Long-wave infrared spectral range background radiation elimination method and system based on long-wave infrared detector

Abstract

The application provides a long-wave infrared spectral segment background radiation elimination method and system based on a long-wave infrared detector. First, all pixel dark background measured values of a certain frame number of the long-wave infrared detector and focal plane temperatures at corresponding moments are obtained. The relationship between the dark background measured values and the focal plane temperatures is fitted. Each pixel obtains a group of fitting coefficients. The dark background estimated values of the current frame of different pixels can be calculated through the fitting coefficients of each pixel and the real-time focal plane temperature. The dark background estimated values are removed from the incident signals, and the influence of the long-wave infrared system background radiation can be effectively eliminated. The above method and system build the relationship between the background radiation of all pixels and the focal plane temperature, calculate the dark background of different pixels from the nature of the background radiation, reduce the intermediate links, eliminate the influence of the non-uniformity of the dark pixels and the transmission error, effectively improve the calculation accuracy, and avoid wasting the detector resources caused by the artificial definition of the dark pixels.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of photoelectric detection, in particular to a long-wave infrared spectral background radiation elimination method and system based on a long-wave infrared detector. BACKGROUND

[0002] With the development of detectors, long-wave infrared detectors are increasingly widely used in the field of space satellites. HgTeCd has the characteristics of adjustable band gap, large optical absorption coefficient, long carrier lifetime, and high electron mobility, which makes HgTeCd an ideal material for preparing long-wave infrared focal plane detectors. However, as the wavelength increases, the background radiation of the detector also increases, which largely occupies the dynamic range of the effective signal, so that the integral capacitor of the detector is already saturated before the detector reaches the required integration time of the system. In addition, the fluctuation of the background radiation also reduces the noise equivalent temperature difference of the system, affecting the imaging quality of the long-wave infrared system. Therefore, it is necessary to remove the background radiation of the infrared system, especially the long-wave infrared.

[0003] The active method of suppressing background radiation needs to keep the focal plane and optical system at an extremely low temperature, which will consume a large amount of resources and is not sustainable. The present application is a passive method, which does not pursue keeping the entire system at an extremely low temperature, but through different methods, the real-time dark background estimation value of all pixels is fitted to remove the dark background estimation value from the incident signal, so as to achieve the purpose of eliminating the background radiation. The prior art is based on the dark pixels of the detector. That is, a part of the detector pixels (referred to as "dark pixels") are shielded so that they are kept outside the entrance pupil of the optical system and cannot receive the radiant energy of the effective signal, but can only output a dark field signal to represent the background radiation of the system. Then the correlation between different pixels and these dark pixels is established to derive the background radiation of all pixels on the focal plane. For example, patent application CN112284535 A progressive on-orbit push-broom mid-short-wave infrared imaging spectrometer dark background removal method, CN105841815 A imaging spectrometer CCD spectral image dark current correction method, CN111432093 A dark current correction method of CMOS image sensor, etc.

[0004] For the passive method of eliminating the background radiation of the infrared spectral region, the prior art is based on the dark pixels of the detector, which needs to define one or more dark pixels in a certain area or several areas of the detector, so that they do not photosensitive to represent the background radiation. This has three disadvantages:

[0005] Limitation: Currently limited by the process, the focal plane size of infrared detectors, especially long-wave infrared detectors, is small, usually less than 1Kx1K area array, and a certain area is defined as a dark pixel, which wastes the number of effective pixels. In order to improve the accuracy, this method usually defines multiple dark pixel regions at different positions of the detector, which wastes more pixels.

[0006] Difference: The non-uniformity between the pixels of the long-wave infrared detector is very obvious, usually about 10%. Since this method uses a few dark pixels to estimate the background radiation of all pixels, it will inevitably lead to inaccurate calculation due to the difference between different pixels.

[0007] Whether the dark pixel is really "dark": The existing technical solution actually implies a premise that in the normal imaging state, the effective incident signal has no response on the dark pixel, and the output of the dark pixel only includes the background radiation. In actual work, it is not so ideal that the effective signal will produce charges on the dark pixel more or less. In general, in order to improve the accuracy of calculation, dark pixels near the effective pixels are selected, and the target incident signal is more likely to "pollute" the dark pixels, which are contradictory to each other. SUMMARY

[0008] Therefore, it is necessary to provide a long-wave infrared spectral band background radiation elimination method and system based on a long-wave infrared detector, which can effectively improve the accuracy of calculation and avoid wasting detector resources caused by artificially defined dark pixels.

