We present a semi-analytical model of optical coherence tomography (OCT) taking into account multiple scattering. The model rests on the assumptions that the measured portion of the backscattered sample field is spatially coherent and that the sample is motionless relative to measurement time. This allows modeling an OCT signal as a sum of spatially coherent fields with random phase arguments-constant during measurement time-caused by multiple scattering. We calculate the mean OCT signal from classical results of statistical optics and a Monte Carlo simulation. Our model is shown to be in very good agreement with a whole range of experimental data gathered in a comprehensive study of cross-talk in wide-field OCT realized with spatially coherent illumination. The study consists of depth scan measurements of a mirror covered with an aqueous suspension of microspheres. We investigate the dependence of cross-talk on important optical system parameters, as well as on some relevant sample properties. We discuss the more complex OCT models based on the extended Huygens-Fresnel principle, which rest on different assumptions since they assume partially coherent interfering fields.
The crucial role played by the source's degree of spatial coherence in wide-field optical coherence tomography is shown experimentally. Spatially coherent illumination, as obtained with a pulsed laser, generates a considerable amount of coherent optical cross-talk. The latter can be suppressed with spatially incoherent illumination as provided by a thermal or a pseudothermal light source. Demonstration is made for a US air force resolution target covered with a scattering solution made of polystyrene microspheres suspended in water. The origin and nature of cross-talk signals are discussed, as well as specific limitations of spatially incoherent sources.
Parallel optical coherence tomography is demonstrated at video rate using a 58 by 58 smart-pixel detector array. A sample volume of 210x210x80 micrometers3 (corresponding to 58x58x58 voxels) was imaged at 25 Hz. A femtosecond mode-locked Ti:Sapphire laser in combination with a free space Michelson interferometer was employed to achieve a 3 micrometer longitudinal resolution. We used 20x microscope objectives in both sample arm and reference arm and measured a 8 micrometer transverse resolution. The sensitivity of the system was 76 dB.
Parallel optical coherence tomography in scattering samples is demonstrated using a 58 by 58 smart-pixel detector array. A femtosecond mode-locked Ti:Sapphire laser in combination with a free space Michelson interferometer was employed to achieve 4micrometers longitudinal resolution and 9mm transverse resolution on a 260x260 micrometers 2 field of view. We imaged a resolution target covered by an intralipid solution with different scattering coefficients as well as onion cells.
We describe the current status of the ELP-OA project in which we try to demonstrate in practice that it is possible to measure the tilt of a wave front using only a polychromatic laser guide star and no natural guide star. The first phase of ELP-OA, consisting of feasibility experiments, has recently been completed successfully. This paper provides an overview over the results of this first phase and over the continuation of the ELP-OA project.
Adaptive optics at astronomical telescopes aims at correcting in real time the phase corrugations of incoming wavefronts caused by the turbulent atmosphere, as early proposed by Babcock. Measuring the phase errors requires a bright source located within the isoplanatic patch of the program source. The probability that such a reference source exists is a function of the wavelength, of the required image quality (Strehl ratio), of the turbulence optical properties, and of the direction of the observation. It turns out that the sky coverage is disastrously low in particular in the visible wavelength range where, unfortunately, the gain in spatial resolution brought by adaptive optics is the largest. Foy and Labeyrie have proposed to overcome this difficulty by creating an artificial point source in the sky in the direction of the observation relying on the backscattered light due to a laser beam. This laser guide star (hereinafter referred to as LGS) can be bright enough to allow us to accurately measure the wavefront phase errors, except for two modes which are the piston (not relevant in this case) and the tilt. Pilkington has emphasized that the round trip time of the laser beam to the mesosphere, where the LGS is most often formed, is significantly shorter than the typical tilt coherence time; then the inverse-return-of-light principle causes deflections of the outgoing and the ingoing beams to cancel. The apparent direction of the LGS is independent of the tilt. Therefore the tilt cannot be measured only from the LGS. Until now, the way to overcome this difficulty has been to use a natural guide star to sense the tilt. Although the tilt is sensed through the entire telescope pupil, one cannot use a faint source because $APEX 90% of the variance of the phase error is in the tilt. Therefore, correcting the tilt requires a higher accuracy of the measurements than for higher orders of the wavefront. Hence current adaptive optics devices coupled with a LGS face low sky coverage. Several methods have been proposed to get a partial sky coverage for the tilt. The only one providing us with a full sky coverage is the polychromatic LGS (hereafter referred to as PLGS). We present here a progress report of the R&D program Etoile Laser Polychromatique et Optique Adaptative (ELP-OA) carried out in France to develop the PLGS concept. After a short recall of the principles of the PLGS, we will review the goal of ELP-OA and the steps to get over to bring it into play. We finally shortly described the effort in Europe to develop the LGS.
