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Abstract
The directional polarimetric camera (DPC) is a polarization sensor with the characteristics of ultra-wide-angle and low-distortion imaging. The multi-angle polarization information is helpful to obtain the spatial distribution of target radiation, and multiple data fusion relies on the non-uniformity calibration of image plane. The non-uniformity consists of many factors such as lens, detector assembly, spatial stray light, etc. The single correction method can not distinguish the error source effectively. In consideration of the in-flight operation mode of DPC based on the adjustment of exposure time, the non-uniformity correction method of the detector based on multi parameters is proposed. Through the electro-optical performance measurement system of the CCD detector, the sensitive factors such as temperature, dark current, exposure time and spectral response are obtained. After a series of preprocessing of the image including removal of dark signal, removal of smearing effect and temperature compensation, the non-uniformity calibration based on multi-parameters is imposed on the detector. The low-frequency unbalanced response difference of the image surface is eliminated, and the high-frequency difference is effectively suppressed. The experimental results show that the photo response non-uniformity of 95% full well single frame data is reduced from 2.86% to 0.36%. After correction, the data noise is shown as shot noise, and the detector has good ability of dynamic range adjustment. The non-uniformity calibration by the proposed method can offer data support for the instrumental calibration and in-flight fast calculation, and provide effective reference for the subsequent polarization remote sensing instruments.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The directional polarimetric camera (DPC) is a satellite sensor with the aim to observe the polarization and directionality of the earth’s reflectance, developed by Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences [1–3]. It was launched successfully on 9 May 2018, aboard the Gao Fen-5 Satellite, a sun-synchronous orbiting satellite at an altitude of 705 km with an inclination of 98°. The multi-angle polarization information can reflect the bidirectional distribution of target polarization [4–6]. The accuracy of multi-angle data is affected by the non-uniformity of radiation response for remote sensing image, which is related to the detector, optical lens, filter and spatial stray light. All of these factors need to be corrected. Firstly, it is necessary to measure the photoelectric performance of the detector and complete the non-uniformity calibration of the detector assembly. The non-uniformity correction of the DPC is completed in the radiometric calibration, including the correction of spatial stray light, the correction of relative radiation and the correction of non-uniformity of polarized channel response [7–9]. The In-flight test and the results of aerosol and cloud products show that the calibration meets the design requirements.
There are two ways to measure the linearity of the detector. One way is to change the brightness of the external light source such as the integrating sphere and calculate the linearity by measuring the change of the response data [10,11]. The other one is to regulate the internal gain such as the exposure time, and measure the response data under the same illumination [12,13]. The DPC in flight mainly includes land mode, ocean mode and custom-defined mode. According to the remote sensing detection target, the corresponding mode is adopted. By adjusting the exposure time, it can adapt to the modulation of dynamic range. Therefore, the laboratory carried out the linearity test based on the exposure time variation, and the non-linearity measurement under different irradiance will be accomplished in the pre-flight calibrations of the DPC [3]. For detectors with good linearity, the two-point and multi-point methods based on linear fitting are usually used for non-uniformity correction [14]. For nonlinear devices, in addition to multi-line correction, the neural network parameter training method and non-uniformity correction method depending on modeling are also used for correction [15].
In this work, the radiometric model of the DPC is utilized to analyze the influence of the detector on remote sensing images and the composition of noise sources of detector. The photo response non-uniformity (PRNU) indicates the inconsistency of the response of different pixels to the same incident radiation, which is related to the difference in quantum efficiency and luminous area of different pixels in the manufacturing process of the device. The non-uniformity of the detector for DPC reflects in high frequency and low frequency. The high frequency difference is reflected in the rapid change of adjacent pixels, and the low frequency difference is reflected in the overall slow change of different field of view. Here, the dark current, smearing effect and spectral response changes caused by temperature drift are analyzed through the electro-optical performance measurement system of the detector. After multi-parameters compensation and correction, the detector shows good linearity. Consequently, multi-point linear fitting is proposed for PRNU calibration, which eliminates the unbalanced low frequency difference and adjacent high frequency difference of the images. The PRNU of 95% full well single frame data is reduced from 2.86% to 0.36%. The experimental results present the effectiveness and superiority of the proposed correction method.
