- Email: [email protected]
Phase conjugation, imaging in biological media and characterization of quantum noise by parametric image amplification
C. R. Acad. Sci. Paris, t. 1, Série IV, p. 627–632, 2000 Solides, fluides : propriétés électroniques et optiques/Solids, fluides: electronic and optical properties (Physique appliquée/Applied physics)
OSCILLATEURS PARAMÉTRIQUES OPTIQUES : FONDEMENTS ET APPLICATIONS OPTICAL PARAMETRIC OSCILLATORS: BASICS AND APPLICATIONS
DOSSIER
Phase conjugation, imaging in biological media and characterization of quantum noise by parametric image amplification Éric LANTZ, Fabrice DEVAUX, Gaëlle LE TOLGUENEC Laboratoire d’optique P.M.-Duffieux, UMR 6603 CNRS, université de Franche-Comté, 25030 Besançon cedex, France E-mail: [email protected] (Reçu le 3 janvier 2000, accepté le 6 mars 2000)
Abstract.
We review recent results about parametric image amplification obtained in our group and in others. First, forward phase conjugation has been used to restore images through aberrant media and to image objects embedded through thick biological tissues. Second, quantum noise in image amplification has been actively studied by several groups, leading to theoretical demonstration of image entanglement and squeezing, as well as experiments on noiseless image amplification and characterization of the correlations in the spatial fluctuations of amplified images. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS nonlinear optics / parametric amplification / imaging
Conjugaison de phase, imagerie dans les milieux biologiques et caractérisation du bruit quantique par amplification paramétrique d’images Résumé.
Cet article présente les résultats récents obtenus en amplification paramétrique d’images dans notre groupe et ailleurs. Tout d’abord, nous avons utilisé la conjugaison de phase vers l’avant dans un milieu quadratique pour restaurer des images ayant subi une distorsion déterministe et pour imager des objets cachés dans des tissus biologiques épais (4 cm). D’autre part, le bruit quantique en amplification d’images a fait l’objet d’études par plusieurs équipes, ayant abouti à la démonstration théorique de la possibilité de reproduction sans bruit d’une image et à la réalisation expérimentale de l’amplification d’une image avec conservation du rapport signal sur bruit. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS optique non linéaire / amplification paramétrique / traitement d’images
Note présentée par Guy L AVAL. S1296-2147(00)00157-8/FLA 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés.
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E. Lantz et al.
OPTICAL PARAMETRIC OSCILLATORS
1. Introduction After the first demonstration of parametric image amplification by Guthals and Sox [1], we experimentally characterized the spatial resolution in the amplified image and then demonstrated edge enhancement by filtering of spatial frequencies, time-gated image recovery and amplification of a polychromatic image [2]. This note aims to summarize more recent results and some promising perspectives. After a brief recall of the principle of parametric image amplification in Section 2, Section 3 is devoted to imaging through aberrant media by forward phase-conjugation. In Section 4, we present imaging through thick biological media, that could be a first step to optical mammography. Section 5 deals with quantum fluctuations in amplified images. 2. Principle of parametric image amplification The partially transparent object is trans-illuminated by a monochromatic plane wave. The scattered light forming the input signal can be considered as a superposition of plane waves, each plane wave being associated to a spatial frequency of the object by the laws of Fourier optics. The pump beam, as well collimated and monochromatic as possible, is superimposed with the signal in a nonlinear birefringent crystal. The formation of an amplified image can be obtained in three different ways: (a) No imaging system is used and the image is formed with the idler wave, that is phase-conjugate of the signal wave [3–6]. (b) The crystal is placed in the Fourier plane of the imaging system [1]. The range of amplified spatial frequencies is then determined in this plane by the transverse cross-section of either the crystal or the pump beam (the latter situation occurs if the diameter of the pump beam is not large enough to ensure uniform illumination of the crystal). On the other hand, the field of view is determined by the angular acceptance that can be derived from the phase-matching conditions. (c) The crystal is placed in a first image plane and a second image is formed on the detector [2]. The field of view is determined by the lateral sizes of the crystal (or of the pump beam), while the amplified spatial frequencies are determined by the phase-matching conditions. In the last case, the resolution is optimum for a phase-matching configuration that is noncritical for the signal [2,7]. The general expression of the phase-mismatch vector that determines the resolution can be found in [8]. 