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Time correlated pixel-by-pixel calibration for quantification and signal quality control during solute imaging
Sensors and Actuators B 115 (2006) 263–269
Time correlated pixel-by-pixel calibration for quantification and signal quality control during solute imaging Niklas Str¨omberg ∗ , Stefan Hulth Department of Chemistry, G¨oteborg University, SE-412 96 G¨oteborg, Sweden Received 22 June 2005; accepted 19 September 2005 Available online 27 October 2005
Abstract Analytical protocols for normalization of artifacts and signal quality control are crucial in the design of intensity-based imaging optodes. In this study, we demonstrate how the time correlated pixel-by-pixel calibration (TCPC) technique could be used to predict analytical sensitivity, limit of detection (LOD) and determination of signal variation (relative standard deviation, R.S.D.) at a pixel level throughout measurements without separate tests. In addition, LOD from the TCPC protocol was used to define the operational lifetime of the sensor. The technique was tested on a recently developed imaging ammonium optode. The predicted parameters using TCPC agreed well with the determinations of the parameters using standard analytical protocols. Predicted limit of detection was 0.7 × 10−6 M compared to 1.3 × 10−6 M determined through a separate LOD determination. The operational lifetime of the optode was 280 h compared to the actual value of 286 h. When exposed to a soil matrix the operational lifetime was significantly reduced to 128 h. The decrease in sensor performance was efficiently tracked by all the statistical parameters, e.g. during a total experimental period of 234 h, the analytical sensitivity changed from 3 × 10−6 M to 14 × 10−6 M between 125 × 10−6 M and 250 × 10−6 M. The technique is exemplified by a long-term (∼10 days) test of a recently developed ammonium fluorosensor, and high-resolution imaging of ammonium concentrations in porous media following dissolution of a fertilizer stick in soil. © 2005 Elsevier B.V. All rights reserved. Keywords: Imaging; Optode; Ammonium; Time correlated pixel-by-pixel calibration; TCPC; Drift
1. Introduction One of the major benefits from optical sensors with chemical recognition (optodes) is that signals can be transferred to imaging sensors. The often small-scale, non-steady-state and heterogeneous characteristics of natural environments make imaging optodes an interesting complement, or alternative, to ion selective electrodes (ISEs) for solute detection. The major drawbacks using ISEs in such systems include electrode brittleness, extensive replication to cover large areas, and limited resolution due to electrode size, which normally make the measurements laborious and extremely time consuming. Nevertheless, using imaging optodes to distinguish the subtle changes in analyte concentrations with high spatial and temporal resolution make great demand on the precision of the measurements made in each pixel.
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Corresponding author. Tel.: +46 31 7722784; fax: +46 31 7722785. E-mail addresses: [email protected] (N. Str¨omberg), [email protected] (S. Hulth). 0925-4005/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2005.09.012
The general principle of imaging optodes is to immobilize solute specific indicators onto/within thin-layer plastic films and fix these onto transparent supports. The sensor in contact with the sample is illuminated using appropriate wavelengths and the emitted fluorescence is captured with a camera. The main overall drawback of intensity-based sensors include leakage and bleaching of reagents, and subsequent drift in signal over time [1]. Large efforts have been undertaken to minimize these problems, e.g. by the development and use of more photo-stable fluorescent dyes and various derivatization and immobilization techniques [2]. In addition to the drift in fluorescence, artifacts associated with e.g. a variable effective dye content and short/long-term variations in excitation light intensity are normally not automatically compensated for and will, thus, interfere with the analytical signal. In contrast to fiber optic chemical sensors, imaging optodes might also suffer from a Gaussian intensity distribution due to the transfer of excitation and emission light through glass lenses in the optical system. Procedures and analytical protocols for normalization of artifacts and signal quality control are therefore crucial in the design of intensity-based imaging optodes.
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For imaging devices, flat fielding [3] and pixel-by-pixel calibration [4] are widely used techniques to compensate for uneven illumination and individual pixel sensitivity, as well as for eventual aberrations in the optical system. However, drift in signal due to photo bleaching and dye leakage is normally not compensated for using these techniques. Ratiometric protocols generally compensate for short-term variations in e.g. excitation light intensity and uneven illumination [5], as well as a heterogeneous distribution of the indicator dye [6]. Additionally, it is generally assumed that fluorescent ratiometry will normalize signal drift over time [1]. Commonly, these sensing schemes make use of wavelength ratiometric probes that are specific to the analyte. A versatile alternative to wavelength ratiometric probes is to utilize the wavelength shift following the transfer of a solvent or potential sensitive indicator dye across a hydrophilic/hydrophobic interface when exposed to the analyte [7]. The fluorescence ratio encompasses the fluorescence emitted from dye molecules in either phase. This approach has been successfully used to image trans-membrane potentials of cells, cell organelles, and membrane vesicles [7–9]. A ratiometric protocol using the solvent sensitive Merocyanine 540 (MC 540) has recently been developed, tested and thoroughly evaluated for an ammonium [5] fluorosensor. Despite normalization procedures aimed to compensate for the systematic drift during measurements, the sensor was found to encounter drawbacks associated with insufficient long-term stability and sensor drift over time (∼10 days). A similar drift in fluorescence ratio has also been recognized for the wavelength ratiometric calcium probe Indo-1 which drifted more than 15% following only 10 min of illumination [10]. These studies imply that ratiometric approaches not necessarily remove drift over time. In order to circumvent this problem, we previously introduced a time correlated pixel-by-pixel calibration (TCPC) procedure for imaging sensors that more or less completely removed time-dependent drift in response [11]. An additional feature of the used calibration technique was the unique possibility to determine the quality of the signal throughout measurements. The overall objective of this study was to demonstrate how the TCPC technique directly could be used to determine analytical sensitivity, limit of detection (LOD) and relative signal variation (i.e. relative standard deviation, R.S.D.) at a pixel level during measurements. In addition, LOD estimated from the calibration procedure was used to define the operational lifetime of the sensor. High-resolution imaging of ammonium concentrations in porous media following dissolution of a fertilizer stick in soil was used as a representative example of a sensor application including signal quality control of the sensing film. 2. Experimental To validate the statistical parameters associated with the calibration technique, ammonium standard solutions (Itot,NaCl+NH+ = 3.0 × 10−3 M) were injected into a custom4 made flow cell during 10 days of experiments. Additionally, a short-time experiment (∼1 day) was performed to measure
