Chapter 4 Results
4.3 Surface Displacement Measurements
The performance of the phase-resolved imaging was tested with a pure phase object consisting of a resolution target (Edmund: NBS 1963A RESOLUTION TARGET_
positive) covered with a chromium layer deposited upon the target surface by evaporation. The thickness of the Chrome coating is 100 nm. Fig. 4.3(a) shows a sketch of the sample, and Fig. 4.3(b) is the sample path configuration. A two-dimensional data set of 50 adjacent A-scans was recorded; the sample was moved by 10µm in the x direction, perpendicular to chromium step, between the A-scans.
Fig. 4.3(c) shows an intensity and Fig. 4.3(d) a phase-difference OCT image. The phase image shows the phase difference on a color scale. Fig. 4.3(e) shows a plot of the phase difference along the surface of air-chromium. The phase difference changes
along the interface of the phase object is ~ 90°, corresponding to step heights of ~ 103 nm, can be observed, which is invisible in the intensity image [Fig. 4.3(c)].
(a) (b)
Fig. 4.3. Resolution target measurement, (a) Schematic of the sample, (b) sample path configuration, (c) intensity image, (d) phase image, (e) phase difference along the Chromium layer.
4.4 Nomarski experiment
A disadvantage of Wollaston is its splits the sample beam in two orthogonally polarized beams separated by∆d =8.7mm, the distance between the focal spots of two separate sample beams lim versal resolution. Therefore, we change to a Nomarski crystal, it can make the two orthogonally polarized beams split very small angle
(
0.06°)
. The distance of separated beam is only mited the trans
µ
52 . In this condition, we measure the chromium layer resolution target (Edmund: NBS 1963A RESOLUTION TARGET_ positive) covered with a cover glass (SUPE RIOR MARIENFELD : Deckgläser Nr.1 cover glasses, 22×22mm, made in Germany ), like Fig. 4.4, and extract the phase information for multi-layer structure.
Fig. 4.4. OCT test sample: schematic of the object structure.
he interferometric signals of two orthogonally polarized beams are shown in Fig. 4.5.
T
The first signal peak is reflected from the surface of a cover glass. The second signal peak is reflected from the interface of the bottom of cover glass and the glass plate or
the chromium layer of resolution target, the phase difference between them will be measured. The third peak is from muliple reflection.
(a) (b)
600 700 800 900 1000 1100 1200 1300 1400 -1
600 700 800 900 1000 1100 1200 1300 1400 -3
600 700 800 900 1000 1100 1200 1300 1400 0
600 700 800 900 1000 1100 1200 1300 1400 0
700 750 800 850 900 950 10001050 11001150 1200 0
Fig. 4.5. The interferometric signals of two orthogonally polarized beams, (a) signal P, (b)signal S, (c) Hilbert P, (d) Hilbert S, (e) combine Hilbert P and Hilbert S.
In Fig. 4.5(e), we discovered the signal P and signal S have displacement shift about µm
20 . This is due to the light passes through Nomarski crystal to make the optical path different. According to Fig. 3.2 and Eq. 3.2.2, we must move Nomarski crystal transversely. But after calculating, the distance of adjustment is too large over the size of crystal. Two orthogonally polarized beams can not interfere in the same time, thus the adjacent phase difference can not be extracted successfully.
Chapter 5. Discussion
This present result shows that our proposed free-space phase contrast optical coherence tomography system achieves sub-nanometer scale displacement sensitivity and is better than some previous systems [2, 7-9]. It may be due to the light passes through the same path before Wollaston, the common phase noise can be canceled by differential phase measurement. Besides, some other noise that caused by environmental perturbations, including temperature fluctuations, air currents, vibration, and moving part of scanning and phase modulation can be priority canceled by using the balanced detection. However, the instability of a mechanical device (i.e.
scanning mirror) in the reference arm (RSOD) of an OCT system decreases the stability of interference fringe carrier frequency thus increases the phase variance in our system.
