Spectroscopic ultrahigh-resolution full-field optical coherence microscopy

: We have developed a full-field optical coherence microscopy system providing intensity-based tomographic images and spectroscopic information with ultrahigh spatial resolution. Local measurements of the backscattered light spectrum center of mass are achieved through short-time Fourier analysis of a stack of en face interferometric images acquired with a Linnik-type microscope. Using a halogen lamp as an illumination source enables us to achieve spectroscopic imaging over a wavelength range from 600 to 900 nm with a spatial resolution of ~ 1 µm. Absorption measurements of a colored gel are reported as a validation of the technique. Enhancement of tissue imaging contrast is demonstrated by imaging a Xenopus Laevis (African frog) tadpole ex vivo.


Introduction
Full-Field Optical Coherence Microscopy (FF-OCM), also referred to as Full-Field Optical Coherence Tomography (FF-OCT), is an efficient technique for ultrahigh-resolution (~1 µm) three-dimensional imaging of biological media [1][2][3][4]. FF-OCM was proposed recently as an alternative method to conventional Optical Coherence Tomography (OCT) [5][6][7]. It uses a CCD camera as an array detector in combination with a spatially and temporally incoherent illumination source for parallel acquisition of en face-oriented (transverse) tomographic images. High detection sensitivity (> 90 dB) can be achieved through the accumulation of multiple images, which is permitted when ex vivo and hence immobile samples are imaged. In vivo full-field OCT imaging is possible with reduced detection sensitivity [8,9]. Spectroscopic OCT is an extension of conventional scanning OCT that is used for performing cross-sectional tomographic imaging and spectroscopic imaging simultaneously [10][11][12]. Information on the spectral content of backscattered light is obtained by detection and processing of the OCT interferometric signal. This method allows the spectrum of backscattered light to be measured over the entire available optical bandwidth, which can extend from 650 nm to 1000 nm using ultrabroad-band Ti:saphire laser technology [11].
Conventional spectrometer systems use a tungsten halogen lamp because of the extremely broad and smooth spectrum of thermal light. Since the usual illumination source of FF-OCM is also a tungsten halogen lamp, the combination of spectroscopy and FF-OCM seemed particularly appropriate. In this paper we present spectroscopic FF-OCM, an extension of the FF-OCM technique that is capable of providing spatially-resolved spectroscopic information with ultrahigh spatial resolution. Absorption measurements with spectroscopic FF-OCM are reported as a validation of the technique. Enhancement of tissue imaging contrast is demonstrated by imaging a Xenopus Laevis (African frog) tadpole ex vivo.

Experimental setup
The experimental setup of spectroscopic FF-OCM is represented schematically in Fig. 1. It is based on an interference microscope in the Linnik configuration, i.e., a bulk Michelson interferometer with identical microscope objectives -Olympus, 10x/0.3 W -in both arms. A Köhler halogen illuminator with a stabilized DC power supply is used as a spatially and temporally incoherent light source. The polished surface of an Y 3 Al 5 O 12 (YAG) crystal is placed at the focal plane of the microscope objective in the reference arm. Since waterimmersion microscope objectives are used, the water/crystal interface constitutes a reference mirror with ~ 2% reflectivity. The object to be imaged is placed in the other arm of the interferometer under an identical water-immersion microscope objective. Identical glass plates ( are placed in both arms of the interferometer. By adjusting the tilt of one of the plates, we can compensate for dispersion mismatch induced by the microscope objectives and the beam splitter. The plates are not tilted while the imaging depth in the imaged biological sample is varied. The numerical aperture of the microscope objectives is 0.3, providing a theoretical transverse (x-y) resolution of ~ 1.4 µm at the mean wavelength λ = 750 nm. The image of the reference mirror and the image of the object are projected with an achromatic doublet lens (500 mm focal length) onto a CCD camera array where they interfere with each other. The CCD camera -DALSA 1M15 -has the following characteristics: frame rate f CCD =15 Hz, 12 bits digitization, and 1024×1024 pixels. The CCD operates with 2×2 pixel binning in order to increase the detection sensitivity. The effective number of pixels is consequently reduced to 512×512. The object can be translated along the optical axis (z) by a computer-controlled piezoelectric transducer (PZT) -Polytech Pi P725 -in steps Δz. At each step p, an adjustable number m of identical interferometric images are captured by the CCD and transferred to the host computer, which calculates their sum. The resulting image p E is then written on the computer hard disk in 32 bit binary format. A stack of N interferometric images 1,..., p N E = is thus recorded, which represents a three-dimensional data-set of 512×512×N elements. The full interferometric signal as a function of depth in the object is thus acquired simultaneously by each CCD pixel. Due to the spectral response of the CCD camera and the optical elements of the experimental setup, the useful wavelengths range from approximately 600 nm to 900 nm. The fringe period (in water) may therefore vary between 225 nm and 340 nm. The PZT step is adjusted to δz = 35 nm, which ensures the sampling of the interferometric signal to be several times above the Nyquist limit. The PZT is equipped with absolute-measuring, directmetrology capacitive sensors to minimize errors and fluctuations in the nominal step value. Data acquisition, camera control and PZT control are performed by a Visual C++ windows application. After recording the full interferometric signal, we can extract both the intensitybased images from the fringe envelope and the spectral information from the fringe pattern through data post-processing.