3. Image restoration by optical phase conjugation With no imaging system, the idler is phase conjugate with the signal, but propagates in the forward direction. Hence, it forms an image of the object plane in a conjugate plane, symmetrically located with respect to the crystal, while the amplified signal still gives a far-field representation of the diffracted wave. The resolution is determined by the smallest value between the phase-matching aperture and the geometric angular aperture, that is the solid angle occupied by the crystal (or by the pump beam) seen from the object [4]. The most promising application of optical phase conjugation is to correct deterministic aberrations. We have shown that, like usual optical phase conjugation in χ(3) media, χ(2) phase conjugation can be used for this purpose [5]. Figure 1 presents our experimental setup. The infrared beam at 1.064 µm is delivered by a Q-switched mode-locked Nd : YAG laser. The radiation is partially frequency-doubled in a KDP crystal. The remaining infrared light is separated from the green light by a dichroïc mirror and is then attenuated and vertically polarized. This beam illuminates a transparency (the object) which is at a distance D = 36 cm of the input face of a 4 × 4 mm wide and 5 mm long KTP crystal. The diffracted signal wave (Σs ) crosses an aberrant plate which is at a distance d = 15 cm of the object. Frequency-doubled light is used as the pump beam. The collimated pump pulse is synchronized with the infrared pulse by means of a delay line and illuminates uniformly the whole crystal. The pump beam diameter is about 1 cm (FWHM) and the power density on the crystal is adjusted at 160 MW/cm2 , corresponding to a mean gain of 4 dB. Since
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Figure 1. Experimental setup for image restoration by three waves mixing phase-conjugation. BS: beam splitter; P: polarizer; F: RG5 filter.
Figure 2. (a)–(c) represent direct images of different parts of the object. (b) corresponds to the group of 3.17 lines/mm. (d)–(f) represent direct images of the same parts of the object through the aberrant plate. (g)–(i) represent restored images formed by the idler wave reflected back through the aberrant plate. On (i), the group of 5.66 lines/mm is resolved.
there is no anti-reflecting coatings on the crystals faces, the output face is used as a mirror (R ∼ 7%) and is exactly turned towards the normal direction of propagation of the pump plane wave. The reflected waves (Σ0s , Σi ) propagate back through the aberrant plate. While the signal wave (Σ0s ) is once more degraded by the backward travel through the aberrant medium, distortions of the idler wave (Σi ) are compensated and the initial diffracted wave is restored. A beam-splitter (BS) directs the counter-propagating waves on a single-shot CCD camera sets in the object conjugate plane at the same distance D of the crystal. A polarizer (P) sets in front of the camera rejects the signal and permits the detection of the idler wave only. Figures 2a–2c present images of different parts of the transparency obtained by a direct imaging system on the CCD camera with no amplification process. Figure 2b corresponds to the group of 3.17 lines/mm. Figures 2d–2f present images of the same parts of the resolution chart with the aberrant plate set between the object and the imaging system. Images are strongly distorted and objects can no more be identified whatever the group of lines. Restored images formed by the idler wave reflected back through the aberrant plate are presented in figures 2g–2i. Distortions are compensated and the group of 5.66 lines/mm (176 µm) are resolved ( figure 2i). The same resolution was measured in phase conjugate images obtained with no
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aberrant medium. This resolution is in a good agreement with the predicted resolution and the aberrant medium does not seem to affect image resolution. 4. Time-resolved imaging through thick biological tissues In the recent years, optical imaging through biological media has attracted a considerable interest, owing to the small absorption in the therapeutic window (600–1300 nm) and the non ionizing character of light. However, the light is strongly scattered and various methods have been proposed to select the least scattered photons [9]. In relatively thin media, a part of the incident light, called ballistic, is not scattered and images are now routinely obtained by using optical coherence tomography, that detects this ballistic light by interferomtry [10]. In thicker media, like human breast, imaging tumors remains challenging, because the optical thickness is so important that ballistic light does not exist any more and images must be formed with scattered photons. Since diffusion in a biological medium is strongly anisotropic, the photons are preferentially scattered in the forward direction and the front part of a short pulse, largely stretched by the medium, is formed with the least scattered photons that have traveled on the shortest paths. Hence, the front part still carries some amount of spatial information, with a resolution that depends on the thickness of the diffusing medium. We have used parametric image amplification to separate this front part from the multi-diffused light [6]. The most efficient scheme, shown in figure 3, combines time-gating and forward phase conjugation for a better rejection of the diffused light. In order to increase the field of view, a virtual image is formed with a 0.1 magnification in the plane symmetrical of the CCD camera with respect to the crystal.
