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The inhe en p ope ies o ligh a e a signi ican sou ce o in o ma ion when used o p obe he p ope ies o
ege al issues1–17. In mic oscopy imaging, i is common o p epa e he samples o be s udied in e y hin sec-
ions o p e en mul iple sca e ing o ligh by he di e en issue s uc u es, which can deg ade image con as
and spa ial esolu ion. Thin sec ions o issues a e in gene al almos anspa en and e y di icul o isualize i
a con as enhancemen echnique is no applied. Chemical s aining is a e y popula app oach because o he
chemical speci ici y o dyes o a ge ed molecules in he issues. The phase con as echnique13 is a widely sp ead
app oach, which does no equi e any s aining, and which can inc ease con as o he hin sec ions p opo ion-
ally o he op ical hickness o he ege al s uc u es p obed.
The use o pola ized ligh o inc ease con as in images used o ege al issue cha ac e iza ion is also a
well-known app oach. Con as enhancemen o images o plan s uc u es is usually ob ained using pola ized
ligh , h ough he measu e o dich oism o bi e ingence18–25. Dich oism is ela ed o he pola iza ion-dependen
abso p ion o ligh by plan s uc u es and i is use ul o de ec speci ic molecules as well as o isualize how
hey a e o ganized in a h ee-dimensional amewo k. Dich oism is success ully used in many s udies de o ed
o e eal he o ganiza ion and concen a ion o chlo oplas s and ela ed o ganelles in plan species19,21. Bi e-
ingence is gene a ed ei he by aniso opic molecules (in gene al pa ially c ys allized mac omolecules) o by
non-iso opic o ganiza ion o non-necessa ily aniso opic mac omolecules. Bi e ingence has been success ully
used o cha ac e ize bi e ingen mac omolecules as cellulose, in ol ed in dis inc ypes o cell p ocesses, such as
cell de elopmen and aging18, p oduc ion o gua d cell p o oplas s19. Bi e ingence has also been used o s udy
he s uc u e o gua d cells hemsel es and hei ela ed s oma a20 o o in es iga e he cell wall composi ion in
phylogene ically dis an g oups o plan s21, and o s udy he s uc u e o ichomes22,23.
Pola ime ic mic oscopes used o plan inspec ion a e mos ly op imized o measu e dich oism o bi e-
ingence, bu o he pola ime ic ea u es, as depola iza ion, a e usually neglec ed. Depola iza ion a ises when
pho ons wi h di e en pola iza ion s a es incohe en ly each he same a ea o he de ec o . In plan s, depola i-
za ion is mainly caused by ligh sca e ed by cells, o ganelles, ex acellula s uc u es, and o he elemen s ha
may be loca ed wi hin he issue. Fo e y hin p epa a ions, sca e ing is usually low and depola iza ion e ec s
ͷǯUǡǡÖǡͶ;ͷͿǡǤǡǡ
ǡǡͿͷͷͶǡǤBo anical Ins i u e o Ba celona
ȋǡǦȌǡͶ;Ͷ;ǡǤͺǡƬǤ
ǡ ǡ Ͷ;Ͷ; ǡǤ ͻDepa men o Applied Physics, Uni e si y o
ǡͷǡͻͶͶͶͿǡǤ *email: albe .[email p o ec ed]
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a e usually dis ega ded, howe e , op ical cha ac e iza ion o plan s is no always pe o med in such condi ions.
To da e, he mos used app oach o accoun o depola iza ion in oduced by plan s is o measu e he so-called
deg ee o pola iza ion (DoP) o sca e ed ligh 26–29. Since DoP depends on he in insic cha ac e is ics o he
cons i uen s o plan s i is a pe inen and in o ma i e obse able o he s a e o a gi en specimen, eason why i
has been used in p eceding s udies. Howe e , a mo e gene al app oach, Muelle pola ime y has been sca cely
used in bo any24,25,30. The la e si ua ion is su p ising compa ed o he ex ensi e use and he s ill g owing in e es
o Muelle pola ime y o s udy ei he human o animal issues31–36.
The goal in he p esen manusc ip is o show ha Muelle pola ime y p o ides bo h, pola iza ion-based
and depola iza ion-based obse ables and ha bo h o hem can b ing in e es ing and independen in o ma ion
abou he physical p ope ies and s uc u e o ege al issues. Pola iza ion-based obse ables can be measu ed
wi h echniques o he han Muelle pola ime y, howe e , Muelle pola ime y has he ad an age compa ed o
o he expe imen al app oaches ha i p o ides all he pola iza ion-based obse ables and he depola iza ion-
based ones as he esul o a single measu emen . The p esen manusc ip is o be ead as a gene al p esen a ion
o imaging Muelle pola ime y applied o plan s and he e iden po en ial bene i s ha bo anis s can ob ain
when implemen ing i in hei cha ac e iza ion ou ines. This pape goes beyond he simple illus a ion o a case
s udy and compa es pola iza ion mic oscopy- ela ed images wi h mic oscopy images ob ained wi h s a e-o - he
a echniques commonly used o isualize and o cha ac e ize plan s. We demons a e how pola iza ion mic os-
copy is an excellen ool o cha ac e iza ion o ege al issues and plan sec ions. I is a pe ec complemen , and
in some cases is ad an ageous, o s anda d mic oscopy me hods, p o iding he po en ial o expand he ield o
op ical ins umen a ion o he s udy o plan s.