Intensity-based tomographic images
A stack of transverse-oriented (x-y) intensity-based tomographic images is obtained from the raw interferometric data by calculating the fringe envelope using a five-frame nonlinear phase-shifting algorithm [13]. Each intensity-based image k I is calculated according to Because the mean wavelength is λ = 750 nm and the PZT step is δz = 35 nm, the adjacent frames in Eq. (1) are separated by a phase of ~ π/2 (considering the refractive index of the medium to be n = 1.33), as required in this phase-shifting algorithm. Each image I k represents the transverse intensity distribution of light emanating from a thin slice orthogonal to the optical axis (z). The data-set ( , , ) i j k I of 512×512×(N-8) elements is thus a three-dimensional image of the internal structures in the object which have backscattered the incident light. The imaging axial (z) resolution can be defined as the full width at half maximum (FWHM) of the fringe envelope along z, i.e., half the source coherence length, which is inversely proportional to the spectral bandwidth [7]. The axial resolution was measured to be 0.8 µm by imaging a silver mirror with a drop of water placed between the mirror and the objective. Since biological tissues consist mainly of water, the use of identical water-immersion microscope objectives in the two interferometer arms minimizes dispersion mismatch introduced by the tissues refractive index heterogeneities. The axial resolution degradation is thus minimized when the imaging depth increases.
Because the sampling step is δz = 35 nm, the fringe envelope along z is actually oversampled. In order to benefit from all the acquired images, we reduce the intensity data-set ( , , ) i j k I to a matrix ( , , ) * i j k I by summing 10 adjacent transverse tomographic images k I . The compression of the data by a factor of 10 does not degrade the axial resolution. Tomographic images in arbitrary orientations, as well as image projections and volume rendering visualizations can then be produced from * ( , , ) i j k I . Calculations are performed in C programming language for maximum speed. Image production and processing are achieved using ImageJ and Matlab TM softwares.
High-resolution optical imaging of biological media requires a high detection sensitivity and a large dynamic range. These requirements in FF-OCM rely on several experimental parameters such as the reference mirror reflectivity and the full well capacity of the CCD pixels [2,3]. The full well capacity can be virtually increased by pixel binning and image accumulating. 2×2 binning is achieved by summing the signal delivered by 4 adjacent pixels. The image magnification on the CCD array is adjusted so that this binning does not reduce the transverse resolution. In order to keep the acquisition time relatively short, we choose to accumulate m = 5 raw images at each PZT step. As explained before, the three-dimensional intensity distribution ( , , ) i j k I is calculated by using a 5-frame phase-shifting algorithm, which means that each element of ( , , ) . With these conditions, the intensity detection sensitivity was measured to be ~ 85 dB.

Spectroscopic measurements
Spectroscopic information is obtained through Fourier analysis of the full interferometric signal recorded by each CCD pixel as a function of depth (z). Spatially-resolved power density spectra are calculated using a short-time Fourier transform. For each value of 1 , 512 i j ≤ ≤ (each "binned" CCD pixel), "fast Fourier transforms" (FFTs) of the interferometric data (a vector of N elements) are calculated over a moving Gauss window. The window is moved in steps of 10 points, so that a power density spectrum is associated with each element of the three-dimensional intensity data-set * ( , , ) i j k I . The choice of the Gauss window size results in a trade-off between spectral resolution and spatial resolution of the spectral data. Our aim is to favor the spatial resolution. As a consequence, spectra will be measured with low spectral resolution. Only spectral shifts resulting from absorption within the tissues and backscattering by the sample microstructures will be measured. We chose a very narrow Gauss window, with width equal to the imaging axial resolution, i.e., a FWHM of 0.8 µm. The spectral impulse response of the system is the Fourier transform of this Gauss window. The spectral resolution, defined as the width (FWHM) of the spectral impulse response, is therefore equal to 240 nm. High spatial resolution of the spectral information is thus realized. Despite a low spectral resolution, high spectral sensitivity is achieved, which is required to measure weak spectral shifts. This point will be discussed later.
Before calculating the FFT, each data-set is increased in size to 4096 points by zeropadding in order to reduce the spectrum sampling step, which, after padding, is , it is necessary to quantify some aspect of the spectra for display. Due to our low spectral resolution, the measured spectra are always peak functions. As spectroscopic metric, we chose the spectrum center of mass.
For simultaneously displaying intensity and spectroscopic information, we use a HSL (hue, saturation, luminance) color map. Hue encodes the spectroscopic information (spectrum center of mass), whereas luminance and saturation together encode the intensity information, as done in [14]. We restrict the Hue variation from 0 to 0.5 (the full available hue range being from 0 to 1), so that the color varies from red to light blue (see color bar in Fig. 4). Luminance ranges from 0 to 1 and saturation from 0.5 to 1.