[0009] To solve the above problems, the technical scheme adopted by the present application is as follows:

[0010] One of the objects of the present application provides a long-wave infrared spectral band background radiation elimination method based on a long-wave infrared detector, comprising the following steps:

[0011] In a dark field environment, obtain the dark background measured values of all pixels of the long-wave infrared detector in several frames and the real-time focal plane temperature of the long-wave infrared detector at the corresponding moment;

[0012] Fit the relationship between the obtained dark background measured values of all pixels in several frames and the real-time focal plane temperature at the corresponding moment;

[0013] Obtain a set of fitting coefficients for each pixel;

[0014] According to the fitting coefficients and the real-time focal plane temperature, the dark background estimated value of the current frame of different pixels is calculated, and the influence of the background radiation is eliminated by removing the dark background estimated value from the incident signal.

[0015] In some embodiments, the step of obtaining the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding time instants comprises the following steps: placing the long-wave infrared detector in a completely dark environment, shielding the target radiant energy from entering the long-wave infrared detector with a cold light screen, and obtaining the measured values of the pixel dark background by the long-wave infrared detector.

[0016] In some embodiments, the step of obtaining the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding time instants comprises the following steps: using a constant current source and a temperature measuring diode, and combining a 32-bit high-precision ADC to obtain the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding time instants, and averaging the values obtained by multiple sampling.

[0017] In some embodiments, the step of fitting the relationship between the obtained dark background measured values of all pixels in several frames and the focal plane real-time temperatures in corresponding time instants comprises the following steps: using different fitting models to fit the relationship between the pixel dark background and the focal plane temperature, and the target is to minimize the residual, wherein the fitting models include polynomial fitting, exponential fitting, and linear fitting.

[0018] The second object of the present application provides a long-wave infrared spectral background radiation elimination system based on a long-wave infrared detector, comprising:

[0019] A data acquisition unit is configured to obtain the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding time instants in a dark field environment.

[0020] A fitting unit is configured to fit the relationship between the obtained dark background measured values of all pixels in several frames and the focal plane real-time temperatures in corresponding time instants.

[0021] A fitting coefficient acquisition unit is configured to obtain a set of fitting coefficients for each pixel.

[0022] A background radiation elimination unit is configured to calculate the dark background estimated values of different pixels in the current frame according to the fitting coefficients and the focal plane real-time temperatures, and remove the dark background estimated values from the incident signal to eliminate the influence of background radiation.

[0023] In some embodiments, the data acquisition unit adopts a constant current source plus a temperature measuring diode, and is matched with a 32-bit high-precision ADC to acquire the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperature of the long-wave infrared detector at corresponding moments, and the average values are obtained through multiple sampling.

[0024] In some embodiments, the fitting unit is configured to fit the relationship between the dark background of pixels and the focal plane temperature at corresponding moments by using different fitting models, such as polynomial fitting, exponential fitting and linear fitting, so as to minimize the residual.

[0025] The application adopts the above technical solutions, and has the following beneficial effects:

[0026] The long-wave infrared spectral band background radiation elimination method and system based on a long-wave infrared detector provided by the application acquires the dark background measured values of all pixels of the long-wave infrared detector in a certain number of frames and the focal plane temperature at corresponding moments before formal imaging, fits the relationship between the dark background of different pixels and the temperature of the focal plane according to the real-time temperature of the focal plane and the dark background measured values of all pixels, minimizes the residual, and obtains a group of fitting coefficients for each pixel. During formal imaging, the dark background estimated values of different pixels can be calculated through the fitting coefficients of each pixel and the real-time temperature of the focal plane, and the influence of background radiation can be eliminated by removing the dark background estimated values from the incident signal. The long-wave infrared spectral band background radiation elimination method and system based on a long-wave infrared detector provided by the application directly constructs the relationship between the background radiation of all pixels and the temperature of the focal plane, calculates the dark background of different pixels from the nature of background radiation, and does not rely on the intermediate medium of "dark pixels", which reduces the intermediate links, eliminates the influence of non-uniformity of dark pixels and the transmission error, effectively improves the calculation accuracy, and avoids wasting the detector resources caused by the artificial definition of dark pixels. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the application, the drawings needed in the description of the embodiments of the application or the prior art will be briefly introduced. Obviously, the drawings described below are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0028] Figure 1 The step flow chart of the long-wave infrared spectral band background radiation elimination method based on a long-wave infrared detector provided by the embodiments of the application.

[0029] Figure 2A structure schematic diagram of a long-wave infrared spectral background radiation elimination system based on a long-wave infrared detector provided by an embodiment of the present application.

[0030] Figure 3 A schematic diagram of a relationship between a pixel dark background measured value and a focal plane temperature provided by embodiment 1 of the present application.

