Laser optical feedback imaging insensitive to parasiticoptical feedback
Olivier Jacquin,* Eric Lacot, Corinne Felix, and Olivier HugonLaboratoire de Spectrométrie Physique, UMR CNRS 5588, Université Joseph Fourier de Grenoble, 140 Avenue de la
Physique, BP 87, Domaine Universitaire, 38402 Saint Martin d’Hères, France
The laser optical feedback imaging (LOFI) techniqueis a sensitive imaging method combining optical het-erodyne interferometry with the dynamic proprietiesof class B lasers [1]. In this method, the interferencetakes place into the laser, between the intracavitylight and the backscattered light by the studied tar-get. The backscattered light is frequency shifted tocreate an intracavity optical beating. The laser out-put is thus modulated at the shift frequency �. Theamplitude and phase measurement of this modula-tion with a lock-in amplifier makes it possible to ob-tain amplitude (or reflectivity) images and phase (orprofilometry) images [2] of a nocooperative target (adiffusing surface or volume, for example). To get themaximum sensitivity, the optical beating frequencymust be resonant with the natural oscillation of thelaser. That is why the shift frequency � must beequal to the laser relaxation frequency �R. In thiscase, one has a great amplification of the optical beat-ing. For a Nd:YAG microchip laser, this LOFI ampli-fication is of the order of 106, which makes it possible
to be extremely sensitive to the light reinjected intothe laser. Reflectivity as low as 10�13 is then easilydetectable with a laser output power of a few mil-liwatts, with a bandwidth detection of 1 KHz [3]. Inthe LOFI technique the laser is the source and thedetector (Fig. 1). The system is then self-alignedsince the laser and the target are conjugated via theoptics of the system, the backscattered photonscome back into the laser cavity according to thereverse path principle. Consequently, the opticalsystem needs no complex alignment. In the LOFItechnique, an image is built up by a point-by-pointscan. Figure 1 shows a schematic of the LOFI ex-periment.
We used a Nd:YAG microchip laser emitting a fewmilliwatts at the wavelength of 1.064 �m. The relax-ation frequency �R is approximately 1 MHz. A two-axis galvanometric mirror scanner allows us to movethe laser beam on the studied target. The frequencyshift is obtained with two acousto-optic modulatorsoperating respectively at 81.5 MHz (order �1) and81.5 MHz � ��2 (order �1). The frequency shift isequal to ��2 when the light crosses the shifter. Aftera round trip, the total frequency shift of the reinjectedlight into the laser is thus equal to �.
Parasitic reflections are inherent in optical systems.They are generated by all the optical interfaces of thesystem, and they are more or less important accord-ing to the quality of the optical elements. These par-asitic reflections are a leading problem in opticaldevices as, for example, in laser chains [4] or in op-tical telecommunication networks [5]. A significantparasitic reflection generated by an optical elementlocated between the frequency shifter and the studiedtarget limits the LOFI sensitivity for amplitude im-ages. It affects amplitude and phase information con-tained in LOFI images. For a parasitic diffusingobject with an effective reflectivity rP and for a targetwith an effective reflectivity rC, respectively locatedat distances dP and dC from the laser, the expressionsof amplitude and phase extracted by the lock-in am-plifier are [6]
� � a tan�rC sin��c� � rP sin��p�rC cos��c� � rP cos��p��, (1)
R � GLOFI�rC2 � rP
2 � 2rCrP cos��C � �p�Pout, (2)
with �p � �2����2dP, �c � �2����2dC, and Pout as theoutput laser power.
If rP �� rC, the previous equations become � � �c
and R � GLOFIrCPout. The phase � is thus directlyproportional to dC, the distance between the targetand the laser, and the amplitude R is directly pro-portional to the effective reflectivity rC of the target.In the following, we will consider no parasitic reflec-tion if rP �� rC, (i.e., if the parasitic reflections have anegligible effect on the measurements).
On the other hand, if the inequality rP �� rC is notsatisfied, the phase behavior is thus no longer linearaccording to the laser–target distance. As a conse-quence, the displacement measurements or profilom-etry images are degraded. One also notices that the Ramplitude depends on rP, rC and the optical path dif-ference between the parasitic signal and the back-scattered signal from the studied target. In thissituation, the least vibrations of the target generatefluctuations of R, which will disturb amplitude image
acquisition. One has the same fluctuations of R for avibration of the parasitic object or for atmosphericoptical distortion between the parasitic object and thetarget. Intuitively, we can also understand that it willbe difficult to detect target reflectivity lower thanthose of the parasitic object, which then limits thesensitivity of the LOFI technique.
To illustrate the effect of parasitic reflection on theR and � parameters, we have introduced a greatparasitic echo �rP � rC� using a microscope slide. Thisparasitic echo is similar to that caused by optics withno antireflective coating. We have measured at thefrequency �, the reflectivity and the phase for a sin-gle point on the target (no scanning), with a move-ment of the target along the optical axis. Thismovement is obtained from a piezoelectric transla-tion. We measure thus the following parameters:R�dC� and ��dC� for a dC variation between 0 and a few�. These measurements are given in polar coordi-nates in Fig. 2.
Figure 2 shows a circle with radius rC, correspond-ing to a constant reflectivity of the target and a lon-gitudinal displacement greater than �. However, thecircle is not centered because the measured ampli-tude R is not constant. Figure 2 shows also that themeasured phase is not proportional to dC. Indeed, ifyou imagine a circle located in the top right frame,then the phase measured by the lock-in amplifier isincluded between 0 and ��2, whereas it actually var-ies between 0 and 2�. In the absence of importantparasitic reflection, i.e., if rP �� rC, the circle is per-fectly centered with a constant amplitude R and aphase � proportional to dC.
