In this paper we present an ultra high speed and highly phase sensitive line-field FD-OCT system for quantitative phase mapping. The system works with a maximum speed of 512 000 A-scan/s (1000 fps) in real time mode. Along the parallel recorded direction excellent phase stability corresponding to a path length variation of only 510 pm was measured. We demonstrate how to exploit this phase accuracy for fast chemical analysis of glucose mixture processes. The system has particular potential for studying micro-fluidic processes.
©2010 Optical Society of America
Phase contrast techniques are of high importance in microscopy to enhance the intrinsic low contrast of many cell samples. Especially for in vivo imaging staining-free methods are necessary. Most techniques do not directly provide quantitative information on these phase changes. Such information is readily obtained in interferometry: the interferometric signal phase gives access to nanometer and even sub-nanometer optical path length variations. For example, motions of such magnitude include the actin-based transport of organelles within the cells , the ruffling of cell membranes , and the reaction of cell volumes to hypertonicity or hypotonicity . On the other hand slight changes in refractive index or in general dispersion due to chemical changes or characteristics of a sample medium equally impact on the signal phase of the reflected or transmitted signal. Detection of these fundamental properties plays key role in a number of optical imaging and microscopy techniques [4–6]. Quantitative dispersion microscopy has recently been proposed for full field refractive index maps of biological samples . The elegant method has only limitations concerning achievable signal-to-noise-ratio (SNR) in order to enhance its phase sensitivity. Another promising method is spatial light interference microscopy, a combination of phase microscopy and Zernike phase contrast . This technique, which operates in trans-illumination mode, yields sub-nanometer precision for differential lateral changes in refractive index.
Employing low coherence light sources in interferometric techniques operating in epi-illumination can help to gate the region of interest in depth and to avoid coherent crosstalk from nearby reflections [8–11]. High precision instruments utilizing Fourier domain optical coherence tomography (FD-OCT) techniques have been introduced, which showed excellent phase stability [12–14]. They can be implemented using a common-path topology  in which virtually all phase noise is common mode between the reference and sample optical fields [16,17]. Common path topologies are nevertheless critical in case of high NA objectives, because back-reflected light from reference interfaces outside the short confocal gate may be completely suppressed. In order to keep the option of imaging with high NA, an en-face OCT system with high transverse imaging speed (40 fps (520 x 200 pixels) was introduced . It was demonstrated how the phase changes owing to jitter, scanner noise, or sample motion can be separated from the phase changes introduced by the sample structure itself. However, several post processing steps need to be performed in order to extract the correct phase information.
A particularly interesting application of highly phase stable partial coherence interferometric systems is the quantitative assessment of analyte concentrations [19,20]. The principle is based on measuring the change in accumulated optical path length due to changes in dispersion as light passes the sample volume. The method is still limited to a single point, since scanning would critically affect the precision of the method. Phase jitter due to beam scanning could be completely suppressed by using a full field approach based on swept source OCT . The limitations of this potentially highly stable setup are the availability of relatively slow array sensors and the phase stability of the source itself.
In the present work we introduce a phase microscopy system based on FD-OCT that records one transverse coordinate in parallel avoiding thus mechanical jitter due to scanning and exhibiting extraordinary phase stability. Such line field system has been introduced before to achieve cross sectional images with high structural viability as is important for example for corneal topographic imaging . We demonstrate how this highly phase sensitive device can be used for studying high-speed changes in refractive index of glucose mixtures.
2. Experimental setup
The optical scheme of the parallel FD-OCT system is shown in Fig. 1 . A Michelson interferometer is illuminated by a superluminescent diode (SLD) with a central wavelength of λ 0 = 832 nm and a spectral full width at half maximum (FWHM) of Δλ FWHM = 17 nm. Outgoing light from the SLD pigtail is collimated with fiber coupler FBC. The cylindrical lens CL1 defines an anamorphotic scheme and produces a line illumination of the sample (~3 mm x 11 μm). The anamorphic beam is split by a non-polarizing beam splitter BS1 into sample and reference beam. At the exit of the interferometer, the light beams returning from the sample and reference arms are recombined collinearly. Light is spatially filtered via a slit (3 mm x 50 µm) and then fed into the spectrometer. The slit is positioned in a conjugate plane to the sample with its long extension parallel to the illuminating line. By rejecting light, in particular multiply scattered light, from adjescent voxels it improves image details and reduces also the incoherent background at the detector . However, such ‚quasi-confocal‘ system does not achieve the confocality of a truly confocal systems, since the slit does not act on the parallel direction. Hammer et al.  compared theoretically and experimentally line illumination techniques with confocal systems and came to the conclusion that the contrast and depth resolution of images is qualitatively similar.
The spectrometer is equipped with a high speed CMOS camera (custom made high speed camera with integrated Solid-State-Disk (1.3 GB\s), 1280 x 1024 @ 500 frames\s, 12 μm square pixel, 59 dB dynamic range, AES Technologie AG). The light is dispersed via transmission grating TG (Wasatch Inc., 1200 lines/mm) and imaged through an achromatic lens (f = 150 mm) onto horizontal detector lines. Hence, each such line yields an A-scan (depth information) after Fourier analysis, whereas the vertical detector coordinate samples the transverse sample structure. One camera acquisition gives therefore a full B-scan. The spectral resolution of 0.07 nm results in a system depth range of 2.7 mm.
