Imaging linear and circular polarization features in leaves with complete Mueller matrix polarimetry
C.H. Lucas Patty, David A. Luo, Frans Snik, Freek Ariese, Wybren Jan Buma, Inge Loes ten Kate, Rob J.M. van Spanning, William B. Sparks, Thomas A. Germer, Győző Garab, Michael W. Kudenov
IImaging linear and circular polarization features inleaves with complete Mueller matrix polarimetry
C.H. Lucas Patty , David A. Luo , Frans Snik , Freek Ariese , Wybren JanBuma , Inge Loes ten Kate , Rob J.M. van Spanning , William B. Sparks ,Thomas A. Germer , Gy˝oz˝o Garab , Michael W. Kudenov *[email protected] Abstract
Spectropolarimetry of intact plant leaves allows to probe the molecular archi-tecture of vegetation photosynthesis in a non-invasive and non-destructive wayand, as such, can offer a wealth of physiological information. In addition tothe molecular signals due to the photosynthetic machinery, the cell structureand its arrangement within a leaf can create and modify polarization signals.Using Mueller matrix polarimetry with rotating retarder modulation, we have1/40 a r X i v : . [ q - b i o . B M ] M a r isualized spatial variations in polarization in transmission around the chloro-phyll a absorbance band from 650 nm to 710 nm. We show linear and circularpolarization measurements of maple leaves and cultivated maize leaves anddiscuss the corresponding Mueller matrices and the Mueller matrix decompo-sitions, which show distinct features in diattenuation, polarizance, retardanceand depolarization. Importantly, while normal leaf tissue shows a typical splitsignal with both a negative and a positive peak in the induced fractional circularpolarization and circular dichroism, the signals close to the veins only display anegative band. The results are similar to the negative band as reported earlierfor single macrodomains. We discuss the possible role of the chloroplast orien-tation around the veins as a cause of this phenomenon. Systematic artefactsare ruled out as three independent measurements by different instruments gavesimilar results. These results provide better insight into circular polarizationmeasurements on whole leaves and options for vegetation remote sensing usingcircular polarization. Keywords
Photosynthesis, Mueller matrix polarimetry, circular dichroism, chloroplast,chlorophyll a
Introduction
One of the most distinctive and characteristic features of life is the homochiralityof its molecular building blocks [1]. Chiral molecules in their most simple formexist in left-handed (L-) and a right-handed (D-) versions, called enantiomers.In non-biological systems, the mixture is expected to be racemic (50 % - 50 %).2/40owever, biological systems tend to have nearly 100 % preference for one type ofenantiomer, which is a feature called homochirality. In fact, the functioning andstructure of biological systems is largely determined by their chiral constituents.Although there are a few exceptions [2], amino acids mainly occur in the L-configuration and sugars occur predominantly in the D-configuration. Apartfrom these small molecules, many large scale molecular architectures, dimensionsof which can range over several orders of magnitude, are chiral. An exampleof such large-scale chirality is displayed by the DNA molecule, which is alwaysright-handed and can be over 2 m long [3]. Chirality can also be observedin the chlorophylls and bacteriochlorophylls, in particular when utilized inphotosynthesis (as their intrinsic signal is very weak due to their planar andalmost symmetrical structure). Additionally, these chlorophylls are organized ina supramolecular structure that itself is chiral too [4].The molecular dissymmetry of chiral molecules has a specific response toelectromagnetic radiation [5] and this response both depends on the intrinsicchirality of the molecules and on the chirality of the supramolecular architecture.Examples of available spectroscopic methods that are based on this interaction arecircular diattenuation (dichroism) and linear diattenuation spectroscopy. Bothmethods are complementary and offer valuable insight into the functionality andstructure of molecules and have a long history in the research on photosynthesis[4]. In circular dichroism spectroscopy, the differential extinction of left- and right-handed circularly polarized light as a function of wavelength is measured. Lineardiattenuation spectroscopy characterizes the change in extinction dependingon the linear polarization of the incident (orthogonal) beams. Usually, onlyisolated molecules or cell constituents are measured, but it has recently beenshown that the circular dichroism of whole leaves can also be determined [6, 7].This is not possible in linear diattenuation spectroscopy, since the