Effect of diffraction on early-arriving photonsduring femtosecond laser transillumination ofhighly scattering media of biological significance

Theodore G. Papazoglou, W. Q. Liu, Alex Vasiliou, Ralf Grassmel, Costas Kalpouzos,and Costas Fotakis

Early-arriving photons of 100-fs laser pulses transmitted through highly scattering media have beendetected by a streak camera. Because of their partial spatial coherence, they are affected by diffractionfrom small hidden discontinuities. The experimental data of the patterns are analyzed with Fresneldiffraction theory and then corrected accordingly. Submillimeter hidden objects were scanned andimaged. Diffraction correction resulted in a significantly improved contrast in the hidden object’simage.Key words: Ultrafast transillumination, diffraction correction, image-contrast improvement.

r 1996 Optical Society of America

1. Introduction

Most of any image-bearing light that propagatesthrough a highly scattering medium undergoes mul-tiple scattering that causes broadening on both thetemporal and spatial point-spread functions.1–3This has a deleterious effect on the attempt to imagehidden objects in the medium on a micrometer scale1microscopy2 for a variety of applications in themedical and biological fields. Various time-resolvedtechniques have been used to detect objects hiddenin turbid media. Early-arriving photons of a trans-mitted ultrashort laser pulse can carry image infor-mation whereas late-arriving photons, because oftheir extensive scattering, bare little information.4Enhancement of the early part of the propagatingpulse through nonlinear techniques or time-gatingimaging have been used to discriminate betweenthese photons.5,6 Both techniques seem to maxi-mize contrast in the hidden object’s image. Al-though early-coming photons bare information for anarrow cross section surrounding the line of propaga-

The authors are with Laser andApplications Division, Instituteof Electronic Structure and Laser, Foundation for Research andTechnology—Hellas, P.O. Box 1527, 711 10 Heraklion, Crete,Greece.Received 15August 1995; revised manuscript received 1 Febru-

ary 1996.0003-6935@96@193759-04$10.00@0r 1996 Optical Society of America

tion of the laser beam, any optical discontinuity inthis region 1a small absorbing or scattering object2combined with the partial coherence of photons canproduce additional noise in the main intensity distri-bution 1the object shadow2 resulting from interference-based effects such as diffraction.7 Laser diffractom-etry has been suggested in the past as a method ofmeasuring cellular dimension changes caused byfluid shear8 1erythrocyte deformability2. This tech-nique, however, has been used only in transparentmedia in which absorption and scattering are re-duced and the contrast in the cells is high.

2. Experimental Methods

We report the results of a series of measurementsthat were taken on one-dimensional and two-dimensional objects that are hidden in highly scatter-ing media. Diffraction patterns were recognizedthrough their dependence on the distance betweenthe object and the detector. Early-arriving photon-based profiles of the discontinuities were fitted byFresnel theory patterns, and the images that re-sulted were replaced by the best-fitting pattern.The experimental imaging system is illustrated in

Fig. 1. Near-IR 1,790-nm2, sub-100-fs pulses areproduced at a rate of ,80 MHz by a Spectra-PhysicsTsunami Ti:sapphire laser pumped by a Spectra-Physics Ar1 laser. The beam diameter was lessthan 2 mm. After neutral density filter attenua-

1 July 1996 @ Vol. 35, No. 19 @ APPLIED OPTICS 3759

tion, less than 100 mW of laser light is relayed to theobject that is positioned in the middle of the scatter-ing medium. The object is also connected to an x–ytranslation stage. The surrounding medium thick-ness was either 20 or 40 mm. The medium con-sisted of concentrations of polystyrene microspheres1400 nm in diameter2 that resulted in point-spreadfunctions corresponding to those created by chickenbreast tissue of similar thickness. The concentra-tions used in the data presented were 1.2 and 2.3g@L. The fitted parameters for the optical coeffi-cients were 11 2 g2µs 5 0.18 mm21 and µa 5 0.03mm21 in the case of the dense solution. Thesevalues are very similar to the ones reported forchicken breast tissue.1 Calculation of these coeffi-cients was based on fitting the experimental data toPatterson’s analytical expression of the pulse timespreading during transmission.1,6 Transmitted lightemerging from the back surface of the medium isdirectly relayed to the input slit of a HamamatsuC1587 streak camera. The slit’s horizontal lengthvaried from 1 mm 1scanning measurements2 to 3 mm1single-position measurements and camera focus-mode measurements2, and its width was 35 µm.The transmitted lightwas imaged onto the photocath-ode through the slit. Before the initiation of theexperiments it was verified that the shade of submil-limeter objects could be imaged on the photocathodewhen they were irradiated by the laser beam in theabsence of the scattering solution. This wasachieved by operating the camera as an imageintensifier 1focus mode2.

