- Email: [email protected]
THREE-DIMENTIONAL COHERENT OPTICAL DIFFRACTION TOMOGRAPHY OF TRANSPARENT LIVING SAMPLES
THREE-DIMENTIONAL COHERENT OPTICAL DIFFRACTION TOMOGRAPHY OF TRANSPARENT LIVING SAMPLES Bertrand Simon†, Matthieu Debailleul†, Vincent Georges† Olivier Haeberlé† and Vincent Lauer‡ † ‡
Laboratory MIPS, IUT Mulhouse, 61 rue Albert Camus, 68093 Mulhouse Cedex France Lauer Optique et Traitement du Signal, 1 Villa de Beauté, 94130 Nogent/Marne, France
Abstract: We present a technique to image living transparent specimens in 3-D, based on coherent optical diffraction microscopy. The sample is successively illuminated by a series of plane waves having different directions. Each scattered wave is recorded by phase-shifting interferometry and a Fourier representation of the object is reconstructed. The specimen, first recorded in Fourier space, is then reconstructed in the object space. This technique permits a 3-D reconstruction of the complex index of refraction distribution, with a resolution of the order on a quarter of the wavelength. Copyright © 2006 IFAC Keywords: Microscopes, Image Reconstruction, Fourier Optics, Tomography, 3DDomain
1. INTRODUCTION The fluorescence microscope is the instrument of choice in biology, because of its unique capabilities for 3-D imaging of living specimens, and thanks to the development of specific fluorescent dyes, which permit to study precise cellular structures or functions. However, the resolution is still limited compared to scanning electronic microscopy or nearfield techniques. This has motivated many works to improve the resolution, speed of acquisition, or depth of observation. Fluorescent techniques however present the possible limitation that one has to label the specimen. The dye may experience bleaching during the acquisition, or induce phototoxicity into the specimen. In some cases, it is therefore preferable not to have to tag the specimen with fluorescent chemicals. The observation of transparent or quasi-transparent specimens is however difficult, especially in 3-D, for two reasons. First, the low contrast does not permit to identify intracellular structures. Secondly, transmission microscopes suffer from a bad resolution along the optical axis, because of the presence of a so-called “missing-cone” in the Optical
Transfer Function (OTF). As a consequence, while the resolution in the (x,y)-plane is often sufficient, the image presents a strong deformation along the optical axis (z-axis). In order to improve the ability of transmission microscopes to detect small, quasi-transparent structures, the phase contrast microscope and the differential phase contrast or Nomarski microscope have been invented. While very successful, these apparatus suffer from the fact that a pseudo-contrast and/or pseudo-relief are recorded. For morphologic studies, the obtained images are often convincing. However, these microscopes all use an incoherent source to build a transmitted image of biological objects. This image is 2-D only, and to obtain a 3-D image, the technique of optical sectioning is used, which requires a translation of the specimen with respect to the microscope objective. The intensity in the image is linked to the absorption and the index of refraction of the specimen, but in a complex manner. As a consequence, the intensity cannot be directly related to a physical quantity of the observed object. We have developed a technique based on coherent optical diffraction, which permits to image transparent specimens in three-dimensions and
(b)
(a)
Scattered waves
Incident wave
Scattered waves
NA
Incident wave
NA
presents two advantages. It both permits a higher resolution and allows recording of the complex index of refraction distribution into the specimen. From these data, various representation of the specimen can then be computed. 2. PRINCIPLE
The idea of diffraction tomography is to increase the set of Fourier components, which can be recorded, by illuminating the sample with successive waves having different angles of incidence (Fig. 1(b)). Holography can in this sense be considered as a special case of coherent diffraction tomography with no angular scanning of the illumination wave. The detection system and the specimen are fixed. As a consequence, when illuminating the specimen with waves having different incidences, one records different sets of Fourier components, which have to be correctly reassigned in the Fourier space, as shown by Figure 1(c). To properly reassign these components, one has first to record both the phase and amplitude, then to precisely measure the actual shift in the 3-D Fourier space between each set. Ideally, this shift is zero for a purely rotational system, but in practice, a dephasing may appear. When using a large set of illumination angles, the well-known butterfly shaped support of the Optical Transfer Function appears (Fig. 1(d)).