In his wo k we ha e conside ed lea es om a specimen o Epip emnum au eum (Linden & And é) G.S.Bun ing
belonging o he A aceae amily as a case o s udy. A pic u e o said specimen is shown in Fig.1a. Compa ison
o imaging pola ime y wi h o he ad anced echniques, such op ical mic oscopy, phase con as mic oscopy,
luo escen mic oscopy, highligh s he po en ial o pola ime y o plan inspec ion. These ad anced imaging
me hods ha will be discussed in he p esen s udy a e cu en ly used in bo any o plan inspec ion. Al hough
he selec ion is no an exhaus i e compila ion, i is mean o be ep esen a i e o he echniques used in he ield
and hey should be in e p e ed he e as a base o compa ison o help he eade o unde s and he po en ial and he
in e es o Muelle pola ime y. No e ha o he me hods could be men ioned bu a e no a ailable in his s udy,
as o ins ance, di e en ial con as mic oscopy (DIC) ha is a ele an ad anced cha ac e iza ion echnique,
and ha p esen s images like hose ob ained by phase con as mic oscopy bu emphasizing lines and edges o
he sample s uc u es by exploi ing he pola iza ion p ope ies o ligh 37. Figu e1b shows one o he lea es used
o he p esen s udy. The squa e inside he lea e highligh s he a ea ha was imaged using he abo e-lis ed
mic oscopic echniques. A desc ip ion o he plan used o he p esen s udy is ound a he Me hods sec ion.
Pola ime ic mic oscopic images o he Epip emnum au eum lea es we e aken wi h a mul imodal mic oscope
wo king in ansmission con igu a ion. The mic oscope can also be used in a way o ob ain images insensi i e o
he pola iza ion o ligh (s anda d op ical mic oscope). Mo e de ails o he mic oscope used can be ound in he
Me hods sec ion. An example o an image aken in non-pola ized mode o he lowe lea su ace o he lea can be
seen in Fig.2a. In he la e image i is possible o dis inguish he p esence o a ew epi helial cells, cha ac e ized
by hei ypical polygonal shape, and a gua d cell and i s ela ed s oma a. These cells a e loca ed jus a he lowe
su ace o he lea . In he image shown, he e is also possible o guess he p esence o an elonga ed s uc u e which
appea s blu ed because i is loca ed inside he lea , a a dis ance om he ocal egion longe han he dep h o
ocus o he objec i e used o ake he images. Because o he blu y and he lack o con as in said image, i is
no possible o pe cei e he de ails, o a leas , o unambiguously iden i y he na u e o he elonga ed s uc u e.
Figu e1. Plan specimen used o he p esen s udy: (a) Epip emnum au eum gene al iew; (b) one o he
measu ed Epip emnum au eum lea es.
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The same po ion o he lea was measu ed in pola ime ic mode and he Muelle ma ix image encoding he
pola ime ic esponse o he sample was ob ained. To ge u he physical in o ma ion om he measu ed Muelle
ma ix image, he la e was decomposed o ob ain a se o subsequen images o pola iza ion and depola iza ion
me ics. Conce ning depola iza ion, in his wo k i is used he depola iza ion index PΔ and a se o obse ables
(P1, P2 and P3) called indices o pola ime ic pu i y (IPPs) ha gi e indica ions abou he way ha a medium
depola izes ligh . Acco dingly, PΔ and IPPs a e sensi i e o classi y di e en mic oscopic elemen s acco ding o
hei abili y o depola ize he illumina ing ligh . I is wo h o no e ha PΔ is a global depola iza ion measu e
while IPP can dis inguish di e en depola iza ion aniso opies ha esul s in o he same PΔ alue. In e es ed
eade s can ound, in he Me hods sec ion and in he Supplemen a y in o ma ion, a de ailed desc ip ion o he
pola iza ion-depola iza ion obse ables and an algo i hm o deduce hem om Muelle ma ices.
Figu e2b–d show he images co esponding o PΔ, he i s IPP, P1, and he di e ence P2–P1, which p o ided
highly con as ed images. Conce ning pola iza ion p ope ies, Fig.2e shows he sinus o he linea e a dance,
which gi es in o ma ion abou he bi e ingence o s uc u es in he imaged a ea o he lea . In Fig.2b–e he
elonga ed shape o an inulin aphide can be also seen. Inulin is a ype o polysaccha ide which c ys allizes in
needle-shaped c ys als; he c ys als end o g oup oge he o o m aphides, which a e ound in pa enchymal
cells in some plan species. In such images, he edges o he aphide can be clea ly dis inguished, and he whole
s uc u e is highly con as ed wi h espec o he backg ound. In ac , in he case o P1 image (Fig.2c), he ed
squa e sec ion o he aphide, has an a e age P1 alue o 0.11 whe eas he g een squa e sec ion, co esponding o
he backg ound, has an a e age P1 alue o 0.29. A compac s uc u e such a aphide sca e s ligh di e en ly ha
he aqueous s uc u e o he su ounding media. The ac ha he alues o P1 a e well clus e ed in wo g oups
a ound 0.11 and 0.29 espec i ely, shows he abili y o he obse able P1 o dis inguish among di e en ypes o
ma e , which would no be possible unde non-pola ized ligh images. The case o P2–P1 channel in Fig.2d is
also exempla y. Acco ding o his obse able, he same sec ion o he aphide is cha ac e ized by alues a ound
0.13 whe eas he same sec ion o he backg ound cells shows he alue 0.02. To quan i y he image con as
be ween wo s uc u es in he image, he so-called isibili y has been used as a me ic. The isibili y is de ined
by he exp ession:
V
=
Is −Iback
/(Is +Iback) , wi h I
s
and Iback being he a e age signal in ensi ies o he
s udied biological s uc u e (in his case he aphide) and he backg ound cells espec i ely. Visibili y alues a e
be ween 0 (null con as ) and 1 (maximum con as ). In he analysed case, he isibili y o he image be ween he
aphide and he backg ound is V = 0.03 o he in ensi y image (Fig.2a), V = 0.24 o PΔ (Fig.2b), V = 0.41 o he
P 1 obse able, (Fig.2c) and a isibili y o V = 0.72 o P2-P1 case (Fig.2d). Visibili y alues o di e en obse ables
a e calcula ed o e he same ed and g een squa e sec ions (Fig.2c) and u he con as analysis, including he
s udy o he s anda d de ia ion o he in ensi y in hese egions, is p o ided in he Supplemen a y in o ma ion.
