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Quantitative phase imaging has been an important labeling-free microscopy modality for many biomedical and material science applications. In which, ultra-fast quantitative phase imaging is indispensable for dynamic or transient characteristics analysis. Conventional wide field optical interferometry is a common scheme for quantitative phase imaging, while its data acquisition rate is usually hindered by the frame rate of arrayed detector. By utilizing novel balanced-photo-detector based digital optics coherent detection techniques, we report on a method of constructing ultra-fast quantitative phase microscopy at the line-scan rate of 100 MHz with ~2 μm spatial resolution.
© 2016 Optical Society of America
1. Introduction
The structural mapping of refractive index distribution contains key information for achieving high quality three dimensional imaging in biological and material characterizations. Not only does the refractive index mapping itself present a direct visualization of the sample [1], but also it can often provide calibration databases for wave-front sensitive imaging techniques, such as fluorescence-based structured illumination microscopy (SIM) [2, 3]. Due to the intrinsic relationship between optical phase and refractive index, quantitative phase imaging (QPI) has emerged as an important tool for studying structures and dynamics of both labeling-free and labeled samples [4]. Compared to Zernike phase contrast microscopy [5] and Nomarski differential interference contrast microscopy [6], QPI techniques are capable of accurate quantification of both optical phase and amplitude, providing a powerful platform for studying topographical or refractive index data [7, 8].
As optical phase cannot be detected directly, optically interferometric schemes are usually used to demodulate the phase. As fields from the optical source interact with specimen, phase shifts are induced in the scattered fields with respect to the un-scattered reference fields. Several different approaches based on optically interfering scheme exist, including common-path based Fourier phase microscopy (FPM), diffraction phase microscopy (DPM) [9], quadriwave lateral shearing interferometry (QWLSI) [10], and off-axis based digital holography (DH) imaging [11]. Such QPI methods are all based on wide-field data acquisition with arrayed detectors, such as CCD and well-suited for single-shot imaging. All information extracted from phase can be processed and then used for cellular identification and biomarker. However, high speed phase information acquisition is often limited by the CCD frame rate. On the other hand, we know that ultra-fast quantitative phase imaging is especially indispensable for dynamic or transient characteristics analysis in high throughput bio-medical or material science study.
Serial time-encoded amplified microscopy (STEAM) has been developed to achieve megahertz imaging frame rate [12, 13]. The imaging information is first encoded into spatially dispersed spectral channels. The modulated spectra are then highly chirped and detected by single channel high-speed opto-electronic receiver. By taking advantage of well-developed high speed opto-electronic components and demodulation techniques in modern optical communication, STEAM provides a unique way to obtain ultra-fast imaging information by serial intensity acquisition. By using optical interferometric detection in the STEAM imaging system, high-speed QPI imaging has been demonstrated [7]. However, stringent polarization alignment between the signal and local oscillator (LO) light is required in the conventional optical interferometric scheme [14]. Otherwise, the system stability will be influenced.
In this paper, we introduce optical digital coherent detection technique for achieving quantitative phase imaging. More specifically, we present a digital coherent time-stretch microscopy system that is capable of delivering ultrafast QPI of fixed cells in a scanning rate up to 100 MHz without averaging. With using the digital coherent detection system, the polarization state is diversified at digital coherent receiver and so the imaging system will not be influenced due to the polarization instability. In addition, the system sensitivity can be improved due to digital coherent and balance detection scheme [15]. The whole imaging system will also become flexible and easy-to-compensation due to digital coherent and sampling technique.
2. Principles
In this work, the quantitative phase image of the sample is retrieved in the optical digital coherent receiver which consists of two homodyne coherent detectors in a polarization-diversity configuration [15]. It requires a local oscillator (LO) that servers as an absolute phase and polarization reference to demodulate the phase and polarization information of the incoming signal. The homodyne coherent detection scheme is shown in Fig. 1(a). The LO is divided to two arms to beat with the two paths of the signal, respectively. One of the LO arms is phase shifted by 90° so that two quadrature components can be detected simultaneously. Two balanced detectors are used to convert the two quadrature components to electrical current, which are given by
where R is the responsivity of the photodiode, PS(t) is the optical power of the signal, PL is the power of the LO light, θS(t) and θL are the phase of the signal and LO respectively, and I and Q represent the in-phase and quadrature components separately. Then the complex amplitude can be expressed asThe amplitude and the phase information then can be restored through digital signal procession (DSP) on the complex signal.
Fig. 1 Three types of coherent detection scheme. (a) Single PD detection. (b) Balanced detection. (c) Homodyne detection receiver.