(d)
(c)
NA
The wave diffracted by a weakly scattering object, when illuminated by a parallel coherent light beam, can be recorded in both amplitude and phase. In the Born approximation, it is then possible from this recorded wave to reconstruct a two-dimensional, spherical subset of the three-dimensional frequency representation of the weakly scattering object. Using a series of illumination beams having different directions, different subsets of the object’s threedimensional frequency representation can be reconstructed. The corresponding equations of diffraction tomography were originally established by Wolf (Wolf 1969) for scalar fields. Figure 1 shows the principle of diffraction tomography, compared to holography. In the Born model, at first order and in the scalar approximation, diffraction is interpreted as a Fourier transformation (Born.and Wolf, 1991). In the Fourier plane, one then records Fourier components of the object index of refraction distribution. The set of Fourier components, which can be recorded, is limited by the numerical aperture (NA) of the microscope objective used in the detection system (Fig. 1(a)). For the sake of clarity, Figure 1 depicts a 2-D, (ν x-νz) representation only. In three dimensions, the set of detected waves corresponds to a cap of the Ewald sphere, limited by the detection numerical aperture. The radius of the Ewald sphere in the Fourier space is linked to the wavevector k=2π/λ, where λ is the wavelength of observation.
Fig. 1. Principle of coherent diffraction tomography. Construction of the set of detected waves. The most straightforward method to record both the phase and amplitude of the scattered wave is phaseshifting holography. However, when successive illumination beams of different directions are used, it is generally not possible to control the relative phase of these beams. As a consequence, each scattered wave detected by phase shifting holography is affected by a non-controlled phase shift, which does not allow reconstruction of the object’s threedimensional representation. We have developed a measurement-oriented approach to diffraction tomography (Lauer, 2002), taking into account not only the scattered wave and the illuminating wave, but also the reference wave and the phase relations between these three waves, giving a more complete description of the field than previous implementations of this apparatus (Devaney and Schatzberg, 1992) This has permitted to successfully use phase shifting holography with successive illumination beams with different directions, as originally suggested by Wolf (Wolf, 1969). This is made possible by an accurate compensation of the non-controlled phase shifts, which itself results from a complete frequency-space analysis of the image acquisition method. Figure 2 explains why the resolution in coherent diffraction tomography is expected to be better than for a classical transmission microscope using incoherent illumination. For the sake of simplicity, a one-dimensional only sketch is given. When using incoherent illumination, under many angles of incidence (role of the condenser in a microscope), the detection bandwidth is limited from –2NA/λ to +2NA/λ in the Fourier space, but higher frequencies are strongly attenuated (dotted line).
the image diaphragm limits the size of the observed part of the object, which in turn avoids undersampling on the CCD sensor placed in a Fourier plane. The wave then passes through lenses to reach the CCD sensor so that a plane wave originating from the object forms a point on the CCD sensor.
OTF
νx ΝΑ/λ
2ΝΑ/λ
Fig. 2. Comparison of Optical Transfer Functions for incoherent transmission microscopy (dotted line), holographic microscopy (solid line), and coherent diffraction tomography (dashed line). In holographic microscopy, the detection bandwidth is more limited from –NA/λ to +NA/λ in the Fourier space. However, these frequencies are detected without attenuation, the transfer function being constant over this interval (solid line). In coherent diffraction tomography, the detection bandwidth is increased by angular scanning of the illumination wave. If the condenser has the same numerical aperture than the objective, one obtains the same detection bandwidth from –2NA/λ to +2NA/λ in the Fourier space, but with constant transmission, thanks to the use of coherent illumination (dashed line). As a consequence, the ability to detect small details is strongly increased by the better optical transfer function of the tomographic microscope, despite the fact that it has the same frequency support than classical transmission microscopes.