Figure 3. Experimental set-up for imaging through biological samples: Σ0 : object plane; Σv : virtual object plane; Σc : phase-conjugated image plane; P1–P3: Glan–Taylor polarizers.
Figure 4. (a) amplified image of the cross without biological tissue. (b)–(c) amplified images through 4 cm thick chicken breast tissue. The delays are respectively 0 and 158 ps. In (b) the strips are resolved and the best SNR ≈ 2 is obtained. (d) resolved image of a 1 cm3 piece of liver embedded in the same chicken breast sample.
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Figure 4 shows experimental results. Figure 4a presents an amplified image of the object, a cross formed by two 9 mm wide metal strips, without biological tissue. Figures 4b and 4c show images of this cross embedded in 4 cm thick chicken breast tissues. The delays are respectively 0 and 158 ps, where the time origin corresponds to the pump and signal pulses synchronized in the crystal in the absence of biological tissue. In figure 4b the 9 mm wide metal strips are resolved and the best signal-to-noise ratio is obtained. When the delay is greater than 33 ps, the strips are no longer resolved and only diffused light is amplified ( figure 4c). Figure 4d shows a resolved image of a 1 cm3 piece of liver embedded in the same biological sample [11]. These results are very promising because the thickness of the biological tissues corresponds to that of human breast in mammography. Though the resolution is in the range of several millimeters, the nonionizing and non-invasive character of the method could be very useful for routine preventive exams. Using parametric image amplification, images in a reflection configuration have been obtained recently with femtosecond pulses [12]. This pulse duration allows precise tomography, but for thinner samples. 5. Characterization of quantum fluctuations and noiseless image amplification Quantum fluctuations in parametrically amplified images have been actively studied in the last years by several groups. For temporal signals, it was experimentally proved some years ago that a phase-sensitive amplifier can preserve the signal-to-noise ratio [13], while a phase-insensitive amplification adds at least 3 dB to the quantum noise. Conditions for noiseless amplification of images have been recently theoretically determined [14] and conservation of the signal-to-noise ratio on each pixel of the amplified image has been experimentally demonstrated [15]. Noise means here temporal fluctuations. In the same way, correlations between homologue pixels of the images formed respectively by the idler and the signal lead to a subpoissonian level for the noise on the intensity difference, that is the signature of image entanglement [16]. The very precise spatio–temporal location of twin photons was already demonstrated in experiments where the image formed by an aperture that spatially modulated the signal beam after the crystal was reproduced on the idler by detecting the coincidences [17]. Although quantum fluctuations are usually detected in the time domain, they can also be observed in the spatial domain. Figure 5 shows spatial fluctuations in the far-field image of parametric fluorescence in a LBO crystal detected at degeneracy [18]. The ring is due to phase-matching and a strong correlation between symmetrical points is evident. While the size of the fluctuations can be connected to the Fourier transform of the pupil in the crystal (in our case, the pump beam), the correlation between the symmetrical points is due to the twin character of the spontaneously down-converted light. These results can be quite accurately reproduced by a numerical simulation that takes in account the coherent amplification with
Figure 5. Sequence of three spatial frequency spectra of parametric fluorescence obtained with the same phase matching conditions and approximately the same pump energy. Each spectrum corresponds to one laser shot. Arrows on the second spectrum underline the central symmetry of the spatial fluctuations. The circle of best phase matching is drawn on the third spectrum.
