Measurement of plant movementin young and mature plants usingelectronic speckle pattern interferometry

Astrid Aksnes Dyrseth

The use of electronic speckle pattern interferometry 1ESPI2 to monitor and measure the surfacemovement of plants is presented. We chose to study the gravitropical response of a coleoptile 1the shootfrom a growing seed2 to illustrate the potentials of the technique for botanical measurements. Acoleoptile represents a very fast growing translucent biological object, a difficult object to recordinterferometrically. Traditional holographic interferometry is not suited to the study of objects withsuch rapid fringe decorrelation. However, ESPI with its short exposure time, fast sampling rate, andhigh sensitivity makes it possible to obtain fringes even on the very tip of the coleoptile where themicrostructure changes most rapidly.Key words: Electronic speckle pattern interferometry, speckle decorrelation, coleoptiles, gravitrop-

ism, plant measurement, TV holography, electronic holography. r 1996 Optical Society of America

1. Introduction

Plant movement has previously been studied withholographic interferometry 1HI2 techniques1 with filmas the recording medium. However, measurementson botanical specimens with HI have been mainlyconfined to mature plants.2–8 In general living ob-jects are more difficult to record interferometricallythan nonliving objects, because the fringe quality isoften poor. This inferior fringe quality is a result ofmany factors9: instability of the object, continuouschanges in the microstructure, and multiple scatter-ing if the light penetrates the surface. In addition,experimental conditions can be difficult. The objectmay be minute, or hard to access; measurementsmust often be obtained quickly and surface reflectiv-ity may be low. Many of these problems can beovercome. For example, scattering can be reducedby careful selection of the laser wavelength. Sur-face reflectivity can be increased by coating thesample, although this should be avoided because itmay influence the response of living tissue.

The author is with the Department of Optics, Division ofPhysics, The Norwegian Institute of Technology, N-7034 Trond-heim, Norway.Received 10 July 1995; revised manuscript received 31 January

1996.0003-6935@96@193695-07$10.00@0r 1996 Optical Society of America

However, the main problem when investigatingbotanical objects is speckle decorrelation caused bychanges in the microstructure, as Briers6,7,10 alsopoints out. To obtain a holographic interferogramof high quality, the exposure time must be shortenough to freeze fluctuations in the interferencepattern and the sampling interval must be shortenough to maintain speckle correlation between thetwo exposures. When film is used as the recordingmedia in HI, the minimum sampling interval forfollowing the object in near real time is equal to thedevelopment time. The two exposures may totallydecorrelate in this time span, which means that nofringes are recorded. Rather than using conven-tional HI, I describe the use of electronic specklepattern interferometry 1ESPI2 tomonitor plantmove-ment in near real time. Phase stepping is used toquantify the movement further.ESPI was introduced almost simultaneously by

Butters and Leendertz,11 Schwomma,12 and Ma-covski et al.13 The technique 1also called TV hologra-phy2 is similar to conventional HI because it permitsfull-field vibration and deformation analysis. Themajor difference between the two techniques is thatESPI uses a video camera as the recording devicerather than a photographic plate. This allows forrecording at high sampling rates 125 Hz2 and withshort exposure times 140 ms2, enabling measurementin near real time. Results can be stored by VCRand frame store for further analysis and documenta-

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tion. However, when video recording rather thanphotographic film is used, the spatial resolution isreduced by approximately two decades for ESPIcompared with HI.14 For many applications this isof minor importance compared with the advantage ofbeing able to record fringes in real time. Anothergreat advantage is that digital-imaging processesare used extensively in ESPI to, e.g., analyze andprocess results, improve visual interpretation, andobtain quantitative measurements. Improvementsin this technology have made ESPI more attractiveand open to new possibilities.

