Abstract
Although long-wavelength infrared imaging technology is crucial in applications such as terrestrial remote sensing and astronomy, it faces a fundamental challenge from the overwhelming thermal background radiation. This background photon flux often pushes conventional detectors to the limits of their background-limited performance (BLIP). The main limiting factor here is not the intrinsic noise of the detector, but the shot noise of the background itself. In this paper, a key classification is demonstrated to distinguish between two superficially similar but fundamentally different detection architectures (difference detector and differential detector). According to the application and implementation of the detector, the background photocurrent of the conventional difference detector sets a background-determined threshold for the detectable signal difference, while the differential detector is a device that directly measures the differences of the target physical quantities at the physical perception level. Only the weak difference signals are integrated, resulting in extensive cumulative sampling to improve the signal-to-noise ratio to an unprecedented level. In particular, the differential detection technology path based on the quantum well infrared photodetector (QWIP) is introduced. QWIP provides an ideal physical basis for realizing high-performance long-wavelength infrared differential detectors with its extremely low dark current, precise electrical controllability and intrinsic spectral selectivity, and has made significant progress in experiments. Finally, Fisher information theory and Cramer-Rao bound are used to provide rigorous theoretical support for differential detectors.
Introduction
Infrared imaging, especially in the long-wavelength infrared atmospheric window (8－14 µm) , is indispensable to many scientific, industrial and defense fields [1-2] . However, ground-based long-wavelength infrared imaging systems face an extreme challenge: the target signal is usually just a tiny temperature or emissivity difference superimposed on the huge thermal background radiation generated by the300 K ambient temperature. This high photon flux means that the ultimate performance of most infrared photodetectors is limited not by their internal noise (such as thermal noise or dark current noise) , but by the intrinsic quantum shot noise of the background photons themselves. This operating state is called the BLIP limit of infrared photodetectors [3].
In order to detect weak targets or subtle changes, a common strategy is to subtract the reference image from the signal image. This has led to the emergence of two completely different architecture concepts-infrared different detector and infrared differential detector. This paper aims to compare and analyze their detection characteristics. Infrared different detector adopts the traditional method, in which an infrared focal plane array collects two independent images (such as a scene containing a target and a reference scene) sequentially or in parallel, and then subtracts the resulting analog or digital signals in post-processing [4]. Infrared differential detector is a new architecture that performs subtraction at the physical level of photoelectric conversion before light is converted into integrated charge. Similar architectures for eliminating background interference have been studied in laser detection, that is, combining the "signal" and "reference" light fields through interference or other means so that the huge, common laser background is cancelled. Ideally, this detector only senses the difference between the "signal" and "reference" light fields [5].
Although both approaches aim to separate different signals, we will demonstrate that infrared different detector architectures face a severe and often insurmountable physical bottleneck in high background radiation environments: the full-well capacity (FWC) of the detector readout circuit [6]. This paper shows that infrared differential detector architectures offer fundamental advantages in sensitivity and information acquisition by circumventing this limitation, demonstrating their uniqueness as a superior class of infrared detectors.
1 Principle and implementation of infrared differential detector architecture
1.1 Dynamic range bottleneck of infrared different detector
Infrared different detector is an intuitive and common architecture. The core idea is to measure two or more total quantities containing signal and background independently, and then subtract these measurement results in the subsequent electronic circuit or digital software to obtain the signal difference. However, this "integrate first, then subtract" model has two fundamental physical defects : (1) the mutual constraints between dynamic range and integration time; (2) quantization noise and failure of digital accumulation.
1.1.1 Mutual constraints between dynamic range and integration time
Modern infrared focal plane array is a hybrid of a detector array and a readout integrated circuit (ROIC) . Each pixel contains an integrating capacitor in the ROIC to accumulate photogenerated charge during exposure. The maximum amount of charge that this capacitor can store is its full-well capacity. This is a finite value, typically between tens of thousands and millions of electrons [7]. In the long-wavelength infrared band, the photon flux from the ambient thermal background is huge. This background infrared flux ΦB generates a large photocurrent IB fills the integration well quickly. To prevent saturation, the integration time tint must be kept very short. If the full-well capacity is Nwell electrons, background photocurrent is generated IB/e electrons (including e is the charge value of the electron) per second, then the maximum integration time is tint, max≈Nwell⋅e/IB. This constraint is the core weakness of the different detector architecture in high infrared light flux scenarios.