Comparing to other reports, Taner Akkm et al. presented a fiber-based optical biosensor, which was capable of detecting ultra-small refractive index changes in highly scattering media with high lateral and longitudinal spatial resolution [21].
The setup is shown in Fig. 5.1(a). The LiNbO3 phase modulator implemented in the reference arm is used to generate a stable interference fringe carrier frequency. The
measurement of phase difference between interferometric frings in two channels eliminates environmental phase noise in this common mode system.
(a)
(c)
optical low coherence tomography. (b) Sample path configuration to scan spatially separated polarization channels on the sample. (c) Measured phase difference of a signal record.
Fig. 5.1. (a) Dual channel phase-sensitive
(b)
Fig. 5.1(c) shows that phase sensitivity for an individual recording is as low as 10-3 radians which allowing measurement of 104 pm path length differences resolution.
Therefore, with fiber-based system and implementation of external phase modulator in the reference arm of our phase contrast OCT, the similar resolution should be achieved.
On the other hand, Christopher Fang-Yen et al. [22] used the dual beam heterodyne interferometer which incorporates both fiber and free-space elements (Fig.
5.2(a)) to measure phase changes of reflected light from a sample relative to a reflective surface above. The light coming out of the second output of the Michelson goes to a reference gap. The reference gap consists of two reflecting surface with adjustable distance. The optical delay created in the Michelson and the noise associated with it was canceled by taking the difference in phase between the sample
and reference signals using Hilbert transform,
(
LS LR)
k ∆ −∆
=
∆φ 0
where k0 is the central wave number of the source. ∆LS and ∆LR are the round-trip optical path length differences between reflections from surfaces 1 and 2 of the sample and of the reference gaps, respectively. It is similar to balanced system.
(a) (b)
Fig. 5.2. (a) DBHI of optical referenced interferometer setup. (b) The phase displacement on the top of coverslip.
Fig. 5.2(b) is the phase displacement on the top of coverslip, averaged over every 0.2ms and the standard deviation of the phase vibrations σ is 0.16 mrad. The stability corresponds to an OPL of 40 picometers. The experiment demonstrated that an optical referencing method has sub-nanometer noise level over a period of 50 ms. But in our balanced system, we can not avoid the optical components for horizontal and vertical polarizations have different optical path delay. The noise with different delay was not canceled completely in our balanced system.
Moreover, because a Wollaston prism splits the sample beam in two orthogonally polarized beams separated by∆d =8.7mm in our system, the distance between the focal spots of the sample beams limited the transversal resolution.
Therefore, we change to a Normaski crystal, it can make the two orthogonally polarized beams split very small angle
(
0.06°)
. The distance of separated beam is onlyµm
52 . However, the Normaski causes two orthogonally polarized beams and they have large optical path difference. Two orthogonally polarized beams can not interfere in the same time, thus the adjacent phase difference can not be extracted successfully.
Another disadvantage of this setup is the mechanical vibrations from the translation stage of sample arm. The sample is mounted on a stage driven by an actuator that moves the sample transversely to the beam propagation direction. The sample stage caused the mechanical vibrations, so we need to spend some time waiting for the stage stability. It makes our measurement spent long time for 2D image. In order to improve the scan speed, we can use galvanomirror scanner instead of moving stage, like Fig. 5.1(b) shows.
Compared to time-domain OCT based phase measurement systems, other methods which based on frequency-domain optical coherence tomography to extract depth-resolved intensity and phase information would have significantly improved phase stability. That is because the frequency-domain OCT do not contain moving parts which can substantially increase the phase noise floor. Moreover, frequency-domain OCT do not require a scanning delay line, they can be built using a
common-path configuration where virtually all phase noise is common mode between the reference and sample optical field [23-25].
For example, Michael A. Choma et al. presented a spectral-domain phase microscopy (SDPM) in 2005. A phase-sensitive functional derivative of spectral-domain OCT that allows for real-time measurement of displacements with picometer-to-nanometer-scale sensitivity was demonstrated (as shown in Fig. 5.3)[26].