Figu e2. Pola ime ic analysis o a small piece o he Epip emnum au eum lea (ma ked wi h a whi e ec angle
in Fig.1b). Di e en images o an inulin aphide, si ua ed close o a s oma, a e p o ided, which we e ob ained
by using di e en channels: (a) In ensi y; (b) PΔ; (c) P1; (d) P2–P1; (e) The sinus o linea e a dance δ (s oma
highligh ed wi h a ed a ow); and ( ) Pseudocolou ed image encoding e a dance modulus and o ien a ion.
Pseudocolou ed image comp ises he linea e a dance o he sample (shown in o a whi e–black scale; adius o
he semi-ci cula colou scale), and he as axis o ien a ion ( ep esen ed wi h di e en colou s; pe ime e o he
semi-ci cula colou scale).
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No e ha he isibili y alues o depola izing obse ables a e signi ican ly be e han hose ob ained o he
pola iza ion insensi i e image. Rega ding he di e en depola izing obse ables, he isibili y o he aphide
is highe in he case o analysing P1 and P2–P1 han PΔ as he aphide depola izes ligh in an aniso opic way.
The e o e, aphides a e easie o iden i y when using hese IPPs obse ables han in he PΔ case.
Raphides a e no he only s uc u es which can be highligh ed hanks o pola ime ic mic oscopy. The e a e
o ins ance gua d cells and hei ela ed s oma a, which can also be isualized and cha ac e ized using bi e in-
gence. Bi e ingence in gua d cells is mos ly due o a p e e en ial alignmen o small cellulose mic o ib ils inside
hei walls. Young and heal hy gua d cells can show egula and in ense bi e ingen pa e n, on he con a y,
dead o non- unc ional gua d cells ha e dis ended walls, and show dis o ed o e y poo bi e ingence pa e ns.
The po ion o he lea shown in Fig.2a– con ains a s oma o abou ~ 50μm s oma al leng h close o he aphide.
Despi e o being bi e ingen , he isibili y o he s oma is lowe han ha o he aphide (also bi e ingen ) and
he e o e somehow sc eened by i in he colou scale chosen o ep esen Fig.2e.
While he s oma has a negligible dich oism, he aphide is cha ac e ized by 0.2 ad o linea dich oism,
which indeed appea ed o be o ien ed along he axis o said aphide. The linea dich oism in aphide may be
due o he aniso opic abso p ion o well aligned inulin c ys als which o m he aphide o o he non-iso opic
sca e ing which a enua es di e en ly ligh pola ized pa allel o pe pendicula o he majo axis o he aphide.
The esul s o a speci ic s udy o elucida e he o igin o dich oism in aphides is ou o he scope o he p esen
wo k bu will be p esen ed elsewhe e. Mo eo e , he non-iso opic sca e ing o ligh due o he elonga ed shape
o he c ys als may be a he o igin o he non-symme ic depola iza ion ha gi es ise o he highly con as ed
P 1 channel wi h espec o PΔ.
A colou encoding o ma is an app op ia e way o highligh di e en pola iza ion and depola iza ion sig-
na u es a once in he same image38. Fo ins ance, Fig.2 shows he sine o he e a dance, al eady shown in
Fig.2e, comple ed wi h he in o ma ion o he o ien a ion o he bi e ingence. In a second igu e, Fig.3a, i is
shown how colou encoding allows o u he isualiza ion o he s oma. The image co esponds o an a ea
o he lea , ee o aphides, whe e s oma, gua d cells and cell memb anes a e p esen . Colou encoding allows
o a clea di e ence be ween he memb anes o he gua d cells and he bounda ies o he s oma. The image in
Fig.3b co esponds o a zoomed iew o he a ea enci cled in Fig.3a and shows how he s uc u e o he s oma
( he po e egion) and he unde lying walls o he associa ed gua d cells can be clea ly dis inguished. No e ha
i is impossible o achie e a simila le el o di e en ia ion by using s anda d, non-pola ime ic, isualiza ion
echniques in mic oscopy wi h uns ained samples; see o ins ance Fig.2a. Wha is mo e, since he colou scale
in Fig.3b is ela ed o di e en o ien a ions o he bi e ingence, quan i a i e in o ma ion abou s ain spa ial
dis ibu ion can be ob ained om he image21.