2. Polarization measurement principle and detector influence analysis
A schematic diagram of the main DPC structure is shown in Fig. 1(a). Figure 1(b) shows the optical system. DPC is a polarization sensor based on large field of view telecentric optics, a rotating wheel module loaded with spectral and polarizing filters, and an area charge coupled device (CCD) detector at the back end of the optical path [16].
The optical system adopts a reversed telephoto telecentric structure and consists of an inverse Galileo telescope followed by a focusing group, which is comprised of three cemented lenses. The focal length is about 4.833 mm, while F# is 4. The field of view is ± 50° along-track, ±50° cross-track and ± 59° in the diagonal. The rotating wheel module between the optics and CCD provides 15 measurement channels, including a background channel dedicated to the dark current measurement of CCD, 5 non-polarized bands (443, 565, 763, 765 and 910nm) and 3 polarized bands (490, 670 and 865nm), each of which is composed of 3 channels equipped with polarizers whose polarization angles are close to 0°, 60° and 120°, respectively. The successive instantaneous earth scenes captured by the instrument are imaged on the CCD detector with 512*512 effective pixels, realizing a high spatial resolution of 3.29 km under a swath width of 1850 km. For an observing object, the DPC provides as much as 9 viewing directions. The main parameters of the DPC are listed in Table 1.
Table 1. Instrumental parameters of DPC sensor
In imaging observation, the filter wheel rotates uniformly to realize time-sharing multi-angle and multi-spectral polarization measurement. The target image points of different bands and angles are distributed in different positions of CCD. The remote sensing data contain 72 groups of data consisting of 8 bands and 9 angles of the measured target. Therefore, the PRNU correction of CCD is particularly important for multi-angle imaging.
The remote sensing data calibration of DPC mainly consists of detector calibration and optical calibration, as shown in Fig. 2. Detector calibration accomplishes the error calibration of CCD detector, including dark current correction, smearing effect correction, temperature compensation correction, exposure time and gain adjustment, and non-uniformity correction. Optical calibration achieves the data calibration of optical system, mainly including radiation correction, polarization correction and geometric correction [3]. Detector calibration provides effective digital signal, which is the basis of optical calibration. Optical calibration obtains the physical information of DPC detection through the effective digital signal to correct the instrument measurement error.
From the imaging model, the non-uniformity correction and correlation processing steps of detector can be analyzed. The radiometric model establishes the conversion relationship between the detection output and the incident radiation. The output signal D for the pixel with the coordinates of (i, j) can be expressed as
Where, k is the spectral band; a is the different installation direction of the polarizer; A is the absolute radiometric calibration coefficient; m is the relative gain coefficient of the electronic amplification gain, t is the exposure time coefficient; f is the temperature compensation coefficient, T is the relative transmittance response coefficient, consisting of the relative transmittance of filter and polarizer, the low frequency transmittance of the optical system and the high and low frequency response coefficient of the detector; C denotes the dark current; (I, Q, U) are the three Stokes vectors of incident light. P1, P2 and P3 are the polarization effect of the instrument, which are expressed as:
Where, $\varepsilon $ is the polarizing degree of the lens, $\theta $ is the field of view angle, $\phi $ is the azimuth angle, $\eta $ is the polarizer efficiency.
According to the radiometric model, there are many factors affecting the data quality of DPC. The instrumental thermal vacuum experiment shows that the dark current and temperature compensation coefficient are mainly related to the detector. The detector parameters are moved to the left of the equation. Considering the non-uniformity of the detector, the calibration function of PRNU is $y = w\cdot x + b$, and then the radiometric model can be described as:
Where the left part of the formula is the detector calibration, the right part is the optical calibration.
The influence of detector on DPC mainly includes several aspects: 1) The influence of CCD dark current, which reflects as ${C_{i,j}}$; 2) the influence of temperature drift on absolute radiometric calibration coefficient ${A^k}$; 3) The influence of smear effect, DPC adopts a frame transfer architecture CCD, the effective data can be obtained by eliminating the smear effect in the data processing. 4) The influence of CCD non-uniformity on the relative transmittance $T_{i,j}^{k,a}$.