This point corresponds to the actual spatial shift of the illuminating beam, which is used to reassign the detected frequencies in the Fourier space. The reference wave is virtually centred on the centre of the image diaphragm and coincides with a wave originating from a centred point source within the observed sample. The piezoelectric mirror is used to shift the phase of the reference beam. The two-level liquid crystal attenuator is a fast-switching device based on a polarization rotator and a polarizer. It serves to modify the intensity of the illumination beam in real time, during image acquisition. By combining various images corresponding to different attenuations, the system’s dynamics can be considerably improved. The microscope also comprises a dedicated computer and appropriate electronics to control the piezoelectric mirror, the tilting mirror and the two-level attenuator, to grab the data acquired by the CCD, and to compute a threedimensional representation of the observed sample. 4. RESULTS Figure 4 shows typical recorded data in the Fourier space. Each set of three phase-shifted holograms permits to obtain a different sphere cap in the 3-D Fourier space.
3. IMPLEMENTATION The prototype of the microscope (Lauer, 2002) is shown in Fig. 3. In order to measure the diffracted function directly in the Fourier space, we have built a prototype in which the CCD sensor is in a Fourier plane, so that each pixel of that sensor corresponds to a given spatial frequency of the diffracted wave leaving the observed sample. A polarized HeNe laser generates a coherent beam, which is divided by a beamsplitter into an illumination beam and a reference beam. This illumination beam is focused on the object focal plane of the aplanatic-, achromatic condenser (NA=1.4), passes through the condenser and leaves it as a plane wave illuminating the object. The direction of this illuminating plane wave can be controlled by modifying the orientation of the tilting mirror: a slight tilt of the mirror generates a large angular variation of the plane wave illuminating the object. The wave scattered by the object passes through the microscope objective (NA=1.4), as well as the non-scattered part of the illuminating wave. An intermediate image is produced and spatially filtered by the image diaphragm. Spatial filtering by
Fig. 3. Photograph of the tomographic microscope. The current prototype works only in transmission.
Fig. 4. 3-D frequency representation of the observed specimen. Top : (νx-νy) cut, bottom : (νx-νz) cut. In the (νx-νy) plane, these portions of spheres appear as circles, as can be noticed on Fig. 4 top. Figure 4 bottom shows a cut along the (νx-νz) plane.
Fig. 5. Specimen (yeast culture) reconstructed in the spatial domain from a Fourier transform of the frequency representation given in Fig. 4 (extended depth of field representation). Scale bar : 5 µm (under the foremost left cell).
(a)
(b)
(c)
As the current prototype only works in transmission, the 3-D optical transfer function suffers from the presence of a so-called missing-cone of undetected frequencies. As a consequence, the resolution along the z-axis will be lower than in the x-y plane, and the detection of structures presenting variations along the z-axis only will be more difficult. Figure 5 shows the reconstructed object in image space, after performing a 3-D Fourier transform of the frequency data set of Fig. 4. The radial lines visible in Fig. 4 top correspond to the limits of the diaphragm clearly visible on Fig. 5. In this image, an extended depth of field representation is given, obtained by averaging the real part of the complex index of refraction along the vertical direction. This data set presents both a large field of view and a high resolution. One advantage of our system is that different representation of the same specimen can directly be given from the same 3-D recorded data set: maximum intensity projection, extended depth of field, optical sectioning. Figure 6 shows a single yeast from Fig. 5 with different representations. Fig. 6(a) shows a horizontal section through the middle of the yeast. The thick cellular membrane is visible. From this image, the lateral resolution can be estimated better than 200 nm (the Abbe criterion giving 226 nm for an incoherent transmission microscope). Fig 6(b) displays a horizontal section through the middle of the vacuole, which shows sharp limits but no thick membrane. Fig 6(c) shows a maximum value projection from a series of (x-y) sections. Previously unnoticed organelles are now visible.
Fig. 6. Different representations of the same yeast. (a) :section through the middle of the yeast. (b) :section through the vacuole. (c) : maximum intensity projection. Scale bar : 5 µm.