Finally, we wan o highligh ano he ele an ad an age o pola ime ic imaging, he abili y o highligh
p ope ies and o imp o e isibili y o objec s which in s anda d condi ions o obse a ions may appea blu y
because hey a e ou o ocus. The la e is discussed h ough he ollowing example, in which he same lea was
used, bu obse ed wi h he co esponding ob e se ace poin ing o he imaging mic oscope objec i e ( he oppo-
si e ace han in p e iously discussed examples). A egion o in e es was selec ed in which a aphide was p esen
in he ield o iew, bu ins ead o ocusing on he aphide (inside he lea ) he image was ocused on he su ace
o he lea . Acco dingly, in Fig.4a, i is shown an image aken unde unpola ized ligh o illus a e how he scene
is iewed unde s anda d isualiza ion condi ions. In his image, he epide mal cell walls a e clea ly isible and
he aphide appea s so ou o ocus and blu y ha i is ba ely iden i iable. The isibili y o he aphide is V ~ 0
( he isibili y is calcula ed by using he associa ed ed and g een squa ed egions o Fig.4b). Howe e , when
he same egion o he lea is measu ed using pola ime y in iden ical imaging condi ions, he p esence o he
aphide is clea ly e ealed in he P2–P1 channel Fig.4b, wi h isibili y equal o 0.67. The same image allows o
he obse a ion o he cell walls which a e also con as ed espec o a black backg ound. Cell walls and aphide
a e isible because bo h sca e ligh mo e e icien ly han he bulk o he cell, and, he e o e hey c ea e mo e
ligh depola iza ion. E en hough he aphide emains ou o ocus, i canno be, by any means, o e looked. We
Figu e3. Pseudocolou ed image o a collec ion o s oma a and he zoomed image o a gi en s oma a e shown
in (a) and (b), espec i ely. The pseudocolou ed image comp ises he linea e a dance in o ma ion o he
sample (shown in o a whi e–black scale; adius o he semi-ci cula colou scale), and he as axis o ien a ion
( ep esen ed wi h di e en colou s; pe ime e o he semi-ci cula colou scale).
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hink ha he abili y o pola ime ic imaging o showing he p esence o s uc u es, e en being ou o ocus, is
a majo ad an age as i allows o he iden i ica ion o biological s uc u es loca ed a di e en axial planes. The
la e pe mi s imaging o a gi en egion a he ocal plane wi hou loss o esolu ion while e ealing some ou o
ocus s uc u es a he same ime. This could be help ul o use s wi hou ap io is ic in o ma ion o samples, as
pola ime ic con as shows o be e y use ul o de ec ele an s uc u es which may be ou o ocus.
So a , in his sec ion we ha e seen he imp o emen associa ed o pola ime ic imaging mic oscopy, wi h
special men ion o he IPPs channels, when compa ed wi h s anda d mic oscopy. Howe e , o he mic oscopy
echniques a e well-s ablished in biopho onics applica ions. Fo he sake o comple eness, we include he e a se
o images aken om he same sample specimen, he Epip emnum au eum lea , ob ained using wo o he main
op ical mic oscopy echniques used in bo anic: phase con as mic oscopy and luo escence mic oscopy.
Phase con as mic oscopy allows o he obse a ion o uns ained cells13 and i is especially use ul o explo e
li ing cells in eal ime because i does no need he e alua ion o mul iple images as in pola ime y. Phase con-
as measu es di e ences in he global phase o a ligh beam be ween adjacen zones in he sample unde exami-
na ion which a e c ea ed by small a ia ions in hickness and densi y ( e ac i e index) among hose zones. In
phase con as mic oscopy, bi e ingence is no needed o c ea e a isible con as be ween wo a eas o a sample.
Phase con as images o an almos anspa en and non-con as ed objec gi e o he human eye he imp ession
o a shaded h ee-dimensional objec . The la e implies a signi ican imp o emen in he pe cep ion o he sam-
ple, and i is in pa wha is behind he success o his echnique. Rep esen a i e images o s oma a and aphides
imaged wi h he phase con as mic oscope a e shown in Fig.5a,b, espec i ely. The lea piece was imaged using
a comme cial Olympus Fluo iew 1000 phase con as mic oscope desc ibed in he Me hods sec ion. Whe eas
he s oma a a e clea ly isible in he phase con as mic oscopy image (Fig.5a), wi h a isibili y o V = 0.38 (V is
calcula ed o e he pu ple and yellow egions o Fig.5a ep esen ing he s oma a and backg ound espec i ely),
he aphides we e no so-well con as ed, p esen ing a isibili y educed o V = 0.14 (V is calcula ed o e he ed
and g een squa ed egions o Fig.5a ep esen ing he aphide and backg ound espec i ely). In Fig.5b, he loca-
ion o a aphide is highligh ed by a iole ellipse o help o isualiza ion. In his example, pola ime ic images
p oduce mo e con as ed and mo e speci ic images han phase mic oscopy. Phase con as pe o med less well
han pola ime y, especially in he case o images o aphides, because he ligh sca e ed by aphides depends
on he pola iza ion o he inciden ligh and phase con as mic oscopy is unable o see ha phenomena as i
illumina es he sample wi h unpola ized ligh . Mo eo e , colou encoding s a egies o enhance image con as
and isibili y can be applied in pola ime ic imaging because pola ime y consis s in mul iple independen
channels o in o ma ion whe eas in phase-con as mic oscopy he in o ma ion is es ic ed o only one chan-
nel. A second eason why phase con as pe o med less well han pola ime y in he example discussed he e is
he ac ha he sample was no hin, i.e., limi ed o a single monolaye o cells. In hese ci cums ances, phase
shi s la ge han 2π can cumula e and p oduce g ey scales which do no linea ly ela e o a ia ions in sample
hickness o densi y, he e o e deg ading he pe o mance o he echnique. Phase con as and pola ime y can
be complemen a y because hey can be used in non-s ained samples. In pola ime y, some channels a e speci ic
o he mani es a ion o a p ope y in he sample, such as e a da ion o dich oism. In his way, while phase-
con as p o ides an enhanced iew o he idimensional con o ma ion o he objec , pola ime ic obse ables
can highligh aspec s ela ed o ce ain speci ic p ope ies o he sample.