ammonium concentration in porous media and thereby illustrate sensor performance and the ratiometric normalization technique in a complex matrix using the statistical parameters described below. 2.1. Ammonium sensor configuration and general principles of the sensing mechanism The general configuration of the ammonium sensor membrane is a detergent-free, two-phase system of 2(dodecyloxy)benzonitrile emulsified in a hydrogel (HYPANTM , HN 80). The hydrogel was doped with an ammonium ionophore (nonactin) and a potential sensitive dye (MC 540). Main principles of the sensing mechanism (coextraction) [12] are that ammonium ions from the sample diffuse into the hydrogel where they are bound to the cyclic carrier molecule nonactin. Phase transfer of the ammonium–nonactin complex across the hydrogel–ether interface most likely proceeds through the simultaneous incorporation or displacement of the negatively charged MC 540 dye molecule in the ether droplets. MC 540 is a solvent/potential sensitive indicator that change excitation:emission (λex :λem ) fluorescence properties upon shift of solvent [13–15]. The λex :λem -maxima of the sensor was separately determined in a spectrofluorometer (Fluoromax-2). In the sensor configuration applied, λex :λem -maxima were shifted from 520:570 nm in the hydrogel to 570:586 nm in the 2(dodecyloxy)benzonitrile emulsion. Quantification of ammonium concentrations during imaging was made through an image ratio (λex 572 nm :λem 592 nm )/(λex 520 nm :em 572 nm ) i.e. close to the λex :λem -maxima of the sensor. 2.2. Reagents and experimental set-up Chemicals and solvents were of analytical grade (PA; Sigma–Aldrich), and aqueous solutions were prepared using UV-oxidized ultra pure (Milli-Q) water. Preparation of sensing foils was performed according to the principles outlined previously [5,16]. In addition, a protective optical isolation (colorit 90) with excellent tear strength in water was attached to the surface of the sensor facing the sample. The sensor support facing the camera was marked with correction fluid (TippexTM ) to facilitate subsequent alignment of the images. The total thickness of the image sensor including the optical isolation was about 2 × 10−4 m. Prior to use, new sensor membranes were for about 5 h treated with solutions of an ionic strength corresponding to that of the samples (Itot,NaCl = 3.0 × 10−3 M). Experiments were performed in a temperature-controlled room at 12 ◦ C and 15% relative humidity. The sensor foil and backing were assembled onto one of two removable sides of a 100 ml custom-made flow cell. Calibration solutions were automatically pumped (100 ml min−1 ) into the flow cell for 20 min before imaging ammonium concentrations. At the end of the calibration procedure, the cell was flushed with blank solution (Itot,NaCl = 3.0 × 10−3 M) for at least 60 min to minimize possible carry-over from ammonium bound in the sensing membrane. Each sensor foil was calibrated before and after the experiments by exposure to ammonium calibrating solutions of 0, 125 and
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250 × 10−6 M for the 10-day experiment, and 0, 125, 250, 375, 500, 1000 and 2000 × 10−6 M for the experiment following ammonium dissolution from a fertilizer stick, respectively. The flow cell was filled with soil pre-treated with tap water before a dissolution experiment. A fertilizer stick (10 mm long and 5 mm in diameter) was carefully inserted into the soil, perpendicular to the sensor assembly. Images of ammonium concentrations during the dissolution of the fertilizer stick were captured during 13.9 h. 2.3. Imaging system A detailed and more complete description of the optical setup is presented elsewhere [11]. The imaging system consisted of a 300 W Xe UV–vis arc lamp (ORC), equipped with a computer controlled dual filter-changer with interference bandpass filters (520:572 nm; full width-half maximum, FWHM; 20:2 nm) at the excitation side. The imbalance in excitation light intensity was used to compensate for the lower fluorescence retrieved at 572 nm compared to at 592 nm when using equivalent excitation bandpass. This procedure significantly reduced the integration time for the images captured through the 572 nm emission bandpass filter. The filtered excitation light was transferred to the sample in a liquid light-guide through focusing lenses. Light emitted by the imaging sensor was collected through a Nikon macro lens and an infinity corrected achromatic lens package. To maximize the throughput of light, the emission bandpass filters (592:572 nm; FWHM 2:2 nm) were mounted in a filter wheel in the infinity region perpendicular to the optical axis between the achromatic lenses (f = 30 mm and 35 mm). The filtered fluorescence signal was detected by a 12-bit thermoelectrically chilled monochrome camera (SPOT RT) equipped with a Kodak KAI 2000 charged coupled device (CCD). The total time for each measurement was less than 3 min. In order to increase the dynamic range of the CCD, the camera was used in a 3 × 3 binning mode (533 pixel × 400 pixel). The data acquisition program (SPOT RT v 3.3) was controlled by a Windows-based P4-2.2 GHz computer.
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position. To remove systematic noise associated with the multiple image capture, images at each wavelength were dark noise subtracted before alignment to the same position. Images were averaged at each wavelength in order to suppress shot noise, and thereafter filtered (3 × 3 median) before and after image ratio. The image filtrations minimized possible mismatches in alignment of images and reduced the influence from eventual white and dark pixels without a major change in optical resolution [11]. For the applied set-up, the optical resolution including filtrations and assembled averaging was previously experimentally determined to 210 × 10−6 M [11]. Two calibration sets were made of stacked ratio images representing each level of the calibration solutions before and after the experiment, respectively. Intermediate concentrations between levels in the calibration set were predicted by linear table-look-up interpolation (Matlab) in each pixel (Fig. 1). Out of range concentrations, were predicted by linear extrapolation using the slope of the last interpolation. Two calibration sets consisting of two complete calibration curves in each pixel were linked at each level by a linear time-dependent response function [11]. Thus, fluorescence ratio in each pixel was evaluated using a unique calibration, individually determined at the time of image capture. The time to pixel calibrate a 100 pixel × 100 pixel image through a script in Matlab was about 2 s. 2.5. Limit of detection and analytical sensitivity To increase the signal-to-noise ratio (S/N) by the principles of ensemble averaging [17], images used for quantification were the average of 10 replicated tiff-images at each wavelength before ratio. The replicated tiff-images that made up the average image ratio were by the relation between the standard deviation
2.4. Image processing and time correlated pixel-by-pixel calibration Tagged image file format (tiff, 12 bit) images were captured using an f-number of 1.8 with 2 s (572 nm) and 10 s (592 nm) integration time, respectively. This file format automatically includes the time of image capture, information essential for the time correlated pixel-by-pixel calibration procedure. Dark noise was determined by collecting 10 images at each wavelength with the lens cap mounted on the macro lens. All experimental images and images used for sensor calibration were processed automatically through specifically designed scripts in Matlab (Mathworks Inc.) by importing two sets (2 × 10 images) of unaligned stacked images captured at 592 nm and 572 nm, respectively. Image alignment was, however, made manually using a script available in Matlab (control point selection tool; cpselect) and the pre-labeled support. Generally, alignment was only needed after the instrumentation, or the flow cell were moved out of
Fig. 1. General principles of the time correlated pixel-by-pixel calibration protocol. Ammonium concentrations between the actual data points in calibration set 1 (filled circles) and calibration set 2 (filled squares) were predicted by table look up interpolation (Matlab). Out of range (x > 1000 × 10−6 M) ammonium concentrations were predicted by a linear extrapolation of the 0–250 × 10−6 M and 750–1000 × 10−6 M levels, respectively. Predicted calibration curves, 53.7 (dotted lines) and 107.5 h (dashes lines) after start of the experiment were calculated from the two calibration sets (solid lines) through a linear time/response function. Shaded areas in the figure represents out of range concentrations.