2. Theory

ESPI has been thoroughly discussed in the litera-ture.14–16 The principle of the technique is thereforeonly outlined here. All speckle 1and hologram2 inter-ferometers combine the object speckle pattern with aseparate carrier wave, the reference wave, to createa primary interferogram. To measure deformation,two such interference patterns of the object arerecorded in their original and deformed states. Theprimary interferograms are combined to create asecondary interferogram inwhich the fringes charac-terize the deformation that has taken place.Figure 1 shows a simplified diagram of the prin-

ciple of ESPI. To record a speckle interferogram,one splits the laser beam into two branches, thereference and the object branches. The laser beamin the object branch is expanded to illuminate theobject. The reflected object wave is a speckle wavecarrying information about the object’s topographyand position. It is focused by a lens onto the video

Fig. 1. Schematic illustration of the ESPI principle.

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camera. Apinhole in the reference branch spatiallyfilters the reference wave to create a uniform wave.The interference of these two waves, the primaryinterferogram, is recorded on the target of the videocamera. It contains full-field information concern-ing the relative optical phase of the object. Toresolve the primary interferogram, an in-line configu-ration with angles between the reference and objectwave of less than 1 deg is necessary because of thelow resolving power of the video camera.14 To intro-duce an optical phase shift of the reference beam, themirror in the reference beam path can be translatedwith a piezoelectric transducer.The recorded video signal contains the cross-

interference term carrying relevant information con-cerning the object movement, as well as the un-wanted reference-beam intensity, the dc term. Thedc term is removed by high-pass filtering. Further-more the signal is rectified 1squared2 to convertnegative terms into positive terms. Figure 2 showsa sketch of this reconstruction process.There are two major categories of analysis in

ESPI, vibration and deformation analyses. Defor-mation analysis has been applied to the botanicalobjects studied in this paper and is used when thedisplacement is slower than the video rate. Twocorrelated video frames must be recorded of theobject, sampled at discrete time intervals. Thedifference between the two recordings depicts theoptical phase change undergone during that sam-pling interval. With in-line illumination and obser-vation, one fringe corresponds to a surface displace-ment of approximately half of the wavelength of thelaser light.

Fig. 2. Reconstruction process.

A. Deformation Analysis

From standard interferometric considerations14 itcan be shown that the resultant instantaneous inten-sity in point 1x, y2 of the video picture is

I1x, y2 5 Ir 1 Io1x, y2 1 2 0g 0 3IrIo1x, y241@2cos f1x, y2, 112

where Ir is the uniform reference-beam intensity andIo1x, y2 is the object-beam intensity; 0g 0 is the normal-ized degree of coherence between Ir and Io1x, y2, ameasure of the fringe visibility, and f1x, y2 is thephase difference between the reference and objectbeams at point 1x, y2.The signal from the video camera is high pass

filtered that discards the dc term Ir. NormallyIo1x, y29 Ir, permitting the simplification

I1x, y2 5 Ia1x, y2 0g 0cos f1x, y2, 122

where Ia1x, y2 5 23IrIo1x, y241@2. This filtered signal isstored as a reference frame. In the normal observa-tion mode the object undergoes a deformation, and anew interferogram is high pass filtered and recorded:

I81x, y2 5 Ia1x, y2 0g 0cos f81x, y2. 132

Here f81x, y2 5 f1x, y2 1 Df1x, y2, where Df1x, y2 is thephase change. The phase change is directly propor-tional to the object deformation Ds1x, y2:

Df1x, y2 54pDs1x, y2

l, 142

where l is the illumination wavelength.The interferograms are subtracted from one an-

other and square law rectified, yielding

Idiff21x, y2 5 4Ia21x, y2 0g 02sin23f1x, y2

1 1⁄2Df1x, y24sin231⁄2Df1x, y24. 152

Equation 152 is the product of two sinusoidal terms.The first term contains the object displacement aswell as the random phase between the object and thereference beams, causing a random speckle noiseterm. The second term is due to object displace-ment and gives rise to the observed interferencefringes.As mentioned above, in our experiment plant

movement has beenmonitored by real-time analysis.A high-pass-filtered reference frame of the object isstored. The following frames, which are high passfiltered, are continuously subtracted from the refer-ence frame and rectified. The resulting sinusoidalfringes are displayed on the monitor or recorded onvideo tape. When the fringes become difficult toobserve because of high fringe density, a new refer-ence frame must be stored.