3. Experimental Results

The object used in the experiments was a 500-µm-thick needle and a cross that served as a two-dimensional object. The size of the cross was 2.7mm 3 2.7 mm, and the thickness of each arm was500 µm. It was formed transparently on an opaqueslide.Data-acquisition involved translation of the object

perpendicularly to the slit in the camera. In Fig. 2 asingle streak measurement is depicted. The verti-cal axis is time, and the horizontal axis is the

Fig. 1. Experimental setup of the imaging system.

3760 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

dimension that corresponds to the camera’s slit.In the middle of the streak the decrease in intensityin the early-arriving portion of the pulse 1snakelikephotons2 corresponds to the shade of the needle,whereas no apparent changes are observed for thelater part of the pulse. At the edges of the shade thedouble peaks of the diffraction pattern are visible.The later-arriving portion of the pulse appears to bespatially uniform.To evaluate the diffraction hypothesis the depen-

dence of the object–detector distance on the patternwas determined. The spatial profiles of a 500-µm-wide needle placed in the middle of the 20-mm-widesolution 12.3 g@L2 are depicted in Figs. 31A2, 31B2, and31C2. These measurements were taken at object–detector distances of 3.8, 15, and 33 cm, respectively.Early-arriving photons were recorded during thefirst 50 ps of the transmitted pulse, diffused photonswere recorded during 75 ps 1with a delay of 100 pswith respect to the pulse rise2, and the whole pulsewas recorded for ,500 ps. The curves have beennormalized to depict the enhanced contrast of theearly-arriving pulse with respect to the shade of theobject. The appearance of a third peak is noted asthe distance increases. This effect is in accordancewith the Fresnel diffraction theory.

4. Experimental and Simulated Results

Because of the small size of the hidden obstacle1millimeters in scale2, the laser beam spreads out intoa diffraction field. The time-gated image could becorrected by Fresnel theory. In this case the Fres-nel integrals can be simplified as

e0

n

exp1ipn2@22dn 5 x1n2 1 iy1n2, 112

Fig. 2. Streak measurement depicting reduced intensity onearly-coming photons caused by the presence of an obstructingobject 1a 0.5-mm-wide needle placed in the middle of a 20-mm-wide scattering solution2. The full vertical scale corresponds to,3.0 mm, whereas the horizontal scale corresponds to ,2 ns.

where

x 5 e0

n

cos1pn2@22dn, y 5 e0

n

sin1pn2@22dn, 122

and n 5 s12@lr21@2, where s is the size of the hiddenobstacle, r is the distance from the sample to the slitof the streak camera, and l is the laser wavelength.If the scattering coefficient 1µs2 of the obstacle islarger than that of the surroundings, the lightdistribution is expected to resemble that of an opaqueobject. If µs of the obstacle is smaller than that ofthe surroundings, the light distribution resembles aslit’s diffraction pattern. The intensity of the distri-bution, after the laser beam has propagated throughthe diffused sample and been obstructed by a smallhidden discontinuity, taking into account the diffrac-tion effect, can now be analytically described by

Ip 5I02

6 3x1n2 1 iy1n24n1n262. 132

The time-gated image could thus be corrected by thisfactor.The diffraction pattern of a 500-µm-wide obstacle

is depicted in Fig. 41A2 and compared with theexperimental spatial profile that was based on the

Fig. 3. Spatial profiles of photon distribution based on theearly-arriving 150 ps2, the whole part 1500 ps2, and the diffused partof the transmitted pulse 175 ps, 100-ps delay2. Graphs 1A2, 1B2, and1C2 depict measurements taken at object–detector distances of 3.8,15, and 33 cm, respectively.

early-arriving photon measurement 150-ps gating2.The latter was obtained at a 38-mm object–detectordistance whereas the obstacle was positioned in themiddle of a 40-mm-thick polystyrene microspheresolution. Experimental data have also been scalecorrected by the factor 12@lr21@2. The side peaksrepresent the diffraction pattern in the near-fieldimage. It is evident that the two curves resembleeach other, although both overestimate, as expected,the real size of the obstacle 1shown by the doublearrow2. The resulting image of the 500-µm needle isshown in Fig. 41B2. This latter was obtained after avertical scanning of the object. To demonstrate theeffect of diffraction, a limited dynamic range ofgray-scale levels was chosen. This procedure, how-ever, created some additional artifacts, such as theblack stripe in the middle that corresponds to thelittle dip in the experimental data. Finally in Fig. 5the image of a transparent cross is depicted. In Fig.51A2 the image based on early-coming photons 1theinitial 30 ps of transmitted pulse, 38-mm object–detector distance2 is shown, whereas in Fig. 51B2 theimage is based on the diffraction patterns best fittedto the experimental cross sections of the two bars ofthe cross. The diffraction patterns were initiallyfitted to the raw data by visual inspection. It isevident that the latter, although representing anoverestimation of the hidden object, exhibits im-proved contrast.