As compared to the conventional optical interferometric scheme for QPI [7], the optical digital coherent receiver has the advantage of improving signal-to-noise ratio (SNR) due to the balance detection used in the receiver [15]. In the conventional optical interferometric scheme as shown in Fig. 1(b), the beating of the signal and the LO is detected by a single photodetector that has the output current
where ωIF is the frequency difference between the signal and LO. The plus and minus sign in Eq. (4) correspond to two output arms. In the output current, the fast-oscillating cosine term is essential for the phase retrieval but the direct current (DC) term should be filtered. When the single PD is replaced by a balanced detector as shown in Fig. 1(c), the DC term from the two arms is subtracted and the amplitude of fast-oscillating cosine term is doubled, resulting in a 3-dB SNR improvement. Additionally, the LO intensity noise can be suppressed by subtracting the two photocurrents.In addition, benefiting from the polarization-diversity configuration, the polarization alignment between the signal and the LO is not required in the optical digital coherent receiver [15]. Two homodyne receivers compose the polarization-diversity receiver as shown in Fig. 2(a). The LO light is polarized at 45 degree relative to the PBS. The signal with an arbitrary polarization state is divided into two orthogonal linear polarization components and demodulated by the two homodyne receivers separately, resulting in two complex amplitudes, IcX and IcY. Although the polarization of the signal may be changed randomly, we can acquire the complex amplitude Ic by rotating the polarization in the subsequent DSP, as shown in Fig. 2(b). The process can expressed as
where IcX and IcY are the complex amplitude of the two polarization components, and θ is the angle between the SOP of incoming signal and x-polarization in the receiver. The angle θ can be solved as arctan(|IcY|/|IcY|). Accordingly, the complex amplitude Ic can be obtained regardless to the polarization of the signal so that the imaging system will not be influenced by the polarization instability.Fig. 2 (a) Scheme of polarization diversity receiver. (b) The rotating of polarization coordinate system.
3. Experimental setup
The schematic diagram of proposed digital coherent ultrafast quantitative phase microscopy is shown in Fig. 3. A home-made Erbium doped fiber mode locked laser (MLL) generated a 100 MHz optical pulse train, which was then band-pass filtered to 14 nm bandwidth around 1550 nm. We chirped the pulse train by using a dispersive fiber of 680 ps/nm group velocity dispersion, which can stretch the pulses to about 9 ns width. An Erbium doped fiber amplifier (EDFA) amplified the chirped pulse train to 20 dBm average power. A 1 × 2 optical power splitter separated the pulses into signal and local oscillator arms with 80:20 power splitting ratio respectively. After passing through an optical circulator (OC), the pulses in the signal arm was then converted into spatial light beam by a fiber collimator. A one-dimensional (1-D) spectral shower was generated by a volume holographic transmission diffraction grating (Wasatch Photonics, Spatial Frequency = 1200 lines/mm). Because the thickness of the sample is generally around tens of micrometers, it is suitable to assume that the dispersion of the sample is negligible. Accordingly, the spatial information of the sample was mapped to the spectrum of the 1-D spectral shower through a double-pass transmission configuration using two objective lenses (both 40x). Then, the beam encoded with spatial information together with the unmodulated reference light from the upper arm were mixed and detected by the optical digital coherent receiver (Picometrix CR-100A). The variable delay line (VDL) in the upper arm was used to tune the relative time delay between two arms. A frequency offset of 4GHz between the LO and signal was achieved by tuning the temporal delay between the two chirped pulses [16]. The average power of signal and LO reaching the digital coherent receiver were about −10 dBm and + 3dBm respectively. Finally, a real-time oscilloscope (LeCroy LabMaster 10Zi) with 80G sampling rate was used to digitize and acquire the I and Q data from the receiver, which can be used to recover the phase and amplitude information of the signal [14].
Fig. 3 Experimental setup of digital coherent ultra-fast quantitative phase imaging system. DCF: dispersion compensating fiber, OBPF: optical band-pass filter.
In the conventional optical interferometric system, polarization controllers are necessary to be introduced to ensure that both the signal and LO have the same SOP. Because the optical digital coherent receiver polarization diversified the signal, then detect both the information at both polarization state, polarization controllers are not necessary between the signal and LO. In addition, the polarization fluctuation in fiber or specimen induced instability of the imaging system can be overcome [15].