B. Four-Frame Phase-Measuring Technique

To obtain quantitative measurements of object defor-mation, phase-measuring techniques can be used.The four-frame phase-measuring technique17 can be

applied to determine the phase. To determine thephase in one state, four frames in that state arestored with phase shifts of 0°, 90°, 180°, and 270°.A piezoelectric transducer in the reference beamcontrols the phase shifts:

I11x, y2 5 Ia1x, y231 1 0g 0cos f1x, y24, 16a2

I21x, y2 5 Ia1x, y231 1 0g 0sin f1x, y24, 16b2

I31x, y2 5 Ia1x, y231 2 0g 0cos f1x, y24, 16c2

I41x, y2 5 Ia1x, y231 2 0g 0sin f1x, y24. 16d2

By proper combination of Eqs. 162, the phase at eachpoint 1x, y2 in the resulting interferogram can becalculated:

f1x, y2 5 arctanI21x, y2 2 I41x, y2

I11x, y2 2 I31x, y2. 172

To determine the phase change caused by deforma-tion, the phase of the object before deformation,f1x, y2, and the phase of the object after deformation,f81x, y2, must be determined by Eq. 172. The phasechange caused by the deformation at point 1x, y2 isthen

Df1x, y25 f81x, y2 2 f1x, y2. 182

We now combine Eqs. 142 and 182 to find the actualdeformation,Ds1x, y2. This technique cannot be usedfor real-time analysis with our present data acquisi-tion and processing because the collection and analy-sis of the information are too time-consuming. It is,however, possible to store recordings on a high-quality VCR or preferably a photo CD and analyzethe phase information later.

C. Visibility and Decorrelation

The coherence between the reference and the objectwaves determines howwell they interfere.18 If thereis full coherence, the interference fringes have maxi-mum contrast, and if the waves are incoherent, nointerference fringes are obtained. For two waveswith equal intensity the fringe visibility or fringecontrast is defined as

V 5Imax 2 IminImax 1 Imin

, 192

where Imax@min is the maximum@minimum intensityin the interference pattern because of constructive@destructive interference. The visibility of the pri-mary interferogram, which is recorded by the TVcamera, is a measure of the coherence between thetwo waves and can also be written

V 52 0g 0 1IrIo21@2

Ir 1 Io, 1102

where 0g 0 is the normalized degree of coherencebetween Ir, the reference-beam intensity, and Io, the

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object-beam intensity. It is evident that the visibil-ity is at its maximum when Ir 5 Io, giving

Vmax 5 0g 0 5 1, 1112

meaning that there is full coherence. In all othercases 0g 0 , 1.When the primary interferogram is recorded in an

ESPI system, the coherence between the object andthe reference wave is dependent on laser coherenceand polarization. Laser coherence is achieved bymatching the optical path length in the two branchesof the interferometer. Equal polarization 1normallylinear2 of the two waves can be achieved by polariza-tion filters. The fringe visibility is deteriorated byelectronic and optical noise as well as fringe move-ment during exposure. If perfect subtraction of theprimary interferograms can be achieved, the opticalnoise will be removed in the secondary interferogram.Fringe movement during exposure can be a result ofinstability of the ESPI system, turbulence, or objectmovement during exposure.When there is object movement, exposure time is

critical. To obtain maximum contrast of the pri-mary interferogram, the movement must be frozen.Otherwise it is integrated, the effect being like alow-pass filter reducing the visibility. The fringesmay disappear altogether when the fluctuations areas rapid as the exposure time and the amplitude ofthe fluctuations is substantial. When a TV camerais used as the recording medium, fairly rapid move-ments can be frozen because the exposure time isonly 40 ms.When deformation analysis is performed, the pri-