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of replicates, and averaged replicates, i.e. standard error (2), also utilized to image analytical sensitivity and limit of detection at a pixel resolution. Thus, the noise in the replicated images that made up the image average (n = 10) at each wavelength was utilized to predict the noise of ten replicated image average using Eq. (2) (n = 10 × 10). Systematic errors are, however, normally not correspondingly cancelled [18]. The effect from systematic errors was, on the other hand, minimized since dark noise of the camera was removed before quantification. LD = 2t1−α,ν σ0 ;
ν ≥ 25
(1)
sm = s0 (n)−0.5 L∗D = 2t1−α,ν sm
(2)
4ν 4ν + 1
;
ν≥5
(3)
Two separate procedures were used to predict limit of detection of the individual pixels during imaging of ammonium concentrations: (i) linear interpolation of pixel LOD calculated from two consecutive calibrations; and (ii) linear interpolation of the fluorescence ratio in each pixel between two consecutive calibrations (Fig. 2A and B). In the direct approach, pixel LOD was calculated during calibrations, and pixel LOD values from two consecutive calibrations were individually linked by a linear function (Fig. 2A). Image LOD could thus not only be calculated at the time of calibration, but also predicted at a pixel resolution between and after calibrations assuming a linear change in response. In the indirect approach, a linear drift in fluorescence ratio was assumed between calibrations. Image LOD was calculated from a predicted calibration set based on the linear function of the fluorescence ratio between two consecutive calibrations (Fig. 2B). For both protocols, LOD in each pixel was calculated (predicted) according to the IUPAC recommendation 1995 (1) in conjunction with standard error (2) to correspond to LOD for image-averaged images (3) [18,19].
Fig. 2. Comparison between the various techniques used to predict limit of detection (LOD): (A) the direct approach, where LOD was calculated from ten individual ratio images and linearly linked to subsequent calculation of LOD; (B) the indirect approach, where values in each pixel of two time-separated measurements were linked with time. The standard deviation (S.D.) of 10 predicted ratio images (predicted calibration set) was thereafter used to calculate LOD.
Parameters denote limit of detection for samples exceeding 25 replicates (LD ), Student’s t-test probability of type 1 (t), false positive errors (α; P = 0.05), degrees of freedom (ν (n − 1)), standard deviation of the population (σ 0 ), standard error (sm ) for image averaged images, standard deviation of a sample of blank measurements (s0 ) and number of blank replicates (n), respectively. Limit of detection (L∗D ) was calculated for a restricted number of replicates (6 < n < 26) according to Eq. (3) using the correction factor (4ν/(4ν + 1)), which implies a difference <1% compared to an infinite number of replicates [18,19] (Eq. (1)). The predicted LOD was compared to a standard LOD determination in a separate test of 20 averaged images. One of the major benefits from sensors compared to a discrete sampling protocol with subsequent analysis is that changes in analyte concentration over time can be determined. The smallest difference in concentration that can be distinguished and resolved between two levels in the calibration curve (analytical sensitivity, d) is related to the standard deviation of the two signals and their absolute concentration. Analytical sensitivity of the image sensor was predicted at a pixel resolution throughout experiments using the same protocol as was used to estimate LOD; i.e. the indirect approach. Eq. (4) has been proposed for sensitivity in quantitative analysis [20]. d = (t1−α/2 + t1−β )sm (2)0.5 (b)−1
(4)
The smallest difference in concentration (d) that can be resolved at a specific concentration is based on the t-values (α = 0.05 two-sided; β = 0.05 one-sided t-test) for the numbers of degrees of freedom with which the standard error (sm (Eq. (2))) was determined. In our case d = 5.76sm /b. The parameter b denotes the slope of the calibration curve between the two concentration data points. 2.6. Predicted operational lifetime and relative standard deviation of measurements The operational lifetime of the sensor was defined for an average of 2500 centered pixels according to criteria corresponding to an average LOD in each pixel of 10 × 10−6 M. Both the direct and the indirect approaches were evaluated and compared to a sensor lifetime derived from interpolating the two concentrations closest to the set criteria. This latter lifetime was considered as the correct operational lifetime of the sensor. Relative standard deviation of the response in each pixel of 10 averaged images was predicted using the TCPC protocol (the indirect method) together with the experimental image and standard error (Eq. (2)). For example, the experimental image was calibrated using a unique calibration at the time of capture calculated through time correlated pixel calibration in each pixel. The standard deviation of the response (Fig. 1) was derived and recalculated to correspond to average (10) images. Finally, the standard deviation (S.D.) was divided by the average value in each pixel to obtain the relative standard deviation at a pixel resolution.
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3. Results and discussion
3.2. Operational lifetime
3.1. Limit of detection and analytical sensitivity
The drift in fluorescence ratio and calculated image LOD was utilized to define the operational lifetime of the ammoniumimaging optode in the specific sample matrix. Analytical sensitivity could in a similar way also constitute a parameter to define the operational lifetime (Eq. (4)). The operational lifetime of the optode using time correlated pixel-by-pixel calibration to calculate image LOD was 280 h (the indirect approach), and 350 h (the direct approach), respectively (Fig. 3). For comparison, interpolation of the two concentrations closest to the set criteria (average LOD of 10 × 10−6 M) corresponded to a lifetime of 286 h. This was considered as the correct operational lifetime of the sensor (Fig. 3). A sensor operational lifetime calculated using the indirect approach thus deviated only 2% from the correct value, compared to 22% using the direct approach.
