Reference Detector Research Articles

Using a small-core graphite calorimeter for dosimetry and scintillator quenching corrections in a therapeutic proton beam

Organic plastic scintillation detectors (PSDs) are known to produce less light per absorbed dose in highly dense radiations in comparison with e.g. 60Co gamma beams. This so-called ionization density quenching can be experimentally determined by comparison of the scintillator output with the absorbed dose established with a reference detector. The hypothesis of this work was that a newly developed small-core graphite calorimeter (core size: ø5mm × 7mm) can be used as reference for such measurements. The potential benefit of a calorimetric reference would be to have a robust and accurate reference with well-understood dosimetry properties even in high-intensity FLASH beams. As a first step, the hypothesis was tested by comparing previously established quenching parameter estimates for the BCF-60 scintillating material with data obtained with the new instrument at different depths along the central axis of a 170 MeV scanned proton beam. After the calorimetric measurements, scintillator measurements were acquired under equivalent conditions by positioning the PSD in a replica graphite core nominally identical to the core used for calorimetry. To experimentally document details of the irradiations, the spot width was mapped along the central beam axis using a new technique based on a PSD and a time-to-distance conversion procedure. Analysing the proton data in the framework of the Birks model, the graphite calorimeter gave a quenching parameter for BCF-60 in agreement with literature values. The consistency between the calorimetric results and the other sources of information supports the validity of the new method, and we therefore aim to apply it for characterization of other detectors in more intense beams where ionometry cannot serve as reference.

An Off-Axis Differential Method for Improvement of a Femtosecond Laser Differential Chromatic Confocal Probe

This paper presents an off-axis differential method for the improvement of a femtosecond laser differential chromatic confocal probe having a dual-detector configuration. In the proposed off-axis differential method employing a pair of single-mode fiber detectors, a major modification is made to the conventional differential setup in such a way that the fiber detector in the reference detector is located at the focal plane of a collecting lens but with a certain amount of off-axis detector shift, while the fiber detector in the measurement detector is located on the rear focal plane without the off-axis detector shift; this setup is different from the conventional one where the difference between the two confocal detectors is provided by giving a defocus to one of the fiber detectors. The newly proposed off-axis differential method enables the differential chromatic confocal setup to obtain the normalized chromatic confocal output with a better signal-to-noise ratio and approaches a Z-directional measurement range of approximately 46 μm, as well as a measurement resolution of 20 nm, while simplifying the optical alignments in the differential chromatic confocal setup, as well as the signal processing through eliminating the complicated arithmetic operations in the determination of the peak wavelength. Numerical calculations based on a theoretical equation and experiments are carried out to verify the feasibility of the proposed off-axis differential method for the differential chromatic confocal probe with a mode-locked femtosecond laser source.

Numerical modeling of the gas gain of low-pressure Tissue-Equivalent Proportional Counters

Proportional counters are radiation detectors widely used in many applications. The design of the counter, to best fit each application, needs an accurate knowledge and physical modeling of the electron avalanche process. A particular proportional counter is the tissue-equivalent proportional counter (TEPC), the reference detector for experimental microdosimetry, which consists of a spherical or cylindrical chamber filled with low-density tissue-equivalent gas to simulate the energy deposition in tissue sites of micrometric size. The lower operation limit of standard TEPCs operated in the pulse-height analysis mode is about 0.3μm. In order to overcome this technological limit, different avalanche-confinement nano-microdosimetric TEPCs capable of measuring microdosimetric spectra in the nanometric domain were designed and constructed.In this work, a novel numerical tool developed for the Monte Carlo simulation of the electron avalanche process inside a low-pressure TEPC is described. The Monte Carlo code allows to simulate complex 3D electric field configurations exploiting COMSOL finite elements analysis. Several models for the electron interactions (i.e. scattering and ionization) are included in the code. The code has been benchmarked with the experimental results of a wall-less avalanche-confinement TEPC in terms of absolute gas gain for different operating conditions (i.e. gas pressures and electrode voltages).The results show that the code is capable of reproducing the absolute value of the gas gain for the avalanche-confinement TEPC simulating some tenths of nanometers in site size. Moreover, the code can reproduce both the extension and the shape of the proportional counter working windows.The code was also applied for simulating the probability of absorption of electrons by the central third electrode: the helix. The results show a non-negligible probability of absorption in the common range of operation. This code will be further applied for optimizing the TEPC design, capable of simulating site sizes closer to the nanometer region.