mary interferograms must be sufficiently correlatedto obtain high-quality secondary interferograms.To maintain correlation, the movement cannot ex-ceed the size of a speckle; it is therefore vital that thesampling interval be short enough. One specklerepresents an area with nearly constant intensityand phase, i.e., an area with high spatial coherence.Its size is equal to the diffraction-limited resolutionof the imaging lens.In summary, the exposure time must be short

enough to freeze fluctuations in the interferencepattern, and the sampling interval must be shortenough to maintain correlation between exposuresto obtain a holographic interferogram with highvisibility.6,10 Parts of the object can, however, losecorrelation, whereas other partsmaintain correlation.This reduces the fringe contrast of the secondaryinterferogram and results in a total loss of fringes ifthe local movements or changes are excessive.In the investigation of biological objects there are

two main sources of decorrelation or loss of visibility.One source of decorrelation is due to displacement ina direction other than that beingmeasured. Plants,for example, grow both in length and in breadth.Correlation is destroyed if there is a large in-planedisplacement whenmeasuring out-of-plane displace-ment and vice versa. Another source is due totime-varying speckle. The amplitude and phase Df

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of the individual speckles vary from changes in themicrostructure. This phenomenon can be observedby illuminating a fast-growing botanical specimenwith laser light where we find the speckle pattern tobe constantly fluctuating 1speckle boiling2. The boil-ing effect is caused by surface movements andchanges in the plant’s surface. In addition, if theillumination penetrates the internal structure,move-ment of and within the cells inside the plant contrib-utes. Oscillations or fluctuations giving rise tospeckle boiling do not necessarily result in totaldecorrelation but the speckle contrast becomes poorer.As mentioned above, fluctuations in amplitude of aspeckle result only in total decorrelation if theamplitude of the fluctuations is substantial and thefluctuations are as rapid as the exposure time.Movement exceeding the size of a speckle from, e.g.,growth, causes decorrelation. If the growth andthus changes in cell structure are uneven over thesurface, corresponding local variations in speckledecorrelation occur.Because the speckle pattern from a botanical

specimen consists of light scattered both from thesurface of the specimen and from within the speci-men, fluctuations can be decreased by optimizing thewavelength of the laser used in the interferometer.In our measurements we are mostly interested insurface movements. Briers3 believes that many ofthe speckle fluctuations are due to rapid movementof the chloroplasts within the cells, causing the greencolor of botanical specimens. If we use, for ex-ample, the green-blue light from an argon laser, theinterferometric observation of plants is almost impos-sible. It turns out that when a He–Ne laser with awavelength of 633 nm is used, speckle fluctuationsare less pronounced because the laser light is acomplementary color to the object. It is believedthat red light is absorbed by the green chloroplastsso that most of the light reflected from the object isdue to specular reflection from the plant surface.

3. Experiment

The main purpose of this research was to investigatethe possibilities of using ESPI on growing plants,preferably with phase stepping to obtain quantita-tive results. In cooperation with the BiophysicsGroup at the University of Trondheim we chose tostudy the gravitropical response of oat coleoptiles.A coleoptile is the young shoot 1or sprout2 from theseed before the primary leaf emerges. Coleoptilesare often chosen as botanical test specimens becausethey respond strongly to phototropic and gravitropicstimuli. Many biological processes that are presentin mature plants are inactive in young plants. Aspecific response can therefore be isolated whencoleoptiles are used as specimens instead of a morecomplicated combination of responses when matureplants are used. Coleoptiles are challenging botani-cal objects to inspect interferometrically because oftheir translucence and rapid growth. The micro-structure changes quickly causing rapid fringe decor-relation.