[0031] Figure 4 An experimental block diagram of a long-wave infrared system provided by embodiment 1 of the present application.

[0032] Fig. 5(a) and (b) are effective signal output diagrams of the detector before and after correction provided by embodiment 1 of the present application.

[0033] Figure 6 A noise equivalent temperature difference diagram before and after correction provided by embodiment 1 of the present application.

[0034] Fig. 7(a) and (b) are effect diagrams of multi-frame merging before and after correction provided by embodiment 1 of the present application. DETAILED DESCRIPTION

[0035] The embodiments of the present application are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar notations represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary, and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0036] In the description of the present application, it is understood that the terms "upper", "lower", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation of the present application.

[0037] In addition, the terms "first", "second" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise specifically limited.

[0038] In order to make the purpose, technical scheme and advantages of the present application more clear and explicit, the present application is further described in detail below by combining with the drawings and embodiments.

[0039] Please refer to Figure 1A step flow chart of a long-wave infrared spectral band background radiation elimination method based on a long-wave infrared detector provided for Embodiment 1, comprising the following steps:

[0040] Step S110: In a dark field environment, acquire the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector at corresponding moments.

[0041] In some embodiments, in the step of acquiring the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector at corresponding moments in a dark field environment, the following steps are specifically included: before formal imaging, the long-wave infrared detector is placed in a completely dark environment, and a cold light screen is used to shield the target radiation energy from entering the long-wave infrared detector, and the long-wave infrared detector acquires the measured values of the pixel dark background. It can be understood that at this time, the pixel output code value only includes the focal plane dark current and the radiation of the instrument itself.

[0042] In some embodiments, in the step of acquiring the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector at corresponding moments, the following steps are specifically included: a constant current source and a temperature measuring diode are used to acquire the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector at corresponding moments, respectively, and a 32-bit high-precision ADC is used to acquire the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector at corresponding moments, and the values are averaged multiple times, so that the real-time temperature of the focal plane can be accurately acquired, and the precision is better than 1mK.

[0043] Step S120: Fit the relationship between the acquired dark background measured values of all pixels in several frames and the focal plane real-time temperatures at corresponding moments.

[0044] In some embodiments, in the step of fitting the relationship between the acquired dark background measured values of all pixels in several frames and the focal plane real-time temperatures at corresponding moments, the following steps are specifically included:

[0045] The acquired dark background measured values of all pixels and the focal plane temperatures at corresponding moments are used to fit the relationship between the pixel dark background and the focal plane temperature by using different fitting models, and the target is to minimize the residual, and the fitting model includes polynomial fitting, exponential fitting and linear fitting.

[0046] Step S130: Acquire a set of fitting coefficients for each pixel.

[0047] It can be understood that the above fitting system is used to represent the relationship between the focal plane temperature and the dark background.

[0048] Step S140: According to the fitting coefficient and the focal plane real-time temperature, the dark background estimation value of the current frame of different pixels can be calculated, and the influence of background radiation can be eliminated by removing the dark background estimation value from the incident signal.

[0049] The long-wave infrared spectral background radiation elimination method based on a long-wave infrared detector provided in the application directly constructs the relationship between the background radiation of all pixels and the focal plane temperature, calculates the dark background of different pixels from the essence of the background radiation, instead of using the intermediate medium of "dark pixels", reduces the intermediate links, eliminates the influence of the non-uniformity of the dark pixels and the transmission error, effectively improves the calculation accuracy, and avoids wasting the detector resources caused by the artificial definition of the dark pixels.

[0050] Please refer to Figure 2 The long-wave infrared spectral background radiation elimination system based on a long-wave infrared detector provided in the embodiment of the application includes a data acquisition unit 110, a fitting unit 120, a fitting coefficient acquisition unit 130, and a background radiation elimination unit 140. The specific implementation modes of each unit are described in detail below.

[0051] Specifically, before formal imaging, the long-wave infrared detector is placed in a completely dark environment, the data acquisition unit 110 shields the target radiation energy from entering the long-wave infrared detector by using a cold light screen, and the long-wave infrared detector acquires the measured value of the dark background of the pixels. It can be understood that the pixel output code value at this time only includes the focal plane dark current and the radiation of the instrument itself.

[0052] The data acquisition unit 110 uses a constant current source and a temperature measuring diode, and is matched with a 32-bit high-precision ADC to respectively acquire the measured values of the dark background of all pixels of the long-wave infrared detector in several frames and the real-time temperature of the focal plane at the corresponding time of the long-wave infrared detector in several frames, and the values are averaged by multiple sampling, so that the real-time temperature of the focal plane can be accurately acquired, and the precision is better than 1mK.