Wavelength discrimination (WLD) detector optimization for time-of-flight positron emission tomography with depth of interaction information

Parallax error in positron emission tomography (PET) scanners degrades image quality away from the center of the field-of-view (FOV). Depth of interaction (DOI) encoding is a common method for mitigating this parallax error in PET scanners. A DOI encoding method based on wavelength discrimination (WLD) has recently been proposed, showing promising results in terms of figure of merit (FOM) values. This method employs an optical filter and a phoswich detector, comprising of LYSO (bottom layer) and GAGG (top layer) scintillators. The main idea behind this method is to place an optical filter between the phoswich detector and one of the two adjacent photodetectors that are used to acquire light photons emitted from the phoswich scintillators, thereby blocking the emission from one of the scintillators. This enables identification of the interacting scintillator, based on the signals detected by the two photodetectors. However, the method has a drawback: light photon loss due to the optical filter degrades the detector’s energy resolution. In this work, experiments were performed to optimize detector configuration of this WLD method. GFAG, a scintillator with a relatively short decay time, was chosen to replace GAGG to improve timing performance. The timing performances of the conventional setup (S50) were measured to be 276 ps and 216 ps for top (GFAG) and bottom (LYSO) layers, respectively. The coincidence resolving time (CRT) for each setup was acquired by using a 3 mm × 3 mm × 5 mm Ce:LYSO scintillator as reference detector. In terms of energy performance, GAGG provided better energy resolutions of 12.9% (top) and 12.6% (bottom) due to its higher light output, compared to 14.7% FWHM and 13.0% for GFAG. Further optimization was performed by reducing the area covered by the optical filter to 25% (S25) and 15% (S15) of the total detector area. The results for S25 were 249 ps (GFAG) and 213 ps (LYSO) for timing performance, and 11.8% and 11.9% for energy resolution of the top and bottom layers, respectively. For S15, the CRTs were 250 ps and 201 ps, while the energy resolutions were 11.2% and 10.8%. Thus, the combination of two fast scintillators (Ce:LYSO and GFAG) and better optical filter placement delivered improvements in timing and energy resolution while preserving WLD’s excellent DOI decoding capability.

Characterization method to achieve simultaneous absolute PDE measurements of all pixels of an ASTRI Mini-Array camera tile

Recently, the Istituto Nazionale di Astrofisica (INAF) has placed a contract with Hamamatsu Photonics to acquire hundreds of Silicon Photomultipliers (SiPM) tiles to build 10 cameras with 37 tiles each for the ASTRI Mini-Array (MA) project. Each tile is made up of 8 × 8 pixels of 7 × 7 mm2 with micro-cells of 75μm. To check the quality of the delivered tiles a complex and accurate test plan has been studied. The possibility to simultaneously analyse as many pixels as possible becomes of crucial importance.Dark Count Rate (DCR) versus over-voltage and versus temperature and Optical Cross Talk (OCT) versus over-voltage can be easily measured simultaneously for all pixels because they are carried out in dark conditions. On the contrary, simultaneous Photon Detection Efficiency (PDE) measurement of all pixels of a tile is not easily achievable and needs an appropriate optical set-up. Simultaneous measurements have the advantage of speeding up the entire procedure and enabling quick PDE comparison of all the tile pixels.The paper describes the preliminary steps to guarantee an accurate absolute PDE measurement and the investigation the capability of the electronics to obtain simultaneous PDE measurements. It also demonstrates the possibility of using a calibrated SiPM as reference detector instead of a calibrated photodiode. The method to achieve accurate absolute PDE of four central pixels of a tile is also described.

A new signal processing method for a differential chromatic confocal probe with a mode-locked femtosecond laser

This paper presents an improved data processing method, which is referred to as the tracking intersection method, for a fibre-based dual-detector differential chromatic confocal probe with a mode-locked femtosecond laser source. In the dual-detector differential confocal system, two fibre detectors of an optical spectrum analyzer are employed to detect the spectra of the confocal signals. One of the fibre detectors, referred to as the measurement detector, is located at the confocal position of the confocal system, and the other fibre detector, referred to as the reference detector, is located at a position with a certain offset from the confocal position. In the tracking intersection method, the Z-directional displacement of a measurement object is derived from tracking the wavelength at the intersection point of the two fibre detector outputs. A new algorithm is proposed to generate a normalized output with a sharp peak at the intersection wavelength, from which the intersection wavelength can be detected with a high-sensitivity while the influence of the non-smooth spectral distribution of the femtosecond laser source can be removed. Compared with the previous tracking local minimum method, the new tracking intersection method is more robust to noises in the fibre detector outputs and consequently can realize better performance such as higher resolution and larger range in measurement of the displacement of the object. The advantages of the new method are demonstrated by simulation and experiment.