The oat coleoptiles were grown in the dark at roomtemperature until they reached a length of 2.5–4.5cm. They grew at a rate of ,1 cm@day or ,0.1µm@s. Balance reactions were studied by placingthe coleoptile horizontally and measuring the verti-cal movement. Some previous experiments indi-cate that the coleoptile bends downward with dis-placement of less than 1 mm before bending upward,whereas some experiments do not find this down-ward movement first.19–21 A reliable technique forstudying these reactions is of interest to botanists.Investigations with mature plants were carried

out first to investigate whether fringes could beobtained on those specimens that are technically lessdemanding to use for measurements. The Oxalisregnellii was chosen because it too is a classicalspecimen used in botanical investigations. The leaf-lets drop from a horizontal position to an almostvertical position with a rhythmic biological cyclerecurring at ,24-h intervals 1circadian movements2.Measurements were performed when the leafletswere nearly vertical.

4. Setup

Conspecs’ RETRA 1000 system for ESPI with a built-inlaser and video camera and REDEF software fordeformation analysis and digital-imaging routineswere used. Figure 3 shows the setup used to studythe gravitropical response. The mirror changes thedirection of the illumination and object beam verti-cally to give a sensitivity to vertical displacement ofthe coleoptile. The setup used to study the Oxalisregnellii is almost the same but without the mirror;thus the sensitivity direction is horizontal.

5. Results

ESPI proved to be well suited to measuring plantmovements ofmature plants inwhich themicrostruc-ture is relatively stable. Measurements of matureplantmovement22 with the four-frame phase-measur-ing technique gave good fringe quality. Figure 4shows the movement of an Oxalis regnellii leaf.The sampling interval was 30 s, which gives ahorizontal 1out-of-plane2 rate of surface movement of,0.27 µm@s.Preliminary experiments were performed to deter-

mine whether fringes could be obtained on a co-leoptile. Because of stringent stability and adjust-ment requirements, fringes were obtained on abouthalf of the 50 samples studied. The coleoptiles were

Fig. 3. Setup used to study the gravitropical response of oatcoleoptiles.

placed horizontally as shown in Fig. 3, and theirvertical out-of-plane movement was logged by thefour-frame phase-measuring technique. Samplingrates varied from 1 to 45 s depending on wheremeasurement took place and on growth. Whencoleoptiles 2.5–4.5 cm long were measured, samplingrates longer than 45 s gave complete fringe decorre-lation in all cases.The decorrelation could be a result of in-plane

1horizontal2 displacement and@or intensity fluctua-tions from movement or changes of and within thecells. It was found experimentally on an inanimateobject that in-plane displacements had to be greaterthan 10 µm before total decorrelation occurred. Inour experiment decorrelation from in-plane displace-ment was negligible because the elongation rate was,0.1 µm@s, which gave a displacement of 4.5 µm in45 s 1the longest sampling period that we achievedbefore speckle decorrelation.2 Strong speckle boil-ing was observed on all the monitored coleoptiles.This boiling did not decorrelate the speckles suffi-ciently to prevent fringe formation, but it reducedfringe contrast. We believe thatmuch of the speckleboiling is caused by rhythmic fluctuations of andwithin the cells. Total speckle decorrelation lead-ing to a complete loss of fringes occurred after ,2–45s, depending on where the coleoptile was beingmonitored, on the tip or near the base. Theserelatively slower changes in the speckle pattern areprobably due to cell division 1growth2 and causeddecorrelation when the overall movement exceededthe size of a speckle or when the surface microstruc-ture had changed. This assumption is supported bythe fact that cell division is most active on the tip ofthe coleoptile where the speckle decorrelation is alsomost pronounced. Uneven changes in cell structuregave corresponding local variations in speckle decor-relations. In fact, plotting the fringe contrast as afunction of position and time would probably alsoprovide valuable information about the growth.Figures 5 and 6 show the vertical movement of the

coleoptile obtained by the four-frame phase-measur-ing technique. We smoothed the recordings using

Fig. 4. Deformation fringes of an Oxalis regnellii leaf 1with kindpermission from J. B. Nysæther222.