In order to improve the signal-to-noise ratio (SNR) , a standard signal averaging technique is used, that is, collecting and averaging K independent frames [8]. The signal-to-noise ratio is proportional to the square root of the number of averages: (SNR) K = K1/2⋅ (SNR) 1. However, since the background forces tint to be very short, the number of frames K that can be collected and averaged within a reasonable observation time is severely limited. This sets a hard upper limit on the achievable signal-to-noise ratio. Therefore, there is a minimum detectable signal threshold for different detectors. If the signal difference is so weak that the charge generated in the brief tint, max is less than the intrinsic noise floor of the system, it cannot be reliably detected because the main means of reducing noise-increasing the integration time-is not available.
1.1.2 Quantization noise and failure of digital accumulation
In order to increase the effective K value, we can quickly read out the integrated charge and perform digital accumulation in the computer to circumvent the limitation of the full-well capacity. However, this method introduces another more hidden bottleneck-quantization noise [9]. In the readout circuit, the analog signal (i.e., the voltage on the integrating capacitor) needs to be converted into a digital signal by an analog-to-digital converter (ADC) . An n-bit ADC divides its full-scale voltage range into 2n discrete quantization levels. The width of each level, i.e., the least significant bit (LSB) , represents the minimum voltage change that the ADC can distinguish [10]. For different detectors, if there is a huge background signal, the background signal occupies the entire dynamic range of the ADC. This means that the voltage change corresponding to a single LSB is often equivalent to many photoelectrons. If the number of charges generated by the weak signal difference caused by the target is less than the number of charges equivalent to a single LSB, then this signal will be completely submerged in the digitization process. The output digital code of the ADC will not reflect the existence of this weak signal. Therefore, simply digitally accumulating these readout values is equivalent to averaging a series of almost unchanged numbers, and any effective signal information cannot be extracted, rendering the digital accumulation strategy ineffective.
1.2 Detection of weak infrared signals by infrared differential detectors under large background interference
Compared with infrared different detectors, infrared differential detectors have the fundamental advantage of breaking through the minimum detectable signal threshold that is limited by the dynamic range in practical applications (especially in high-background, weak-signal infrared imaging scenarios) . One technical approach to realizing infrared differential detectors is to apply the photoconductive properties of quantum well infrared detectors, as shown in Figure1.
Fig.1Schematic diagram of infrared differential detector.
Figure1 shows that two coupled photoconductive devices obtain the photocurrent IB from the background infrared light and the photocurrent IB+IS from the background and target signal respectively. When the two reach a precise balance against the background, the output background photocurrent is zero. At this time, only the signal photocurrent is output, and theoretically, there is no lower limit to this detectable signal photocurrent. In such an infrared differential detector architecture, its subtraction operation at the physical level occurs before the charge integration, so through precise balance, the huge common-mode background photocurrent that does not contain target information is offset.
Therefore, what is injected into the integration capacitor is only the tiny difference current associated with the slight difference in the target. The benefit is that since the amount of injected current is so small, the integration capacitor will hardly be filled. This means that the single integration time can be greatly extended, or a very large number (a very large K value) of accumulated samples can be performed within a fixed readout period. Therefore, in principle, there is no detection threshold determined by the background for the differential detector.
Since the background is eliminated, the entire dynamic range can be used to measure the difference. In theory, as long as the measurement time is long enough (that is, K is large enough) , any non-zero small difference can eventually be extracted from the noise, thereby increasing the signal-to-noise ratio to a level sufficient for clear identification. It is precisely because it breaks through the measurement threshold set by the dynamic range that the measured difference can approach the concept of mathematical infinitesimal without failure . This is perfectly consistent with the idea that differential is the limit of difference in calculus. Therefore, this detector that directly measures the difference at the physical perception level and is not limited by the background dynamic range is defined as a differential detector, to distinguish it from the different detector that is subject to this limitation. This is reasonable in academic research and technological development.
1.3 Implementation path of long-wavelength infrared differential detector: unique advantages of QWIP
In the practice of applying the differential detection principle to long-wavelength infrared imaging, it is crucial to select appropriate photoelectric conversion materials and device structures. Recent research work by the Shanghai Institute of Technical Physics, Chinese Academy of Sciences, shows that QWIP provides a unique technical path for realizing high-performance long-wavelength infrared differential detectors [11]. In particular, the localized joint control method using photoelectric technology has improved the peak external quantum efficiency of QWIP devices. This lays the necessary foundation for the detection sensitivity of QWIP for differential detector architecture. As shown in Figure2, the highest peak external quantum efficiency currently achieved in the long-wavelength infrared band is 28%.