The predicted LOD was found to be a good estimate of the actual LOD during measurements. Limit of detection from the assembled image average (n = 10) was 0.7 × 10−6 M, while LOD determined from the separate test (i.e. 10 replicated average, n = 10 × 10 images) was 1.3 × 10−6 M. Accompanying experimental investigations have demonstrated that a linear drift in fluorescence ratio over time could be approximated with good precision and accuracy [11]. We assumed that limit of detection was a sensor parameter with similar characteristics. However, in this investigation, we experimentally demonstrated that LOD of the ammonium imaging sensor changed exponentially, rather than linearly, over time (Fig. 3). Therefore, calculations of LOD using the direct approach relatively poorly predicted LOD of the images captured between calibrations. The indirect approach, however, provided a better estimate of LOD (giving an exponential shape) where residuals less than 1 × 10−6 M between modeled and measured LOD were found for images between the calibration sets (Fig. 3). Analytical sensitivity is an important parameter to evaluate the performance of the imaging ammonium sensor as the response curve might be non-linear [16] and change shape over time (Fig. 1). At a fixed time, analytical sensitivity was found proportional to analyte concentration, generally between 1 and 1.8% of the concentration investigated for a fresh sensor. However, as the sensor response degrades over time this value might change considerably. For example, during a total experimental period of 234 h analytical sensitivity changed from 3 (∼1%) to 14 × 10−6 M (∼6%) between 125 and 250 × 10−6 M.
Fig. 3. Comparison between averaged predicted () and actual (×) limit of detection (LOD) based on 2500 centered pixels. The dashed line represents a linear prediction of LOD (direct approach) between the calibrations, while the dotted line corresponds to LOD (indirect approach) predicted by the time correlated pixel-by-pixel calibration procedure. The intercept of the solid lines corresponds to sensor lifetime (∼280 h @ LOD < 10 × 10−6 M).
3.3. Ammonium imaging in a complex matrix As an example of sensor applications in heterogeneous and non-steady-state environments, the imaging sensor was used to study ammonium concentrations and diffusive transport in porous media. Release and mobilization of ammonium to the pore water following the dissolution of a fertilizer stick with a proclaimed long-term effect (60 days) was studied with time from insertion in soil. The statistical parameters LOD and analytical sensitivity were predicted and used for quality control of the retrieved signal (the indirect approach) during imaging. In addition, images from the dissolution experiment were supported by an image describing the predicted relative signal variation (relative standard deviation) between 10 replicated average images of ammonium concentrations (n = 10 × 10) at a pixel resolution (Fig. 4B). High-resolution imaging of ammonium concentrations close to the fertilizer stick visualized (as expected) sharp concentration gradients (200–4500 × 10−6 M) over distances of less than 10 mm (Fig. 4A). The highest values were predicted by extrapolation of the slope between 1000 and 2000 × 10−6 M in the calibration curve, i.e. clearly out of range. Furthermore, the top left corner indicated ammonium concentrations exceeding those found in immediate adjacent areas. However, the image displaying relative signal variation demonstrated an inconsistent sensor response in this region of the image (R.S.D. > 6%; Fig. 4B). An erratic response and a possible damage of the sensing film were supported also by the images of LOD (>10 × 10−6 M; Fig. 4C) and analytical sensitivity (>100 × 10−6 M; Fig. 4D). Similar arguments of an erratic response were demonstrated also in the lower left corner. Thus, images displaying the statistical parameters LOD and analytical sensitivity could be used in conjunction with images of the relative signal variation of measured concentrations for image quality control at a high spatial (2 × 10−4 M) and temporal (minutes) resolution throughout measurements. Important features of the TCPC protocol include the possibility to estimate the minimal detectable change in concentration (d), i.e. analytical sensitivity (Eq. (4)). For example, in the light blue region (1000–2000 × 10−6 M) close to the fertilizer stick (Fig. 4A) the predicted analytical sensitivity was on average 30 × 10−6 M
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could be detected at specific times. In addition, the technique facilitated unambiguous determination of the expected operational lifetime of individual sensor foils exposed to a specific matrix without a separate experiment. Evidently, the operational lifetime was found dependent on sample composition as there was a significant difference found in operational lifetime between sensors exposed to solution and soil, respectively. The predicted statistical parameters were most accurately determined using an indirect approach (using the drift in fluorescence ratio) rather than a direct calculation. Fluorescence ratio might drift significantly over time but even if there appears to be no drift in absolute terms, the S/N relation will definitely change over time. Regardless, time correlated pixel-by-pixel calibration provides analytical measures throughout the experiment and the total procedure efficiently removes artifacts as well as absolute drift if present. Acknowledgements The CCD camera was provided by Assoc. Prof. Franck Gilbert. We thank Tobias Larsson for Matlab assistance. This study was funded by the Swedish Natural Science Research Council (VR), the Foundation for Strategic Environmental Research (MISTRA), and the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (FORMAS). References Fig. 4. (A) Time correlated pixel-by-pixel calibrated ratio image of the dissolution of nutrients from a fertilizer stick, inserted in soil perpendicular to the image view. The inner frame defines the region of interest (ROI) used for calculation of the B–D images. The experimental image was captured 8.65 h after the first calibration. (B) Relative signal variation (relative standard deviation, R.S.D.) of the ROI. (C) Predicted LOD of ROI. (D) Predicted analytical sensitivity of ROI between 1000 × 10−6 M and 2000 × 10−6 M.