retrieval of3/40tructural information is dependent on the molecular alignment of the sample.In a randomly oriented sample, such as in a leaf, this information is thereforeaveraged out.Mueller matrix polarimetry allows a thorough characterization of the polar-ization properties of a sample. The complete Mueller matrix is a 4 × in vivo induced circular polarization studies onphototrophic organisms are available. We previously showed that the amountof induced circular polarization of unpolarized light is equivalent to the differ-ential absorbance of incident circularly polarized light for in vivo transmissionmeasurements on leaves [7]. These results are evidence for at least a generalcross sectional isotropy in the fractional circular polarizing/absorbing component.Little, however, is known about the possible spatial variation in the polarizingcomponents of leaves which can offer more information about the origin of thepolarization signals.Depending on the area of the leaf that is measured, such spatial variationsmight lead to inaccuracies if the molecular architecture is investigated. Thisis especially important for in vivo measurements on leaves carried out usingcommercial dichrographs (due to the relatively small area of measurement) andit might also be important to consider when scaling up fractional polarizationmeasurements to remote sensing applications.The typical circular polarization signal observed from chloroplasts is theresult of the superposition of two relatively independent signals resulting fromdifferent chiral macrodomains [18]. These result in bands of opposite sign thatdo not have the exact same spectral shape and thus do not cancel each other outcompletely. The existence of these macrodomains was first demonstrated usingdifferential circular polarization scattering [19] and the different domains werelater imaged using differential polarization microscopy showing separately the5/40ositive and negative bands [18, 20]. While both positive and negative signalsprevail in the image averages over the whole membrane (thus including multiplemacrodomains), the circular polarization spectrum is heavily influenced by thealignment of the chloroplasts [20, 21, 22]. Local alignments of the chloroplastsmight therefore affect the spatial variation in circular polarization and thusoverall the signal on a leaf and canopy scale.In the present study we will investigate the spatial components of polarizationin vegetation using imaging Mueller matrix polarimetry in transmission in orderto get more insight into the polarizing and depolarizing components of vegetationleaves. Various measurements on cultivated maize and maple leaves were takenwithin the relevant wavelength range (650 nm to 710 nm) of the vegetationabsorption band in the red. We show that these measurements improve ourunderstanding of the signals obtained on whole leaves and ultimately aid ininterpreting the signals in vegetation remote sensing using circularly polarizedlight. Materials and Methods
Sample preparation
Maize (
Zea mays ) was grown in the laboratory of Colleen Doherty, Departmentof Molecular and Structural Biochemistry, North Carolina State University. Thewild types we used were N78S and N74R. No differences in their growth features(V3) were observed during the measurements. The plants were cultivated in sandat a 16h/8h light-dark regime (at a photon flux density of 600 µ mol m − s − photosynthetically active radiation (400 nm to 700 nm)) at room temperature.All spectroscopic measurements on the maize leaves were carried out with theleaves still attached to the plant. Maple ( Acer rubrum ) leaves were collected in6/40ovember from trees growing at the Centennial Campus, North Carolina StateUniversity in Raleigh. In order to prevent dehydration, the petioles or stems ofthe leaves were placed in water after collection and during the measurement.
Polarization and Mueller matrix decomposition
Polarization in general is often described in terms of the four parameters of theStokes vector S . With the electric field vectors E x in the x direction (0 ◦ ) and E y in the y direction (90 ◦ ), the Stokes vector is given by: S = IQUV = (cid:10) E x E ∗ x + E y E ∗ y (cid:11)(cid:10) E x E ∗ x − E y E ∗ y (cid:11)(cid:10) E x E ∗ y − E y E ∗ x (cid:11) i (cid:10) E x E ∗ y − E y E ∗ x (cid:11) = I ◦ + I ◦ I ◦ − I ◦ I ◦ − I − ◦ I RHC − I LHC . (1)The Stokes parameters I , Q , U and V refer to intensities which thereby relateto measurable quantities. The absolute intensity is given by Stokes I . Stokes Q and U denote the differences in intensity after filtering linear polarizationat perpendicular directions, where Q gives the difference between horizontaland vertical polarization and U gives the difference in linear polarization butwith a 45 ◦ offset. Finally, V gives the difference between right-handed andleft-handed circularly polarized light. If we know the absolute intensity I , thepolarization state can be completely described by the normalized quantities Q/I , U/I and