Alanine dosimetry in strong magnetic fields: use as a transfer standard in MRI-guided radiotherapy

Reference dosimetry in the presence of a strong magnetic field is challenging. Ionisation chambers have shown to be strongly affected by magnetic fields. There is a need for robust and stable detectors in MRI-guided radiotherapy (MRIgRT). This study investigates the behaviour of the alanine dosimeter in magnetic fields and assesses its suitability to act as a reference detector in MRIgRT.Alanine pellets were loaded in a waterproof holder, placed in an electromagnet and irradiated by 60Co and 6 MV and 8 MV linac beams over a range of magnetic flux densities. Monte Carlo simulations were performed to calculate the absorbed dose, to water and to alanine, with and without magnetic fields. Combining measurements with simulations, the effect of magnetic fields on alanine response was quantified and a correction factor for the presence of magnetic fields on alanine was determined.This study finds that the response of alanine to ionising radiation is modified when the irradiation is in the presence of a magnetic field. The effect is energy independent and may increase the alanine/electron paramagnetic resonance (EPR) signal by 0.2% at 0.35 T and 0.7% at 1.5 T. In alanine dosimetry for MRIgRT, this effect, if left uncorrected, would lead to an overestimate of dose. Accordingly, a correction factor, , is defined. Values are obtained for this correction as a function of magnetic flux density, with a standard uncertainty which depends on the magnetic field and is 0.6% or less.The strong magnetic field has a measurable effect on alanine dosimetry. For alanine which is used to measure absorbed dose to water in a strong magnetic field, but which has been calibrated in the absence of a magnetic field, a small correction to the reported dose is required. With the inclusion of this correction, alanine/EPR is a suitable reference dosimeter for measurements in MRIgRT.

Performance Assessment of Amplification and Discrimination Electronic Devices for Passive Neutron Measurements

The assessment of fissile material mass is a key requirement to enhance radioactive waste management and to ensure a high level of safety in the nuclear industry. The assessment of plutonium fissile mass by passive coincidence measurements is usually obtained by detecting the neutrons generated by the spontaneous fissions of Pu isotopes. The detection and the quantification of a fissile mass in the radioactive waste can also be carried out using active neutron interrogation with a pulsed D-T neutron generator. The 14-MeV neutrons are moderated to induce fissions in the uranium and plutonium-contaminated waste. The emitted neutron signal can be analyzed by considering their detection time after the generator pulse. Data are measured according to the principles of the neutron measurement techniques. As proportional counters filled with 3He gas display high neutron detection efficiency and good gamma-ray immunity, they are the reference detector for passive neutron coincidence counting. A charge preamplifier or a current amplifier, depending on applications, collects the electric pulse produced by neutron interaction in the 3He gas, and a threshold discriminator produces a logic pulse used for neutron counting. This article describes the performance assessment of different commercially-available electronics from Mirion Technologies, Precision Data Technology (PDT), Mesytec, as well as MONACO electronics originally developed by CEA LIST for fission chamber measurements in experimental reactors. Comparative passive neutron measurements are carried out with these electronics at CEA/DEN Nuclear Measurement Laboratory in Cadarache. Overall, PDT and Mesytec electronics show similar detection efficiency as the ACH-NA98 charge amplifier, which is commonly used in our laboratory for such applications. However, MONACO electronics have a lower detection efficiency, similar to the Mirion 7820 current amplifier used in specific high-count rate applications. An optimization of MONACO settings would probably be necessary to adapt to 3He counters instead of fission chambers.

The unified imaging condition of Fourier-transform ghost imaging in the far field

In general, the unequal distance between the two detectors and the thermal light source can lead to poor imaging quality in the Fourier-transform ghost diffraction (FGD) system, while the rule does not hold in the far field. Based on the numerical simulations and experimental results, the imaging condition of the FGD pattern is analyzed in the far field. It is shown that the condition is quite different from that in the near field. When the difference between the distance from the light source to the reference detector and the one from the object to the light source are in the far field, the better diffraction pattern can also be kept when the equivalent distance from the object to the test detector is in the far field, although the lengths of the test path and the reference path are not equal.