Fig.2Summary of peak external quantum efficiency of long-wavelength infrared QWIP devices (the national flag indicates that the experimental data comes from the report of the research institute in the corresponding country, and the data points with the increase of year are from the literature [12-25]) .
QWIP is particularly suitable for differential detector architectures because it has the following advantages:
(1) Extremely low intrinsic device noise. Related studies have shown that the pixel dark current of the hyperspectral long-wavelength QWIP focal plane array used on China's Yaogan-37 satellite can be suppressed to an extremely low level (about 2 pA) , and when the peak external quantum efficiency is further increased from 3% to 20%, the pixel dark current can still be maintained at 8 pA [11]. These dark current values are further reduced compared to the results reported by the U.S. Army Research Laboratory [18-19], and the extremely small device dark current ensures that the device intrinsic noise can be kept at a very low state. Under low-temperature operating conditions, the main noise source is the shot noise caused by background photon fluctuations, so the device intrinsic noise (dark current noise) is much smaller than the background photocurrent noise. This provides an ideal premise for common-mode suppression of background photocurrent: since the interference of the device intrinsic noise is extremely small, the physical subtraction operation can be performed more accurately on the background photocurrent, thereby achieving a higher common-mode suppression ratio.
(2) Precise electrical controllability. The photocurrent gain of the QWIP is sensitive to its bias voltage and has a linear response. This property provides a powerful and precise means of electrical control. By fine-tuning the bias voltage applied to the detector pixel, its response to the background photocurrent can be precisely controlled, thereby achieving a high-precision "zero-point balance" to the common-mode background signal in the different structure. This electrical operability is far more flexible and stable than mechanical or optical fine-tuning.
(3) Intrinsic spectral selectivity. Through designs such as band engineering and critical coupling, QWIP can achieve very high wavelength selectivity and quantum efficiency (peak external quantum efficiency can reach more than 20%) . This can be clearly seen in Figure3 [11]. Therefore, we can construct a pair of detection units that have differential responses to different wavelengths or spectral features. When there is a temperature difference between the target and the background, their spectral distributions are naturally different. Therefore, even if the total photon flux in the two optical paths is the same, the photocurrents generated after passing through the QWIP detection unit with a specific spectral response will be different. In this way, once the wide-spectrum photocurrent difference from the background is accurately balanced to zero using electrical control, any non-zero photocurrent caused by the difference in the target spectral characteristics will be accumulated as a pure differential signal.
Fig.3Response spectra of different pixels on a single QWIP under different micro-nanostructure manipulations: The peak external quantum efficiency of each response peak can reach more than 20%, and is about 9 times higher than the standard light coupling structure (45° grinding angle) formed by the material represented by black (note that the black curve expresses the value after multiplying its experimental value by 9) .
Based on the above advantages, the Shanghai Institute of Technical Physics, Chinese Academy of Sciences has successfully developed a demonstration device consisting of a320×256 QWIP long-wavelength infrared differential detector [11]. The device uses two different wavebands (see Figure4 (a) ) to detect targets. As shown in Figure4 (b) , when dynamic balance is used to image the human hand target during the photoelectric conversion process, the background can be completely balanced in advance, so that only the image of the hand is present in the entire imaging, eliminating other background signals. The feasibility of this technical path was preliminarily verified through the imaging demonstration of room-temperature targets. The results show that its target recognition ability has been improved by an order of magnitude compared to the traditional different mode [11]. This progress provides strong experimental evidence for the differential detector to move from theoretical framework to practical application (especially challenging the applicability problem of infrared recognition technology development in the long-wavelength infrared field) .
Fig.4(a) Two detection wavebands used by the differential detector (their peaks are on both sides of the10 μm wavelength) ; (b) Imaging of a human hand (the scattered points on the image and the blue horizontal lines reflect the inhomogeneity or blind spots of the device) .
1.4 Application of differential detection architecture in other detection technology applications
Thanks to the characteristics of quantum well infrared detectors, the concept of differential detection has achieved a breakthrough in long-wavelength infrared imaging devices. However, this concept has also been applied in other physical dimensions and technical fields, indicating that the differential detection architecture has its universality, especially in the technical function of background common-mode signal suppression.
For example, in the field of laser detection, as the most classic differential detector in the field of optics, the balanced photodetector directly subtracts the two photocurrents after the photocurrent is generated and before any significant electronic amplification, thereby effectively suppressing the relative intensity noise of the laser [26]; in the field of magnetic field detection, the magnetic gradiometer directly measures the spatial gradient of the magnetic field by using two magnetometers separated by a fixed baseline, and has a natural immunity to the distant, spatially uniform magnetic field noise [27]; in wavefront measurement, the common-path interferometer makes the signal light and the reference light overlap on most of the path, thus having a strong suppression ability for common-mode noise sources such as mechanical vibration and temperature drift [28]; in the frequency domain of signal processing, the phase-locked amplifier uses phase-sensitive detection technology to extract only the signal component that is exactly the same as the reference frequency, and regards all other frequency noise as the suppressed "common-mode background" [29] .