Fig. 7. Vertical section of the yeast depicted in Fig. 6. Scale bar : 5 µm. The acquired data set actually being a 3-D one, one can also reconstruct (x-z) sections of the specimen, as shown on Fig. 7. However, as explained previously, the resolution is clearly much lower along the z-axis, and stronger deformations and blur can be noticed. There exists other 3-D microscopy imaging techniques, like for example Confocal Laser Scanning Microscopy (CLSM) or Electron Microscopy Tomography (EMT) (Leapman et al.,
2004). In terms of resolution, our instrument has similar or better lateral performances than the confocal microscope and lower performances along the vertical axis (because of the missing-cone), and much lower than EMT. We however would like to emphasize, that it gives access to another physical quantity (after proper calibration): the optical index of refraction distribution within the specimen. Confocal Laser Scanning Microscopy is based on fluorescence, so gives a fluorescence distribution image, which requires a specimen labelling procedure, while our method might be used on unstained specimens. Electron Microscopy Tomography gives another contrast: the specimen electron absorption, but its big disadvantage compared to our method is that the observation is incompatible with life specimens, because of the sample preparation, while our method works on living samples. 5. CONCLUSIONS We have developed a coherent diffraction tomographic microscopy technique, which permits three-dimensional imaging of transparent living specimens. Our prototype permits a better lateral resolution than the optical transmission microscope working with incoherent light. Because the built prototype only works in transmission, it however presents similar limitations in terms of resolution along the optical axis. In principle, one can however complete the detection of the diffracted wave in order to also record its reflected component, which should greatly improve the resolution along the optical axis too. We are now working on an improved version of this instrument, to combine fluorescence microscopy with tomographic microscopy, by modifying a commercial fluorescence microscope. In a second step, we intend to combine reflection tomography with transmission tomography, in order to greatly improve the axial resolution. This technique permits to record the complex index of refraction distribution into the observed specimen. Then, different rendering of the specimen can easily be computed (optical sectioning, maximum intensity projection, extended depth of field) from data directly connected to physical quantities, the real part of the refraction index describing the refraction properties of the specimen, while the imaginary part describes the absorption of light by the specimen. Coherent diffraction tomography may therefore facilitate the study of unprepared specimen, by providing access for the biologists to physical parameters not yet available by other microscopy techniques.
REFERENCES Born, M. and Wolf, E. (1991) Principles of Optics Pergamon Press. Devaney, A.J. and Schatzberg, A. (1992) The coherent optical tomographic microscope. SPIE Proc. 1767, 62-71. Lauer, V. (2002) New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope. J. Microscopy 205, 165-176. Leapman, R.D. et al. (2004), Three-dimensional distributions of elements in biological samples by energy-filtered electron tomography. Ultramicr. 100, 115-125. Wolf, E. (1969) Three-dimensional structure determination of semitransparent objects from holographic data. Opt. Comm. 1, 153–156.
Laboratory MIPS, IUT Mulhouse, 61 rue Albert Camus, 68093 Mulhouse Cedex France Lauer Optique et Traitement du Signal, 1 Villa de Beauté, 94130 Nogent/Marne, France
Abstract: We present a technique to image living transparent specimens in 3-D, based on coherent optical diffraction microscopy. The sample is successively illuminated by a series of plane waves having different directions. Each scattered wave is recorded by phase-shifting interferometry and a Fourier representation of the object is reconstructed. The specimen, first recorded in Fourier space, is then reconstructed in the object space. This technique permits a 3-D reconstruction of the complex index of refraction distribution, with a resolution of the order on a quarter of the wavelength. Copyright © 2006 IFAC Keywords: Microscopes, Image Reconstruction, Fourier Optics, Tomography, 3DDomain
1. INTRODUCTION The fluorescence microscope is the instrument of choice in biology, because of its unique capabilities for 3-D imaging of living specimens, and thanks to the development of specific fluorescent dyes, which permit to study precise cellular structures or functions. However, the resolution is still limited compared to scanning electronic microscopy or nearfield techniques. This has motivated many works to improve the resolution, speed of acquisition, or depth of observation. Fluorescent techniques however present the possible limitation that one has to label the specimen. The dye may experience bleaching during the acquisition, or induce phototoxicity into the specimen. In some cases, it is therefore preferable not to have to tag the specimen with fluorescent chemicals. The observation of transparent or quasi-transparent specimens is however difficult, especially in 3-D, for two reasons. First, the low contrast does not permit to identify intracellular structures. Secondly, transmission microscopes suffer from a bad resolution along the optical axis, because of the presence of a so-called “missing-cone” in the Optical