Development and Implementation of an End-To-End Test for Absolute Dose Verification of Small Animal Preclinical Irradiation Research Platforms

Lack of standardization and inaccurate dosimetry assessment in preclinical research is hampering translational opportunities for new radiation therapy interventions. The aim of this work was to develop and implement an end-to-end dosimetry test for small animal radiation research platforms to monitor and help improve accuracy of dose delivery and standardization across institutions. The test is based on a bespoke zoomorphic heterogeneous mouse and WT1 Petri dish phantoms with alanine as a reference detector. Alanine measurements within the mouse phantom were validated with Monte Carlo simulations at 0.5 mm Cu x-ray reference beam. Energy dependence of alanine in medium x-ray beam qualities was taken into consideration. For the end-to-end test, treatment plans considering tissue heterogeneities were created in Muriplan treatment planning systems (TPS) and delivered to the phantoms at 5 institutions using Xstrahl's small animal irradiation platforms. Mean calculated dose to the pellets were compared with alanine measured dose. Monte Carlo simulations and in phantom alanine measurements in NPL's reference beam were in excellent agreement, validating the experimental approach. At 1 institute, initial measurements showed a larger than 12% difference between calculated and measured dose caused by incorrect input data. The physics data used by the calculation engine were corrected, and the TPS was recommissioned. Subsequent end-to-end test measurements showed differences <5%. With an anterior field, 4 of the participating institutes delivered dose within 5% to both phantoms. An end-to-end dosimetry test was developed and implemented for dose evaluation in preclinical irradiation with small animal irradiation research platforms. The test was capable of detecting treatment planning commissioning errors and highlighted critical elements in dose calculation. Absolute dosimetry with alanine in relevant preclinical irradiation conditions showed reasonable levels of accuracy compared with TPS calculations. This work provides an independent and traceable dosimetric validation in preclinical research involving small animal irradiation.

Wavelength discrimination (WLD) TOF-PET detector with DOI information

Depth-of-interaction (DOI) encoding can contribute to improving spatial resolution uniformity and sensitivity in positron-emission-tomography (PET) scanners. In addition, time-of-flight (TOF) PET scanners with DOI encoding have received considerable interest because of their potential for improving the spatial resolution, sensitivity, and image quality of the overall system. In this study, a new DOI detector configuration utilizing scintillators’ emission wavelength is proposed, and experimental results on the energy, timing, and DOI performance of the detector are provided.The DOI information from the proposed phoswich-type detector can be acquired at the detector level without complex signal processing by utilizing a single optical filter with customized optical properties. For this, we used either a short pass filter (SPF) or a long pass filter (LPF) that allows light photons of a specific wavelength to pass. The two-layered phoswich detector was configured with two scintillators with different photon-emission spectra. In this study, we used Ce:GAGG (3 mm × 3 mm × 10 mm) and LYSO:Ce (3 mm × 3 mm × 10 mm) as the top and bottom layer scintillators, respectively. A digital silicon photomultiplier (dSiPM) was used as the photosensor and for data acquisition. The phoswich detector was placed in the center of two dSiPM pixels, where one of the dSiPM pixels was covered with the optical filter, and the light guide was placed on the other pixel. The detector was tested for energy, timing, and DOI encoding performance.When an SPF was used, the energy resolutions of 16.2% and 11.8% were achieved for the Ce:GAGG (top layer) and LYSO:Ce (bottom layer) respectively without correcting for saturation effect. With a small (3 mm × 3 mm × 5 mm) LYSO crystal as the reference detector, CRTs (coincidence-resolving times) of 338 ps and 244 ps were recorded for the top and bottom layers respectively. The detector configuration also provides an excellent DOI-separation figure-of-merit (FoM) value of 1.9.In the case of LPF, the energy resolutions of 12.0% and 12.9% were achieved for the Ce:GAGG (top layer) and LYSO:Ce (bottom layer), respectively. CRTs (coincidence resolving times) of 314 ps and 263 ps were recorded for the top and bottom layers, respectively. The DOI-separation FoM value of 1.5 was achieved in this setup.Results show that the proposed method can provide excellent discrete DOI positioning accuracy without compromising the timing performance of the detector.