Since the phase of depth dependent function is a linear function of small displacement
δ , the changes in subresolution position of the sample reflector can be x measured with respect to an arbitrary zero point taken at a reference time t0 :
)]
Fig. 5.3. (A) FD SDPM interferometer. (B) SS SDPM interferometer. The insets show the displacement signals recorded from a clean coverslip.
They demonstrate SDPM using both Fourier-domain and swept source OCT had a displacement sensitivity of 53pm and 780pm, respectively, and can be used to measure cellular motion with exquisite sensitivity. Its spectral-domain system has intrinsically higher phase stability than time-domain techniques. Additionally, the phase of spectral-domain common-path interferometry obviates the need for dual-beam interferometers that are necessary to achieve phase stability in time-domain systems.
In the same year, Chulmin Joo et al. presented a novel quantitative phase imaging modality, referred to as spectral-domain optical coherence phase microscopy (SD-OCPM)(as shown in Fig. 5.4)[27]. Because SD-OCPM acquires depth-resolved information without mechanical scanning of the reference mirror, it can generate a three-dimensional quantitative phase-contrast image of a specimen simply by scanning the beam laterally as it measures phase profiles in depth.
Fig. 5.4. (a) Schematics of the SD-OCPM system. (b) Sample placed between a coverslip and a microscope slide. SDPM measures phase distribution of a sample referenced to the top surface of the coverslip.
The depth dependent function is obtained by a discrete Fourier transform,
The phase sensitivity is an important performance factor in SD-OCPM, and can be characterized by the standard deviation of the phase, and it is expressed as an explicit function of the signal-to-noise ratio.
2SNR 1
2 ≈
∆φ
The measured SNR was 100.4 dB, under which condition the theoretical sensitivity is 0.4 pm. The measured sensitivity in SD-OCPM was 25 pm in air. The difference between the theoretical and measured sensitivities may be due to the influence of external disturbances such as vibrations in the coverslip during the measurement.
In 2006, Marinko et al. developed a full-field swept-source phase microscopy (FF SS PM) technique for quantitative nanoscale surface profiling of samples in reflection[28]. This technique utilizes swept-source optical coherence tomography in a full-field common path interferometer for phase-stable cross-sectional acquisition without scanning as illustrated in Fig. 5.5
Fig. 5.5. Full-field swept-source OCT setup with a 4f common path interferometer.
Fig. 5.6. illustrates the procedure for processing the acquired data. Each interferogram is interpolated, windowed, and zero padded prior to performing a fast Fourier transform. Subwavelength variations are observed as variations in the phase at a particular depth slice.
Fig. 5.6. Processing steps to acquire phase-sensitive data using the full-field swept-source OCT system.
The phase stability of the FF SS PM was characterized both spatially and temporally by use of a glass coverslip. The spatially phase stability was measured from standard deviation across the coverslip surface in a 100*100 pixel region near the center of the
beam (i.e. 1.3 nm). The temporal phase stability was measured from the average standard deviation of the phase over 50 min. The standard deviation calculated for an area of 60 * 80 pixels was 2.5 nm.
In 2007, Desmond C. Adler et al. used buffered Fourier domain mode-locked (FDML) lasers and demonstrated a dynamic phase-sensitive optical coherence tomography (OCT) and 3D OCT phase microscopy[29]. Systems are operated at sweep speeds of 42, 117, and 370 kHz, the displacement sensitivities of 39, 52, and 102 pm were achieved, respectively. Their system is shown in Fig. 5.7.
Fig. 5.7. Setup for phase-sensitive OCT measurements.
Displacement sensitivities (DS) are measured by recording the phase at the back surface of the 210 mµ coverslip, relative to the front surface. Differential displacement sensitivities (DDS) are calculated by subtracting the measured phase of consecutive axial scans, ∆φ1−∆φ0. The result is shown in Table 1.
Table 1. Displacement Sensitivity Using Conventional and FDML Lasers.
Sensitivities are comparable to spectrometer-based OCT phase microscopy systems, but much faster acquisition speeds are possible. The differential displacement sensitivities of buffered FDML lasers are comparable with single-measurement
displacement sensitivities and would provide an additional 2 improvement in Doppler OCT sensitivity when compared with conventional swept lasers or nonbuffered FDML lasers.