The change of electronic gain and exposure time can be neglected in correction. In flight, when the dynamic range meets the measurement requirements, the electronic gain of the detector will not be adjusted and is usually set to a constant. The exposure time is obtained from DPC level 0 data and directly calculated by ratio.
This work mainly discusses the non-uniformity calibration process of the detector, including dark current correction, smearing effect correction, temperature compensation and non-uniformity correction.
3. Experimental sections
The DPC is an earth observation instrument, and its spectral responsivity is shown in Fig. 3, which is distributed from visible to near-infrared bands [17]. The radiation responsivity of the instrument will attenuate differently with the change of space environment and time, so it is necessary to perform in-flight radiometric calibration appropriately [18,19]. In order to improve the adaptability of environmental variety, there are three operating modes on orbit, namely land, ocean and custom-defined pattern. The DPC has established a dynamic range adjustment mechanism to reply with the changes of the main observation targets. The difference between the operating mode is the various exposure time of the detector. The parameter adjustment needs to consider the target reflectivity, spectral responsivity and on orbit radiometric calibration results and the decision is made by the ground data system. The calibration method of detector assembly based on exposure time adjustment was studied in the laboratory.
Figure 4 shows the structure of CCD image acquisition system, which is used to obtain high-quality image signal. The image analog signal of CCD is amplified by the pre-amplifier and processed by the analog front-end video signal processor for signal adjusting and analog-to-digital conversion. Then it is forwarded to the single Field programmable gate array (FPGA) chip for packaging according to the scientific data format, through the low voltage differential signaling (LVDS) data bus uploading the image data to the NI industrial computer for real-time image storage and display. FPGA has advantages such as high integration, strong expandability, convenient online debugging and low power dissipation. FPGA realizes the sequential logic control and image data acquisition of the whole image acquisition system. Through the communication between USB and RS232 serial port on the NI computer, it can realize the modification of exposure time, analog front-end gain and offset, imaging cycle and other working parameter settings.
The noise source of detector assembly mainly includes photon shot noise, readout noise and dark current noise in the time domain, and fixed pattern noise in spatial domain [20]. The photon shot noise can be reduced by the average coupling of multi frame images, and the readout noise can be reduced by using correlation double sample technique. The dark current noise is greatly affected by the working temperature of detector, which can be suppressed by CCD refrigeration. The image noise distributed in spatial domain can be compensated by non-uniformity correction. In the present work, the processing methods of non-uniformity correction are analyzed comprehensively.
The non-uniformity of the frame transfer type CCD detector using by DPC was comprehensively detected by the CCD electro-optical performance measurement system, and the variation law of CCD output was studied under different exposure time conditions. Figure 5 shows the whole test equipment, which is composed of segmented uniform illumination light source, CCD image acquisition system, dark room and detector refrigeration system. The integrated sphere built-in tungsten halogen lamp is used as the illumination source, the filter of the same batch as DPC is placed at the integrated sphere port to ensure the test lighting spectrum consistent with the working spectrum of DPC. A standard detector is placed in parallel with the tested detector which is used for the standard transmission of light source energy. A temperature sensor is pasted on the back of the detector to monitor its working temperature through the Agilent data collector. The image data from the image acquisition system are collected by industrial computer in real time.
The diameter of the integrating sphere is 25cm, and the diameter of the light outlet is 5cm. The detector is placed about 40cm away from the integrating sphere output port, which meets the requirements of light uniformity and irradiance simultaneously. The illumination uniformity of the integrating sphere is calibrated based on the unit detector, the calibration results show that the light uniformity is greater than 99.3% when the ratio of detector distance to the aperture of the integrating sphere is 8 times.
The experimental steps of non-uniformity calibration of the detector based on DPC are as follows:
- 1) Adjust the position of CCD image plane to the center of the optical outlet of integrating sphere radiation source;
- 2) By adjusting the output of integrating sphere, the full range of signal detection can be achieved and the preheating can be carried out to a stable state;
- 3) Run the test system, set the temperature point and preheat the detector to a stable state;
- 4) Set different exposure time to test the output response of the detector;
- 5) During the experiment, the energy of integrating sphere light source and the working temperature of detector were monitored in real time.