Timing performance of a Micro-Channel-Plate Photomultiplier Tube

The spatial dependence of the timing performance of the R3809U-50 Micro-Channel-Plate PMT (MCP-PMT) by Hamamatsu was studied in high energy muon beams. Particle position information is provided by a GEM tracker telescope, while timing is measured relative to a second MCP-PMT, identical in construction. In the inner part of the circular active area (radius r<5.5 mm) the time resolution of the two MCP-PMTs combined is better than 10 ps. The signal amplitude decreases in the outer region due to less light reaching the photocathode, resulting in a worse time resolution. The observed radial dependence is in quantitative agreement with a dedicated simulation. With this characterization, the suitability of MCP-PMTs as t0 reference detectors has been validated.

Impact of theoretical reactor flux uncertainties and of the near detector on the JUNO measurements

JUNO is medium-baseline reactor neutrino experiment that will probe the neutrino spectrum mass ordering (MO) and will measure the mass-mixing oscillation parameters with unprecedented sub-percent precision. It will be complemented with a ton-level, high energy resolution liquid scintillator reference detector, TAO, that will measure the reactor neutrino spectrum with unprecedented accuracy. In this work we study if the limited knowledge of the reactor antineutrino spectrum and of its fine structure can have a significant effect on the mass ordering determination and on the precision measurements of the oscillation parameters, and try to assess the advantages of having the TAO reference detector.

STUDIES ON THE DETERMINATION OF THE TOTAL HARDNESS OF THE DRINKING WATER COMING FROM THE "FÂNTÂNILE RECI" SPRING IN MARAMUREŞ

The paper showcases research conducted in order to determine the total hardness of the drinking water coming from the "Fântânile Reci" spring, located at the edge of the DN18 road, at the end of the Mara town, in Maramures, Romania. A HI97735 advanced portable photometer was used for this experiment. The photometer can perform low, medium and high range measurements of the total hardness of the water samples. The counter comes equipped with a superior optical system which uses a reference detector and a narrowband interference filter used for extremely quick and repeatable measurements. The values obtained as the result of the experiment are: 204 mg/l CaCO 3 (Total Hardness MR), 15,2 °E, 12,2°dH and 21,7°f. The LED light sources are superior compared to the tungsten lamps. LED lights are more efficient, providing more light while using less energy, and they produce little heat, which could otherwise affect the electrical balance.

Key comparison EURAMET.PR-K2.a.2011—spectral responsivity in the range of 900 nm to 1600 nm

The Euramet.PR-K2.a comparison on spectral responsivity for the wavelength range 900 nm to 1600 nm, as described in this report, was carried out to establish the degree of equivalence for the participating European laboratories with respect to the Key Comparison Reference Value (KCRV) of the CCPR-K2.a-2003 comparison. Seven laboratories, including pilot and link laboratory, participated. The comparison was piloted by VSL (Netherlands). Both VSL and NPL (UK) act as link laboratories to the CCPR-K2.a-2003 comparison.Most laboratories show a DoE within 1 % from the CCPR KCRV for almost the full wavelength range, with some slightly larger differences mostly above 1450 nm. One laboratory shows larger deviations, up to 3%.This report provides an overview of the comparison, a description of the characterization of the reference detectors, the data-analysis, participant results and their uncertainties and the degree of equivalence of participating laboratories with the CCPR KCRV. The full Technical Reports of the participants are included in the Appendix of the comparison report.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCPR, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Performance assessment of amplification and discrimination electronic devices for passive neutron measurements

The knowledge of the fissile material mass is a key challenge to enhance radioactive waste management and to ensure a high level of safety in nuclear industry. Data is analyzed according to the principles of the neutron measurement techniques. As proportional counters filled with 3He gas display high neutron detection efficiency and a good gamma-ray discrimination, they are the reference detector for passive neutron coincidence counting. A charge preamplifier or a current amplifier, depending on applications, collects the electric pulse produced by neutron interaction in the 3He gas and a threshold discriminator produces a logic pulse used for neutron counting. This paper describes the performance assessment of different commercially available electronics from Mirion Technologies, Precision Data Technology (PDT), Mesytec, as well as MONACO electronics originally developed by CEA LIST for fission chamber measurements in experimental reactors. Comparative passive neutron measurements are carried out with these electronics at CEA/DEN Nuclear Measurement Laboratory in Cadarache. Overall, PDT and Mesytec electronics show similar detection efficiency as the ACH-NA98 charge amplifier, which is commonly used in our laboratory for such applications. However, MONACO electronics have a lower detection efficiency, similar to Mirion 7820 current amplifier used in specific high-count rate applications. An optimisation of MONACO settings would probably be necessary to adapt to 3He counters instead of fission chambers.