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a random noise at the input at a level of one photon per spatio–temporal mode. We plan to experimentally demonstrate the conservation of the signal-to-noise ratio in phase-sensitive amplification, where noise means spatial fluctuations. An applications could be precise lateral displacement measurements [19]. The first experimental step has been the measurement of the amplification gain versus the input phase and the spatial frequency [20]. The results are in good agreement with theory [21]. 6. Conclusion In the last years, various groups have used parametric amplification of images, with goals going from quantum optics to protection against laser attacks [22]. Because of the promising results, this effort will undoubtedly continue in next years. References [1] Guthals D., Sox D., Quantum limited optical parametric image amplification, in: Proc. Internat. Conf. Lasers ’89, D.G. Harris, T.M. Shay (Eds.), STS, Mclean, VA, 1990, pp. 808–815. [2] Lantz E., Devaux F., Parametric amplification of images, Quantum Semiclass. Opt. 9 (1997) 279–286. [3] Lefort L., Barthélémy A., Revisiting optical phase conjugation by difference-frequency generation, Opt. Lett. 21 (1996) 848–850. [4] Devaux F., Le Tolguenec G., Lantz E., Phase conjugate imaging by type II parametric amplification, Opt. Commun. 147 (1998) 309–312. [5] Devaux F., Guiot E., Lantz E., Image restoration through aberrant media by optical phase conjugation in a type II three-wave mixing interaction, Opt. Lett. 23 (1998) 1597–1598. [6] Le Tolguenec G., Devaux F., Lantz E., Two-dimensional time-resolved direct imaging through thick biological tissues: a new step toward noninvasive medical imaging, Opt. Lett. 24 (1999) 1047–1049. [7] Devaux F., Lantz E., Lacourt A., Gindre D., Maillotte H., Doreau P.A., Laurent T., Picosecond parametric amplification of a monochromatic image, Nonlinear Opt. 11 (1995) 25–37. [8] Lantz E., Devaux F., Phase-mismatch vector and resolution in image parametric amplification, J. Opt. A, in print. [9] See for example, Alfano R.R., Fujimoto J.G. (Eds.), OSA TOPS on Advances in Optical Imaging and Photon Migration, Orlando, USA, March 1996. [10] Tearney G.J., Bouma B.E., Boppart S.A., Golubovic B., Swanson E.A., Fujimoto J.G., High speed optical coherence tomography, in: TOPS on Advances in Optical Imaging and Photon Migration, Orlando, USA, March 1996, p. 224. [11] Devaux F., Le Tolguenec G., Lantz E., 2D time-resolved direct imaging through thick biological tissues by parametric amplification, in: Light for Life Meeting, Cancun, Mexico, July 1999. [12] Doulé C., Lépine T., Georges P., Brun A., Imaging through scattering media with fentosecond non-colinear parametric amplification, Summer School, Waves and Imaging Through Complex Media, Cargèse, France, August 1999, p. 25. [13] Levenson J.A., Abram I., Rivera T., Grangier P., Reduction of quantum noise in optical parametric amplification, J. Opt. Soc. Amer. B 10 (1993) 2233–2238. [14] Sokolov I., Kolobov M., Lugiato L.A., Quantum fluctuations in traveling-wave amplification of optical images, Phys. Rev. A 60 (1999) 2420–2430. [15] Choi Sang-Kyung, Vasilyev M., Kumar P., Noiseless optical amplification of images, Phys. Rev. Lett. 83 (1999) 1938–1941. [16] Gatti A., Brambilla E., Lugiato L.A., Quantum entangled images, Phys. Rev. Lett. 83 (1999) 1763–1766. [17] Pittman T.B., Strekalov D.V., Klyshko D.N., Rubin M.H., Sergienko A.V., Shih Y.H., Two-photon geometric optics, Phys. Rev. A 53 (1996) 2804–2815. [18] Devaux F., Lantz E., Spatial and temporal properties of parametric fluorescence around degeneracy in type I LBO crystal, Europhys. J. D 8 (2000) 117–124. [19] Fabre C., Fouet J.B., Maître A., Quantum limits in the measurement of very small displacements in optical images, Opt. Lett. 25 (2000) 76–78. [20] Devaux F., Lantz E., Gain in phase sensitive parametric image amplification, Phys. Rev. Lett., in print. [21] Devaux F., Lantz E., Parametric amplification of a polychromatic image, J. Opt. Soc. Amer. B 12 (1995) 2245– 2252. [22] Faure J.P., Giraudo O., Modelling of parametric beam conversion: application to image amplification with optical self-limiting, Nonlinear Opt. 21 (1999) 447–459.