Moreover, the combination of SD-OCPM and multiphoton microscopy (SD-OCP-MPM) was proposed by Chulmin Joo et al. in 2007[30]. It can obtain phase contrast and multiphonton fluorescence imaging simultaneously. The setup is shown in Fig. 5.8.
Fig. 5.8. Schematic of SD-OCP/MPM.
Fig. 5.9. Spatial and temporal phase stability of SD-OCP–MPM. (a) The 2D phase repeatability map demonstrates ~ 0.5 nm repeatability in air. (b) Phase fluctuation for a stationary beam; the standard deviation was 53 pm at a SNR of 63.4 dB.
Fig. 5.9 (a) shows the spatial phase stability. The standard deviation across the field of view was measured as ~ 0.5 nm in air, which may be in part attributed to the motion
jitter of the scanners. For the temporal phase stability, the phase fluctuation was recorded as all X, Y, and Z scanners are set to a fixed value (0 V) [Fig. 5.9 (b)]. The measured phase stability was ~ 53 pm in air at a SNR of 63.4 dB.
In 2007, Adrian H. Bachmann et al. presented a dualbeam heterodyne Fourier domain optical coherence tomography[31]. The authors indicate any phase noise due to sample motion or mechanical beam scanning will cause signal degradation as well as insufficient suppression of mirror terms, so they developed a dual beam FDOCT variant that profits from the high phase stability of a common path configuration, without sacrificing measurement depth range, and keeping the flexibility for beam scanning as well as the possibility of dispersion balancing. A dual beam configuration is shown in Fig. 5.10., both reference and sample light share the same path and thus exhibit high relative phase stability. The Dual beam principle is that the output of an interferometer with a relative delay of 2∆zIILS between the two light beam intensities IR and IS is pre-compensated for the relative distance between R1 (reference surface) and R2 (sample). The configuration presents a small relative distance z∆ between reference surface (R1) and sample (R2) and up to four cross correlation terms might occur. The blue beam can be considered as the reference beam.
Fig. 5.10. Dual beam heterodyne FDOCT. Inlet A depicts synchronization of the line detector. Inlet B shows the reference arm added and used for phase stability comparison between the dual beam and the standard configuration.
In order to demonstrate the advantage of dual beam versus standard FDOCT in terms of phase stability, the SNR of the signal peak was adjusted to approximately 26.5dB.
For the standard FDOCT configuration, it could be measured that the phase fluctuations are strongly varying (see Fig. 5.11). The strong fluctuations of the standard signal peak intensity are mainly due to fringe washout and stress-induced polarization state changes in the perturbed fiber, resulting in reduced interference fringe contrast. These measurements proof clearly the advantage of dual beam FDOCT over standard FDOCT.
(a) (b)
Fig. 5.11. (a) The dual beam signal (red) remains stable even if the fiber is perturbed whereas the signal peak corresponding to the standard setup (blue) is heavily perturbed. (b) The red and blue lines indicate the standard deviation σdual =0.05 rad and σstd =0.72 rad of the phase fluctuations, respectively. The shown tomogram depth is approximately 400 mµ (in air),
SNR 26.5dB. ≈
Chapter 6. Summary
We have developed balanced OCT configurations to yield phase information by incorporating the RSOD into a Mach-Zehnder interferometer. The designs that used balanced indicated a more improvement than the standard OCT interferometer. Using this system we have shown that sub-nanometer optical path differences, which are invisible in conventional intensity-based OCT image, can be successfully imaged by phase-resolved OCT. The phase drift caused by environmental disturbance may due to the free-space system configuration. With fiber-based system and implementation of external phase modulator in the reference arm of our phase contrast OCT, the better resolution should be improved. Possible fields of application might include not only biomedicine (e.g. tissue surface profilometry, cell response to various stimuli, etc.) but also, e.g., the semiconductor or the thickness of layered structures is of interest.
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