Transfer Function (OTF). As a consequence, while the resolution in the (x,y)-plane is often sufficient, the image presents a strong deformation along the optical axis (z-axis). In order to improve the ability of transmission microscopes to detect small, quasi-transparent structures, the phase contrast microscope and the differential phase contrast or Nomarski microscope have been invented. While very successful, these apparatus suffer from the fact that a pseudo-contrast and/or pseudo-relief are recorded. For morphologic studies, the obtained images are often convincing. However, these microscopes all use an incoherent source to build a transmitted image of biological objects. This image is 2-D only, and to obtain a 3-D image, the technique of optical sectioning is used, which requires a translation of the specimen with respect to the microscope objective. The intensity in the image is linked to the absorption and the index of refraction of the specimen, but in a complex manner. As a consequence, the intensity cannot be directly related to a physical quantity of the observed object. We have developed a technique based on coherent optical diffraction, which permits to image transparent specimens in three-dimensions and
(b)
(a)
Scattered waves
Incident wave
Scattered waves
NA
Incident wave
NA
presents two advantages. It both permits a higher resolution and allows recording of the complex index of refraction distribution into the specimen. From these data, various representation of the specimen can then be computed. 2. PRINCIPLE
The idea of diffraction tomography is to increase the set of Fourier components, which can be recorded, by illuminating the sample with successive waves having different angles of incidence (Fig. 1(b)). Holography can in this sense be considered as a special case of coherent diffraction tomography with no angular scanning of the illumination wave. The detection system and the specimen are fixed. As a consequence, when illuminating the specimen with waves having different incidences, one records different sets of Fourier components, which have to be correctly reassigned in the Fourier space, as shown by Figure 1(c). To properly reassign these components, one has first to record both the phase and amplitude, then to precisely measure the actual shift in the 3-D Fourier space between each set. Ideally, this shift is zero for a purely rotational system, but in practice, a dephasing may appear. When using a large set of illumination angles, the well-known butterfly shaped support of the Optical Transfer Function appears (Fig. 1(d)).
(d)
(c)
NA
The wave diffracted by a weakly scattering object, when illuminated by a parallel coherent light beam, can be recorded in both amplitude and phase. In the Born approximation, it is then possible from this recorded wave to reconstruct a two-dimensional, spherical subset of the three-dimensional frequency representation of the weakly scattering object. Using a series of illumination beams having different directions, different subsets of the object’s threedimensional frequency representation can be reconstructed. The corresponding equations of diffraction tomography were originally established by Wolf (Wolf 1969) for scalar fields. Figure 1 shows the principle of diffraction tomography, compared to holography. In the Born model, at first order and in the scalar approximation, diffraction is interpreted as a Fourier transformation (Born.and Wolf, 1991). In the Fourier plane, one then records Fourier components of the object index of refraction distribution. The set of Fourier components, which can be recorded, is limited by the numerical aperture (NA) of the microscope objective used in the detection system (Fig. 1(a)). For the sake of clarity, Figure 1 depicts a 2-D, (ν x-νz) representation only. In three dimensions, the set of detected waves corresponds to a cap of the Ewald sphere, limited by the detection numerical aperture. The radius of the Ewald sphere in the Fourier space is linked to the wavevector k=2π/λ, where λ is the wavelength of observation.
Fig. 1. Principle of coherent diffraction tomography. Construction of the set of detected waves. The most straightforward method to record both the phase and amplitude of the scattered wave is phaseshifting holography. However, when successive illumination beams of different directions are used, it is generally not possible to control the relative phase of these beams. As a consequence, each scattered wave detected by phase shifting holography is affected by a non-controlled phase shift, which does not allow reconstruction of the object’s threedimensional representation. We have developed a measurement-oriented approach to diffraction tomography (Lauer, 2002), taking into account not only the scattered wave and the illuminating wave, but also the reference wave and the phase relations between these three waves, giving a more complete description of the field than previous implementations of this apparatus (Devaney and Schatzberg, 1992) This has permitted to successfully use phase shifting holography with successive illumination beams with different directions, as originally suggested by Wolf (Wolf, 1969). This is made possible by an accurate compensation of the non-controlled phase shifts, which itself results from a complete frequency-space analysis of the image acquisition method. Figure 2 explains why the resolution in coherent diffraction tomography is expected to be better than for a classical transmission microscope using incoherent illumination. For the sake of simplicity, a one-dimensional only sketch is given. When using incoherent illumination, under many angles of incidence (role of the condenser in a microscope), the detection bandwidth is limited from –2NA/λ to +2NA/λ in the Fourier space, but higher frequencies are strongly attenuated (dotted line).
the image diaphragm limits the size of the observed part of the object, which in turn avoids undersampling on the CCD sensor placed in a Fourier plane. The wave then passes through lenses to reach the CCD sensor so that a plane wave originating from the object forms a point on the CCD sensor.