V /I . I ◦ , I ◦ , I ◦ and I − ◦ are the intensities oriented in the planesperpendicular to the propagation axis and I LHC and I RHC are, respectively, theintensities of right- and left-handed circularly polarized light.Furthermore, in the Stokes formalism, any optical element can be describedby the 4 × M : 7/40 out = MS in = m m m m m m m m m m m m m m m m · IQUV in . (2)The Mueller matrix elements relate to the Stokes vector by: M = I → I Q → I U → I V → II → Q Q → Q U → Q V → QI → U Q → U U → U V → UI → V Q → V U → V V → V (3)Any set of optical elements in a system can be described by a total systemmatrix, the product of the multiplication of the n individual elements: M = M n M n − . . . M M . In the case of depolarizing samples such as leaves, usingpolar decomposition, the experimental M can be further decomposed into theproduct of a depolarizer Mueller matrix M ∆ , a retarder Mueller matrix M R anda diattenuator Mueller matrix M D . These matrices do not commute and theresult thus depends on the order of multiplication [23, 24, 25]. As there were nosignificant differences between illuminating a maize leaf’s adaxial or abaxial side(i.e., the upper side or the under side), we have used the polar decomposition asdescribed by Lu and Chipman [24]: M = M ∆ M R M D . (4)The depolarization, and the retardance, diattenuation and their orientation8/40an then readily be determined. The diattenuation vector D is given by: D ≡ D ˆ D ≡ D H D D C , (5)where ˆ D = D | D | and D H is the horizontal linear diattenuation, D the 45 ◦ lineardiattenuation and D C the circular diattenuation. The direction of D is definedto be along the eigenpolarization with larger transmittance (1 , ˆ D T ) T .The diattenuation D can be defined as: D = | D | = (cid:113) D + D + D . (6)It follows that: D H = m m , D = m m , D C = m m . (7)The linear diattenuation D L is defined as: D L = (cid:113) D + D . (8)The diattenuation Mueller matrix can be described by: M D = D T D m D , (9)9/40ith m D given by: m D = a + bm bm m bm m bm m a + bm bm m bm m bm m a + bm , a = (cid:112) − D , b = 1 − √ − D D (10)Similarly, the polarizance P , which is the polarization of unpolarized incidentlight, can be defined as: P = | P | = (cid:113) P + P + P , (11)where the diattenuation is given by the first row of M , the polarizance is givenby the first column of M . It thus follows that: P ≡ P H P P C , P H = m m , P = m m , P C = m m . (12)We can then define: M (cid:48) ≡ MM − = M ∆ M R , m (cid:48) = m ∆ m R (13)where M (cid:48) and its submatrix m (cid:48) have no diattenuation but are also not a pureretarder because of the depolarization. The depolarization ∆ can be defined as:∆ = 1 − | tr( M ∆ ) | , ≤ ∆ ≤ , (14)10/40here tr( M ∆ ) is the sum of the main diagonal of M ∆ . M ∆ can be given by: M ∆ = P − mD − D m ∆ , (15)and m ∆ can be obtained by: m ∆ = ± [ m (cid:48) ( m (cid:48) ) T + ( (cid:112) λ λ + (cid:112) λ λ + (cid:112) λ λ ) I ] − × [ (cid:112) λ + (cid:112) λ + (cid:112) λ m (cid:48) ( m (cid:48) ) T + (cid:112) λ λ λ ] , (16)where λ , λ , λ are the eigenvalues of m ∆ . The sign depends on the determinantof m (cid:48) ; when the determinant is negative the sign is negative and vice versa. Thelinear depolarization ∆ L is then given by:∆ L = 1 − (cid:12)(cid:12) m ∆(11) (cid:12)(cid:12) + (cid:12)(cid:12) m ∆(22) (cid:12)(cid:12) , (17)and the circular depolarization ∆ C by:∆ C = 1 − (cid:12)(cid:12) m ∆(33) (cid:12)(cid:12) . (18)The retardance describes a rotation on the sphere of Poincar´e and theretardance Mueller matrix M R can by described by: M R = m R , (19)which can be obtained by: M R = M ∆ − MM D − (20)11/40he retardance vector and its fast axis R can be defined as: R ≡ R ˆ R = Ra Ra Ra ≡ R H R R C , (21)where the retardance, R , is the length of R , ˆ R is the unit vector, R H is thehorizontal linear retardance, R the 45 ◦ linear retardance and R C the circularretardance. The length of R is given by: R = arccos (cid:20) tr( M R )2 − (cid:21) , (22)where tr( M R ) is the sum of the main diagonal of M R ) with a fast-axis orientationdefined by: ˆ R = a a a , a i = 12 sin R (cid:88) j,k =1 ε ijk ( m R ) jk , (23)following: ( m R ) ij = δ ij cos R + a i a j (1 − cos R ) + (cid:88) k =1 ε ijk a k sin R,i, j = 1 , , . (24)where ε ijk is the Levi-Civit´a permutation symbol, m R is a 3x3 submatrix of M R excluding the first row and column and δ ij is the Kronecker delta. 12/40 SG LP QWP
PSA
QWP LP
DetectorLight sourceand Monochr. Sample θ p =180º Figure 1.
