Full-field Optical Coherence Tomography and its Adaptive Optics 

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Low coherence interferometry (LCI)

Interferometry is an important method for the measurement of small optical path length changes, from which small displacements, refractive index changes or surface irregularities can be extracted. As mentioned before, OCT is based on a so called low coherence interferometry (figure 1.5(a)) to detect the magnitude and echo time delay of the backscattered light for sample structure reconstructions. Interferometry measures the electric field of the optical beam rather than its intensity. The function form of the electric field in a light wave is E(t) = E0cos(2πνt − 2π λ z). (1.1) As show in figure 1.5a, the most commonly used interferometer in LCI is Michelson interferometer. Light Ei(t) from the source is directed into the beamsplitter that splits the beam into the reference arm and a sample arm. The sample arm beam incident on the tissue and undergoes partial reflection whenever it encounters a structure or surface within the tissue. Thus the sample reflected beam Es(t) contains multiple echoes from the interfaces within the tissue. The reference arm beam is directed to a reference mirror and reflected Er(t). Both beams travel back toward the beamsplitter, recombined and interfered, result in the output beam, which is the sum of the electromagnetic fields of both arms Eo(t) ∼ Es(t) + Er(t).

OCT performances

The OCT system performances are typically defined by several important parameters such as resolution, field of view and sensitivity. Figure 1.6 illustrate the basic sample arm geometrics of typical OCT systems.

Axial resolution

The dependence of the interference range on the temporal coherence length lc of the broadband source in LCI, as explained in section 1.3, distinguishs OCT from traditional microscopy techniques, in which both axial and lateral resolution is dependent on the numerical aperture (NA) of the objectives. In OCT techniques, the determination of the axial resolution is independent of the beam focusing, given by the width of the electromagnetic field autocorrelation function. With a Gaussian-shaped spectrum, the OCT axial resolution is calculated as Δz = 2ln2 π · λ2 Δλ (1.4) in which λ is the center wavelength of the light source and Δλ is the full-width-half-maximum (FWHM) of the spectrum.

Direct wavefront sensing

Wavefront sensing deals with the aberration determination. Many AO systems nowadays do have a way to sense the optical wavefront directly with enough spatial resolution and speed to apply a real-time correction with wavefront correctors. There are various kinds of direct wavefront sensing techniques have been developed such as curvature sensing [100,101], pyramid wavefront sensor [102, 103], coherence-gated wavefront sensing [104, 105]. Beside these, Shack- Hartmann wavefront sensor is probably the simplest in concept and most widely used in both astronomy and ophthamology applications.

Shack-Hartmann wavefront sensor

Invented in 1971, the Shark-Hartmann wavefront sensor is an optical system derived from the Hartmann method [106] for a number of measurements like human eye aberration determination, laser beam quality evaluation, and astronomical aberration measurement. As shown in figure 2.6 Shark-Hartmann wavefront sensor is composed of a 2D array of miniaturized lenslets that is placed in front of a detector at a distance equal to the focal length of the lenslets. Typically, the lenslets array is conjugated with the pupil plane of an optical system. When there is no aberration, the wavefront arriving at the lenslets array is planar thus the incoming light is formed into many small spots onto the detector as shown in figure 2.6(a). When aberration presents, the small spots focused on the detector is shifted from the center optical axis position as shown in figure 2.6(b). These displacements of the small spots corresponding to the local slope of the wavefront arriving at the lenslets. With centroid algorithm [107] and wavefront reconstruction method [108], the wavefront within the subaperture could be estimated.

Indirect wavefront measurement based on image analysis

The performance of direct wavefront measurement in AO systems could be limited by many sources of errors such as the accuracy of the wavefront sensor, non-common path errors, bac reflection from lens based systems, etc. Also the lack of guiding star in many situations makes wavefront measurement ambiguous as the wavefront sensor would response to all the light impinging upon it and one cannot be sure whether the measured wavefront corresponds to the aberration that are induced to the light coming from the focal plan. For these reasons, Indirect methods that rely on the optical image itself, which is formed by the light coming from the focal plan, as the source for wavefront measurement has been developed. The basic principle is to use the effects of aberrations on the image to optimize the image quality. With a wavefront corrector in the optical beam path, known aberrations are generated before images are recorded. By analysing how the additional known test aberrations changes the image quality, optimization could be achieved by various algorithms to decide the best aberration correction parameters for wavefront corrector. In contrary to the direct wavefront measurement which invariably adds extra hardware like Shack-Hartmann wavefront sensor, indirect methods needsonly the wavefront corrector. Up to today, methods like metric-based sensorless algorithms, phase diversity and pupil segmentation have been developed and applied to various applications like microscopy or OCT.