Images o he same a eas o he lea explo ed unde phase con as imaging we e aken wi h he same Olympus
Fluo iew 1000 comme cial mic oscope p e iously ci ed, ope a ed in luo escen mode. The use o speci ic dyes
selec ed o link o he molecules ha a e o in e es o he obse a ions, makes luo escence mic oscopy a highly
speci ic and highly esol ed echnique. By using wo di e en luo escen dyes, images o well con as ed and
di e en ia ed s oma a (Fig.5c) and aphide (Fig.5d) we e ob ained. Al hough he isualiza ion o he aphide
s uc u e is compa able wi h ha ob ained by using pola ime ic channels (Fig.2b–d), he s oma image shows
Figu e4. Figu e (a) shows he in ensi y image o an inulin aphide ou o ocal plane (de ocused). The
co esponding image ob ained by using he P2–P1 channel is p o ided in (b).
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some cha ac e is ics and de ails which canno be eached by pola ime ic means (Fig.5c). Howe e , some physi-
cal in o ma ion p o ided by pola ime ic images is no p esen in luo escence image, such as mechanical s ess
(which in u n c ea es bi e ingence) ha may occu in cell walls. Pola ime ic and luo escence echniques a e
compa ible in he sense ha bo h can be applied o s ained samples. S aining may enhance pola ime ic p op-
e ies, in pa icula dich oism, in places whe e he dye links o he molecules o he sample because in many
cases dyes a e aniso opic and dich oic. Fluo escence mic oscopy wo ks well wi h samples p epa ed as e y hin
sec ions made o a monolaye o cells. Fo ela i ely hick samples, like he one used he e, he ligh emi ed by
dyes can be sca e ed wi hin he issue and hen o end up by deg ading he spa ial esolu ion o he images i a
con ocal con igu a ion is no used. Wo king wi h hick samples is no a p oblem in pola ime y, p o ided ha
an adequa e sepa a ion be ween pola iza ion and depola iza ion channels can be done as shown in his wo k.
Finally, he alidi y o he analysis pe o med on he Epip emnum au eum lea es by pola ime ic me hods
is con i med by high esolu ion images om scanning elec on mic oscopy (SEM) aken on he same lea es o
he same plan . F om SEM images, we obse ed a concen a ion o inulin aphides which a e in ag eemen in
size and shape o he s uc u es obse ed in Fig.2b–d and iden i ied as aphides. An elec on mic oscope image
showing a ep esen a i e inulin aphide in he s udied Epip emnum au eum plan is shown in Fig.6a. Ano he
inulin aphide is shown in Fig.6b, bu he size o his aphide canno be well de e mined because i was b oken
du ing he sample p epa a ion. P epa ing he sample wi hou damaging he aphides is e y challenging and
equi es a high deg ee o echnical expe ise. The images p o ided by SEM also con i m he p esence o s oma a
p e iously shown in Figs.2, 3 and 5. Two s oma a wi h open and closed po es espec i ely a e shown in Fig.6c,d.
The p esence o o he s uc u es, no de ec ed by p e ious me hods, such as inny sal c ys als which a e obse ed
abo e and a ound he s oma a po es can also be obse ed due o high esolu ion o SEM.
The p esen pape highligh s he in e es o pola ime ic mic oscopy o he s udy o an Epip emnum au eum
lea , bu he sui abili y o pola ime ic me hods he e discussed was also obse ed by us in di e en specimens o
Hede a ma occana McAll., Spa hiphyllum sp., Hibiscus sy iacus L., Pho inia × ase i D ess, P unus dulcis (Mill.)
D.A.Webb, A um i alicum Mill., Hede a helix L., and Vi is ini e a L. Fo comple eness, mic oscopic pola ime -
ic images o He ede a Helix and Vi is ini e a a e p o ided in he Supplemen a y in o ma ion as illus a i e
examples. In he case o he Epip emnum au eum, pola ime ic channels clea ly show he p esence o aphides
and s oma a in he plan . S oma a play an impo an ole in he in e ac ion be ween plan s and en i onmen 39.
Figu e5. Images o Epip emnum au eum s oma a ob ained wi h a phase (a) and a luo escence (c) mic oscope.