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OSCILLATEURS PARAMÉTRIQUES OPTIQUES : FONDEMENTS ET APPLICATIONS OPTICAL PARAMETRIC OSCILLATORS: BASICS AND APPLICATIONS
DOSSIER
Phase conjugation, imaging in biological media and characterization of quantum noise by parametric image amplification Éric LANTZ, Fabrice DEVAUX, Gaëlle LE TOLGUENEC Laboratoire d’optique P.M.-Duffieux, UMR 6603 CNRS, université de Franche-Comté, 25030 Besançon cedex, France E-mail: [email protected] (Reçu le 3 janvier 2000, accepté le 6 mars 2000)
Abstract.
We review recent results about parametric image amplification obtained in our group and in others. First, forward phase conjugation has been used to restore images through aberrant media and to image objects embedded through thick biological tissues. Second, quantum noise in image amplification has been actively studied by several groups, leading to theoretical demonstration of image entanglement and squeezing, as well as experiments on noiseless image amplification and characterization of the correlations in the spatial fluctuations of amplified images. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS nonlinear optics / parametric amplification / imaging
Conjugaison de phase, imagerie dans les milieux biologiques et caractérisation du bruit quantique par amplification paramétrique d’images Résumé.
Cet article présente les résultats récents obtenus en amplification paramétrique d’images dans notre groupe et ailleurs. Tout d’abord, nous avons utilisé la conjugaison de phase vers l’avant dans un milieu quadratique pour restaurer des images ayant subi une distorsion déterministe et pour imager des objets cachés dans des tissus biologiques épais (4 cm). D’autre part, le bruit quantique en amplification d’images a fait l’objet d’études par plusieurs équipes, ayant abouti à la démonstration théorique de la possibilité de reproduction sans bruit d’une image et à la réalisation expérimentale de l’amplification d’une image avec conservation du rapport signal sur bruit. 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS optique non linéaire / amplification paramétrique / traitement d’images
Note présentée par Guy L AVAL. S1296-2147(00)00157-8/FLA 2000 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés.
627
E. Lantz et al.
OPTICAL PARAMETRIC OSCILLATORS
1. Introduction After the first demonstration of parametric image amplification by Guthals and Sox [1], we experimentally characterized the spatial resolution in the amplified image and then demonstrated edge enhancement by filtering of spatial frequencies, time-gated image recovery and amplification of a polychromatic image [2]. This note aims to summarize more recent results and some promising perspectives. After a brief recall of the principle of parametric image amplification in Section 2, Section 3 is devoted to imaging through aberrant media by forward phase-conjugation. In Section 4, we present imaging through thick biological media, that could be a first step to optical mammography. Section 5 deals with quantum fluctuations in amplified images. 2. Principle of parametric image amplification The partially transparent object is trans-illuminated by a monochromatic plane wave. The scattered light forming the input signal can be considered as a superposition of plane waves, each plane wave being associated to a spatial frequency of the object by the laws of Fourier optics. The pump beam, as well collimated and monochromatic as possible, is superimposed with the signal in a nonlinear birefringent crystal. The formation of an amplified image can be obtained in three different ways: (a) No imaging system is used and the image is formed with the idler wave, that is phase-conjugate of the signal wave [3–6]. (b) The crystal is placed in the Fourier plane of the imaging system [1]. The range of amplified spatial frequencies is then determined in this plane by the transverse cross-section of either the crystal or the pump beam (the latter situation occurs if the diameter of the pump beam is not large enough to ensure uniform illumination of the crystal). On the other hand, the field of view is determined by the angular acceptance that can be derived from the phase-matching conditions. (c) The crystal is placed in a first image plane and a second image is formed on the detector [2]. The field of view is determined by the lateral sizes of the crystal (or of the pump beam), while the amplified spatial frequencies are determined by the phase-matching conditions. In the last case, the resolution is optimum for a phase-matching configuration that is noncritical for the signal [2,7]. The general expression of the phase-mismatch vector that determines the resolution can be found in [8]. 