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Table of contents :

I Optical Coherence Tomography and Adaptive Optics in RetinalmImaging 
1 Optical coherence tomography (OCT) 
1.1 Imaging in scattering media
1.2 Introduction of OCT
1.3 Low coherence interferometry (LCI)
1.4 OCT performances
1.4.1 Axial resolution
1.4.2 Lateral resolution
1.4.3 Field of view
1.4.4 Sensitivity
1.5 OCT techniques
1.5.1 Scanning OCT
1.5.2 Parallel OCT
2 Wavefront correction with adaptive optics 
2.1 Wavefront aberration
2.2 Aberration representation with Zernike polynomials
2.3 Strehl ratio
2.4 Adaptive optics (AO)
2.4.1 Introduction of AO
2.4.2 Wavefront corrector
2.4.3 Direct wavefront sensing
2.4.4 Indirect wavefront measurement based on image analysis
2.5 Computational adaptive optics
3 The human eye and retinal imaging 
3.1 Imaging properties of human eye
3.1.1 The structure and geometry of human eye
3.1.2 Eye aberrations
3.1.3 Eye movements
3.2 Retinal imaging
3.2.1 Flood illuminated fundus camera
3.2.2 Scanning laser ophthalmoscope
3.2.3 OCT retinal imaging
II Full-field Optical Coherence Tomography and its Adaptive Optics 
4 Full-field optical coherence tomography (FFOCT) 
4.1 Introduction
4.2 Basic principles of FFOCT
4.2.1 Basic layout
4.2.2 Image acquisition
4.3 FFOCT performances
4.3.1 Resolution
4.3.2 Field of view
4.3.3 Sensitivity
4.3.4 Comparison of FFOCT with other OCT techniques
4.4 LightCT scanner
4.5 FFOCT applications
4.5.1 Histological evaluation of ex vivo tissues
4.5.2 Dynamic FFOCT imaging
4.5.3 Inner fingerprint imaging
5 FFOCT resolution insensitive to aberrations 
5.1 Aberration fuzziness and PSF
5.2 The unexpected PSF determination using nanoparticles in FFOCT
5.3 Optical coherence
5.3.1 Temporal coherence
5.3.2 Spatial coherence
5.4 Theoretical system PSF analysis in various OCTs
5.4.1 Scanning OCT with spatially coherent illumination
5.4.2 WFOCT with spatially coherent illumination
5.4.3 FFOCT with spatially incoherent illumination
5.5 Experimental confirmation with extended object
5.5.1 USAF imaging with defocus
5.5.2 UASF imaging with random aberration
6 Adaptive optics FFOCT (AO-FFOCT) 
6.1 Simplifying AO for low order aberrations in FFOCT
6.1.1 Plane conjugation in AO induce system complexity
6.1.2 Non-conjugate AO for eye’s low order aberration correction
6.1.3 Wavefront sensorless method further simplify the system
6.2 The compact AO-FFOCT setup
6.3 Aberration correction algorithm
6.4 LCSLM-induced aberration correction
6.4.1 Non-conjugate AO
6.4.2 Conjugate AO
6.5 Sample induced aberration correction
6.5.1 Ficus leaf experiment: weak aberration correction
6.5.2 Mouse brain slice: strong aberration correction
6.6 AO-FFOCT retinal imaging of artificial eye model
III In vivo Human Retinal Imaging with FFOCT 
7 Combing FFOCT with SDOCT for in vivo human retinal imaging 
7.1 Introduction
7.2 Combining FFOCT with SDOCT
7.3 Eye safety analysis
7.4 System performance validation with artificial eye model
7.5 In vivo human retinal imaging
7.5.1 FFOCT retinal imaging of the fovea
7.5.2 FFOCT retinal imaging of retinal near periphery
Conclusions and perspectives
Publications
References

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