A time-driven FPGA-based fast nuclear charge digitization method

Abstract Without the need of high-speed analog-to-digital converters (ADCs), the method of translating the shape of nuclear pulses into a time width for charge measurement provides the possibility of multi-channel system implementation with commercialized discrete components. In this paper, we propose such a circuit scheme based on field programmable gate array (FPGA) to realize nuclear charge digitization. Compared with other charge digitizing methods using discrete components, the proposed scheme has a shorter measurement dead time and high measurement performance. Since some logic units of the FPGA are developed to replace discrete analog devices, only one additional analog amplifier for each channel is required outside of the FPGA, which makes the circuit scheme compact and feasible for the implementation of multi-channel systems. Combining with a positron emission tomography (PET) detector module that consists of LYSO crystals coupled with a SiPM array for 22Na coincidence measurement, the circuit can achieve the energy resolution of 12.3% with a typical measurement dead time of 500 ns. Using a reference detector with 164.7 ps time resolution, the coincidence time resolution of the two detectors is evaluated as 367.1 ps, which means the proposed circuit also has an acceptable time performance for some applications.

An FPGA-Based Fast Linear Discharge Readout Scheme Enabling Simultaneous Time and Energy Measurements for TOF-PET Detectors

The readout electronics in time-of-flight positron emission tomography (TOF-PET) detector modules conventionally contain a separate timing circuit and a separate energy measurement circuit. For channel-by-channel readouts, the front-end electronics will be unacceptably large and must rely on application specific integrated circuit (ASIC) chips. In this paper, we present a novel field programmable gate array (FPGA)-based readout scheme that unifies the time and energy measurements with only one analog amplifier per channel in addition to the FPGA. By constructing a simple and effective fast linear discharge circuit, one time-to-digital converter (TDC) per channel can implement time and energy readouts simultaneously with a short measurement dead time. To evaluate the performance of the new approach, a 16-channel PET detector module consisting of LYSO crystals coupled with a silicon photomultiplier (SiPM) array was constructed connecting to the readout electronics. Using a reference detector with a 164.7-ps time resolution to perform 22Na coincidence measurements, the average energy, and time resolution among 16 channels were measured as 12.44% and 372.6 ps, respectively. The typical measurement dead time is approximately 300 ns. The test results show the simplicity and feasibility of the proposed readout scheme, which is particularly useful for laboratory instrumentation.

Application of the Wiener filter for intensity noise reduction in fiber optic gyroscopes.

An essential issue for the low-noise system application of the fiber optic gyroscope (FOG) is to reduce its noise level. The relative intensity noise (RIN) of the light source is the dominant noise of the FOG when the light power on the detector reaches a certain level. The noise subtraction method is effective for RIN reduction and easy to implement in a FOG. This paper theoretically analyzes the factors that influence the result of the method and deduces the function to calculate the noise suppression ratio that can be achieved. A method that uses an optimum filter design based on the Wiener filter in the reference detector signal is proposed to improve the subtraction result. A FOG system is set up to test the feasibility of the method. The experiment results meet with the theoretical analysis, and by using the Wiener filter, the achieved noise subtraction factor reaches the limitation that restrains the optical system and detection circuit.

Optimized noise reduction scheme for heterodyne spectroscopy using array detectors.

In this work, we optimize and further advance a noise reduction scheme for heterodyne spectroscopy. This scheme linearly combines data from reference detectors to predict the noise statistics in the signal detector through an optimized coefficient matrix. We validate this scheme for visible white-light-continuum and 800-nm light sources using un-matched CMOS arrays and show that the signal-to-noise ratio can approach the noise floor of the signal detector while using only ~5% of the energy for reference detection. We also optimize the strategy for estimating the coefficient matrix in practical applications. When combined with elaborate algorithms to perform pixel data compression and expansion, our scheme is applicable in difficult situations, including when the sample position is rapidly scanned, when detectors exhibit nonlinear response, and/or when laser fluctuations are large. The scheme is generalized to scenarios with complex chopping or phase cycling patterns, and a simple approach is provided for the chopping case. Finally, a robust and computationally efficient method is devised to remove multiplicative noise.