3. Image restoration by optical phase conjugation With no imaging system, the idler is phase conjugate with the signal, but propagates in the forward direction. Hence, it forms an image of the object plane in a conjugate plane, symmetrically located with respect to the crystal, while the amplified signal still gives a far-field representation of the diffracted wave. The resolution is determined by the smallest value between the phase-matching aperture and the geometric angular aperture, that is the solid angle occupied by the crystal (or by the pump beam) seen from the object [4]. The most promising application of optical phase conjugation is to correct deterministic aberrations. We have shown that, like usual optical phase conjugation in χ(3) media, χ(2) phase conjugation can be used for this purpose [5]. Figure 1 presents our experimental setup. The infrared beam at 1.064 µm is delivered by a Q-switched mode-locked Nd : YAG laser. The radiation is partially frequency-doubled in a KDP crystal. The remaining infrared light is separated from the green light by a dichroïc mirror and is then attenuated and vertically polarized. This beam illuminates a transparency (the object) which is at a distance D = 36 cm of the input face of a 4 × 4 mm wide and 5 mm long KTP crystal. The diffracted signal wave (Σs ) crosses an aberrant plate which is at a distance d = 15 cm of the object. Frequency-doubled light is used as the pump beam. The collimated pump pulse is synchronized with the infrared pulse by means of a delay line and illuminates uniformly the whole crystal. The pump beam diameter is about 1 cm (FWHM) and the power density on the crystal is adjusted at 160 MW/cm2 , corresponding to a mean gain of 4 dB. Since
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DOSSIER
OPTICAL PARAMETRIC OSCILLATORS
Figure 1. Experimental setup for image restoration by three waves mixing phase-conjugation. BS: beam splitter; P: polarizer; F: RG5 filter.
Figure 2. (a)–(c) represent direct images of different parts of the object. (b) corresponds to the group of 3.17 lines/mm. (d)–(f) represent direct images of the same parts of the object through the aberrant plate. (g)–(i) represent restored images formed by the idler wave reflected back through the aberrant plate. On (i), the group of 5.66 lines/mm is resolved.
there is no anti-reflecting coatings on the crystals faces, the output face is used as a mirror (R ∼ 7%) and is exactly turned towards the normal direction of propagation of the pump plane wave. The reflected waves (Σ0s , Σi ) propagate back through the aberrant plate. While the signal wave (Σ0s ) is once more degraded by the backward travel through the aberrant medium, distortions of the idler wave (Σi ) are compensated and the initial diffracted wave is restored. A beam-splitter (BS) directs the counter-propagating waves on a single-shot CCD camera sets in the object conjugate plane at the same distance D of the crystal. A polarizer (P) sets in front of the camera rejects the signal and permits the detection of the idler wave only. Figures 2a–2c present images of different parts of the transparency obtained by a direct imaging system on the CCD camera with no amplification process. Figure 2b corresponds to the group of 3.17 lines/mm. Figures 2d–2f present images of the same parts of the resolution chart with the aberrant plate set between the object and the imaging system. Images are strongly distorted and objects can no more be identified whatever the group of lines. Restored images formed by the idler wave reflected back through the aberrant plate are presented in figures 2g–2i. Distortions are compensated and the group of 5.66 lines/mm (176 µm) are resolved ( figure 2i). The same resolution was measured in phase conjugate images obtained with no
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aberrant medium. This resolution is in a good agreement with the predicted resolution and the aberrant medium does not seem to affect image resolution. 4. Time-resolved imaging through thick biological tissues In the recent years, optical imaging through biological media has attracted a considerable interest, owing to the small absorption in the therapeutic window (600–1300 nm) and the non ionizing character of light. However, the light is strongly scattered and various methods have been proposed to select the least scattered photons [9]. In relatively thin media, a part of the incident light, called ballistic, is not scattered and images are now routinely obtained by using optical coherence tomography, that detects this ballistic light by interferomtry [10]. In thicker media, like human breast, imaging tumors remains challenging, because the optical thickness is so important that ballistic light does not exist any more and images must be formed with scattered photons. Since diffusion in a biological medium is strongly anisotropic, the photons are preferentially scattered in the forward direction and the front part of a short pulse, largely stretched by the medium, is formed with the least scattered photons that have traveled on the shortest paths. Hence, the front part still carries some amount of spatial information, with a resolution that depends on the thickness of the diffusing medium. We have used parametric image amplification to separate this front part from the multi-diffused light [6]. The most efficient scheme, shown in figure 3, combines time-gating and forward phase conjugation for a better rejection of the diffused light. In order to increase the field of view, a virtual image is formed with a 0.1 magnification in the plane symmetrical of the CCD camera with respect to the crystal.