Fig. 4. Comparison of the spatial profile of early-arriving pho-tons 150 ps2 with a pattern predicted by Fresnel diffraction theory1A2 1a 0.5-mm-wide needle placed in the middle of a 40-mm-widescattering solution2. The resulting image of the needle 1B2 isbased on the experimental raw data.

1 July 1996 @ Vol. 35, No. 19 @ APPLIED OPTICS 3761

5. Discussion and Conclusions

The method described in this study may be signifi-cant in biomedical applications in which opaque oralmost opaque material is imaged through turbidmedia. It is expected that microscopic measure-ments of small structures such as erythrocytes 1ekta-cytometry82 may be possible even when the cells aresurrounded by a highly scattering medium. At-tempting to observe diffraction effects is worthwhilewhen the difference in the scattering coefficientbetween the hidden object and the environment issmall. The objective in this case is to determine theminimum change in µs that can create interferencepatterns observable over the noise. This study isunder way.Another extension of this study that is being

investigated is the case in which more than onehidden object is imaged through the turbid medium.Initial results show that interference patterns areobserved although it is difficult to relate them to thesize of the hidden objects and the distance between

(a)

(b)

Fig. 5. Comparison between 1a2 an early-arriving photon-basedimage of a transparent cross placed in a 20-mm-wide 2.3-g@Lsolution of scattering spheres and 1b2 that predicted by thediffraction theory spatial distribution resulting from the patternsbest fitted to the experimental cross sections of the bars.

3762 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

them. Other groups have indicated that, by selec-tively detecting the information-carrying light andusing spatial filtering, time-resolved detection, or acombination of both, the image quality can be im-proved greatly.9 It is expected that the efficiency ofthe method improves once it is combined with simpleor confocal microscopy, although special consider-ation needs to be taken in the temporal alteration ofthe probing femtosecond pulse by the microscopeoptics.Finally the diffraction pattern simulations can be

improved further by using a running least-squaresfit between the experimental data and the Fresnelintegral calculation. Then the size of the objectthat corresponds to the test fit can be used for thefinal image correction.In conclusion, we have demonstrated that the

detailed diffraction pattern, carried by the early-coming photons during transillumination, of a hid-den object in a highly scattering medium can be usedto improve further the quality of the object’s image.

The authors acknowledge the support of Hama-matsu Photonics Deutschland and the Large Instal-lations Plan—DGXII 1Hunyay Capital and Mobilityprogram ERBCHGECT9200072.

References1. F. Liu, K. M. Yoo, and R. R. Alfano, ‘‘Transmitted photon

intensity through biological tissues within various time win-dows,’’ Opt. Lett. 19, 740–742 119942.

2. B. B. Das, K. M. Yoo, F. Liu, J. Cleary, R. Prudente, E. Celmer,and R. R. Alfano, ‘‘Spectral optical-density measurements ofsmall particles and breast tissues,’’ Appl. Opt. 32, 549–553119932.

3. J. C. Hebden and D. T. Delpy, ‘‘Enhanced time-resolved imag-ing with a diffusion model of photon transport,’’ Opt. Lett. 19,311–313 119942.

4. S. Andersson-Engels, R. Berg, S. Svanberg, and O. Jarlman,‘‘Time-resolved transillumination for medical diagnosis,’’ Opt.Lett. 15, 1179–1181 119902.

5. J. C. Hebden, ‘‘Evaluating the spatial resolution performanceof a time-resolved optical system,’’ Med. Phys. 19, 1081–1087119922.

6. K. Yoo, Q. Xing, and R. R. Alfano, ‘‘Imaging objects hidden inhighly scattering media using femtosecond second-harmonic-generation cross-correlation time gating,’’ Opt. Lett. 16, 1019–1021 119912.

7. T. G. Papazoglou, W. Q. Liu, and A. Manolopoulos, ‘‘Utilizationof diffraction patterns in detection of hidden discontinuities inturbid media of biological significance,’’ in 1994 Conference onLasers and Electro-Optics 1CLEO@Europe2, 1994 Technical Di-gest Series 1Optical Society of America, Washington, D.C.,19942, pp. 214–215.

8. W. Groner, N. Mohandas, and M. Bessis, ‘‘New optical tech-nique formeasuring erythrocyte deformability with the ektacy-tometer,’’ Clin. Chem. 26@10, 1435–1442 119802.

9. G. E. Anderson, F. Liu, and R. R. Alfano, ‘‘Microscope imagingthrough highly scattering media,’’ Opt. Lett. 19, 981–983119942.