[0053] The fitting unit 120 is used to fit the relationship between the dark background of all pixels and the focal plane temperature by using different fitting models, and the target is to minimize the residual error. The fitting models include polynomial fitting, exponential fitting, and linear fitting.

[0054] The fitting coefficient acquisition unit 130 is used to acquire a set of fitting coefficients of each pixel. The fitting system is used to represent the relationship between the focal plane temperature and the dark background.

[0055] The background radiation elimination unit 140 is used for calculating the dark background estimation value of different pixels in the current frame according to the fitting coefficient and the focal plane real-time temperature, and removing the dark background estimation value from the incident signal to eliminate the influence of the background radiation.

[0056] The long-wave infrared spectral background radiation elimination system based on a long-wave infrared detector provided in the application directly constructs the relationship between the background radiation of all pixels and the focal plane temperature, calculates the dark background of different pixels from the nature of the background radiation, instead of using the intermediate medium of the dark pixel, reduces the intermediate links, eliminates the influence of the non-uniformity of the dark pixel and the transmission error, effectively improves the calculation accuracy, and avoids wasting the detector resources due to the artificial definition of the dark pixel.

[0057] Embodiments

[0058] A Stirling refrigeration (60K) long-wave infrared detector is selected, the pixel size is 320x256, the spectral range is 8-12.5 μm, the dark current is 1.5 nA, the dark background occupies a large part of the dynamic range, and limits the increase of the integration time. In addition, the dark background fluctuates with time, which also affects the noise equivalent temperature difference of the system.

[0059] Firstly, although the focal plane temperature is controlled by the Stirling refrigerator to be about 60K, there is still a slight fluctuation, and this slight fluctuation causes the fluctuation of the dark background. A constant current source + diode is used, and a 32-bit high-precision ADC is used to accurately obtain the real-time temperature of the focal plane, and the temperature measurement accuracy is improved by multiple sampling and averaging, and the final temperature measurement frequency is 250 times / s.

[0060] Next, the relationship between the pixel dark background and the focal plane temperature is found. The system is placed in a completely black environment, the dark background output of different pixels is measured, and the focal plane temperature is recorded. As shown in Figure 3 The solid line is the dark background DN value (left vertical coordinate), the dashed line is the focal plane temperature (right vertical coordinate), and the horizontal coordinate is the frame number (representing time). Firstly, it can be seen that the pixel dark background fluctuates greatly, and the peak-to-peak value is 40 DN; secondly, although the fluctuation range of the focal plane temperature is only 0.016K, it is very consistent with the fluctuation of the dark background, that is, the consistency is very good; finally, it can be seen that the temperature curve has a delay of 20 frames (200 ms) compared with the change of the dark background. Our temperature measurement frequency is 25 times / s, and the temperature measurement period is 4 ms, so this delay is not caused by the temperature measurement frequency, but by the delay caused by the conduction of the temperature from the focal plane to the diode. This delay can be corrected by subsequent data processing.

[0061] In the laboratory, the above experiment can be repeated to obtain a large number of focal plane temperature and pixel dark background data, and the relationship between the dark background of each pixel and the focal plane temperature can be obtained by neural network fitting of Matlab, which can be expressed by a polynomial (each pixel has a separate polynomial), and each pixel obtains a set of fitting coefficients. In the actual work of the imaging system, these fitting coefficients are written into the FPGA of the circuit in advance, the temperature of the focal plane is accurately sampled in real time, and the current dark background estimation value of each pixel is calculated in real time, which is removed from the effective incident signal, so that the influence of the infrared spectral background radiation on the imaging quality can be eliminated.

[0062] Finally, the effect of this method is verified by experiment, and the experimental device block diagram is shown in Figure 4 . The verification effect is divided into two parts.

[0063] The first part directly gives the comparison before and after the dark background correction, as shown in Figs. 5(a) and (b), which represents the effective signal output of the detector before and after the correction. The incident light source is a uniform constant temperature plane array black body, which represents constant and unfluctuating incident energy. Before correction, the focal plane temperature changes irregularly with time, and the background radiation of the pixel fluctuates with the focal plane temperature, so the detector output also fluctuates with time; after correction, the dark background component is basically eliminated, so the detector output basically remains stable, only white noise (shot noise) exists.

[0064] The second part is verified by noise equivalent temperature difference. Since the background radiation of the pixel fluctuates with time, it will increase the noise equivalent temperature difference of the system. The noise equivalent temperature difference of the system before and after correction is compared, as shown in Figure 6 , which represents the noise equivalent temperature difference before and after correction. The noise equivalent temperature difference of the system before correction is greater than 1.4K in different spectral ranges; after correction, it is reduced to about 0.5K. It can be seen that after the focal plane temperature is used for dark background correction, the noise equivalent temperature difference is obviously reduced.