Figure 3. Experimental set-up for imaging through biological samples: Σ0 : object plane; Σv : virtual object plane; Σc : phase-conjugated image plane; P1–P3: Glan–Taylor polarizers.
Figure 4. (a) amplified image of the cross without biological tissue. (b)–(c) amplified images through 4 cm thick chicken breast tissue. The delays are respectively 0 and 158 ps. In (b) the strips are resolved and the best SNR ≈ 2 is obtained. (d) resolved image of a 1 cm3 piece of liver embedded in the same chicken breast sample.
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Figure 4 shows experimental results. Figure 4a presents an amplified image of the object, a cross formed by two 9 mm wide metal strips, without biological tissue. Figures 4b and 4c show images of this cross embedded in 4 cm thick chicken breast tissues. The delays are respectively 0 and 158 ps, where the time origin corresponds to the pump and signal pulses synchronized in the crystal in the absence of biological tissue. In figure 4b the 9 mm wide metal strips are resolved and the best signal-to-noise ratio is obtained. When the delay is greater than 33 ps, the strips are no longer resolved and only diffused light is amplified ( figure 4c). Figure 4d shows a resolved image of a 1 cm3 piece of liver embedded in the same biological sample [11]. These results are very promising because the thickness of the biological tissues corresponds to that of human breast in mammography. Though the resolution is in the range of several millimeters, the nonionizing and non-invasive character of the method could be very useful for routine preventive exams. Using parametric image amplification, images in a reflection configuration have been obtained recently with femtosecond pulses [12]. This pulse duration allows precise tomography, but for thinner samples. 5. Characterization of quantum fluctuations and noiseless image amplification Quantum fluctuations in parametrically amplified images have been actively studied in the last years by several groups. For temporal signals, it was experimentally proved some years ago that a phase-sensitive amplifier can preserve the signal-to-noise ratio [13], while a phase-insensitive amplification adds at least 3 dB to the quantum noise. Conditions for noiseless amplification of images have been recently theoretically determined [14] and conservation of the signal-to-noise ratio on each pixel of the amplified image has been experimentally demonstrated [15]. Noise means here temporal fluctuations. In the same way, correlations between homologue pixels of the images formed respectively by the idler and the signal lead to a subpoissonian level for the noise on the intensity difference, that is the signature of image entanglement [16]. The very precise spatio–temporal location of twin photons was already demonstrated in experiments where the image formed by an aperture that spatially modulated the signal beam after the crystal was reproduced on the idler by detecting the coincidences [17]. Although quantum fluctuations are usually detected in the time domain, they can also be observed in the spatial domain. Figure 5 shows spatial fluctuations in the far-field image of parametric fluorescence in a LBO crystal detected at degeneracy [18]. The ring is due to phase-matching and a strong correlation between symmetrical points is evident. While the size of the fluctuations can be connected to the Fourier transform of the pupil in the crystal (in our case, the pump beam), the correlation between the symmetrical points is due to the twin character of the spontaneously down-converted light. These results can be quite accurately reproduced by a numerical simulation that takes in account the coherent amplification with
Figure 5. Sequence of three spatial frequency spectra of parametric fluorescence obtained with the same phase matching conditions and approximately the same pump energy. Each spectrum corresponds to one laser shot. Arrows on the second spectrum underline the central symmetry of the spatial fluctuations. The circle of best phase matching is drawn on the third spectrum.