Schematic representation of the rotating retarder Mueller matrixellipsometer setup in transmission, where PSG = polarization state generator,PSA = polarization state analyzer, LP = linear polarizer and QWP = quarterwaveplate.
Mueller matrix polarimeter
The imaging Mueller matrix polarimeter was built by the Optical Sensing Lab(North Carolina State University). A diagram of the setup is presented in Figure1 and the wavelength dependency for the Mueller matrix elements of an emptysystem is given in Figure 2. All measurements were carried out in transmission.The system was additionally verified in reflectance using a BK7 glass blockand BK7 right angled prism to verify the elements relating to respectivelythe diattenuation and retardance. The polarimeter is based on the commonlyused dual-rotating-retarder configuration as first described by Azzam [26]. Togenerate the polarization states, a white LED optical source, which was selecteddue to the high stability over time (MBB1L3, Thorlabs, USA) , was placedin front of a collimator and a monochromator with 8 nm FWHM resolution(Micro-HR, Horiba, Japan), which were followed by a polarization state generator(PSG). Hereafter the light interacted with the sample which was followed by thepolarization state analyzer (PSA) for the analysis of the polarization state. A50-mm focal length objective ( f / .
4, AF Nikkor, Nikon, Japan) then focusedthe light onto a 1.2 million pixel CCD with a total spatial resolution of less than0.1 mm per pixel (Manta G125-B, Allied Vision, Germany). Both the PSG and Any mention of commercial products within this paper is for information only; it does notimply recommendation or endorsement by the authors or their affiliated institutions.
Data acquisition
The polarimeter was designed to take 37 measurements for every single Muellermatrix. Obtaining a single Mueller matrix took approximately 7 minutes. Theretarders rotate harmonically by a 1:5 ratio [27]; per measurement the PSGQWP rotates stepwise from 0 to 180 degrees in 5 degrees increments while thePSA QWP rotates stepwise from 0 to 900 degrees in 25 degrees increments, thusresulting in different temporal modulations. The measured Stokes vector is thengiven by: [28]: S out = AM sample GS in , (25)where A is the Mueller matrix of the PSA ( A = M LP M QWP ), G the Muellermatrix of the PSG ( G = M QWP M LP ) and S in the Stokes vector of the incidentlight. As only the intensity is measured: I = c AM sample S G , (26)where c is the proportionality constant from the absolute intensity and S G = GS in , this can be reduced to: I = c (cid:88) i,j =1 µ ij m ij , (27)14/40here µ i,j = a i p j , with a i the first row of A and p j the first column of G . Asonly the first row of A is involved: a a a a . . . .. . . .. . . . · m m m m m m m m m m m m m m m m · P P P P = I... out . (28)which upon multiplication gives: I = (cid:88) i,j =1 µ ij m ij , (29)the sample Mueller matrix can then be reconstructed by multiplying the pseudo-inverse of µ ij with the measured intensities. Spectropolarimetry on maple leaves
The induced fractional circular polarimetric measurements ( m ) on maple( Acer pseudoplatanus ) leaf veins were additionally measured on TreePol, adedicated circular spectropolarimetric instrument (see [7] for a description ofthe instrument). The leaves (n=3) were illuminated from the adaxial side, and acircular area of radius ≈ a v e l eng t h [ n m ] MM value . m - - m - - m - m - m . m - - - m - . - . m - . - . m - m . m - - . - m - m - . - . m . - m . m Figure 2.
