that the at least one calibration coefficient includes one or more of the calibration coefficients a, b, c, where the linearized optical signal I MEAS associated with the measured optical signal I LINEAR is generated as I LINEAR = aexp(bI MEAS ) + c.

[0119] Example 16 includes the subject matter according to any one of Examples 14-15, and further specifies that the at least one calibration coefficient includes the calibration coefficient b, where the linearized optical signal I MEAS associated with the measured optical signal ILINEAR is generated as I LINEAR = exp(bI MEAS ).

[0120] Example 17 includes the subject matter according to any one of Examples 14 - 16, and further specifies that the memory device stores at least one dynamic calibration coefficient, wherein the processor linearizes the optical signal based on the at least one calibration coefficient and the at least one dynamic calibration coefficient.

[0121] Example 18 includes the subject matter according to any one of Examples 14 - 17, and further specifies that the at least one dynamic calibration coefficient is associated with the calibration coefficient b.

[0122] Example 19 includes the subject matter according to any one of Examples 14 - 18, and further specifies that the at least one dynamic calibration coefficient includes two dynamic calibration coefficients A and B such that the calibration coefficient b = A(E eff ), + B, where E eff is associated with the average power of the modulated light beam.

[0123] Example 20 includes the subject matter according to any one of Examples 14 - 19, and further includes linearizing the measured optical signal to I LINEAR = exp(bI MEAS ), where I LINEAR is the linearized optical signal associated with the measured optical signal I MEAS .

[0124] Example 21 includes the subject matter according to any one of Examples 14 - 20, and further includes a DC - coupled amplifier coupled to the photodetector.

[0125] Example 22 includes the subject matter according to any one of Examples 14 - 21, and further specifies that: the amplifier includes a first amplifier and a second amplifier, wherein the first amplifier is a DC amplifier coupled to the photodetector; and the processor is coupled to provide a variable gain and offset to the second amplifier and linearizes the optical signal based on the at least one calibration coefficient and the variable gain and offset.

[0126] Example 23 includes the subject matter according to any one of Examples 14 - 21, and further specifies that E is determined based on the measured optical signal or the offset applied to the second amplifier eff .

[0127] Embodiment 24 includes the subject matter according to any one of Embodiments 14-23, and further specifies that the processor is coupled to linearize the optical signal based on a reverse calculation of the received optical signal to a network node between the first amplifier and the second amplifier.

[0128] Embodiment 25 includes the subject matter according to any one of Embodiments 14-25, and further includes a digital potentiometer and a digital-to-analog converter coupled to the processor and the second amplifier to establish the variable gain and offset.

[0129] Embodiment 26 includes the subject matter according to any one of Embodiments 14-25, and further includes a current source that supplies current to the photodetector based on an average photocurrent generated in response to the illumination of the photodetector.

[0130] Embodiment 27 includes the subject matter according to any one of Embodiments 14-26, and further specifies that the at least one dynamic calibration coefficient includes two dynamic calibration coefficients A and B such that the calibration coefficient b = A(R eff ) + B, where E eff is associated with the average power of the modulated light beam.

[0131] Embodiment 28 includes the subject matter according to any one of Embodiments 14-27, and further includes a current source that supplies current to the photodetector based on the photodetector dark current.

[0132] In view of the fact that the principles of the present invention disclosed can be applied to many possible embodiments, it should be recognized that the illustrated embodiments are only preferred examples and should not be considered as limiting the scope of the present disclosure.

Claims

1. An FTIR system, the FTIR system comprises: a photodetector; a memory device that stores at least one calibration coefficient associated with the photodetector; and a processor coupled to receive an optical signal in response to illumination of the photodetector and linearize the optical signal based on the at least one calibration coefficient.

2. The FTIR system according to claim 1, wherein the at least one calibration coefficient includes one or more of calibration coefficients a, b, and c, wherein the linearized optical signal I MEAS associated with the measured optical signal I LINEAR is generated as I LINEAR = a exp(bI MEAS ) + c.

3. The FTIR system according to claim 1, wherein the at least one calibration coefficient includes a calibration coefficient b, wherein the linearized optical signal I MEAS associated with the measured optical signal I LINEAR is generated as I LINEAR = exp(bI MEAS ).

4. The FTIR system according to claim 3, wherein the memory device stores at least one dynamic calibration coefficient, and wherein the processor linearizes the optical signal based on the at least one calibration coefficient and the at least one dynamic calibration coefficient.

5. The FTIR system according to claim 3, wherein the at least one dynamic calibration coefficient is associated with the calibration coefficient b.

6. The FTIR system according to claim 4, wherein the at least one dynamic calibration coefficient includes two dynamic calibration coefficients A and B such that the calibration coefficient b = A(E eff ) + B, where E eff is associated with the average power of the modulated beam.

7. The FTIR system according to claim 6, wherein the FTIR system further linearizes the measured optical signal into I LINEAR = exp(bI MEAS ), where I LINEAR is the linearized optical signal associated with the measured optical signal I MEAS .

8. The FTIR system according to claim 1, the FTIR system further comprising a DC-coupled amplifier coupled to the photodetector.

9. The FTIR system according to claim 8, wherein: the amplifier includes a first amplifier and a second amplifier, wherein the first amplifier is a DC amplifier coupled to the photodetector; and the processor is coupled to provide a variable gain and offset to the second amplifier and linearize the optical signal based on the at least one calibration coefficient and the variable gain and offset.

10. The FTIR system according to claim 8, wherein E is determined based on the measured optical signal or the offset applied to the second amplifier eff .

11. The FTIR system according to claim 6, wherein the processor is coupled to linearize the optical signal based on a reverse calculation of the received optical signal to a network node between the first amplifier and the second amplifier.

12. The FTIR system according to claim 8, the FTIR system further comprising a digital potentiometer and a digital-to-analog converter coupled to the processor and the second amplifier to establish the variable gain and offset.

13. The FTIR system according to claim 12, the FTIR system further comprising a current source that provides current to the photodetector based on an average photocurrent generated in response to the illumination of the photodetector.

14. The FTIR system according to claim 1, wherein the at least one dynamic calibration coefficient includes two dynamic calibration coefficients A and B such that the calibration coefficient b = A(E eff ) + B, where E eff is associated with the average power of the modulated beam.

15. The FTIR system according to claim 1, the FTIR system further comprising a current source that provides current to the photodetector based on a photodetector dark current.

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