Due to the low quantum efficiency of the used CMOS detector (7% at 800 nm) and the limited bit depth of 8 bit, a sensitivity of ~74 dB has been measured at the maximum intensity position with an exposure time of 1 ms. In addition the sensitivity depends on the intensity distribution across the B-scan direction as shown in Fig. 2 .
The sensitivity is clearly not sufficient for in vivo OCT measurements. However, the high potential of this detector lies in its fast frame rate: one B-scan consists of 512 A-scans and the system works with a maximum speed of 1000 fps in real time mode. This is equivalent to 512 000 A-scan/s with 512 x 1280 pixels. The field of view (z, y) of the system is ~2.7 mm x 3 mm, with a depth resolution of 18 μm and transversal resolution of 11 μm.
The aim of the present work is to exploit the ultra high speed of the employed CMOS camera together with the intrinsic high phase stability of the parallel detection scheme in order to extract slight dynamic phase changes, caused by the sample, due to optical path length changes in the order of nano- and subnanometer along the sample path.
2.1 Phase measurements on the resolution test target
The performance of the system with respect to transverse resolution can be best characterized on a USAF resolution test target (RTT). In order to extract the phase map from an en-face image of the structure, a full 3D data set needs to be recorded. For lateral scanning (x axis), the RTT was placed on a piezo translation stage and shifted in horizontal direction at constant speed of 2 mm/s during the measurement. 3D data set, consisting of ~1000 tomograms (exposure time 1 ms/tomogram) of 512 x 1280 pixels, was captured in ~1 s.
After FFT of all spectra we obtain a complex valued 3D data set (Fig. 3(b) ). The en-face intensity map and associated phase map image were taken at maximum of the intensity of the front reflex from the RTT target.
The full scan intensity plot is shown in Fig. 4(a) . The cross-section along the group 5 (Fig. 4(b)) allows determining the lateral resolution of the system as 11 µm (element 4 of group 5 of the RTT target), which corresponds well to the theoretical estimation of 10 µm. Due to the high transversal stability, we obtain the lateral phase image (Fig. 5(b) ) directly from the original phase image (Fig. 5(a)) with no additional phase correction in post-processing except phase unwrapping and background subtraction. The measured phase of the interferometric signal consists of following terms:
The background subtraction is effectively a phase referencing to a lateral line along the scanning coordinate that samples only the glass plate surface. It sufficiently deletes the phase noise terms in Eq. (1), which equally affect the phases at each point along the parallel direction. We finally observe the quantitative phase change introduced by the height profile and phase shift introduced by reflection of the chromium layer (Fig. 5(b)). There is a strong phase change visible at the edges of the chromium lines. We attribute this change to diffraction effects as the beam with finite width crosses the edge of the chromium line on glass. It is interesting to note that this effect is more pronounced in the scanning direction than in the parallel-recorded direction.
2.2 Phase stability of the system
The phase stability and the associated error of the path length difference of the system can be quantified by the following formula :Eq. (2) we have calculated the theoretical error of the path length difference with 240 pm. In order to calculate the standard deviation Δς of the phase fluctuations along the parallel-recorded line at the mirror surface we first need to subtract the constant phase offset for each pixel. This offset is readily obtained by averaging the phases of 200 lines. The measured standard deviation was then 510 pm. Such phase fluctuation of that small magnitude extent has so far only been reported with self-referenced common-path configurations. On the other hand, the standard deviation obtained from 200 successive frames in time at a single position on the mirror surface at maximum SNR was 5 nm. This value reflects the stability (mechanical vibrations, thermal fluctuations, etc.) of our system during the measurement time of 200 ms with an exposure time of 100 μs and is comparable with that of standard OCT systems.
2.3 Phase sensitive detection of glucose-water concentration
The motivation behind this experiment is the observation that any change in optical path length assessed via OCT signal phase can have two origins. Firstly, a simple change in geometric path length d geom such as in case of axial sample motion or surface profile changes, or secondly, a change of refractive index n along the optical path. The latter effect produces Doppler signatures for static sample reflections underneath flowing liquid with inhomogeneous refractive index distribution such as blood (see Fig. 8(a) ). Here, the origin is the change in optical path length of light that traverses the flowing liquid, which is independent of multiple scattering. Mathematically we write for the change in optical path length d opt = nd geom, where d geom is the geometric path length and n is the group refractive index of the medium:
Let us now assume a homogeneous glucose-water solution within a cuvette of known thickness d. The concentration of glucose can be directly related to the change in optical path length of light that traverses the cuvette twice as:
To demonstrate this linear dependence we have measured six different glucose concentrations in the range 1-10 mg/ml (ambient temperature: 24.4 ± 0.1 °C, humidity: 34 ± 1%). The sample light passes through the cuvette of thickness d = 10 mm, is reflected on a mirror, passes a second time through the glucose solution and interferes with the reference arm light. We extracted then the phase of the cross correlation signal corresponding to the mirror interface behind the solution. Data set was referenced to pure distilled water. Figure 6 verifies the linear dependence of the phase shift on the concentration of glucose.
