A dark signal temperature dependence correction method for miniature spectrometer modules is described in this paper. It is based on laboratory measurements of dark signal temperature dependence at few different integration times. A set of parameters are calculated which make it possible to estimate dark signal at any temperature and integration time within reasonable range. In field conditions, it is not always possible to take frequent dark signal readings during spectral measurements. If temperature is recorded during the measurement, this method can be used for estimating dark signal for every single spectral measurement. The method is validated on two different miniature spectrometers.
Miniature spectrometer modules are becoming increasingly available. They provide a cost-effective way for designing small and lightweight spectrometer systems.
There are several possible fields of use for miniature spectrometer modules, for example, agriculture [
Dark signal is an inherent property of a spectrometer. It is the output signal of the spectrometer when the optical entrance is closed. During a target measurement, the output signal is the sum of the target signal and the dark signal. For extracting target signal, therefore, a precise knowledge of the dark signal is necessary. It is most important in spectral bands where measured signal is low either because of weak optical signal or low sensitivity of the sensor array.
Dark signal of a spectrometer is mainly the sum of two components. One is caused by the dark current,
Two airborne spectrometer systems UAVSpec2 and UAVSpec4SWIR have been designed in Tartu Observatory [
Three different miniature spectrometer modules manufactured by Carl Zeiss Jena GmbH are examined in this study. Those are a near infrared (NIR) enhanced version of MMS-1 with a spectral range of 400–1100 nm, NIR-PGS-1.7 with a spectral range of 960–1690 nm, and NIR-PGS-2.2 with a spectral range of 1000–2170 nm. Dark signal dependence on temperature and integration time is measured for all the spectrometers. A correction algorithm is developed, and it is validated on MMS-1 and NIR-PGS-1.7.
Big and expensive spectrometers usually come with built-in temperature corrections, but this information is often company business secret and it is not publicly available. So, it is not possible to directly compare the method described in this paper with previously used temperature correction methods. To the best of our knowledge, this is the first reported literature on the dark signal temperature dependence correction method for miniature spectrometer modules.
MMS-1 spectrometer module is built around a solid glass body. The imaging grating and 256-pixel Si linear array sensor are rigidly attached to the glass body. The spectrometer has a fiber optic input with cross-section converter—single fibers of the fiber bundle in linear configuration form the entrance slit [
NIR-PGS-series modules have a collimator and focusing lens with a plane grating. Sensors are thermoelectrically (TE) cooled InGaAs linear arrays. NIR-PGS-1.7 uses a standard-type InGaAs sensor with 256 or 512 pixels. The one used in this study has a 256-pixel sensor array. NIR-PGS-2.2 is equipped with a long wavelength-type 256-pixel InGaAs detector. Fiber optic input is similar to the MMS-1 spectrometer module. NIR-PGS-series also have built-in preamplifiers [
Table
Parameters of the devices under test.
Module | MMS-1 | NIR-PGS-1.7 | NIR-PGS-2.2 |
---|---|---|---|
Serial number | 028582 | 047934 | 046973 |
Sensor type | NIR-enhanced Si | InGaAs | Long wavelength type InGaAs |
Spectral range, nm | 400–1100 | 960–1690 | 1000–2170 |
Sensor cooling | None | 1-stage TE | 2-stage TE |
Temperature controller | None | PELTIER-tc | PELTIER-tc |
Compatible FEE | FEE-HS | FEE-1M | FEE-1M |
For each spectrometer, two external thermistors are used for temperature measurements. One is glued to the analog to digital converter (ADC) integrated circuit (IC) at FEE. Another thermistor measures the temperature of the sensor module. For MMS-1, it is attached to the body of the spectrometer module. For NIR-PGS-series, the thermistor is glued next to the operational amplifier and voltage reference ICs at the preamplifier board.
All the spectrometer modules are connected to a laptop or desktop personal computer (PC) via in-house designed microprocessor-controlled interface cards. The microprocessor controlles the integration time and handles the data transmission between the PC and FEE. It also measures supply voltage level and temperatures with its internal ADC. The acquisition software running on the PC is in-house designed as well.