4. Results and discussion
4.1 Data processing flow
The output effective signal of the detector needs to be calibrated, and the effective value can only be obtained by non-uniformity correction to reduce the error of the detector itself. The detector output effective value is the basis of DPC pre-flight and in-flight calibration. The related processing steps of detector calibration are analyzed from the radiometric model, expressed as Eq. (4), which represents the effective value of consistent response of all pixels for an ideal detector.
Due to the manufacturing process and product batch, the radiation response of each pixel of the detector is different, which affects the data quality of DPC multi-angle observation and the signal accuracy requirements of optical calibration. During in-flight operation, the gain coefficient and exposure time are usually constants. Dark current, temperature, smear effect and non-uniformity correction are primarily considered in the detector calibration. The data correction process is shown in Fig. 6, which is consistent with the in-flight correction process.
The original data and multi-parameter data of the DPC, including temperature monitoring data and light source monitoring data, are obtained to correct temperature changes and light source brightness changes. The original images need to be preprocesssed in order to obtain accurate key parameters of the detector, including multiple images averaging, removal of defect pixels, removal of darkness signal, correction of smearing effect, temperature change compensation and external light source stability compensation. After multi-parameter correction, the signal-to-noise ratio is improved and the influence of noise is reduced, then, PRNU correction coefficient is calculated by multi-point linear fitting method. The effective image signal can be converted into digital number (DN) data through the correction of detector component.
4.2 Dark current correction
The dark current noise belongs to thermally generated electronic noise, in the normal exposure process of CCD, dark current and photo generated current accumulate at the same time in the potential well, resulting in a smaller space for storing useful optical signal. The changes of exposure time, temperature, on orbit environment and instrument decay will affect the dark current. The overall amplitude of dark current occupies about 3% of the detector full well, which has an obvious impact on low reflectivity targets such as the ocean. A background channel is set up on the rotating wheel, which can provide dark current value of a full field frame image during a measurement period for real-time correction and pixel quality monitoring.
The dark current of CCD is measured under different temperatures, as shown in Fig. 7. By changing the exposure time of the detector without illumination, 16 points are selected for testing at the equal interval of 20ms from 0ms to 300ms. Then, the exposure time is taken as the abscissa and the output signal is taken as the ordinate. The measurement data are fitted with the least square method. The slope of the straight line is the dark current per unit time of the detector.
The relationship between dark current and temperature can be described as Eq. (5).
Where T is the working temperature of the detector (in Kelvin), ${\textrm{Q}_{\textrm{d0}}}$ is the dark signal at 293K,${\textrm{Q}_\textrm{d}}$ is the measured dark signal at temperature T.
It can be seen from Fig. 7 that the dark current raise quickly in the high temperature range. The research results show that the working temperature is increased 6°C, the dark current is increased about 1 times, and the dark current at 20°C is about 8.4 times of 0°C.
4.3 Smearing effect correction
The smear effect refers to the charge transfer mode of the detector. Each pixel not only collects the photo charge but also realizes the charge transfer [21]. In the process of charge output, the charge moves line by line and keeps exposure at the same time, resulting in non-uniformity response of pixels. Through the measurement and analysis of the detector smear effect, the effective data can be obtained by eliminating the smear effect in the data processing. In order to explain clearly, the central field of view test data is utilized to illustrate. The comparison is shown in Fig. 8 before and after the smearing effect correction, where the influence signal is eliminated.
Fig. 8. The comparison before and after the smear correction (a) Original image (b) Smearing effect corrected image (c) Gray value of row 150
4.4 Temperature and illumination compensation
The quantum efficiency(QE) of CCD has a stronger temperature dependence for the near-infrared wavelengths. As the working temperature decreases, the energy gap of silicon becomes wider, and the probability of photogenerated charge jumping through the energy gap becomes smaller, then the QE decreases accordingly [22]. The variety of spectral response curve of detector assembly under different temperature conditions is shown as Fig. 9, which shows that QE in near infrared band is greatly affected by temperature. Therefore it is important to control the stability of the detector working temperature. Before the non-uniformity correction, the temperature compensation coefficient correction should be added to eliminate the influence of temperature change.
