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Sun-induced leaf fluorescence was inferred by using high resolution (0.5 cm-1) radiance measurements and simulated spectra of the solar irradiance at the ground level, in the region of the O2-B absorption band. The minimization of a cost function was performed in the Fourier transform domain in order to make an accurate fit of the Instrumental Line-Shape that convoluted the simulated spectrum. Second- order polynomials were used to fit the leaf fluorescence and reflectance in the 100-cm-1-wide spectral window. The scale and the instrumental conversion factor were also fitted in order to obtain an accuracy that could not be attained by using the radiance measurements alone.
©2008 Optical Society of America
1. Introduction
The sun-induced fluorescence of plants in the red and far-red part of the visible- near infrared spectrum is a very small emission that is due to chlorophyll. It represents about 1% of the radiation which plants receive from the sun, and its emission adds to a generally much higher reflected radiation signal [1].
For the remote sensing of vegetation, one of the most useful frequency ranges has been located in the atmospheric O2-B absorption band [1]. Interest in this band was motivated by its position (i.e. next to the maximum of the red fluorescence band) and by the advantage of its having a reduced reflected signal. Furthermore, the molecular oxygen absorption of the sun radiance influences chlorophyll fluorescence minimally in this spectral window. Absolute measurements of chlorophyll fluorescence are very difficult to obtain and need careful calibration.
Generally, to be independent of the instrument characterization and detection geometry as much as possible [2], the on-ground radiance measurements have to be normalized to a reference spectrum.
Unfortunately, signals deriving from reference and vegetation radiance measurements may differ in amplitude and noise for practical reasons that are linked to the measurement set-up [3]. This fact can represent a source of additional uncertainty.
Furthermore, for any feasibility study of fluorescence retrieval from space, a simulation is required in order to assess the sensitivity of plant reflectance and fluorescence to any variation in the atmospheric factors that determine the attenuation of radiance from the top of the atmosphere (TOA) to the bottom of atmosphere (BOA) and back.
In this paper, we demonstrate an intelligent use of the simulated function of the solar radiance transmission. In particular, we were able to determine certain instrumental characteristics by means of a dedicated fitting process that made use of a the simulated source and a reference spectrum. Estimated values were employed for retrieving sun-induced fluorescence and reflectance with high accuracy.
In the final section, we performed a comparisons of our results with those deduced by means of a direct method which employed the actual spectra reflected by the reference and by the vegetation, where the latter included the fluorescence. From this comparison we could appreciate the importance of being able to make a fit of the instrumental characteristics.
To carry out the analysis, we availed of the knowledge of the chlorophyll fluorescence spectral features that were deduced by means of techniques based on laser induced fluorescence. These techniques make it possible to derive a disperse spectrum by using a fixed lasing wavelength. They are used to correlate the plant stresses to a change in the fluorescence spectrum, and are possible candidate to future space missions.
The work that we present was devoted to an actual mission which is based on passive (i.e. The work that we present was devoted to an actual mission based on passive (i.e. sun-induced) leaf radiance measurements.
2. Chlorophyll fluorescence and reflectance retrieval
The mathematical model that we used to retrieve fluorescence and reflectance was represented by the equations reported below, as a function of the wavenumber k:
where ML (k) is the measurement of the radiation emitted and reflected by the leaf, MW (k) is the measurement of the radiation reflected by the reference, S(k) is the source spectrum (time- and place-dependent), R(k) is the leaf reflectance, F(k) is the leaf fluorescence, and ILS(k) is the Instrumental Line Shape by which the simulated source was convoluted. In (1) and (2), β is the factor that converts counts to irradiance, since the measurements were in count units and the source was in W/m2/cm-1. In (1) the reflectance of the reference was assumed to be unity.
3. The source spectrum
The TOA solar spectrum was computed as a Planck function at 5800 K, and was corrected by means of a forward model that simulates the atmosphere [4] in order to deduce the BOA solar spectrum.
The BOA solar spectrum (referred to as “source spectrum” here as follows) was computed for a “clear sky” condition at a sampling rate of 0.02 cm-1. The section of the spectrum within the detection window used in the experiment is shown in Fig. 1.