Dark signal temperature dependence at several different integration times was measured for all the spectrometers. A portable refrigerator which had both cooling and warming ability was used for controlling the ambient temperature. For each spectrometer, the temperature was recorded approximately once per second. Since the refrigerator did not have a temperature controller, it was not possible to measure dark signal after the stabilization of the temperature. Therefore, the measurements were made simultaneously with changing the temperature and refrigerator supply voltage was adjusted to limit the temperature change rate. The maximum temperature change rate was 0.7°C /min and the average was 0.15–0.35°C/min for different spectrometers. Dark signal was measured at seven integration times: 120, 240, 480, 600, 1000, 2000, and 3000 ms. A script running on the PC looped through these settings and recorded 11–88 dark signal readings at every integration time. In addition, the sensor module and FEE were heated one at a time with a hot air gun to determine which part is more sensitive to temperature change.
For NIR-PGS-1.7 the Peltier current, setpoint voltage, and sensor temperature measured with the internal thermistor of the linear array were recorded from the PELTIER-tc temperature controller with a Campbell 21X datalogger. The experiment setup can be seen in Figure
Experiment setup. The section inside dotted rectangle applies only to experiments with NIR-PGS-series spectrometer modules. The dashed rectangle represents the refrigerator.
Heating the spectrometer module and FEE separately revealed that dark signal depends significantly only on the temperature of the spectrometer module (see Figure
Dark signal during heating of MMS-1 and FEE separately with a hot air gun. Integration time was 3000 ms.
In Figure
Dark signal temperature dependence of band no. 150 of MMS-1 at different integration times.
The dark signal temperature dependence of NIR-PGS-1.7 is shown in Figure
Dark signal temperature dependence of band no. 150 of NIR-PGS-1.7 at different integration times.
When the ambient temperature was increased from 12°C to 41°C, the thermistor voltage measured from PELTIER-tc increased from 99.7 mV to 101.5 mV which corresponds to the decrease of sensor temperature from 6.99°C to 6.55°C [
The dark signal temperature dependence of NIR-PGS-2.2 is plotted in Figure
Dark signal temperature dependence of band no. 150 of NIR-PGS-2.2 at different integration times.
In Figure
The dark signal temperature dependence measurements were carried out simultaneously with changing the temperature. If the recorded dark signal is plotted against measured ambient temperature, a hysteresis can be seen as in Figure
The effective temperature
For MMS-1,
In the case of NIR-PGS-1.7, there was virtually no time delay between the change of the measured temperature and spectrometer signal. Therefore,
For NIR-PGS-2.2,
After calculation of effective temperature for each measured spectrum, dark signal temperature dependence can be corrected. For this, dark signal was measured at seven different integration times while varying ambient temperature.
The second order polynomial function
Parameters
Parameters
Parameters
Parameters
Parameters
Parameters
If we know fitted parameters
The agreement between modelled and measured dark signal for MMS-1 can be seen in Figure
Integration time and sensor temperature are not the only parameters affecting dark signal. It can depend on other factors as well, for example, long-term deterioration of electronic components. Therefore, during each measurement campaign actual dark signal measurement
To test the correction algorithm in field conditions, an airborne measurement with closed input apertures was made for MMS-1 and NIR-PGS-1.7 spectrometer modules. After the subtraction of the dark signal, the remaining target signal should be 0, since there was no optical radiation incident on the detectors. UAVSpec2 and UAVSpec4SWIR were mounted to the frame of a Robinson R22 helicopter during a 40-minute flight. The integration times were 150 ms and 100 ms for MMS-1 and NIR-PGS-1.7, respectively. The weather conditions during the test flight were similar to those during actual field spectroscopic measurements. When the helicopter was on the ground, the sun warmed the instruments. After takeoff, the air flow generated by the main rotor and flight airspeed cooled the instruments and temperature decreased rapidly several degrees, dropping more than one degree in a minute. During flight, temperature changed a few degrees depending on flight speed, altitude, and the helicopter position relative to the Sun. After landing, the temperature of the instruments started to increase again due to the stop of the air flow and warmth of the sun.