Images o an Epip emnum au eum inulin aphide, ob ained wi h he same phase and luo escence mic oscopes
(b,d), espec i ely.
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These s uc u es egula e gas exchange and wa e loss in plan s, being bo h key p ocesses in a con ex o inc ease
o CO2 a mosphe ic concen a ion and wa e s ess p oduced by ex eme d ough s. Despi e he con as ing
esponses o s oma a o clima e change40, he s udy o hese s uc u es in li ing plan s is especially ele an in
he cu en scena io o de e mine he plan p oduc i i y by analysing i s wa e use e iciency41. Measu emen s
o s oma a a e ypically conduc ed using a silicon ubbe imp ession echnique42 ollowed by a posi i e eplica
o he imp ession ma e ial made by using nail a nish43. Pola ime y is p esen ed as a non-con ac al e na i e
echnique ha is as e and easie o implemen . Mo eo e , pola ime y b ings new in o ma ion ela ed wi h he
dis ibu ion o bi e ingence, p obably due o mechanical s ain, in he s oma a cell walls21.
Raphides a e p esen in many plan species, hei abundance and mo phology (size, shape…) p esence
oge he wi h he c ys al s uc u e and mo phology seems o be cha ac e is ic o axonomic g oup o plan s.
These s uc u es, which may be pa o he de ence mechanism o he plan due o hei oxici y, a e pa icula ly
equen in he A aceae amily. They a e used in ood and pha ma indus ies44,45 and hey ha e se e al medicinal
applica ions, hough hey can also cause se e al side e ec s. In addi ion, he s udy o he aphides can be used
in he cha ac e iza ion o some plan species and in hei sys ema ic classi ica ion46 and o in o m abou he
oxici y o wild edible plan s included in e ie al s a egies47. Elec on mic oscopy is ou inely used o obse e
he c ys als in de ail, bu he echnique equi es speci ic sample p epa a ion. Pola ime y is p esen ed as a non-
in asi e echnique wi h an easie implemen a ion.
The esul s shown in his a icle ha e been selec ed o illus a e he p esence o di e en pola iza ion and
depola iza ion esponses in plan issues and he e o e how hey can be used o cha ac e ize plan sec ions o
speci ic ege al s uc u es. Raphides a e cha ac e ized by a well-de ined depola izing and dich oic esponse, and
s oma a by hei e a dance. These cha ac e is ic pola ime ic esponses allow o an easy iden i ica ion o he
men ioned s uc u es (Figs.2, 3 and 4), while being almos in isible o he mos used op ical ins umen a ion
echniques. The e o e, i has been shown how pola ime ic imaging p o ides e y p ac ical and use ul ools ha
allow o he isualiza ion o some plan cha ac e is ics no obse ed when s anda d non-pola ized images a e
used. In addi ion, pola ime ic me hods can e eal some s uc u es hidden because hey a e ou o ocus bu
ha e a dis inc pola ime ic esponse (Fig.4). Al hough elabo a e sample p epa a ion, such as clea ing, ixing,
cu ing, o moun ing can o cou se help o imp o e image quali y, hey a e no manda o y o do pola ime ic
imaging, which g ea ly simpli y he sample handling and cha ac e iza ion p ocedu es.
Figu e6. Scanning elec on mic og aph showing he ul as uc u e o a bunch o inulin aphides (a) and (b) in
he pa enchyma cell o he s udied Epip emnum au eum lea . S oma ul as uc u e is also shown wi h an open
(c) and closed (d) po e.
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Thanks o he sensi i i y o pola iza ion o speci ic p ope ies which a e gene ally loca ed in well-de ined pa s
o plan , pola ime y can be complemen a y o e en mo e use ul han o he s anda d cha ac e iza ion echniques.
In ac , pola ime y can be combined wi h o he op ical echniques wi hin he same op ical ins umen 35. As
an impo an ad an age, pola ime ic me hods can p o ide unique physical in o ma ion, as was he case o he
non-homogeneous physical p ope ies o he s oma e ealed by pola iza ion (Fig.3a,b), ha was hidden when
using any o he o he me hods desc ibed in his manusc ip , including elec on mic oscopy.
The images p o ided by SEM (Fig.6) con i m he esul s ob ained by using pola ime ic mic oscopy. Elec-
onic images p o ide he bes isualiza ion o plan s uc u es, when compa ed wi h op ical echniques p e i-
ously discussed. Howe e , op ical, in pa icula pola ime ic me hods a e much mo e accessible han elec onic
mic oscope and could be used o dynamic applica ions (snapsho image s). Pola ime e s a e based on compac
(an e en ually po a i e) op ical con igu a ions48, which can be used o ou doo s measu emen s.
Summa izing, he esul s p o ided in his manusc ip illus a e he po en ial o Muelle pola ime ic mic os-
copy o plan cha ac e iza ion and bo anical applica ions, and also hey illus a e he bene i s o he ecen ly
de ised depola iza ion-based obse ables in complemen o he commonly used pola iza ion-based ones. Muelle
pola ime y p o ides complemen a y in o ma ion no accessed using o he op ical echniques, as phase con as
o luo escen mic oscopy. Elec on mic oscopy p o ides images wi h high esolu ion bu is less p ac ical han
pola ime y o o he op ical me hods. Mo eo e , pola ized ligh mic oscopy is a non-in asi e echnique (as i is
he case o luo escen mic oscopy) and can be combined wi h o he op ical echniques in he same ins umen
jus by including e y easible se ups (pola ime e s) in he common pa h o s anda d op ical mic oscope se up. In
addi ion, some image pola ime e a chi ec u es a e e y compac 48 and can be used ou doo s, hus being alid o
pe o m insi u and in i o measu emen s o plan s. Unde his scena io, we hink ha Muelle pola ime y is a
e y in e es ing and p omising echnique o be used alone o in complemen o o he app oaches o s udy plan s.