[0065] In addition, in order to further verify the effect of correction, the images are merged. According to the system noise formula, when the system noise is white noise, multi-frame merging can effectively reduce the noise equivalent temperature difference, and the reduction factor is approximately the square root of the number of merged frames. Figs. 7(a) and (b) show the effect of multi-frame merging before and after correction. Before correction, due to the existence of background radiation and the continuous fluctuation with time, white noise (shot noise) does not dominate, and multi-frame merging has basically no effect; after correction, due to the elimination of the interference of background radiation, white noise dominates, and after multi-frame merging, the noise equivalent temperature difference is greatly reduced, and after 32 frame merging, it can reach 0.3K (without considering bad pixels).

[0066] According to the above examples and the comparison of experimental results before and after correction, it can be proved that the technical scheme of the present application is feasible and effective.

[0067] It can be understood that any combination of the technical features in the above-described embodiments can be made, and for the sake of brevity, not all possible combinations of the technical features in the above-described embodiments are described, however, as long as the combination of the technical features does not exist contradictory, it should be considered within the scope of the present disclosure.

[0068] The above are only the preferred embodiments of the present application, and only the technical principles of the present application are specifically described, and these descriptions are only for the purpose of explaining the principles of the present application, and cannot be interpreted in any way as a limitation on the scope of protection of the present application. Based on the explanation here, any modification, equivalent replacement and improvement made within the spirit and principle of the present application, and other specific embodiments of the present application which can be easily thought by those skilled in the art without creative labor, should be included in the protection scope of the present application.

Claims

1. A method for eliminating background radiation in a long-wave infrared spectral range based on a long-wave infrared detector, characterized in that, The method comprises the following steps: In a dark field environment, acquiring dark background measured values of all pixels of the long-wave infrared detector in several frames and focal plane real-time temperatures of the long-wave infrared detector in corresponding moments; Fitting the relationship between the acquired dark background measured values of all pixels in several frames and the focal plane real-time temperatures in corresponding moments; Acquiring a set of fitting coefficients of each pixel; According to the fitting coefficients and the focal plane real-time temperatures, calculating the dark background estimated values of different pixels in the current frame, and removing the dark background estimated values from the incident signal to eliminate the influence of background radiation; In the step of acquiring the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding moments in a dark field environment, the following steps are specifically included: Placing the long-wave infrared detector in a completely dark environment, shielding the target radiation energy from entering the long-wave infrared detector with a cold light screen, and acquiring the measured values of the pixel dark background by the long-wave infrared detector; In the step of acquiring the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding moments, the following steps are specifically included: using a constant current source plus a temperature measuring diode, and matching a 32-bit high-precision ADC to acquire the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding moments, and repeatedly sampling and averaging the values; In the step of fitting the relationship between the acquired dark background measured values of all pixels in several frames and the focal plane real-time temperatures in corresponding moments, the following steps are specifically included: Using different fitting models to fit the relationship between the pixel dark background and the focal plane temperature, and the target is to minimize the residual, the fitting models include polynomial fitting, exponential fitting and linear fitting.

2. A long-wave infrared spectral range background radiation elimination system based on a long-wave infrared detector, characterized in that The method comprises: A data acquisition unit, configured to acquire dark background measured values of all pixels of the long-wave infrared detector in several frames and focal plane real-time temperatures of the long-wave infrared detector in corresponding moments in a dark field environment; A fitting unit, configured to fit the relationship between the acquired dark background measured values of all pixels in several frames and the focal plane real-time temperatures in corresponding moments; A fitting coefficient acquisition unit, configured to acquire a set of fitting coefficients of each pixel; A background radiation elimination unit, configured to calculate the dark background estimated values of different pixels in the current frame according to the fitting coefficients and the focal plane real-time temperatures, and remove the dark background estimated values from the incident signal to eliminate the influence of background radiation; The data acquisition unit uses a constant current source plus a temperature measuring diode, and matches a 32-bit high-precision ADC to acquire the dark background measured values of all pixels of the long-wave infrared detector in several frames and the focal plane real-time temperatures of the long-wave infrared detector in corresponding moments, and repeatedly samples and averages the values; The fitting unit is used for fitting the relationship between the dark background of all pixels and the focal plane temperature at the corresponding moment by using different fitting models, and the target is to minimize the residual error, wherein the fitting models include polynomial fitting, exponential fitting and linear fitting.

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