Wavelength dependence of the normalized Mueller matrix of anempty system (n=1). Error bars denote the standard error, but are often smallerthan the graph’s linewidth. 16/40 esults
Mueller matrices
The transmission wavelength dependence of the (normalized) Mueller matrices ofthe normal tissue and the veins of maize leaves are shown in Figure 3. Similarly,the wavelength dependence of the (normalized) Mueller matrices of the normaltissue and the veins of maple leaves as a function of wavelength are shown inFigure 4. Comparing the two leaf types, roughly similar features in the individualMueller matrix elements are visible, although with a noticeable offset in variouselements. Some structure is visible in the Mueller matrix elements relatingto linear polarizance ( m , m ) and dichroism ( m , m ). For maize theseelements show a much stronger and gradual signal as compared to maple, whichmight result from the positioning of the maize leaves within the setup, whichwas always very similar, in combination with the parallel venation. With theexception of the elements m and m , the signals per leaf type are generallyvery similar between the veins and the normal tissue, but with various offsetvalues. The variation between the maple leaves, and thus the standard error,was much larger than that in maize leaves. These differences are likely due tothe larger amount of absorbance within the maple leaves as compared to themaize leaves. 17/40 a v e l eng t h [ n m ] MM value . m - . - . - . m - . . . m - . . m - . - . - . m . m - . - . - . m . . m - . . m - . - . - . m - . . m - . . . m - . . . m - . . m - . - . . m - . . m Figure 3.
Wavelength dependence of the normalized Mueller matrix of maize leaf normal tissue (blue) and veins (orange dashed), averaged for 3 leaves. Theborder areas are excluded. Error bars denote the standard error. 18/40 a v e l eng t h [ n m ] MM value . m - . . m - . . . m - . - . . m - . . m . m - . . . m - . - . m - . - . . m - . - . - . m . m - . - . . m - . - . . m - . . . m - . . . m . . . m Figure 4.
Wavelength dependence of the normalized Mueller matrix of maple leaf normal tissue (blue) and veins (orange dashed), averaged for 3 leaves. Theborder areas are excluded. Error bars denote the standard error. 19/40 ueller matrix elements m and m Figure 5 shows that for a maize leaf the average Mueller matrix elements m and m are of similar shape and magnitude within the standard error. Theelements m and m represent the induced fractional circular polarization anddifferential circular absorbance, respectively. The largest difference betweenthese two elements can be found at 680 nm, which coincides with the chlorophyllmaximum absorbance band and is positioned on the slope between the negativeand positive peak observed in the V /I signal. m m Figure 5.
Wavelength dependence of the normalized Mueller matrix elements m and m (representing the induced fractional circular polarization anddifferential circular absorbance, respectively), averaged for 3 maize leaves. Theshaded areas denote the standard error. Spatial differences in polarization between veins and nor-mal tissue
As is shown in Figure 6 for a maize leaf and Figure 7 for a maple leaf, cleardifferences in the circular polarization features ( m ) for the selected tissuecategories can be distinguished. The three categories, normal tissue, border areaand veins, are discriminated on the basis of the large contrast observed in m ,and comparing this with the total intensity ( I ) images (data not shown). InFigures 6 and 7, the subplots A , C and E show the false colored image of a20/40ingle measurement at 710 nm (because of the higher transmittance) of m in order to highlight their spatial distributions. Excluding the white area, theaverage spectra (MM element m ) of the colored areas are shown in Figures 6and 7: B D and F .Figure 6 A and B show that the circular polarization per wavelength ofnormal maize tissue is in line with the typical signal one can expect from themeasurements of thylakoid membranes [4] and is similar to earlier measurementson whole leaves [6, 7]. In the border category, Figure 6 C and D , a slight decreasein the positive circular polarization band can be observed. However, looking atonly the circular polarization of the veins, Figure 6 E and F , we can see thatthe positive band has almost completely disappeared while the negative band isstill present and much larger in magnitude.These differences in structural categories can be seen even more clearly formaple leaves (Figure 7). Looking at the normal tissue (Figure 7 A and B ), theshape is similar to earlier measurements on whole leaves [6, 7]. In the categoryborder area (Figure 7 C and D ) and in the veins (Figure 7 E and F ) it is shownthat the positive band is absent while the negative band has increased in signalintensity.Circular polarization measurements specifically on veins were repeated withTreePol [7]. These measurements show a signal that is similar in shape to theMueller matrix measurements as is visible in Figure 8 for maple leaves. TreePolhas a much higher spectral resolution and shows more structure in the signal.Also shown in Figure 8 are the results from earlier measurements on maple leavescarried out on the dual PEM polarimeter [17, 16]. While not specifically aimedat measuring the veins, the result show a signal that is very similar to that ofmaple veins even though the amount of leaf tissue versus the amount of veins inthese measurements is unknown. 21/40 igure 6. The different isolated spatial features of a maize leave (upper row)and the accompanying spectral features of Mueller matrix element m (bottomrow) (n=3). A and B : normal leaf tissue. C and D : the border area. E and F : the veins. Per category, the area shown in white is excluded. Scale bars inthe lower left of A , C and E are approximately 0.4 cm. Error bars denote thestandard error. Border area m m m Figure 7.