Ǥ We measu ed a lea o Epip emnum au eum (Linden & And é) G.S.Bun ing, which
is a synonym o Po hos au eus Linden & And é. This species, belonging o he A aceae amily, occu s in o es s
om Sou heas Asia o opical Aus alia. The adul lea es a e usually pe o a ed and o en ha e anslucen
spo s along he mid ib. These e e g een climbing plan s a e cul i a ed o hei a ac i e oliage. A he ba ium
ouche o he s udied species is deposi ed in he He ba ium o he Bo anical Ins i u e o Ba celona (BC843412).
An image o he measu ed Epip emnum au eum is gi en in Fig.1a. The lea measu ed is shown in Fig.1b.
Ǥ Pola iza ion o ligh is in gene al modi ied when i in e ac s wi h ma e ial
media. The o malism ollowed in his wo k o desc ibe he pola ime ic modi ica ions is he Muelle ma ix
app oach. Wi hin his app oach, he s a es o pola iza ion o ligh a e ep esen ed by means o ou eal pa am-
e e s, which a e he componen s o he so-called S okes ec o . The physical meaning o he ou componen s
o he S okes ec o is ela ed o he ellip ici y, ε, and he azimu h, θ, o he pola iza ion ellipse49. The pola iza-
ion ellipse is he ajec o y ollowed by he end poin o he elec omagne ic ield when ligh p opaga es in a
gi en media. Acco dingly, he modi ica ion o he pola iza ion s a e p oduced du ing ligh -ma e in e ac ions is
desc ibed by using a 4 × 4 ma ix called he Muelle ma ix, in such a manne ha he S okes ec o o he ou pu
ligh is gi en by he p oduc o he Muelle ma ix and he S okes ec o o he inpu ligh .
The de e mina ion o he expe imen al Muelle ma ix equi es he use o a Muelle pola ime e , which
measu es he pola ime ic cha ac e is ics o he sample by con olling he pola iza ion o he illumina ion ligh
and analysing he s a e o pola iza ion o he ligh e en ually modi ied du ing he ligh -ma e in e ac ion.
The de e mina ion o a Muelle ma ix is ob ained om a se o adiome ic measu emen s esul ing om he
illumina ion o he sample wi h ligh p epa ed in di e en pola iza ion s a es, and he subsequen analysis o
he pola iza ion o imaged (o de ec ed) ligh beam. This si ua ion is ma hema ically desc ibed by means o he
ollowing exp ession:
whe e I is a n × n ma ix composed by he measu ed in ensi ies, MSample is he 4 × 4 Muelle ma ix o he sample,
SPSG is a 4 × n ma ix whose n columns ep esen he S okes ec o s o he di e en pola iza ion s a es used o
illumina e he sample, and SPSA is a n × 4 ma ix whose ows p o ide he n di e en ansposed S okes ec o s
which ep esen he se o analysis pola iza ion s a es o e which he pola iza ion s a e eme ging om he sample
is p ojec ed o be analyzed. The Muelle ma ix can be de i ed om he Eq.(3) by calcula ing he pseudoin e se
o he analyze and he illumina ion ma ices ( ˜
S
−1
P
SA
and ˜
S
−1
P
SG
) his leading o he ollowing ela ion,
A leas ou illumina ing and analyzed s a es a e needed o measu e he ull Muelle ma ix. The e o e, a
leas 16 measu emen s a e equi ed o ully de e mine MSample.
Ǥ In he wo k p esen ed he e, we make use o di e en pola i-
me ic me ics o analyze he op ical esponse o ege al samples. These me ics a e calcula ed om he expe i-
men al Muelle ma ix and hey a e ela ed o he main pola ime ic con en o he sample, i.e., dia enua ion,
e a dance and he deg ee o depola iza ion. Al hough a ew me ics can be di ec ly ga he ed om he Muelle
ma ix, such as he dia enua ion D, o he me ics can be ob ained a e decomposi ion o he Muelle ma ix
o a se o simple ma ices. The e a e di e en ypes o ma ix decomposi ion schemes, such as p oduc , sum
and di e en ial50,51 ones, each decomposi ion is adap ed o pa icula and well-de ined expe imen al condi ions.
(1)
I
=SPSAMSampleSPSG
,
(2)
MSam
p
le =˜
S−1
PSAI
˜
S−1
PSG
.
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Acco dingly, he choice o one o ano he decomposi ion scheme mus conside he expe imen al condi ions
and he sample s uc u e. In he con ex o he p esen wo k a p oduc decomposi ion known as Lu-Chipman
decomposi ion49,50 was used o ob ain he pola ime ic p ope ies om expe imen al da a. In gene al, he pola-
ime ic p ope ies de i ed om di e en decomposi ions may di e o each o he , he la e being due o he
non-commu a i i y o he di e en algeb aic ope a ions needed o be done in o de o implemen he decom-
posi ion. Be o e doing a inal choice o p esen he da a o his wo k, he pola ime ic da a ob ained wi h he
Lu-Chipman decomposi ion, he symme ic decomposi ion and he di e en ial decomposi ion we e compa ed.