The attenuation effects of solar irradiance - e.g. aerosols (scattering from particles) and molecular (Rayleigh) scattering - that modify the simulated source can be accounted for by means of a (slightly) wavelength-dependent multiplicative-factor applied to the source. These effects will be considered in detail in a future paper.
The method that we propose can also be used with other sources, since only one set of independently simulated data is needed to represent the source in the retrieval process.
4. Experimental apparatus
Radiance measurements were performed with a high resolution dispersion apparatus consisting of a low-stray-light double monochromator and high f-number equal to 7.8. An intensified diode array of 510 active elements, each 25 µm-wide, was used to detect the filtered light. The resolution of the system was limited by the single element dimension of the array, which represents a standard for commercially-available instruments. The same single element dimension determined the sampling of the measured spectrum, which corresponded to approximately 0.2 cm-1 in the spectral window used in the experiment.
The measured full width at half maximum FWHM of a He-Ne laser line, which was detected using the same entrance slit width of 40 µm used in the experiment, corresponded roughly to a Voigt function that took into account the effects of both the double monochromator and the detection system. The fitted Voigt function that represented the Instrumental Line Shape (ILS) had a FWHM equal to 0.54 cm-1. The Lorentzian contribution was mainly due to cross-talk between adjacent elements.
The radiation from a single leaf was collected using an optic fiber, and was fed directly into the entrance slit of the monochromator without the use of any adapting optics. This simplified coupling penalized the amount of energy that could be collected, as the radiation was partially stopped by the slit. However, it avoided aberrations caused by additional collecting and focusing optics in front of the slit. A Spectralon standard (Labsphere, North Sutton, NH) was used for the diffuse-reflectance white reference panel.
All data were collected over the same integration time (i.e. 12 s). This fact ensured almost the same background contribution to signals collected from both the leaf and reference surfaces. This single scan time was chosen in order to obtain an adequate integrated signal with respect to the noise, while keeping the period still comparable to the one available for measurements from satellites. The signal background was subtracted at each scan.
5. The chlorophyll fluorescence bands
The red fluorescence band of the leaves is correlated to the chlorophyll content. It peaks in a range between 685 and 690 nm [5], and is about 30 nm at FWHM. The far red chlorophyll fluorescence band is sited in the far red and peaks at about 760 nm. Its red tail contributes in part to the signal that we detected in the O2-B absorption band which is mainly due to the red fluorescence band.
The shape of these bands was found to be almost Gaussian, as revealed by means of fittings performed on the leaf radiances of different plants measured at low resolution, using a laser source to induce fluorescence [6].
The peak position and intensity of the red fluorescence of leaves undergo variations due to stresses and environmental changes, and can be utilized for monitoring the status of health of plants. For example, a line-shape study in this regard was performed in [7].
Since the detection window was situated around 687 nm, i.e. very close to an expected maximum of the red fluorescence band, a second order polynomial was considered sufficiently accurate for modelling fluorescence in this relatively small (5 nm) part of the chlorophyll fluorescence band and for discovering a peak [8].
Furthermore, since reabsorption influences the fluorescence signal from the rear and front parts of the leaves [9] in a different way, we performed the measurements on both the front and rear sides of a leaf, in order to put the method to the test by detecting these differences.
A second order polynomial was also used to fit reflectance, because no inflection point for this function is expected in this part of the spectrum.
5. Three-step fitting
The procedure that we used consisted of three minimization steps for determining the: 1) ILS(k), β and wavenumber scale, 2) fine tuning of the scale, ILS(k) and β, and 3) reflectance and fluorescence.
Steps 1) and 2) were used to determine the instrumental parameters. Notwithstanding it was possible in principle to do the procedure in one step, we preferred to perform it in two separated step for the highest control of the instrument characteristics. In particular the first step was the most general wavenumber scale construction while the second step was addressed to a local resampling to correct any pixel failure.
5.1 Instrumental parameters
An adequately accurate instrumental line shape is needed to convolve the simulated source. In accordance with the results obtained by means of a He-Ne laser, a Voigt function was used to fit the ILS(k) profile. To increase the precision, we made this analysis in the Fourier transform domain.
For β, we considered a first order (2 parameters) polynomial function of the intensity on the sensor I (k).