Adaptive optics at astronomical telescopes aims at correcting in real time the phase corrugations of incoming wavefronts caused by the turbulent atmosphere, as early proposed by Babcock. Measuring the phase errors requires a bright source, which is located within the isoplanatic patch of the program source. The probability that such a reference source exists is a function of the wavelength of the observation, of the required image quality (Strehl ratio), of the turbulence optical properties, and of the direction of the observation. Several papers have addressed the problem of the sky coverage as a function of these parameters (see e.g.: Le Louarn et al). It turns out that the sky coverage is disastrously low in particular in the short (visible) wavelength range where, unfortunately, the gain in spatial resolution brought by adaptive optics is the largest. Foy and Labeyrie have proposed to overcome this difficulty by creating an artificial point source in the sky in the direction of the observation relying on the backscattered light due to a laser beam. This laser guide star (hereafter referred to as LGS) can be bright enough to allow us to accurately measure the wavefront phase errors, except for two modes which are the piston (which is not relevant in this case) and the tilt. Pilkington has emphasized that the round trip time of the laser beam to the mesosphere, where the LGS is most often formed, is significantly shorter than the typical tilt coherence time; then the inverse-return- of-light principle causes deflections of the outgoing and the ingoing beams to cancel. The apparent direction of the LGS is independent of the tilt. Therefore the tilt cannot be measured only from the LGS. Until now, the way to overcome this difficulty has been to use a natural guide star to sense the tilt. Although the tilt is sensed through the entire telescope pupil, one cannot use a faint source because approximately equals 90% of the variance of the phase error is in the tilt. Therefore, correcting the tilt requires a higher accuracy of the measurements than for higher orders of the wavefront. Hence current adaptive optics devices coupled with a LGS face low sky coverage. Several methods have been proposed to get a partial or total sky coverage for the tilt, such as the dual adaptive optics concept, the elongation perspective method, or the polychromatic LGS (hereafter referred to as PLGS). We present here a progress report of the R&D program Etoile Laser Polychromatique et Optique Adaptative (ELP-OA) carried out in France to develop the PLGS concept. After a short recall of the principles of the PLGS, we will review the goal of ELP-OA and the steps to get over to bring it into play.
KEYWORDS: Laser guide stars, Telescopes, Sodium, Stars, Global system for mobile communications, Oscillators, Wavefronts, Adaptive optics, Calibration, Photometry
We present results from measurements of the return flux from a polychromatic sodium laser guide star produced in Pierrelatte, France during the PASS-2 experiment. In the experiment, photometry of light at 330, 569, 589, and 589.6 nm emitted by mesospheric sodium under two-color laser excitation (569 and 589 nm) was performed. The variation of oscillator and laser configurations as well as simultaneous measurements of the atmospheric coherence length and the mesospheric sodium density permit a comparison of the results with atomic physics models. Using the results, we can determine the setup that produces the maximum return flux from the polychromatic laser guide star. The knowledge gained will be used to aid the ELP- OA project, which has as its goal the design, testing, and implementation of an adaptive optics system that uses a polychromatic laser guide star for wave front tilt measurements.
PASS-2 is an experiment designed to perform photometry of the polychromatic laser guide star. The tilt of an atmospherically distorted wave front coming from an astronomical object cannot be determined with a monochromatic laser guide star. If it is possible to produce a laser guide star that emits light at different wavelengths, however, the tilt can be determined from the measurable differences between the tilts at the different wavelengths. This is the concept of the polychromatic laser guide star. The PASS-2 experiment is a step towards an implementation of an adaptive optics system that uses a polychromatic laser guide star for the wave front tilt measurement. The goal of the experiment is to validate the feasibility of a polychromatic laser guide star adaptive optics system and to determine the laser parameters that produce the optimal return flux from the polychromatic laser guide star. To this end, the return flux from the polychromatic laser guide star at 330 and 589.6 nm will be measured as a function of laser parameters, atmospheric conditions, and the density of the mesospheric sodium layer.
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