After linearization of the results, we have measured that glucose induces changes in the phase of 0.10 rad/(mg/ml) in the 10 mm thick cuvette. The averaged standard deviation over 200 phase measurements for different glucose concentrations was ± 3.5 mrad, which is in good agreement with previously reported work using phase sensitive low coherence reflectometry and phase sensitive spectral domain OCT . This value corresponds to a glucose concentration precision of 0.035 mg/ml. For comparison, physiologic glucose concentrations are between 60 and 100 mg/dl, i.e., 0.6 and 1 mg/ml.
Having measured the dependence of phase and glucose concentration we will now proceed to dynamic mixture processes where we can fully exploit the speed advantage of the CMOS sensor.
To demonstrate the applicability of the method for measurements of fast processes, we image an injection of 10 mg/ml glucose solution into distilled water within a cuvette of same geometry as before. The drawing of the experiment is shown in Fig. 7 . As the light travels twice through the cuvette volume, it will pick up all phase changes due to changes in refractive index of the liquid. We measure the intensity and accumulated phase after double transit through the sample. Clearly this experiment does not resolve local changes along the optical axis, but it is highly sensitive to accumulated relative transverse changes in refractive index. In order to relate measured phase differences to glucose concentrations we reference the phase values at time t to the original phase distribution without glucose injection at time t = 0, i.e., ΔΦ(t,x) = Φ(t,x) − Φ(t = 0,x).
Figure 8(a) shows the en-face OCT intensity M-scan image of liquid injection (beginning) extracted at the probing light beam position. The calculated glucose concentration map obtained with the help of Fig. 3 is shown in Fig. 8(b).
Note that this map shows the accumulated phase change corresponding to the optical path length through the cuvette at each lateral position along the parallel-recorded coordinate and at each point in time (cf. Figure 3, where time replaces x axis). The data set was captured with ultra high speed of 512 000 equivalent A-scans/s (1000 frames (tomograms)/s, 512 x 1280 pixels) and an exposure time of 100 μs.
The high chemical sensitivity of the system was demonstrated by performing the same experiment with 5x decreased glucose concentration of 2 mg/ml (Fig. 9 ). Figure 9(a) shows the OCT intensity M-scan image of liquid injection extracted at the axial mirror position. Figure 9(b) shows the corresponding concentration map. Whereas we cannot observe any changes in the OCT intensity M-scan image (Fig. 9(a)), the phase map of same M-scan (Fig. 9(b), 9(c)) clearly reveals the temporal evolution of low concentration glucose liquid solution during the injection. The phase of the interferometric signal, as a most sensitive parameter, can enhance the image contrast similar to the Schlieren method .
The applicability of the method for the quantitative assessment of fast processes was demonstrated by imaging the injection process of glucose into water. A critical parameter was the phase stability during the injection process as the injection was performed by the operator. This causes the appearance of background phase variations along time in Fig. 9(b). These drawbacks can be suppressed by implementation of a microfluidic chip and using a syringe pump for precise dosing and actuation of liquid flow.
Microfluidics deals with the behavior, precise control and manipulation of fluids that are geometrically constrained to a small (sub-millimeter) scale [26–28]. Advances in microfluidics technology are revolutionizing molecular biology procedures for enzymatic analysis (e.g., glucose and lactate assays), DNA analysis, and proteomics. Another emerging application area for biochips is clinical pathology, especially the immediate point-of-care diagnosis of diseases. In addition, microfluidics-based devices, capable of continuous sampling and real-time testing of air/water samples for biochemical toxins and other dangerous pathogens, can serve as an always-on “bio-smoke alarm” for early warning. These technologies are based on the manipulation of continuous liquid flow through micro-fabricated channels. Obviously, the presented phase sensitive parallel FD-OCT method has a high potential to be exploited in various applications of microfluidics.
In conclusion, we have introduced a new ultra-high speed and highly phase sensitive parallel FD-OCT system for quantitative phase mapping. The system works with a maximum speed of 512 000 A-scan/s (1000 fps) in real time mode. The field of view (z,y) of the system is approximately ~2.7 mm x 3 mm, with a depth resolution of 18 μm and transversal resolution of 11 μm. We have demonstrated excellent phase stability along the transversal (parallel, non-scanning) direction. The measured precision of the method to detect small changes in optical path lengths was 510 pm. The averaged standard deviation of ± 0.0035 rad obtained from the phase measurements of different concentrations of aqueous glucose solution demonstrates the high accuracy of the system to follow high speed refractive index changes. Hence, implementation of the principle with micro-fluidics could exploit its potential in various applications as for studying mixture dynamics or for fast chemical analysis of micro-fluids.
The authors would like to acknowledge financial assistance from the European Fund (FP7-HEALTH-A) Grant 201880 FUNOCT.
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