The different isolated spatial features of a maple leaf (upper row)and the accompanying spectral features of Mueller matrix element m (bottomrow) (n=3). A and B : normal leaf tissue. C and D : the border area. E and F : the veins. Per category, the area shown in white is excluded. Scale bars inthe lower left of A , C and E are approximately 0.4 cm. Error bars denote thestandard error. 22/40 igure 8. Transmission measurements of the veins of maple leaves carried outwith TreePol, the Mueller matrix polarimeter element m and of general mapleleaf surfaces with the dual PEM polarimeter. Error bars and shaded area denotethe standard error. 23/40 ueller matrix decomposition The diattenuation for maize and maple leaves is shown in Figure 9, where thespatial variation of the linear diattenuation at 710 nm for respectively maize andmaple leaves are shown in Figure 9 A and B . In the same images the orientationof the linear diattenuation is superimposed as a vector field. In Figure 9 C and D the circular diattenuation is shown. The averages over wavelength for bothlinear and circular diattenuation are shown in Figure 9 E and F for respectivelymaize and maple. Again, similar to the associated Mueller matrix elementsthe linear diattenuation is observed to be larger in maize than in maple wherethe value is averaged out. Similarly, the polarizance is shown in Figure 10.For the maize leaves, the circular and linear polarizance and diattenuation arealmost identical. A larger difference between those features is observed for themaple leaves, although the differences in linear and circular diattenuation andpolarizance are not significant.The linear and circular depolarization for maize and maple leaves are shownin Figure 11. Figure 11 A and B show the spatial variation at 710 nm of thelinear depolarization for respectively maize and maple and Figure 11 C and D show the spatial variation at 710 nm of the circular depolarization for respectivelymaize and maple. In general, the amount of linear depolarization is much largerin the veins than in the normal tissue, which is even more pronounced for circulardepolarization which is almost completely depolarized in the veins. Both thelinear and circular depolarization in the veins slightly decreases in magnitudearound the main chlorophyll absorbance band in the maize leaves, while thiseffect is larger in the maple leaves (Figure 11 E for maize and F for maple).Lastly, the retardance is shown in Figure 12. To account for systematicoffsets in the setup a rotation matrix was applied on R . The spatial variationin linear retardance is shown for maize in Figure 12 A and for maple in 12 B .24/40he orientation of the retardance fast-axis of the veins is shown as a vector fieldsuperimposed on the linear retardance. In both maize and maple, the retardancefast axis orientation is almost horizontal in the figure for the normal tissue, butnot for the veins. Additionally, clear differences in retardance values can beobserved, between the veins and the normal tissue. The circular retardanceshowes more noise in the veins and as a result is slightly larger. However, noclear structures can be seen (shown in Figure 12 C and D for maize and maplerespectively). No large differences in retardance are observed over wavelength ascan be concluded from Figure 12 E (maize) and F (maple). 25/40 igure 9. Spatial variations in linear diattenuation at 710 nm for A : maize and B : maple. The vectors depict the diattenuation orientation. Spatial variationsin cirular diattenuation at 710 nm for C : maize and D : maple. Averaged linearand circular diattenuation over wavelength for E maize and F maple ( n =3).Error bars denote the SE. 26/40 igure 10. Spatial variations in linear polarizance at 710 nm for A : maize and B : maple. The vectors depict the polarization orientation. Spatial variationsin cirular polarizance at 710 nm for C : maize and D : maple. Averaged linearand circular polarizance over wavelength for E maize and F maple ( n =3). Errorbars denote the SE. 27/40 igure 11. Spatial variations in linear depolarization at 710 nm for A : maizeand B : maple. Spatial variations in cirular depolarization at 710 nm for C : maizeand D : maple. Averaged linear and circular depolarization over wavelength for E maize and F maple ( n =3). Error bars denote the SE. 28/40 igure 12. Spatial variations in linear