(Fig. 4D) at the time of capture. Thus, in this region signal changes less than 30 × 10−6 M were not statistically supported (P = 0.95). Over the center of the fertilizer stick the predicted LOD was on average (out of 2500 pixel) 1.4 × 10−6 M and the predicted operational lifetime was 128 h. The relative signal variation in this region was 0.26% (R.S.D.) representing the spread of 10 assembled images at the time of capture. Compared to a replicate sensor (sensor from same batch) exposed to solutions in the long-term experiment the operational lifetime was considerably lower (about half) in the soil sample. 4. Conclusions Statistical parameters such as analytical sensitivity, limit of detection and relative signal variation were directly (automatically calculated through scripts) predicted throughout measurements using the TCPC protocol. The technique was found useful for sensor quality control to highlight low response-areas of the sensor foil and to estimate the smallest change in signal that
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Time correlated pixel-by-pixel calibration for quantification and signal quality control during solute imaging Niklas Str¨omberg ∗ , Stefan Hulth Department of Chemistry, G¨oteborg University, SE-412 96 G¨oteborg, Sweden Received 22 June 2005; accepted 19 September 2005 Available online 27 October 2005
Abstract Analytical protocols for normalization of artifacts and signal quality control are crucial in the design of intensity-based imaging optodes. In this study, we demonstrate how the time correlated pixel-by-pixel calibration (TCPC) technique could be used to predict analytical sensitivity, limit of detection (LOD) and determination of signal variation (relative standard deviation, R.S.D.) at a pixel level throughout measurements without separate tests. In addition, LOD from the TCPC protocol was used to define the operational lifetime of the sensor. The technique was tested on a recently developed imaging ammonium optode. The predicted parameters using TCPC agreed well with the determinations of the parameters using standard analytical protocols. Predicted limit of detection was 0.7 × 10−6 M compared to 1.3 × 10−6 M determined through a separate LOD determination. The operational lifetime of the optode was 280 h compared to the actual value of 286 h. When exposed to a soil matrix the operational lifetime was significantly reduced to 128 h. The decrease in sensor performance was efficiently tracked by all the statistical parameters, e.g. during a total experimental period of 234 h, the analytical sensitivity changed from 3 × 10−6 M to 14 × 10−6 M between 125 × 10−6 M and 250 × 10−6 M. The technique is exemplified by a long-term (∼10 days) test of a recently developed ammonium fluorosensor, and high-resolution imaging of ammonium concentrations in porous media following dissolution of a fertilizer stick in soil. © 2005 Elsevier B.V. All rights reserved. Keywords: Imaging; Optode; Ammonium; Time correlated pixel-by-pixel calibration; TCPC; Drift
1. Introduction One of the major benefits from optical sensors with chemical recognition (optodes) is that signals can be transferred to imaging sensors. The often small-scale, non-steady-state and heterogeneous characteristics of natural environments make imaging optodes an interesting complement, or alternative, to ion selective electrodes (ISEs) for solute detection. The major drawbacks using ISEs in such systems include electrode brittleness, extensive replication to cover large areas, and limited resolution due to electrode size, which normally make the measurements laborious and extremely time consuming. Nevertheless, using imaging optodes to distinguish the subtle changes in analyte concentrations with high spatial and temporal resolution make great demand on the precision of the measurements made in each pixel.
∗
Corresponding author. Tel.: +46 31 7722784; fax: +46 31 7722785. E-mail addresses: [email protected] (N. Str¨omberg), [email protected] (S. Hulth). 0925-4005/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2005.09.012
The general principle of imaging optodes is to immobilize solute specific indicators onto/within thin-layer plastic films and fix these onto transparent supports. The sensor in contact with the sample is illuminated using appropriate wavelengths and the emitted fluorescence is captured with a camera. The main overall drawback of intensity-based sensors include leakage and bleaching of reagents, and subsequent drift in signal over time [1]. Large efforts have been undertaken to minimize these problems, e.g. by the development and use of more photo-stable fluorescent dyes and various derivatization and immobilization techniques [2]. In addition to the drift in fluorescence, artifacts associated with e.g. a variable effective dye content and short/long-term variations in excitation light intensity are normally not automatically compensated for and will, thus, interfere with the analytical signal. In contrast to fiber optic chemical sensors, imaging optodes might also suffer from a Gaussian intensity distribution due to the transfer of excitation and emission light through glass lenses in the optical system. Procedures and analytical protocols for normalization of artifacts and signal quality control are therefore crucial in the design of intensity-based imaging optodes.
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For imaging devices, flat fielding [3] and pixel-by-pixel calibration [4] are widely used techniques to compensate for uneven illumination and individual pixel sensitivity, as well as for eventual aberrations in the optical system. However, drift in signal due to photo bleaching and dye leakage is normally not compensated for using these techniques. Ratiometric protocols generally compensate for short-term variations in e.g. excitation light intensity and uneven illumination [5], as well as a heterogeneous distribution of the indicator dye [6]. Additionally, it is generally assumed that fluorescent ratiometry will normalize signal drift over time [1]. Commonly, these sensing schemes make use of wavelength ratiometric probes that are specific to the analyte. A versatile alternative to wavelength ratiometric probes is to utilize the wavelength shift following the transfer of a solvent or potential sensitive indicator dye across a hydrophilic/hydrophobic interface when exposed to the analyte [7]. The fluorescence ratio encompasses the fluorescence emitted from dye molecules in either phase. This approach has been successfully used to image trans-membrane potentials of cells, cell organelles, and membrane vesicles [7–9]. A ratiometric protocol using the solvent sensitive Merocyanine 540 (MC 540) has recently been developed, tested and thoroughly evaluated for an ammonium [5] fluorosensor. Despite normalization procedures aimed to compensate for the systematic drift during measurements, the sensor was found to encounter drawbacks associated with insufficient long-term stability and sensor drift over time (∼10 days). A similar drift in fluorescence ratio has also been recognized for the wavelength ratiometric calcium probe Indo-1 which drifted more than 15% following only 10 min of illumination [10]. These studies imply that ratiometric approaches not necessarily remove drift over time. In order to circumvent this problem, we previously introduced a time correlated pixel-by-pixel calibration (TCPC) procedure for imaging sensors that more or less completely removed time-dependent drift in response [11]. An additional feature of the used calibration technique was the unique possibility to determine the quality of the signal throughout measurements. The overall objective of this study was to demonstrate how the TCPC technique directly could be used to determine analytical sensitivity, limit of detection (LOD) and relative signal variation (i.e. relative standard deviation, R.S.D.) at a pixel level during measurements. In addition, LOD estimated from the calibration procedure was used to define the operational lifetime of the sensor. High-resolution imaging of ammonium concentrations in porous media following dissolution of a fertilizer stick in soil was used as a representative example of a sensor application including signal quality control of the sensing film. 2. Experimental To validate the statistical parameters associated with the calibration technique, ammonium standard solutions (Itot,NaCl+NH+ = 3.0 × 10−3 M) were injected into a custom4 made flow cell during 10 days of experiments. Additionally, a short-time experiment (∼1 day) was performed to measure