OTF
νx ΝΑ/λ
2ΝΑ/λ
Fig. 2. Comparison of Optical Transfer Functions for incoherent transmission microscopy (dotted line), holographic microscopy (solid line), and coherent diffraction tomography (dashed line). In holographic microscopy, the detection bandwidth is more limited from –NA/λ to +NA/λ in the Fourier space. However, these frequencies are detected without attenuation, the transfer function being constant over this interval (solid line). In coherent diffraction tomography, the detection bandwidth is increased by angular scanning of the illumination wave. If the condenser has the same numerical aperture than the objective, one obtains the same detection bandwidth from –2NA/λ to +2NA/λ in the Fourier space, but with constant transmission, thanks to the use of coherent illumination (dashed line). As a consequence, the ability to detect small details is strongly increased by the better optical transfer function of the tomographic microscope, despite the fact that it has the same frequency support than classical transmission microscopes.
This point corresponds to the actual spatial shift of the illuminating beam, which is used to reassign the detected frequencies in the Fourier space. The reference wave is virtually centred on the centre of the image diaphragm and coincides with a wave originating from a centred point source within the observed sample. The piezoelectric mirror is used to shift the phase of the reference beam. The two-level liquid crystal attenuator is a fast-switching device based on a polarization rotator and a polarizer. It serves to modify the intensity of the illumination beam in real time, during image acquisition. By combining various images corresponding to different attenuations, the system’s dynamics can be considerably improved. The microscope also comprises a dedicated computer and appropriate electronics to control the piezoelectric mirror, the tilting mirror and the two-level attenuator, to grab the data acquired by the CCD, and to compute a threedimensional representation of the observed sample. 4. RESULTS Figure 4 shows typical recorded data in the Fourier space. Each set of three phase-shifted holograms permits to obtain a different sphere cap in the 3-D Fourier space.
3. IMPLEMENTATION The prototype of the microscope (Lauer, 2002) is shown in Fig. 3. In order to measure the diffracted function directly in the Fourier space, we have built a prototype in which the CCD sensor is in a Fourier plane, so that each pixel of that sensor corresponds to a given spatial frequency of the diffracted wave leaving the observed sample. A polarized HeNe laser generates a coherent beam, which is divided by a beamsplitter into an illumination beam and a reference beam. This illumination beam is focused on the object focal plane of the aplanatic-, achromatic condenser (NA=1.4), passes through the condenser and leaves it as a plane wave illuminating the object. The direction of this illuminating plane wave can be controlled by modifying the orientation of the tilting mirror: a slight tilt of the mirror generates a large angular variation of the plane wave illuminating the object. The wave scattered by the object passes through the microscope objective (NA=1.4), as well as the non-scattered part of the illuminating wave. An intermediate image is produced and spatially filtered by the image diaphragm. Spatial filtering by
Fig. 3. Photograph of the tomographic microscope. The current prototype works only in transmission.
Fig. 4. 3-D frequency representation of the observed specimen. Top : (νx-νy) cut, bottom : (νx-νz) cut. In the (νx-νy) plane, these portions of spheres appear as circles, as can be noticed on Fig. 4 top. Figure 4 bottom shows a cut along the (νx-νz) plane.
Fig. 5. Specimen (yeast culture) reconstructed in the spatial domain from a Fourier transform of the frequency representation given in Fig. 4 (extended depth of field representation). Scale bar : 5 µm (under the foremost left cell).