In practice, we used the equations in (1) in order to deduce both ILS(k) and β in correspondence with the largest signal variations and lowest signal-to-noise ratio. In fact, the reference signal variations were larger than those of the leaf signal, and were characterised by a lower noise. Hence, the use of (1) resulted in a more accurate determination of β. Furthermore, no signal extrapolation was necessary to deduce the non-linearity in the leaf radiance measurements. Moreover, we chose to down-sample the source to a rate close to the expected mean value of the experimental samples.
Since in our set-up different detector elements were related to different wavenumber increments, the scale of the instrument in step 1) was fitted by means of a second-order polynomial function of k (three parameters), for the transformation from element units of the linear detector to wavenumber increments. The 4 (for ILS and β)+3 (for the scale) values found at the end of step 1) were the initial guesses we used in step 2).
In step 2), the mapping between the ordinal position of each pixel and its corresponding wavenumber was represented by a spline function linked to 301 points uniformly distributed over the full range. The individual tuning ranges, dk, were constrained in order to make them narrower than the corresponding scale samplings. In this case, we minimized a cost function based on 509 equations of type (1) for a total number of 301 (for the limits of 300 different tuning ranges) +4 (for ILS and β) fitted parameters.
The new scale was used to resample the radiance measurements on the source scale.
5.2 Fluorescence and reflectance parameters
In step 3), the 4 values for β and ILS that we found at the end of step 2) were used as initial guesses in the set of equations in (2). The 509 cost functions were minimized with respect to 6 new parameters for deducing fluorescence (3 parameters) and reflectance (3 parameters).
6. Modeling of β parameter
The analysis of residuals as a function of the source intensity was first performed by making β equal to an unknown constant in both (1) and (2). The residuals of the reference radiance ResW, normalized to the maximum intensity of the source Smax, are shown in Fig. 2(a) as a function of the normalized source intensity S/Smax.
Non-linear behavior is clearly visible for S/Smax values that were greater than 0.8. The same feature was not equally noticeable in the much noisier residuals of the leaf radiance, the intensity variations of which as a function of k were about six times smaller compared to those of the white screen radiance.
Fig. 2. Normalized residuals as a function of source intensity for a constant (a) and variable (b) β parameter.
In Fig. 2(b) we show the residuals resulting from the minimization process performed with the assumption of a variable β.
The percentage non-linearity NL was computed as:
and was found to be 2.4% for the leaf signal. In (3), I was the detected signal, L(I) was the best linear approximation of I/β,, Lmax and Imax were the maximum fitted and measured values, respectively, and Imin was the minimum measured value. In fact, the NL was found to be effectively very small, and could be deduced only from extremely accurate measurements.
7. Measured and simulated reference radiance spectra
The simulated radiance spectrum of the reference white panel sW(k)=S(k) ⊗ ILS(k) and W(k), the measured radiance Mw(k) multiplied by β, are shown in Fig. 3 after their normalisation to Smax. Both sW(k) and W(k) derived from the results of the fitting step 2). The residuals of the fit (ResW/Smax) are also shown in the same figure.
There were four types of contributions to the residuals: a) lines that were not properly modelled by the source, such as those close to 14525 cm-1, b) false signals due to the array detector that were particularly evident at the end of the spectral window in correspondence with 14458 cm-1, c) noise fluctuations of about 2% of Smax, which were visible in the continuum, d) oscillations due to lines that were barely resolved, such as those close to 14555cm-1.
In fine-tuning the scale, we found that the range with the maximum deviation of the scale (37% of the frequency sampling interval) was close to 14555 cm-1.
The FWHM of the ILS was 0.50 cm-1, which derived from a variation in the Gaussian standard deviation σ of +27% and in the Lorentzian half width γ of -30%, as compared to the corresponding values that were found in the evaluation of the He-Ne laser line shape.
8. Measured and simulated leaf radiance spectra
In Fig. 4, we show the simulated leaf front radiance sLF(k)=[S(k)R(k)+F(k)] ⊗ ILS(k) and LF, the measured leaf front radiance ML(k) multiplied by β, both normalized to Smax.
In this case, the spurious effects of type a) were less evident in the normalized ResLF/Smax residuals (lower trace in Fig. 4), because the mean value of the measurement noise was higher than that of the white screen.