Interpretation of spectroscopic OCT measurements
Spectroscopic OCT is theoretically able to reveal spectral changes of light propagating in biological tissues due to elastic scattering and absorption. However, these two mechanisms are very different. Absorption takes place over the entire optical path, while scattering takes place at the local interfaces of refractive index inhomogeneities. In essence, absorption measurements are not truly spatially-resolved. In contrast, scattering measurements are more localized indicators. The contributions of both effects, however, are difficult to distinguish [15][16][17].
The spectral changes due to single-particle backscattering are related to the size of that particle [18]. In theory, spectroscopic OCT could be used in determining the size of scattering particles. In practice, the absolute determination of particle size by spectroscopic OCT is particularly difficult for several reasons: * The wavelength-dependant attenuation of light due to absorption and scattering during the propagation from the sample surface to the imaged particle and back from the imaged particle to the sample surface. * The presence of multiple scatterers in the coherence volume (the three-dimensional pointspread function) will generate interference, causing spectral modulations [14,16]. The number of scatterers in the coherence volume affects the spectral modulation. If the number of scatterers is large, the spectral modulation tends to be averaged out spatially. If the number of scatterers is small, dramatic modulation effects on the spectrum will occur. This situation is more likely to happen in high-resolution OCT, especially in FF-OCM where the coherence volume is ~ 1 µm 3 . Even if the spectral modulations are not resolved by spectroscopic OCT (as is the case in our spectroscopic FF-OCM system), they may cause a spectral shift. Since it is often difficult to know whether one or several particles are present in the coherence volume, it is difficult to be certain whether the measured spectral shift is a result of single-particle backscattering or multi-particle backscattering. Consequently, the determination of particle size is considerably hampered. * The sample is not illuminated by a plane wave. Indeed the sample is illuminated with a distribution of incidence angles defined by the numerical aperture of the objective. This geometrical effect modifies the fringe period of the interferometric signal causing an apparent shift of the calculated spectrum. [16,19,20].
A few works have been published on wavelength-dependent scattering measurements achieved by spectroscopic OCT [16,17,21]. For the reasons cited above and due to the inhomogeneous properties of tissue scatterers, such as variations in size, refractive index, and density, the quantitative interpretation of scattering effects detected by spectroscopic OCT is still a challenge.
In contrast, a larger number of studies have focused on measuring the wavelengthdependent absorption from either endogenous or exogenous absorbers [15,22,23]. According to Beer's law, for an absorber to significantly shift the spectrum of backscattered light, the absorber either needs to have a large absorption cross-section, be present in high concentration or the length of the absorber region needs to be large. In order to maximize the imaging penetration depth, OCT uses near-infrared light where the absorption of biological tissues is minimal (so-called therapeutic window). Except for a few biological constituants such as melanin and blood (absorption peak of deoxy-hemoglobin at 760 nm and the haemoglobin isosbestic point at around 800 nm), endogeneous biological molecules have a very weak absorption cross-section in this spectral region. Finally, since OCT images structures at a typical depth between 0 and 1-2 mm, the effect of absorption is integrated over a small optical path. Consequently, the spectral modifications are generally faint.

Validation of the technique by absorption measurements
In order to validate spectroscopic measurements achieved by FF-OCM, we imaged the surface of a microscope slide (glass plate) covered by a layer of colored Agarose gel as depicted in Fig. 2 left. A microscope cover-slip was placed on top of the gel at an angle such that the gel acts as a wedge-shaped absorbing medium. The coloration was obtained by introducing blue ink during the gel preparation before solidification. The dispersion introduced by the microscope cover-slip was compensated for by placing an identical cover-slip in the other arm of the interferometer between the microscope objective and the beam splitter. A typical transmission spectrum of the ink (contained in a 1 mm thick glass cell), measured by a conventional grating-based spectrometer, is shown Fig. 2 right. Since the effective illumination spectrum of FF-OCM spreads from 600 nm to 900 nm, the absorption of the blue ink is expected to induce measurable spectral changes. Values of the spectrum center of mass shift measured with FF-OCM as a function of wedge thickness are reported in Fig. 3. As expected, the spectrum of the reflected light is shifted towards longer wavelengths at positions where the wedge is thicker. The theoretical shift was calculated assuming a Gaussian illumination spectrum ( ) illum with a gel, i.e. a reflectivity of ~ 0.35%, which is higher than the reflectivity of most biological structures. The spectral sensitivity when imaging biological tissues is degraded due to a lower signal-to-noise ratio. In the image presented in Fig. 4(B), for example, the spectral sensitivity varies from one point to another, depending on the intensity of the detected signal. The average spectral sensitivity over this entire image was measured to be ∼ 20 nm. Melanocytes (indicated by white arrows) are the most backscattering structures; the spectral sensitivity in these regions was estimated to be ∼ 10 nm.