2 . Reasoning based on information theory
To provide a deeper theoretical basis for the superiority of the differential detector, we go beyond the traditional SNR analysis and enter the field of information theory. Fisher information theory and the Cramer-Rao bound provide us with powerful mathematical tools for this rigorous comparison [30].
2.1 Fisher information: a measure of extractable information
Fisher information I (θ) quantifies the amount of information a measurement carries about the unknown parameter θ [30]. The larger its value, the higher the potential accuracy of estimating θ from the data. The Cramer-Rao bound links this concept to actual measurements, which states that the variance of any unbiased estimator θ′ (i.e., the square of the measurement uncertainty) cannot be less than the inverse of the Fisher information [31], that is, Var (θ′) ≥1/I (θ) . Therefore, the fundamental performance of a measurement architecture can be evaluated by the amount of Fisher information it provides for the target parameter.
2.2 Information theory comparison of the two architectures
The following compares the amount of Fisher information that the differential detector architecture and the differential detector architecture can provide when measuring the difference parameters d=A−B.
2.2.1 Different detector architecture
(1) Perform two independent measurements to obtain the observed value mA=A+nA and mB=B+nB.
(2) Assuming noise nA and nB is independent Gaussian noise with variance σ2.
(3) The difference estimator is d′=mA−mB=d+ (nA−nB) .
(4) The variance of this estimator is Var (d′) =σ2+σ2=2σ2.
(5) Therefore, the Fisher information provided by this architecture about the parameter d is
(1)
2.2.2 Differential detector architecture
(1) Perform a direct measurement to obtain the observed value md=d+nd.
(2) The noise nd comes from a single detection link, and its variance is σ2d. In a well-designed system, σ2d is comparable to the noise variance of a single channel, i.e.σ2d≈σ2.
(3) The Fisher information provided by this architecture is
(2)
The conclusion after comparison is as follows: Idirect (d) =2Idiff (d) . This result clearly shows that the differential detector retains twice as much information about the difference parameter in a single measurement as the different detector. The different architecture, due to its separate measurement process, permanently loses half of the information by introducing double noise at the initial stage.
2.3 The role of signal averaging and information accumulation
Signal averaging is a common method to improve measurement accuracy. For K independent measurements, the total Fisher information is K times the individual information [26]. However, the two architectures differ greatly in their ability to accumulate information: for different detectors, the average number Kdiff that can be performed is strictly limited by the dynamic range; for differential detectors, since the background is eliminated, the average number Kdirect can theoretically approach infinity. Therefore, in practical applications, there is a huge difference in the total amount of information that the two architectures can accumulate:
(3)
(4)
(5)
This provides a quantitative theoretical expression from the fundamental level of information theory for the overwhelming advantages of differential detectors when facing high background flux and weak signal challenges.
3 . Conclusion
Through a comprehensive analysis of physical principles, existing technologies and information theory, we specifically define infrared detectors that directly measure differences at the physical perception level and are not limited by the background dynamic range as infrared differential detectors, in order to distinguish them from different detectors that are subject to this limitation. This distinction is not a simple difference in terminology, but a definition of two fundamentally different measurement modes.
Infrared different detectors represent the idea of measuring first and then calculating. It is subject to the superposition of noise from each independent channel, and is even more constrained by the dynamic range of the detector itself in practical applications, especially in scenarios with high background flux, where there is an insurmountable lower limit of detection. Infrared differential detectors embody the concept of calculation in perception. Through clever physical design, it extracts the core difference information before the information is contaminated by noise and background. This method is not only more efficient in information theory, but more importantly, it breaks the shackles of the dynamic range by eliminating the influence of background signals on the integral capacitor, making it possible to detect extremely weak signals by averaging a large number of signals.
The technical path represented by quantum well infrared detectors fully utilizes its advantages such as low dark current and electrical controllability, provides strong support for the realization of infrared differential detectors, and has verified its great potential in experiments. The technology in this area needs to continue to focus on the engineering realization of infrared differential detector focal plane arrays. The key challenges include further improving the accuracy and stability of background suppression, and developing matching high-speed, low-noise readout circuits to promote the leap of weak target feature recognition technology under strong infrared background interference.