retardance at 710 nm for A : maize and B : maple. The vectors depict the orientation for the retardance fast-axis andare shown only for the veins. Spatial variations in cirular retardance at 710nm for C : maize and D : maple. Averaged linear and circular retardance overwavelength for E maize and F maple (n=3). Error bars denote the SE. 29/40 iscussion We have carried out full Mueller matrix polarimetry on various maize and mapleleaves and separated the spatial features corresponding to the veins and thenormal leaf tissue. While the linear diattenuation and polarizance of maize leavesshowed clear differences, these properties were averaged out in maple. This is alsovisible in the associated Mueller matrix elements, and we accredit the observeddifferences to the parallel venation of maize and the leaf orientation duringthe measurements which was similar for all maize leaves measured. Distinctdifferences between veins and normal tissue were visible in linear retardance andlinear depolarization for both maize and maple.The linear polarization of vegetation has been investigated before as a remotesensing tool on Earth [8, 9, 10, 11, 12]. While indicative of leaf structuralchanges that can be associated with drought stress [11], the linear polarizationspectral reflectance around the chlorophyll absorbance band is generally verysmooth and free of structure. We did not observe the typical sharp featuresassociated with chloroplast linear polarization [4] (for Mueller matrix elements m , m , m , m ) either, although the maize leaf veins show a smooth featuresomewhat relatable to intensity.We observed a large difference in circular polarizance and diattenuation andthe associated values of Mueller matrix elements m , m , between normalleaf tissue and leaf veins (Figures 3, 4, 6 and 7). Normally, the spectrum ofchloroplasts shows a very typical split signal around the chlorophyll absorbanceband. It has been shown that this split signal is the result of the superpositionof two relatively independent signals resulting from different domains [18]. Thenegative band has been mainly associated with the stacking of the thylakoidmembranes, whereas the positive band is generally associated with the lateralorganization of the chiral domains [29, 30, 31]. In our measurements, the normal30/40eaf tissue shows a typical split signal for Mueller matrix element m , but theveins display only a negative band. This effect was observed for both maize andmaple leaves. The measurements on maple veins were repeated using TreePol,showing a roughly similar result and the overall absence of the positive band.The observed differences are not only due to a difference in biomolecularstructures. While the bundle sheath cells in maize veins can contain chloroplastswith unstacked thylakoid membranes [32] (which might have led to the lowersignals observed in maize veins as compared to maple veins) it is known thatmaple does not contain similar differences between chloroplasts. Although thereare definitely fewer chloroplasts and pigments around the veins, this would onlylead to a smaller V /I signal and would not affect the ratio between the positiveand negative band.It is on the other hand also unlikely that the effects are purely due to multiplescattering. While multiple scattering events can create circular polarization,it is not likely that scattering alone results in bands with such narrow widthssince scattering polarization is usually a phenomenom leading to a very gradualwavelength dependence [33]. We do assume that multiple scattering events occurnear the veins, which is evident from the large amount of depolarization (seeFigure 11). The depolarization hardly changes over wavelength (Figure 11 E and F ), so it is therefore unlikely that the positive band is completely depolarizedwhile the negative band is not.While the different macrodomains within the chloroplasts show single bandsof either a positive or a negative signal, it has been reported that both bandspersist in the chloroplast averages [20] (a representation of these bands is shownin Figure 13). If these bands contribute in equal amount, the superposition ofthe bands results in the typical split signal as observed in normal leaf tissueand randomly oriented chloroplasts in suspension. These bands do not always31/40 avelength [nm] V / I V / I Wavelength [nm]
A B
Figure 13.