Demonstration of imaging contrast enhancement
In order to illustrate the system's performances in imaging biological media, we imaged a Xenopus Laevis tadpole (ex-vivo). The tadpole was placed in a tank filled with phosphatebuffered saline (PBS, pH 7) for animal preservation and to provide index matching. A stack of N = 5000 images was recorded, which represents a three-dimensional data-set of 512×512×5000 elements (5 GigaBytes). The physical size of the imaged volume is 530µm×530µm×175µm (x×y×z). A vertical (x-z) tomographic image extracted from the threedimensional data-set is shown in Fig. 4 with intensity-based contrast (A) and combined spectroscopic/intensity-based contrast (B). The same image with combined spectroscopic/intensity information is shown in Fig. 4(B). We point out the ultrahigh spatial resolution of the spectroscopic information displayed in this image. Melanocytes (see arrows) appear red with our colormap, indicating an average spectral shift of ~ 35 nm towards longer wavelengths as compared to the mean spectrum center of mass over the entire image. The possible physical mechanisms responsible for this spectral shift are scattering and absorption. Melanocytes are relatively strong light scatterers (see Fig. 4(A). According to Rayleigh's theory, the amount of scattering increases sharply as the wavelength of the light decreases. A blue-shift of the backscattered light spectrum would then happen, which is in contradiction with the observation. One possible explanation is that light scattering by the melanocytes is not described by Rayleigh theory, because the size of the scattering structures is not very small compared to the optical wavelength. However, even with Mie theory, scattering cannot explain the measured spectral shift. Below the melanocytes, a shadow is observed, which is due to a strong absorption of light by these biological structures. The absorption of melanin decreases monotonically with the wavelength in the visible and near infrared [11,24]. We think that absorption is therefore the predominant effect responsible for the spectral changes of light backscattered by the melanocytes. A "red" spectral shift immediately below the melanocytes is not observed because the transmission of light through theses biological structures is too weak. At sufficient depths, the shadow disappears because light is able to pass around the melanocytes due to the relatively high numerical aperture of the microscope objective (look at the small melanocyte on the right of the image). For this light, absorption has not occurred, and significant spectral changes are consequently not observed. Similar results have been reported with conventional spectroscopic OCT [11]. A slight red-shift of the measured spectra with increased imaging depth can be observed in the image. This tendency is consistent with the fact that longer wavelengths penetrate deeper than shorter wavelengths due to reduced scattering [11,14]. However, the imaging depth is not large enough here (175 µm) to make this phenomenon clearly visible.
The acquisition time of the three-dimensional data-set was ( ) hard disk. The size of the acquired raw data-set is considerable (~ 10 9 "points"). Because of the acquisition time, the technique is presently not appropriate for in vivo imaging. Nevertheless, as demonstrated here, it may be applicable in the biomedical domain on ex vivo or immobile samples.

Conclusion
In summary, we have developed a FF-OCM system capable of providing combined spectroscopic/intensity three-dimensional images. Spatially-resolved measurements of the spectrum of light backscattered by the sample are achieved through short-time Fourier analysis of a stack of en face-oriented interferometric images. Intensity images with ultrahigh spatial resolution (~ 0.8 µm × 1.4 µm, axial × transverse) are extracted from the interferometric image stack using a non-linear 5-frame image combination. Due to the broad and smooth spectrum of the illumination source (halogen lamp), spectroscopic imaging is possible over a wavelength range from 600 to 900 nm. The centers of mass of the lowresolution measured spectra are calculated to provide local spectroscopic information.
As a validation of the spectroscopic FF-OCM technique, we have carried out absorption measurements in a model sample (a colored Agarose gel). We have demonstrated that spectroscopic FF-OCM may enhance the contrast of biomedical imaging, making differentiation of distinct tissues easier. At the price of an increase of the acquisition time, spectroscopic FF-OCM may provide improved imaging compared to conventional FF-OCM.