ammonium concentration in porous media and thereby illustrate sensor performance and the ratiometric normalization technique in a complex matrix using the statistical parameters described below. 2.1. Ammonium sensor configuration and general principles of the sensing mechanism The general configuration of the ammonium sensor membrane is a detergent-free, two-phase system of 2(dodecyloxy)benzonitrile emulsified in a hydrogel (HYPANTM , HN 80). The hydrogel was doped with an ammonium ionophore (nonactin) and a potential sensitive dye (MC 540). Main principles of the sensing mechanism (coextraction) [12] are that ammonium ions from the sample diffuse into the hydrogel where they are bound to the cyclic carrier molecule nonactin. Phase transfer of the ammonium–nonactin complex across the hydrogel–ether interface most likely proceeds through the simultaneous incorporation or displacement of the negatively charged MC 540 dye molecule in the ether droplets. MC 540 is a solvent/potential sensitive indicator that change excitation:emission (λex :λem ) fluorescence properties upon shift of solvent [13–15]. The λex :λem -maxima of the sensor was separately determined in a spectrofluorometer (Fluoromax-2). In the sensor configuration applied, λex :λem -maxima were shifted from 520:570 nm in the hydrogel to 570:586 nm in the 2(dodecyloxy)benzonitrile emulsion. Quantification of ammonium concentrations during imaging was made through an image ratio (λex 572 nm :λem 592 nm )/(λex 520 nm :em 572 nm ) i.e. close to the λex :λem -maxima of the sensor. 2.2. Reagents and experimental set-up Chemicals and solvents were of analytical grade (PA; Sigma–Aldrich), and aqueous solutions were prepared using UV-oxidized ultra pure (Milli-Q) water. Preparation of sensing foils was performed according to the principles outlined previously [5,16]. In addition, a protective optical isolation (colorit 90) with excellent tear strength in water was attached to the surface of the sensor facing the sample. The sensor support facing the camera was marked with correction fluid (TippexTM ) to facilitate subsequent alignment of the images. The total thickness of the image sensor including the optical isolation was about 2 × 10−4 m. Prior to use, new sensor membranes were for about 5 h treated with solutions of an ionic strength corresponding to that of the samples (Itot,NaCl = 3.0 × 10−3 M). Experiments were performed in a temperature-controlled room at 12 ◦ C and 15% relative humidity. The sensor foil and backing were assembled onto one of two removable sides of a 100 ml custom-made flow cell. Calibration solutions were automatically pumped (100 ml min−1 ) into the flow cell for 20 min before imaging ammonium concentrations. At the end of the calibration procedure, the cell was flushed with blank solution (Itot,NaCl = 3.0 × 10−3 M) for at least 60 min to minimize possible carry-over from ammonium bound in the sensing membrane. Each sensor foil was calibrated before and after the experiments by exposure to ammonium calibrating solutions of 0, 125 and
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250 × 10−6 M for the 10-day experiment, and 0, 125, 250, 375, 500, 1000 and 2000 × 10−6 M for the experiment following ammonium dissolution from a fertilizer stick, respectively. The flow cell was filled with soil pre-treated with tap water before a dissolution experiment. A fertilizer stick (10 mm long and 5 mm in diameter) was carefully inserted into the soil, perpendicular to the sensor assembly. Images of ammonium concentrations during the dissolution of the fertilizer stick were captured during 13.9 h. 2.3. Imaging system A detailed and more complete description of the optical setup is presented elsewhere [11]. The imaging system consisted of a 300 W Xe UV–vis arc lamp (ORC), equipped with a computer controlled dual filter-changer with interference bandpass filters (520:572 nm; full width-half maximum, FWHM; 20:2 nm) at the excitation side. The imbalance in excitation light intensity was used to compensate for the lower fluorescence retrieved at 572 nm compared to at 592 nm when using equivalent excitation bandpass. This procedure significantly reduced the integration time for the images captured through the 572 nm emission bandpass filter. The filtered excitation light was transferred to the sample in a liquid light-guide through focusing lenses. Light emitted by the imaging sensor was collected through a Nikon macro lens and an infinity corrected achromatic lens package. To maximize the throughput of light, the emission bandpass filters (592:572 nm; FWHM 2:2 nm) were mounted in a filter wheel in the infinity region perpendicular to the optical axis between the achromatic lenses (f = 30 mm and 35 mm). The filtered fluorescence signal was detected by a 12-bit thermoelectrically chilled monochrome camera (SPOT RT) equipped with a Kodak KAI 2000 charged coupled device (CCD). The total time for each measurement was less than 3 min. In order to increase the dynamic range of the CCD, the camera was used in a 3 × 3 binning mode (533 pixel × 400 pixel). The data acquisition program (SPOT RT v 3.3) was controlled by a Windows-based P4-2.2 GHz computer.
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position. To remove systematic noise associated with the multiple image capture, images at each wavelength were dark noise subtracted before alignment to the same position. Images were averaged at each wavelength in order to suppress shot noise, and thereafter filtered (3 × 3 median) before and after image ratio. The image filtrations minimized possible mismatches in alignment of images and reduced the influence from eventual white and dark pixels without a major change in optical resolution [11]. For the applied set-up, the optical resolution including filtrations and assembled averaging was previously experimentally determined to 210 × 10−6 M [11]. Two calibration sets were made of stacked ratio images representing each level of the calibration solutions before and after the experiment, respectively. Intermediate concentrations between levels in the calibration set were predicted by linear table-look-up interpolation (Matlab) in each pixel (Fig. 1). Out of range concentrations, were predicted by linear extrapolation using the slope of the last interpolation. Two calibration sets consisting of two complete calibration curves in each pixel were linked at each level by a linear time-dependent response function [11]. Thus, fluorescence ratio in each pixel was evaluated using a unique calibration, individually determined at the time of image capture. The time to pixel calibrate a 100 pixel × 100 pixel image through a script in Matlab was about 2 s. 2.5. Limit of detection and analytical sensitivity To increase the signal-to-noise ratio (S/N) by the principles of ensemble averaging [17], images used for quantification were the average of 10 replicated tiff-images at each wavelength before ratio. The replicated tiff-images that made up the average image ratio were by the relation between the standard deviation
2.4. Image processing and time correlated pixel-by-pixel calibration Tagged image file format (tiff, 12 bit) images were captured using an f-number of 1.8 with 2 s (572 nm) and 10 s (592 nm) integration time, respectively. This file format automatically includes the time of image capture, information essential for the time correlated pixel-by-pixel calibration procedure. Dark noise was determined by collecting 10 images at each wavelength with the lens cap mounted on the macro lens. All experimental images and images used for sensor calibration were processed automatically through specifically designed scripts in Matlab (Mathworks Inc.) by importing two sets (2 × 10 images) of unaligned stacked images captured at 592 nm and 572 nm, respectively. Image alignment was, however, made manually using a script available in Matlab (control point selection tool; cpselect) and the pre-labeled support. Generally, alignment was only needed after the instrumentation, or the flow cell were moved out of
Fig. 1. General principles of the time correlated pixel-by-pixel calibration protocol. Ammonium concentrations between the actual data points in calibration set 1 (filled circles) and calibration set 2 (filled squares) were predicted by table look up interpolation (Matlab). Out of range (x > 1000 × 10−6 M) ammonium concentrations were predicted by a linear extrapolation of the 0–250 × 10−6 M and 750–1000 × 10−6 M levels, respectively. Predicted calibration curves, 53.7 (dotted lines) and 107.5 h (dashes lines) after start of the experiment were calculated from the two calibration sets (solid lines) through a linear time/response function. Shaded areas in the figure represents out of range concentrations.