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neighborhood averaging to improve visual interpre-tation. This improves fringe quality, but the back-ground becomes more pronounced and noisy. Eachfringe corresponds to ,0.3-µm displacement. Fig-ure 5 shows that even movement on the very tip of acoleoptile where the microstructure changes mostrapidly can be logged. The movement logged hereis mainly due to upward bending and growth on theunderside of the coleoptile caused by the gravitropi-cal response as well as the out-of-plane growth of thecoleoptile caused by an increase in thickness. Thedetailed behavior of the coleoptile was not analyzed.It was seen, however, that when the coleoptile wasplaced horizontally the rate of vertical movementvaried depending on where the coleoptile was stud-ied 1on the tip or close to the holder2 and where in thebending@growing process it was.Video films were taken of five of the coleoptiles in

real time following their movement for 20 min. Wehad to update the reference frame continuously tomaintain correlation when logging the plant move-ment. Figure 7 shows an example of a real-timerecording. The reference frame had been recorded45 s earlier. Changes in the direction of the co-leoptile movement could be monitored by followingthe real-time fringe movement. The direction offringe movement and coleoptile displacement is di-rectly related.

Fig. 5. Phase recording of ,0.8 cm of the tip of a 3.5-cm-long oatcoleoptile with a sampling interval of 5 s and a vertical rate ofmovement of ,0.2 µm@s.

Fig. 6. Phase recording of ,1 cm of a 3.5-cm-long oat coleoptilewith a sampling interval of 30 s and a vertical rate of movement of,0.05 µm@s.

3700 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

No change in the direction of movement waslogged for most of the samples. One sample did,however, bend downward before bending upward.This coleoptile was 5.5 cm, whereas the others were2.5–4.5 cm, indicating that the weight or maturity ofthe plant might play a role in the reaction. Furtherexperiments must be carried out in amore controlledenvironment to verify this.

6. Discussion

We have shown that ESPI is well suited for measur-ingmovements ofmature plants that are not translu-cent and where the microstructure is fairly stable.To obtain interferometric fringes on growing botani-cal objects, the movement that we are trying torecordmust be large enough to be resolved before thefringes decorrelate. This might be expected to limitthe technique somewhat for measurement on co-leoptiles or other biological objects having rapiddecorrelation times. We have shown, however, that,because of its short exposure time and rapid sam-pling, ESPI can also be used to study the surfacemovement of fast-growing botanical specimens suchas coleoptiles. Fringes were obtained on the verytip of the coleoptile where themicrostructure changesmost rapidly. Movement could be followed in nearreal time as long as is desired, and it could berecorded with a VCR. Traditional interferometricholography techniques where film development isinvolved are not suited to the study of such move-ments6,7 and do not permit real-time observation.We have shown that quantitative results can also

be obtained by the four-frame measuring techniquecombined with digital-image-processing routines.However, a slight movement of the object can beexpected between frames, which results in a smallerror in the calculated phase. To obtain more exactquantitative measurements, other techniques mustbe used. It is possible, for example, to record thephase shifts of the object on a single frame.23,24 Thiseliminates error from the object movement betweenframes.The optical setup used in this experiment recorded

the surface movement of the plant in one directiononly because we were mainly concerned with loggingthe gravitropical response of the coleoptile. Tomea-sure the absolute growth rate, an optical setup that

Fig. 7. Real-time recording of ,1 cm of a 4.5-cm-long oatcoleoptile; the reference frame was recorded 45 s earlier.

illuminates and records the object from three direc-tions is necessary.In conclusion, the possibility of following move-

ment in real time with a video camera is one of thegreat advantages of ESPI. Digital-imaging rou-tines to manipulate the data, e.g., filtering or patternrecognition, open many possibilities. The tech-nique has potential for many biological and biomedi-cal applications in which traditional interferometricholography routines are not suited. In combinationwith microscopic techniques the mutual interactionbetween cells may be investigated possibly withESPI. Further effort will be made to improve thetechnique for biological and biomedical applications.

This researchwas supported byNorges Forskning-sråd. The author thanks Ole Johan Løkberg andHans Magne Pedersen for useful comments. Theauthor also thanks Anders Johnsson for interest inthe measurements of botanical specimens and forproviding the seeds.

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