The formula of correction algorithm in the range of working temperature can be expressed as Eq. (6).
Where T is the temperature of detector, ${L_0}$ is the calculated output radiance value, ${T_x}$ is the relative reference temperature point, ${f_x}$ is the calculation coefficient of ${T_x}$, and L is the corrected output radiance value. The experimental results of the thermal balance of DPC show that the temperature coefficient of 910 nm band is 0.28%/°C, then ${f_x}\textrm{ = 0}\textrm{.0028}$, The temperature drift change rate of 865nm is 0.17%/°C, then ${f_x}\textrm{ = 0}\textrm{.0017}$. During the non-uniformity experiment, the temperature change is less than 1°C, and the temperature effect of other bands can be neglected. After adopting thermal control design and temperature compensation method, the measurement error caused by temperature fluctuation is less than 0.1%. The measurement data of radiance at the light outlet of integrating sphere at band k of DPC under temperature T can be expressed as ${L_{k,t}}$, which is expressed as Eq. (7).
Where L(λ) is the spectral radiance of the reference light source at the wavelength λ, which is the measuring result of the spectral radiometer, r(λ) is the relative spectral responsivity of the instrument, λ1 and λ2 are the upper and lower wavelengths of the k-band filter, and the temperature correction coefficient is the relative value of the relative temperature reference point. The radiance is expressed by the digital number value of the DPC to simplify the calculation.
During the non-uniformity experiment, the temperature monitoring data of the detector is shown as Fig. 10. Here 0°C is selected as the calibration temperature point, the overall temperature change is less than 0.15°C, the temperature control is good, and the temperature drift is very small.
The monitoring data of standard detector is used to compensate for the influence of light source illumination change. The stability of light source and the safety of instrument are considered in the experiment. The measurement is conducted after the light source reaches the thermal stable state. In order to reduce the error influence, the experiment requires that the maximum variation of light source within 30 min is less than 0.5%. The stability data of the light source is shown as Fig. 11, and the maximum deviation is 0.0258%. The integrating sphere light source is stable and meets the experimental requirements.
4.5 Non-uniformity correction
When the light source irradiance is fixed and the exposure time of CCD is changed, a total of 11 groups of signals from 0 to 180ms are obtained. After dark current, smearing effect, temperature and illumination correction, the linear response of the average image plane are shown as Fig. 12. When the exposure time is 180ms, the DN value is close to 3000, and the detector is in 95% full well, which mean that the linearity of the detector is good. When the exposure time is 0ms, the gray value is very small, and the linear bias is close to 0. The dark current correction, smearing effect correction and other multi-parameter correction have achieved ideal consequences, and the experimental data conform to the calculation conditions of linear regression fitting.
According to the linear regression theory, the calibration model is established as Eq. (8).
Where D is the effective signal value after multi-parameter correction and compensation, ${\boldsymbol D} = {[{D{N_1},D{N_2},\ldots ,D{N_n}} ]^\textrm{T}}$, P is the reference value of the input signal, ${\boldsymbol P} = [{{t_1},1;{t_2},1;\ldots ,{t_n},1} ]$, A is the parameter quantity ${\boldsymbol A} = [{a,b} ]$, E is the amount of deviation, ${\boldsymbol E} = {[{{e_1},{e_2},\ldots ,{e_n}} ]^\textrm{T}}$. According to the linear regression fitting, the linear parameter matrix ${{\boldsymbol A}_{i,j}}$ and mean parameter matrix ${{\boldsymbol A}_{\textrm{mean}}}$ of every pixel are obtained. The PRNU correction matrix ${\boldsymbol A}_{i,j}^{\textrm{PRNU}}$ is obtained by a linear transformation and stored as K1 slope matrix and K2 intercept matrix, and the non-uniformity correction of detector is realized by the coefficient matrix.
The PRNU refers to the response difference between different pixels under uniform illumination. The corrected evaluation method can be expressed as Eq. (9).
Where m, n is the number of rows and columns of the photosensitive pixel of the area CCD, ${\mu _{i,j}}$ is the gray value of row m and column n pixel after correction, and $\overline \mu $ is the average gray value of effective pixels in the image after correction.