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a random noise at the input at a level of one photon per spatio–temporal mode. We plan to experimentally demonstrate the conservation of the signal-to-noise ratio in phase-sensitive amplification, where noise means spatial fluctuations. An applications could be precise lateral displacement measurements [19]. The first experimental step has been the measurement of the amplification gain versus the input phase and the spatial frequency [20]. The results are in good agreement with theory [21]. 6. Conclusion In the last years, various groups have used parametric amplification of images, with goals going from quantum optics to protection against laser attacks [22]. Because of the promising results, this effort will undoubtedly continue in next years. References [1] Guthals D., Sox D., Quantum limited optical parametric image amplification, in: Proc. Internat. Conf. Lasers ’89, D.G. Harris, T.M. Shay (Eds.), STS, Mclean, VA, 1990, pp. 808–815. [2] Lantz E., Devaux F., Parametric amplification of images, Quantum Semiclass. Opt. 9 (1997) 279–286. [3] Lefort L., Barthélémy A., Revisiting optical phase conjugation by difference-frequency generation, Opt. Lett. 21 (1996) 848–850. [4] Devaux F., Le Tolguenec G., Lantz E., Phase conjugate imaging by type II parametric amplification, Opt. Commun. 147 (1998) 309–312. [5] Devaux F., Guiot E., Lantz E., Image restoration through aberrant media by optical phase conjugation in a type II three-wave mixing interaction, Opt. Lett. 23 (1998) 1597–1598. [6] Le Tolguenec G., Devaux F., Lantz E., Two-dimensional time-resolved direct imaging through thick biological tissues: a new step toward noninvasive medical imaging, Opt. Lett. 24 (1999) 1047–1049. [7] Devaux F., Lantz E., Lacourt A., Gindre D., Maillotte H., Doreau P.A., Laurent T., Picosecond parametric amplification of a monochromatic image, Nonlinear Opt. 11 (1995) 25–37. [8] Lantz E., Devaux F., Phase-mismatch vector and resolution in image parametric amplification, J. Opt. A, in print. [9] See for example, Alfano R.R., Fujimoto J.G. (Eds.), OSA TOPS on Advances in Optical Imaging and Photon Migration, Orlando, USA, March 1996. [10] Tearney G.J., Bouma B.E., Boppart S.A., Golubovic B., Swanson E.A., Fujimoto J.G., High speed optical coherence tomography, in: TOPS on Advances in Optical Imaging and Photon Migration, Orlando, USA, March 1996, p. 224. [11] Devaux F., Le Tolguenec G., Lantz E., 2D time-resolved direct imaging through thick biological tissues by parametric amplification, in: Light for Life Meeting, Cancun, Mexico, July 1999. [12] Doulé C., Lépine T., Georges P., Brun A., Imaging through scattering media with fentosecond non-colinear parametric amplification, Summer School, Waves and Imaging Through Complex Media, Cargèse, France, August 1999, p. 25. [13] Levenson J.A., Abram I., Rivera T., Grangier P., Reduction of quantum noise in optical parametric amplification, J. Opt. Soc. Amer. B 10 (1993) 2233–2238. [14] Sokolov I., Kolobov M., Lugiato L.A., Quantum fluctuations in traveling-wave amplification of optical images, Phys. Rev. A 60 (1999) 2420–2430. [15] Choi Sang-Kyung, Vasilyev M., Kumar P., Noiseless optical amplification of images, Phys. Rev. Lett. 83 (1999) 1938–1941. [16] Gatti A., Brambilla E., Lugiato L.A., Quantum entangled images, Phys. Rev. Lett. 83 (1999) 1763–1766. [17] Pittman T.B., Strekalov D.V., Klyshko D.N., Rubin M.H., Sergienko A.V., Shih Y.H., Two-photon geometric optics, Phys. Rev. A 53 (1996) 2804–2815. [18] Devaux F., Lantz E., Spatial and temporal properties of parametric fluorescence around degeneracy in type I LBO crystal, Europhys. J. D 8 (2000) 117–124. [19] Fabre C., Fouet J.B., Maître A., Quantum limits in the measurement of very small displacements in optical images, Opt. Lett. 25 (2000) 76–78. [20] Devaux F., Lantz E., Gain in phase sensitive parametric image amplification, Phys. Rev. Lett., in print. [21] Devaux F., Lantz E., Parametric amplification of a polychromatic image, J. Opt. Soc. Amer. B 12 (1995) 2245– 2252. [22] Faure J.P., Giraudo O., Modelling of parametric beam conversion: application to image amplification with optical self-limiting, Nonlinear Opt. 21 (1999) 447–459.
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