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of replicates, and averaged replicates, i.e. standard error (2), also utilized to image analytical sensitivity and limit of detection at a pixel resolution. Thus, the noise in the replicated images that made up the image average (n = 10) at each wavelength was utilized to predict the noise of ten replicated image average using Eq. (2) (n = 10 × 10). Systematic errors are, however, normally not correspondingly cancelled [18]. The effect from systematic errors was, on the other hand, minimized since dark noise of the camera was removed before quantification. LD = 2t1−α,ν σ0 ;
ν ≥ 25
(1)
sm = s0 (n)−0.5 L∗D = 2t1−α,ν sm
(2)
4ν 4ν + 1
;
ν≥5
(3)
Two separate procedures were used to predict limit of detection of the individual pixels during imaging of ammonium concentrations: (i) linear interpolation of pixel LOD calculated from two consecutive calibrations; and (ii) linear interpolation of the fluorescence ratio in each pixel between two consecutive calibrations (Fig. 2A and B). In the direct approach, pixel LOD was calculated during calibrations, and pixel LOD values from two consecutive calibrations were individually linked by a linear function (Fig. 2A). Image LOD could thus not only be calculated at the time of calibration, but also predicted at a pixel resolution between and after calibrations assuming a linear change in response. In the indirect approach, a linear drift in fluorescence ratio was assumed between calibrations. Image LOD was calculated from a predicted calibration set based on the linear function of the fluorescence ratio between two consecutive calibrations (Fig. 2B). For both protocols, LOD in each pixel was calculated (predicted) according to the IUPAC recommendation 1995 (1) in conjunction with standard error (2) to correspond to LOD for image-averaged images (3) [18,19].
Fig. 2. Comparison between the various techniques used to predict limit of detection (LOD): (A) the direct approach, where LOD was calculated from ten individual ratio images and linearly linked to subsequent calculation of LOD; (B) the indirect approach, where values in each pixel of two time-separated measurements were linked with time. The standard deviation (S.D.) of 10 predicted ratio images (predicted calibration set) was thereafter used to calculate LOD.
Parameters denote limit of detection for samples exceeding 25 replicates (LD ), Student’s t-test probability of type 1 (t), false positive errors (α; P = 0.05), degrees of freedom (ν (n − 1)), standard deviation of the population (σ 0 ), standard error (sm ) for image averaged images, standard deviation of a sample of blank measurements (s0 ) and number of blank replicates (n), respectively. Limit of detection (L∗D ) was calculated for a restricted number of replicates (6 < n < 26) according to Eq. (3) using the correction factor (4ν/(4ν + 1)), which implies a difference <1% compared to an infinite number of replicates [18,19] (Eq. (1)). The predicted LOD was compared to a standard LOD determination in a separate test of 20 averaged images. One of the major benefits from sensors compared to a discrete sampling protocol with subsequent analysis is that changes in analyte concentration over time can be determined. The smallest difference in concentration that can be distinguished and resolved between two levels in the calibration curve (analytical sensitivity, d) is related to the standard deviation of the two signals and their absolute concentration. Analytical sensitivity of the image sensor was predicted at a pixel resolution throughout experiments using the same protocol as was used to estimate LOD; i.e. the indirect approach. Eq. (4) has been proposed for sensitivity in quantitative analysis [20]. d = (t1−α/2 + t1−β )sm (2)0.5 (b)−1
(4)
The smallest difference in concentration (d) that can be resolved at a specific concentration is based on the t-values (α = 0.05 two-sided; β = 0.05 one-sided t-test) for the numbers of degrees of freedom with which the standard error (sm (Eq. (2))) was determined. In our case d = 5.76sm /b. The parameter b denotes the slope of the calibration curve between the two concentration data points. 2.6. Predicted operational lifetime and relative standard deviation of measurements The operational lifetime of the sensor was defined for an average of 2500 centered pixels according to criteria corresponding to an average LOD in each pixel of 10 × 10−6 M. Both the direct and the indirect approaches were evaluated and compared to a sensor lifetime derived from interpolating the two concentrations closest to the set criteria. This latter lifetime was considered as the correct operational lifetime of the sensor. Relative standard deviation of the response in each pixel of 10 averaged images was predicted using the TCPC protocol (the indirect method) together with the experimental image and standard error (Eq. (2)). For example, the experimental image was calibrated using a unique calibration at the time of capture calculated through time correlated pixel calibration in each pixel. The standard deviation of the response (Fig. 1) was derived and recalculated to correspond to average (10) images. Finally, the standard deviation (S.D.) was divided by the average value in each pixel to obtain the relative standard deviation at a pixel resolution.
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3. Results and discussion
3.2. Operational lifetime
3.1. Limit of detection and analytical sensitivity
The drift in fluorescence ratio and calculated image LOD was utilized to define the operational lifetime of the ammoniumimaging optode in the specific sample matrix. Analytical sensitivity could in a similar way also constitute a parameter to define the operational lifetime (Eq. (4)). The operational lifetime of the optode using time correlated pixel-by-pixel calibration to calculate image LOD was 280 h (the indirect approach), and 350 h (the direct approach), respectively (Fig. 3). For comparison, interpolation of the two concentrations closest to the set criteria (average LOD of 10 × 10−6 M) corresponded to a lifetime of 286 h. This was considered as the correct operational lifetime of the sensor (Fig. 3). A sensor operational lifetime calculated using the indirect approach thus deviated only 2% from the correct value, compared to 22% using the direct approach.