The results can be seen in Figures
Validation of dark signal temperature dependence correction algorithm for MMS-1.
Validation of dark signal temperature dependence correction algorithm for NIR-PGS-1.7.
The use of correction algorithm improved the results for both spectrometers. For MMS-1, the root mean square error (RMSE) of the target signal during the time of flight decreased 36%. In case of NIR-PGS-1.7, RMSE of the target signal decreased 68%.
Due to lack of field data, the algorithm was not validated in field conditions for NIR-PGS-2.2. However, the modelled dark signal agrees well with the data measured in the refrigerator experiment, as can be seen in Figure
Although the physical model of dark current temperature dependence of an uncooled junction-based detector can be described with an exponential function, a second-order polynomial function was used instead. In a limited temperature range, the polynomial function is accurate enough. The coefficients of polynomial terms are linearly related to integration time and are not very sensitive to small fitting errors. In case of the exponential function, the dependence of coefficients on integration time is more complex and even a small change in the exponential terms coefficients causes a significant change in the result.
The dark signal temperature dependence of MMS-1 and NIR-PGS-1.7 are very different. The reason is that NIR-PGS-1.7 has an InGaAs detector array which is thermoelectrically cooled and kept at a constant temperature. Nevertheless, there is still some correlation between the temperature and dark signal. When ambient temperature is increased, the setpoint voltage of PELTIER-tc also increases which causes the slight decrease of sensor array temperature. This may be caused by the increased Peltier current which warms the PELTIER-tc module. When the module is heated with a hot air gun, setpoint voltage also increases. However, this cannot be the cause of the temperature dependence visible in Figure
Despite having a thermally stabilized detector, NIR-PGS-2.2 has a very strong dark signal temperature dependence. One possible explanation to this is that in addition to dark current, thermal background may become more predominant at longer wavelengths. Only the sensor chip is cooled, but it is still sensitive to thermal radiation from surrounding mechanics [
The sensor temperatures in Figures
It is clear from (
Parameter
If the same integration time is used for target and dark signal measurements,
A linear detector array consists of several independent detectors. The dark signal of each detector should be dealt with independently. The need for an individual set of correction coefficients for each band should be evident when looking at Figures
Figures
The measured target signal may have high dynamic range. The signal reflected from green vegetation under natural illumination conditions measured with MMS-1 has about 100 times difference between 350 nm and 750 nm bands. If signal at 750 nm band is 20000 DN, then dark signal error of 10 DN is insignificant for this band, but at the same time it is already 5% of the signal at 350 nm band.
Integration time and temperature are the two factors that have the strongest effect on the dark signal of a spectrometer. Integration time is always known, but it is not necessarily the same for all the measurements. Miniature spectrometer modules with uncooled sensor arrays do not have an internal thermistor for measuring the temperature of the sensor array. The spectrometers with cooled sensor arrays have a thermistor inside the sensor which is used for controlling the Peltier current. In this case, the dark signal temperature dependence is not caused by the sensor but can still be significant and should be taken into account, especially for long wavelength-type InGaAs sensors. External temperature sensor should be added to the spectrometer module and temperature should be recorded during the measurements. The temperature dependence correction method for miniature spectrometer modules described in this paper makes it possible to estimate dark signal at any temperature and integration time within reasonable range. Only six parameters for each band and one temperature modelling parameter common to all bands are needed. In field conditions, it is not always possible to take frequent dark signal readings during spectral measurements. If temperature is recorded during the measurement, this method can be used for estimating dark signal for every single spectral measurement.
This study was supported by research Grants nos. 7725 and 6812 from the Estonian Science Foundation. The author would like to thank Raul Kangro and Helina Kitsing for discussion on the modelling of effective temperatures. Valuable comments by Andres Kuusk and Jan Pisek are greatly appreciated.