The DPC has three polarized bands and five non-polarized bands and provides as much as nine viewing directions for the same observing object. In this work the 910nm band is selected to implement the non-uniformity correction of the detector. The influence of CCD noise and non-uniformity will increase with the increase of signal amplitude. By choosing 95% full well single frame data the correction effect can be evaluated more effectively. As shown in Fig. 13, the PRNU correction coefficient is used to correct single frame data, and the PRNU of single frame data is reduced from 2.86% to 0.36%. Before correction, the low-frequency non-uniformity is obvious, as shown in Fig. 13(a), and the low-frequency imbalance difference is eliminated after correction, as shown in Fig. 13(b).
Fig. 13. Comparison of single frame image before and after PRNU correction (a) The original single image at 95% full well (b) The single image after PRNU correction
The correction effect of high frequency non-uniformity was analyzed by histogram. Although most of the shot noise effects can be eliminated by multiple images averaging, the non-uniform noise cannot be reduced by the method of averaging the original data, which can be seen by comparing the histogram of single frame image, as shown in Fig. 14(a), and histogram after averaging 10 images, as shown in Fig. 14(c). Due to the influence of superimposed shot noise, as shown in Fig. 14(b), the correction effect of high-frequency non-uniformity cannot be judged after single frame data correction, so the impact of shot noise needs to be eliminated to evaluate the effectiveness of PRNU correction.
Fig. 14. The histogram of data before and after non-uniformity correction (a) Histogram of single image(b) Histogram of single image after PRNU correction(c) Average histogram of ten images(d) PRNU correction of average histogram for ten images
After multiple images averaging, most of the shot noise is eliminated, and then the non-uniformity correction is carried out. The effect is shown as Fig. 14(d). After correction, the PRNU is reduced to less than 0.2%, the shot noise and non-uniformity are eliminated simultaneously, and the non-uniformity of the detector is effectively corrected.
The non-uniformity correction has also been carried out in the other working spectral bands. The statistical results of the PRNU calibration in different bands are listed in Table 2.
Table 2. The statistical results of the PRNU calibration in different bands
From the above analysis, it can be seen that the correction effect of 95% full well single frame image shows that the low-frequency non-uniformity of image plane in different field of view and the high-frequency non-uniformity of neighborhood pixels are effectively corrected, which is less than the influence of shot noise. For the principal noise sources of the detector, the non-uniformity noise and dark current noise of the detector are effectively calibrated to meet the multi-angle data application.
5. Conclusion
The DPC is the first Chinese satellite sensor for multi-angle polarized earth observation. It acquires the two-dimensional image of the earth with large field of view and a high spatial resolution (3.29 km) in 8 spectral bands. The non-uniformity of full field of view affects the quality of multi-angle data, so a variety of correction methods should be adopted to correct step by step. In view of the in-flight dynamic range of DPC based on exposure time adjustment, the non-uniformity correction method of detector based on multi-parameters is proposed. The linearity of photo response under different exposure time is analyzed through the multi-parameter monitoring measurement of the detector. Through dark current correction, smearing effect correction, temperature compensation and light source energy variation correction, the photo response of the detector shows good linearity. The non-uniformity of full image plane is corrected by multi-point fitting. The PRNU of 95% full well single frame image at 910nm band is reduced from 2.86% to 0.36%. The non-uniformity noise and dark current noise are effectively calibrated, and the remaining noise after PRNU correction is shot noise. After 10 images are averaged, the PRNU is reduced to less than 0.2%, and the shot noise is corrected effectively. The non-uniformity calibration of the detector provides data basis for further pre-flight calibration of the whole instrument, which meets the multi angle data application and provides effective reference for the subsequent instrument development.
Funding
Major special project of high resolution earth observation system (civil part) (30-Y20A19-9007-15/17); the Satellite Data Simulation Technology (50-Y20A38-0509-15/16).
Acknowledgments
The authors are grateful to all of those who were involved in this work. We also thank the reviewers for their useful suggestions.
Disclosures
The authors declare no conflicts of interest.
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