The predicted LOD was found to be a good estimate of the actual LOD during measurements. Limit of detection from the assembled image average (n = 10) was 0.7 × 10−6 M, while LOD determined from the separate test (i.e. 10 replicated average, n = 10 × 10 images) was 1.3 × 10−6 M. Accompanying experimental investigations have demonstrated that a linear drift in fluorescence ratio over time could be approximated with good precision and accuracy [11]. We assumed that limit of detection was a sensor parameter with similar characteristics. However, in this investigation, we experimentally demonstrated that LOD of the ammonium imaging sensor changed exponentially, rather than linearly, over time (Fig. 3). Therefore, calculations of LOD using the direct approach relatively poorly predicted LOD of the images captured between calibrations. The indirect approach, however, provided a better estimate of LOD (giving an exponential shape) where residuals less than 1 × 10−6 M between modeled and measured LOD were found for images between the calibration sets (Fig. 3). Analytical sensitivity is an important parameter to evaluate the performance of the imaging ammonium sensor as the response curve might be non-linear [16] and change shape over time (Fig. 1). At a fixed time, analytical sensitivity was found proportional to analyte concentration, generally between 1 and 1.8% of the concentration investigated for a fresh sensor. However, as the sensor response degrades over time this value might change considerably. For example, during a total experimental period of 234 h analytical sensitivity changed from 3 (∼1%) to 14 × 10−6 M (∼6%) between 125 and 250 × 10−6 M.
Fig. 3. Comparison between averaged predicted () and actual (×) limit of detection (LOD) based on 2500 centered pixels. The dashed line represents a linear prediction of LOD (direct approach) between the calibrations, while the dotted line corresponds to LOD (indirect approach) predicted by the time correlated pixel-by-pixel calibration procedure. The intercept of the solid lines corresponds to sensor lifetime (∼280 h @ LOD < 10 × 10−6 M).
3.3. Ammonium imaging in a complex matrix As an example of sensor applications in heterogeneous and non-steady-state environments, the imaging sensor was used to study ammonium concentrations and diffusive transport in porous media. Release and mobilization of ammonium to the pore water following the dissolution of a fertilizer stick with a proclaimed long-term effect (60 days) was studied with time from insertion in soil. The statistical parameters LOD and analytical sensitivity were predicted and used for quality control of the retrieved signal (the indirect approach) during imaging. In addition, images from the dissolution experiment were supported by an image describing the predicted relative signal variation (relative standard deviation) between 10 replicated average images of ammonium concentrations (n = 10 × 10) at a pixel resolution (Fig. 4B). High-resolution imaging of ammonium concentrations close to the fertilizer stick visualized (as expected) sharp concentration gradients (200–4500 × 10−6 M) over distances of less than 10 mm (Fig. 4A). The highest values were predicted by extrapolation of the slope between 1000 and 2000 × 10−6 M in the calibration curve, i.e. clearly out of range. Furthermore, the top left corner indicated ammonium concentrations exceeding those found in immediate adjacent areas. However, the image displaying relative signal variation demonstrated an inconsistent sensor response in this region of the image (R.S.D. > 6%; Fig. 4B). An erratic response and a possible damage of the sensing film were supported also by the images of LOD (>10 × 10−6 M; Fig. 4C) and analytical sensitivity (>100 × 10−6 M; Fig. 4D). Similar arguments of an erratic response were demonstrated also in the lower left corner. Thus, images displaying the statistical parameters LOD and analytical sensitivity could be used in conjunction with images of the relative signal variation of measured concentrations for image quality control at a high spatial (2 × 10−4 M) and temporal (minutes) resolution throughout measurements. Important features of the TCPC protocol include the possibility to estimate the minimal detectable change in concentration (d), i.e. analytical sensitivity (Eq. (4)). For example, in the light blue region (1000–2000 × 10−6 M) close to the fertilizer stick (Fig. 4A) the predicted analytical sensitivity was on average 30 × 10−6 M
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could be detected at specific times. In addition, the technique facilitated unambiguous determination of the expected operational lifetime of individual sensor foils exposed to a specific matrix without a separate experiment. Evidently, the operational lifetime was found dependent on sample composition as there was a significant difference found in operational lifetime between sensors exposed to solution and soil, respectively. The predicted statistical parameters were most accurately determined using an indirect approach (using the drift in fluorescence ratio) rather than a direct calculation. Fluorescence ratio might drift significantly over time but even if there appears to be no drift in absolute terms, the S/N relation will definitely change over time. Regardless, time correlated pixel-by-pixel calibration provides analytical measures throughout the experiment and the total procedure efficiently removes artifacts as well as absolute drift if present. Acknowledgements The CCD camera was provided by Assoc. Prof. Franck Gilbert. We thank Tobias Larsson for Matlab assistance. This study was funded by the Swedish Natural Science Research Council (VR), the Foundation for Strategic Environmental Research (MISTRA), and the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (FORMAS). References Fig. 4. (A) Time correlated pixel-by-pixel calibrated ratio image of the dissolution of nutrients from a fertilizer stick, inserted in soil perpendicular to the image view. The inner frame defines the region of interest (ROI) used for calculation of the B–D images. The experimental image was captured 8.65 h after the first calibration. (B) Relative signal variation (relative standard deviation, R.S.D.) of the ROI. (C) Predicted LOD of ROI. (D) Predicted analytical sensitivity of ROI between 1000 × 10−6 M and 2000 × 10−6 M.
(Fig. 4D) at the time of capture. Thus, in this region signal changes less than 30 × 10−6 M were not statistically supported (P = 0.95). Over the center of the fertilizer stick the predicted LOD was on average (out of 2500 pixel) 1.4 × 10−6 M and the predicted operational lifetime was 128 h. The relative signal variation in this region was 0.26% (R.S.D.) representing the spread of 10 assembled images at the time of capture. Compared to a replicate sensor (sensor from same batch) exposed to solutions in the long-term experiment the operational lifetime was considerably lower (about half) in the soil sample. 4. Conclusions Statistical parameters such as analytical sensitivity, limit of detection and relative signal variation were directly (automatically calculated through scripts) predicted throughout measurements using the TCPC protocol. The technique was found useful for sensor quality control to highlight low response-areas of the sensor foil and to estimate the smallest change in signal that
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