The use of antireflective-coated optics [7] at theworking wavelength in the optical device makes itpossible to avoid parasitic reflections to verify theinequality rP �� rC. However, it is difficult and�orexpensive to verify this inequality for rC reflectivityas low as 10�13. For example, if the LOFI techniqueis coupled with a microscope to realize biological im-ages [8], it is difficult to find objectives with
Fig. 1. Description of the classical LOFI experiment.
Fig. 2. R and � are given in polar coordinates versus the distancedC, with parasitic reflection in the optical system.
antireflective coating at the wavelength of 1.064�m and expensive or not reasonable to use anantireflective-coated microscope slide. The surfaceof the sample also causes an important echo thatlimits the possibilities of investigations under thissurface. These examples highlight the importanceof being able to avoid the adverse effects caused byparasitic reflections.
3. Antireflection LOFI Device
The aim of this work is to present a LOFI device thatallows the measurement of a backscattered signal bythe target without the adverse effects caused by par-asitic reflections. For that purpose, the studied targetis lighted by two laser beams instead of one singlelaser beam. The principle of the experiment is shownin Fig. 3. The laser beam is split by a 50�50 beamsplitter located before the frequency shifter. TheLOFI system is thus composed of two parallel opti-cal arms. The optical frequency is not the same forboth arms. For the top arm in Fig. 3, there is nofrequency shift because the light does not crossthe frequency shifter, whereas there is a frequencyshift for the bottom arm. Both laser beams are fi-nally focused in a single point of the target by alens. The scanning is still performed by two galva-nometric mirrors.
The backscattered light then has two possibilitiesto be reinjected into the laser. Indeed, it can comeback by the bottom arm or by the top arm (Fig. 3). Ineach case, the frequency shift is different. If thelaser–target path and the target–laser path are dif-ferent, then the frequency shift is ��2, because thereinjected light has crossed the frequency shifter onlyonce. If the laser–target path and the target–laserpath are the same, then the frequency shift is � orzero because the reinjected light has crossed the fre-quency shifter twice or never. If there is a parasiticreflection, it takes place before the target, outside theoverlapping point of both beams, which means thatthe laser–target path and the target–laser path arenecessarily the same. Hence, the frequency shift forparasitic reflection is � or zero. Thus, an amplitudeand phase measurement at frequency ��2 with thedevice presented in Fig. 3 makes it possible to avoidthe adverse effects caused by parasitic reflections.
4. Experimental Results
To validate the principle of the optical device pre-sented in Fig. 3, we have realized the same experi-ment as the one described in Section 2. The parasiticoptical feedback is generated by a microscope slideplaced on both arms just after the frequency shifter.We have measured at the frequency ��2 the reflec-tivity and the phase for a single point on the target(no scanning), with a movement of the target alongthe optical axis. We measure thus the following pa-rameters: R�dC� and ��dC� for dC variations between 0and a few �. These measurements are plotted in polarcoordinates in Fig. 4. It shows a centered circle thatmeans measurements of R and � parameters insen-sitive to the parasitic reflection contribution. The Ramplitude is constant, corresponding to the point ofinvestigation on the target. The measured amplitudewith the lock-in amplifier is thus directly propor-tional to rC, the effective reflectivity of the target atthis point. The measured phase � is also correct.Indeed, it is directly proportional to dC, the distancebetween the laser and the target. These results val-idate the possibility of avoiding the adverse effectscaused by parasitic reflections with the optical sys-tem proposed in Fig. 3.
With the optical device presented in Fig. 3, we havealso realized an image with a controlled parasiticreflection. Images have been realized at the frequen-cies � and ��2. The imaged object is a piece of ametallic ruler. Figure 5 shows images obtained fordifferent investigated configurations. Figures 5(a)and 5(b) give images realized without parasitic re-flection. For measurement at the frequency �, the toparm of the optical system is shut to approach as muchas possible a classical LOFI set up. Figure 5 showsthat images (a) and (b) realized respectively at thefrequencies � and ��2 without significant parasiticreflection �rP �� rC� are of the same quality. Then wehave realized the same images with significant par-asitic reflection �rP � rC� caused by a microscope slidein the optical system (Fig. 3). We note that the imageFig. 3. LOFI device insensitive to optical parasitic reflection.
Fig. 4. R and � given in polar coordinates measured at ��2frequency with antireflection system.
realized at the frequency � is completely drowned inthe noise generated by the parasitic reflection, theimage obtained is a continuous amplitude corre-sponding to the amplitude of light reinjected into thelaser by the parasitic reflection. On the other hand,we note that the measurement at the frequency ��2yields an image of the same quality with or withoutparasitic reflection. We can conclude from these re-sults that the proposed device allows us to realize aLOFI image without the adverse affect caused byparasitic reflections in the optical system.
5. Conclusion
In this paper, we have shown that parasitic reflec-tions damage the amplitude and phase informationcontained in LOFI images. To avoid these adverseeffect, we have presented a LOFI device insensitive tooptical parasitic reflection. The experimental resultsshow that the proposed device allows us to avoid theadverse effect caused by a parasite in the opticalsystem on amplitude and phase LOFI images. Thenext step is to propose an equivalent system self-aligned, in which it is not necessary to overlap bothlaser beams as in the proposed device in this paper.For that, we could, for example, use birefringent op-tics to split the laser beam and to select the round-trip path.
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Fig. 5. LOFI images realized respectively at the frequencies �and ��2, with and without parasitic reflection (i.e., with and with-out the microscope slide placed before the metallic ruler) to vali-date the principle of the antireflection scheme for the LOFItechnique. (a) Detection frequency �, without parasitic reflection;(b) detection frequency ��2, without parasitic reflection; (c) detec-tion frequency �, with parasitic reflection; (d) detection frequency��2, with parasitic reflection.