To highlight the sensitivity of the method, in Fig. 5 we show the ResLNF/Smax residuals that were obtained by removing fluorescence in the model and by eliminating F(k) in (2). Consequently, we found that the method rejected the fluorescence signal that appeared in the ResLNF/Smax residuals while the reflectance was left almost unchanged.
In the same figure, we also show ResLF/Smax. The ResLNF/Smax residuals were higher than the ResLF/Smax, and were probably correlated to the convoluted source structure.
Fig. 4. Simulated (sLF) and measured (LF) spectra of the front leaf radiance and residuals (ResLF), both normalized to Smax.
This fact is emphasised by Dif_Res, the difference signal between the two residuals which is also shown in Fig. 5. This signal points out a deterministic aspect that was partially hidden by the noise components in ResLNF/Smax.
Fig. 5. Residuals normalized to Smax for the front leaf radiance obtained with (ResLF) and without (ResLNF) fluorescence included in (2), and the difference (Dif_Res) between the two residuals.
9. Fluorescence and reflectance of the leaf
The fitted reflectance R and normalized fluorescence F/smax are reported in Fig. 6. In this figure, FF and RF refer to fluorescence and reflectance on the front of the leaf; FR and RR refer to fluorescence and reflectance on the back of the leaf.
Due to reabsorption effects, the front side of the leaf fluorescence was flattened with respect to that of the back side, which peaked at about 14495.3 cm-1 (or 689.9 nm).
Fig. 6. Simulated normalized fluorescence F/Smax and reflectance R for the front (FF and RF) and rear (FR and RR) sides of the leaf, respectively.
In the fitting procedure, the two peaks were evidenced only by the application of fitting step 2). Otherwise, with the simple second-order polynomial fitting for the scale determination, the peaks were shifted to the low-frequency cut-off point.
10. Comparison with an approximated fitting procedure
To further emphasise the accuracy of the three-step method, we report the results that we obtained using the simplified model consisting of the equations in (4) reported below:
which employed only the measured spectra, and was derived from (1) and (2). In (4), Fc represents the unknown fluorescence in count units. This set of equations was employed in a minimization least square process, in order to deduce both reflectance and fluorescence as second-order polynomials without any correction for the non linearity of the instrument and with no fine tuning of the scale.
In Fig. 7, a dramatic change can be observed in the FF1, FR1, RF1 and RR1 fits equivalent to those reported in Fig. 6, which were obtained by means of the three-step method. In particular, the front leaf reflectance was higher by about 55% than the value found when using (1) and (2). Furthermore, the fluorescence reversed its convexity, and was found to be about 35% lower.
The lack of a correction for the intensity dependence of the β parameter was the main reason for these discrepancies.
Fig. 7. Simulated normalized fluorescence F/Smax and reflectance R for the front (FF1 and RF1) and back (FR1 and RR1) sides of the leaf, respectively
11. Conclusion
We demonstrated the possibility of a high-resolution determination of sun-induced leaf fluorescence and reflectance by performing high-resolution measurements and simulations for an effective vegetation monitoring. The fits were analyzed by means of residuals. The characterization of the instrument, performed by means of a dedicated fitting procedure, was an integral part of the method and was responsible for the accuracy that was obtained. The reflectance fitting showed itself to be useful in evaluating the sensitivity of the method for the evaluation of both fluorescence and reflectance. The accuracy in the fluorescence retrieval was comparable to that of a second-order polynomial function approximation of the unknown real function in the presence of accidental errors equal to a few percent of the measured source irradiance. The systematic errors were clearly localized in the spectrum of the residuals, and could easily be reduced after a line identification in order to further increase the reliability of the source.
Acknowledgments
M. Mazzoni wishes to acknowledge Piero Mazzinghi, who first promoted this work, and Giovanni Agati, Bruno Carli, Guido Toci, Donatella Guzzi, Ivan Pippi, and the FLEX (Fluorescence Explorer) community for their help during the development of the study. This work was financed by the National Research Council as a grant to M. Mazzoni and by the European Space Agency (ESA) within the “FLEX Performance Analysis and Requirements Consolidation Study.
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