Representation of the chloroplast images and spectral resultsby Garab et al. and Finzi et al. [18, 21] including our data (normalizedto superposition results). When probed using differential circular absorbancemicroscopy, macrodomains can be imaged having single spectral bands of oppositesign (red and blue). A : If the total signal (solid black line) is the superpositionof ≈
60 % positive band and ≈
40 % negative band the signal is comparable tothe m results for the normal tissue (dotted black). B : If the total signal (solidblack line) is the superposition ≈
25 % positive band and ≈
75 % negative bandthe signal is comparable to the m results observed for the veins (dotted black).contribute in an equal amount, as is evident from measurements on magneticallyaligned chloroplasts in suspension; the alignment of the chloroplast, be it face-aligned or edge-aligned, results in different signals [20, 21, 22]. It should also benoted that a spectral difference was observed comparing both the negative andpositive peak from the different domains in either (magnetically aligned) face oredge-aligned chloroplasts [18]. Possibly, the apparent existence of four bands isthe result of superposition of two bands still persisting in the measurements on thelocalized ’islands’, although the difference in face and edge-aligned measurementsmight be indicative of a spatial anisotropy in the dipole moments.From the images in the same study [18] it also appears that a rotationaldissymetry in circular dichroism is present in the chloroplasts. As such, it seemslikely that the chloroplast circular dichroism average depends on which side ofthe chloroplast is measured. Consequently, this feature determines the extent towhich both the positive and negative bands contribute.We hypothesize that around the veins the chloroplasts are oriented in such away towards the observer that the resulting signal is dominated by the negativeband. In Figure 13 A we show that the spectral behavior of the Mueller matrix32/40lement m for the normal tissue of maple leaves can be reconstructed out of thetwo spectral bands if these have a more or less equal contribution. Figure 13 B shows the same results but in unequal contribution (25 % - 75 % for respectivelythe postive and negative bands). In this ratio the superposition is very similarto the spectral behavior of Mueller matrix element m observed in the veinsof maple leaves. In both figures our data is red-shifted as compared to thesuperposition signal, but only by a few nanometers.Additionally, it was shown that these separate signals from the macrodomainshave a magnitude much larger than the superimposed signal [18]. We do notobserve such large signals near the veins, which we attribute to the depolarizationof the veins. The negative signal observed in maple leaf veins is still severaltimes larger than the negative band in the split signal of leaf averages.These findings underline that caution should be taken when scaling upsmall area leaf measurements to possible remote sensing applications or whenevaluating measurements that use polarization modulated incident light of wholeleaves to get insight into photosynthesis functioning. To illustrate this, we alsoincluded a set of measurements taken with the PEM polarimeter which were notparticularly aimed at measuring the veins or the normal leaf tissue, but weretaken as a general measure of leaves (see Figure 8). Although there is somevariation between the three methods they essentially show the same pattern andany variations might be due to different contributions of the positive or negativeband or slight physiological variations between the different leaves.Importantly, these differences in circular polarization should also be consid-ered in the evaluation of remote sensing observations itself. The measurementsof whole leaves by the PEM polarimeter [17, 16] were dominated by the neg-ative band (Figure 8), but this was only the case for measurements of leavesthat were collected later in the growth season. Young leaves did display the33/40xpected typical split signal (results not shown). These signals could thereforealso be indicative of growth stage, depending on species, although additionalmeasurements are required. Additionally, from an astrobiological point of view,examining the chiroptical evolution of a revolving planet might underline thepresence of dynamically changing signatures of life.Follow-up polarization microscopy studies on chloroplasts will be crucial infurther evaluating these observed differences. Orientation-dependent polarizationmeasurements using optical tweezers (see e.g. [34]) should in theory allow athree-dimensional reconstruct of the chloroplast circular dichroism, which couldprovide a more fundamental understanding of the signal. Conclusion
Using transmission imaging Mueller matrix polarimetry we have demonstratedthat leaves show distinct spatial variations in linear and circular polarizationcharacteristics as a function of wavelength. Especially in circularly polarized lightwe observed distinct differences in the produced fractional circular polarizationand differential circular absorbance for veins and normal tissue. While thenormal tissue shows the typical split sign signal comparable to circular dichroismmeasurements on isolated chloroplasts, the veins show only a negative band. Weattribute these effects to a preferential orientation of the chloroplasts near theveins, resulting in a larger contribution of the macrodomains that display onlythe negative band. Although not measured in depth in this study, previouslyobtained data suggest a correlation with vegetation maturation. As such, thesefindings suggest possible applications in vegetation monitoring and may offernew prospects for the detection of extraterrestrial life by evaluating a planet’schiroptical evolution. 34/40 cknowledgments
This work was supported by the Planetary and Exoplanetary Science Programme(PEPSci), grant 648.001.004, of the Netherlands Organisation for ScientificResearch (NWO). We acknowledge Colleen Doherty, Department of Molecularand Structural Biochemistry, North Carolina State University, for providing uswith the maize samples. 35/40 eferences
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