(a)
(b)
(c)
As the current prototype only works in transmission, the 3-D optical transfer function suffers from the presence of a so-called missing-cone of undetected frequencies. As a consequence, the resolution along the z-axis will be lower than in the x-y plane, and the detection of structures presenting variations along the z-axis only will be more difficult. Figure 5 shows the reconstructed object in image space, after performing a 3-D Fourier transform of the frequency data set of Fig. 4. The radial lines visible in Fig. 4 top correspond to the limits of the diaphragm clearly visible on Fig. 5. In this image, an extended depth of field representation is given, obtained by averaging the real part of the complex index of refraction along the vertical direction. This data set presents both a large field of view and a high resolution. One advantage of our system is that different representation of the same specimen can directly be given from the same 3-D recorded data set: maximum intensity projection, extended depth of field, optical sectioning. Figure 6 shows a single yeast from Fig. 5 with different representations. Fig. 6(a) shows a horizontal section through the middle of the yeast. The thick cellular membrane is visible. From this image, the lateral resolution can be estimated better than 200 nm (the Abbe criterion giving 226 nm for an incoherent transmission microscope). Fig 6(b) displays a horizontal section through the middle of the vacuole, which shows sharp limits but no thick membrane. Fig 6(c) shows a maximum value projection from a series of (x-y) sections. Previously unnoticed organelles are now visible.
Fig. 6. Different representations of the same yeast. (a) :section through the middle of the yeast. (b) :section through the vacuole. (c) : maximum intensity projection. Scale bar : 5 µm.
Fig. 7. Vertical section of the yeast depicted in Fig. 6. Scale bar : 5 µm. The acquired data set actually being a 3-D one, one can also reconstruct (x-z) sections of the specimen, as shown on Fig. 7. However, as explained previously, the resolution is clearly much lower along the z-axis, and stronger deformations and blur can be noticed. There exists other 3-D microscopy imaging techniques, like for example Confocal Laser Scanning Microscopy (CLSM) or Electron Microscopy Tomography (EMT) (Leapman et al.,
2004). In terms of resolution, our instrument has similar or better lateral performances than the confocal microscope and lower performances along the vertical axis (because of the missing-cone), and much lower than EMT. We however would like to emphasize, that it gives access to another physical quantity (after proper calibration): the optical index of refraction distribution within the specimen. Confocal Laser Scanning Microscopy is based on fluorescence, so gives a fluorescence distribution image, which requires a specimen labelling procedure, while our method might be used on unstained specimens. Electron Microscopy Tomography gives another contrast: the specimen electron absorption, but its big disadvantage compared to our method is that the observation is incompatible with life specimens, because of the sample preparation, while our method works on living samples. 5. CONCLUSIONS We have developed a coherent diffraction tomographic microscopy technique, which permits three-dimensional imaging of transparent living specimens. Our prototype permits a better lateral resolution than the optical transmission microscope working with incoherent light. Because the built prototype only works in transmission, it however presents similar limitations in terms of resolution along the optical axis. In principle, one can however complete the detection of the diffracted wave in order to also record its reflected component, which should greatly improve the resolution along the optical axis too. We are now working on an improved version of this instrument, to combine fluorescence microscopy with tomographic microscopy, by modifying a commercial fluorescence microscope. In a second step, we intend to combine reflection tomography with transmission tomography, in order to greatly improve the axial resolution. This technique permits to record the complex index of refraction distribution into the observed specimen. Then, different rendering of the specimen can easily be computed (optical sectioning, maximum intensity projection, extended depth of field) from data directly connected to physical quantities, the real part of the refraction index describing the refraction properties of the specimen, while the imaginary part describes the absorption of light by the specimen. Coherent diffraction tomography may therefore facilitate the study of unprepared specimen, by providing access for the biologists to physical parameters not yet available by other microscopy techniques.
REFERENCES Born, M. and Wolf, E. (1991) Principles of Optics Pergamon Press. Devaney, A.J. and Schatzberg, A. (1992) The coherent optical tomographic microscope. SPIE Proc. 1767, 62-71. Lauer, V. (2002) New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope. J. Microscopy 205, 165-176. Leapman, R.D. et al. (2004), Three-dimensional distributions of elements in biological samples by energy-filtered electron tomography. Ultramicr. 100, 115-125. Wolf, E. (1969) Three-dimensional structure determination of semitransparent objects from holographic data. Opt. Comm. 1, 153–156.