Fo he case analysed in his a icle i was ound ha all he decomposi ions es ed p o ided equi alen esul s.
The choice o he Lu-Chipman decomposi ion was done because i p o ided sligh ly be e esul s in e ms o
nume ical noise compa ed o he symme ic decomposi ion, and because i can be applied o measu emen s in
ansmission and e lec ion con igu a ions, con a ily o he di e en ial decomposi ion, only alid o measu e-
men s in ansmission.
The Lu-Chipman decomposi ion desc ibes he Muelle ma ix as a p oduc o h ee 4 × 4 eal ma ices sepa-
a ing he main pola ime ic in o ma ion encoded in M,
whe e MΔ ep esen s a depola ize , MR, a gene alized e a de , and MD is a gene alized dia enua o . These ma i-
ces can be used o ob ain he alues o he linea and ci cula e a dance and he linea and ci cula dich oism.
Mo eo e , he o ien a ion o he axis de ining linea e a dance and dich oism can also be ob ained om ma ices
MR and MD, espec i ely. The de ails abou he implemen a ion o he Lu-Chipman decomposi ion ha e been
la gely discussed in he li e a u e and a e included in he ex ended in o ma ion sec ion o eade ’s con enience.
To cha ac e ize he depola izing con en o he bo anical samples, in his s udy i is discussed he use o
a ull depola iza ion space ins ead o a single obse able. A depola iza ion space is an abs ac ma hema ical
space made o h ee o mo e depola iza ion- ela ed me ics which a e no ully independen bu ela ed o each
o he . A depola iza ion space gi es in o ma ion no jus on how much ligh is depola ized bu also on how i
is depola ized by he sample. The de ini ion o a depola iza ion space is no unique52,53 and a choice mus be
done based on mul iple c i e ia such as disc imina ion powe be ween depola iza ion me ics, compu a ion
ime, adequacy o he physical p oblem ea ed among o he s54. The depola iza ion space used in his wo k is
composed by he IPPs55, which can be di ec ly deduced om he measu ed Muelle ma ix o he sample. The
se o IPPs is composed o h ee eal magni udes labelled as P1, P2, and P3 (wi h alues om 0 o 1 each) de ined
as espec i e combina ions o he ou eigen alues ( aken in dec easing o de λ0 ≥ λ1 ≥ λ2 ≥ λ3) o he co a iance
ma ix H which is associa ed wi h he Muelle ma ix, M55.
IPP pa ame e s a e es ic ed by he ollowing inequali ies55,
The idea behind IPPs is ha he esponse o any depola ize can be syn hesized as he incohe en sum o ou
componen s wi h di e en weigh s, which a e egula ed by he IPPs50,56. Acco dingly, P1 is associa ed wi h he
ela i e po ion o a non-depola izing componen , P3 wi h he po ion ha is no ully depola ized, and P2–P1
measu es he ela i e po ion o a pa allel componen composed o an equip obable mix u e o wo non-depo-
la izing elemen s50. In his con ex , IPPs allows o he di e en ia ion be ween di e en ypes o depola ize s56,57,
o , in o he wo ds, be ween di e en ypes o depola iza ion mechanisms, which may un eil di e ences among
he s uc u es and o gans in he sample issue. In con as o he IPP, which p o ide comple e quan i a i e in o -
ma ion o depola iza ion, he depola iza ion index PΔ58, commonly used in he pola ime ic communi y, only
p o ides an o e all measu e o he depola izing powe o he sample. No e ha PΔ can e en ually be calcula ed
om he IPPs as55,
Ǥ The op ical mic oscope is he same used in he pola ime ic mic oscope (desc ibed
below), bu wi hou he co esponding PSG and PSA.
Ǥ Pola ime ic images (Figs.2, 3 and 4) we e ob ained wi h a mul imodal mic o-
scope pola ime e . The mul imodal mic oscope is an inno a i e pola ime ic imaging sys em ha can be ope -
a ed in wo imaging modes, he eal plane, and he Fou ie plane (also called conjuga e space plane). In eal
plane imaging mode, he mic oscope p oduces images o he s udied sample, while in Fou ie imaging mode he
images co espond o he angula dis ibu ion o ligh ansmi ed o sca e ed by he sample. The ins umen
is coupled o a whi e ligh LED as a sou ce, ollowed by a na ow-band spec al il e cen ed a a wa eleng h o
533nm wi h a spec al wid h o 15nm. The mic oscope is moun ed in ansmission con igu a ion; he sample
is loca ed be ween wo iden ical mic oscope objec i es (one o imaging and ano he o illumina ion). The
mic oscope objec i es can be selec ed among di e en magni ica ions; 50×, 20×, o 5 × depending on he needs
o a speci ic esolu ion and a nume ical ape u e o a desi ed image.
(3)
M
=
M
MRM
D
,
(4)
P1≡
0−
1
H,P2≡
0+
1−2
2
H,P3≡
0+
1+
2−3
3
H.
(5)
0
≤
P
1≤
P
2≤
P
3.
(6)
P
=
1
√
32P2
1+
2
3
P2
2+
1
3
P2
3.