4. Experimental results
To demonstrate the feasibility of the system to obtain the information of QPI, we replace the optical circulator and the spatial light setup in Fig. 1 with liquid crystal on silicon (LCOS) based WaveShaper (Finisar WaveShaper 4000S), which can be programmed to simulate the arbitrary amplitude and phase change. The amplitude and phase modulation of the WaveShaper is equivalent to the process of spectral modulation in the imaging system.
Firstly, the WaveShaper was set to all-pass mode, the solved amplitude and phase data could be regarded as the references. Then, a sinusoidal amplitude attenuation and sinusoidal phase shape are simultaneously programmed on the signal arm through the WaveShaper. The solved and normalized amplitude and phase are shown in Fig. 4(a) and Fig. 4(c) respectively. To compare, the spectrum of the shaped optical signal acquired from an Optical Spectrum Analyzer (OSA) is shown in Fig. 4(b), which is consistent with the normalized amplitude. Similarly, the programmed phase of the WaveShaper is shown in Fig. 4(d), which is consistent with the normalized phase.
Fig. 4 (a) Normalized amplitude of the sinusoidal shaped signal. (b) Optical spectra acquired from OSA. (c) Normalized phase of the sinusoidal modulated signal. (d) The phase spectra programmed on WaveShaper.
Then, a silicon chip based Dammann grating [17] was used as the imaging sample. The Dammann grating had alternative phase change of 0 and π rad, which was realized through etching a specified depth change on the chip. The imaged area was in the rectangular box in Fig. 5(a), which was captured by a commercial light microscope with a slow imaging speed. The spectral shower covers about 230 μm and a total of 400 scans with a step of 0.5 μm are performed along the y-axis (the arrow direction).Benefiting from digital coherent receiver, we can retrieve intensity and phase information with high quality simultaneously. Because of the improved Signal to Noise Ratio (SNR) of the proposed imaging method, the amplitude and phase images in the following figures were processed without averaging. So we can achieve an effective line-scan rate as high as 100 MHz. As the intensity image shown in Fig. 5(b), except the boundaries between the different phases, the reflectivity of all the chip was nearly 100% in either 0 or π phase area. However, light reflected by different phase area had different Optical Path Length (OPL), which could be presented in the phase image. By translating the phase to depth, a 3D image shows the real depth information of the silicon chip grating (Fig. 5(c)). To see clearly, the projecting portion in Fig. 5(c) represents the deeper area. Relating to the phase resolution, the vertical resolution of ultrafast quantitative phase imaging could be as high as nanometer [18].
Fig. 5 (a) Light microscope image of the silicon chip based Dammann grating. (b) Intensity image by our method. (c) Reconstructed depth information based on phase image.
The lateral resolution of the digital coherent time-stretch microscopy was experimentally demonstrated by capturing the time-stretch image of the smallest feature on a resolution target with a negative pattern coating (Thorlabs USAF-1951). The imaged area covered all the group 7 is shown in Fig. 6(a), which was taken by the conventional optical microscope. By capturing the surface reflection light, the intensity 2D image was reconstructed as shown in Fig. 6(b). The high speed image showed quality similar to that obtained from the low speed microscope and resolved well the smallest line feature (a linewidth of 2.2 μm in Element 6 of Group 7). Based on our proposed system configuration and following the analysis presented in Ref [19], the spatial lateral resolution was calculated to be ∼2 μm. Again, a depth 3D image of the resolution target was reconstructed as shown in Fig. 6(c) and resolved well similarly. The height between the area with coated and without coated was assessed as ~150 nm.
Fig. 6 (a) Light microscope image of the resolution target. (b) Intensity image by our method. (c) Reconstructed 3D image based on quantitative phase imaging.
To further demonstrate the potential application of the high speed quantitative phase imaging performance for biological specimen, we performed imaging of fixed cell cultured samples on glass slides. By scanning the samples in the direction orthogonal to the spectral shower with a step size of 0.5 μm and 100 MHz line-scan rate, a 2-D image is acquired. Figure 7(a) and Fig. 7(c) show two groups of unstained nasopharyngeal carcinoma cells captured by conventional phase contrast microscope. Cells in Fig. 7(c) and Fig. 7(a) were cultured with and without tumor suppressor drugs respectively. Cells in Fig. 7(c) had more condensed morphology compared to the control cells. The high-speed time-stretch image on the same region of interest were shown in Fig. 7(d) and Fig. 7(b) respectively, which showed the morphology difference of the two groups of cells. More importantly, we acquired the quantitative phase profile of the cells at an ultrahigh line-scan rate of 100 MHz. The quantitative phase information can be used to further characterize the individual cells by analyzing the parameters such as refractive index, cell volume and cell dry mass [20]. It should be noted that large population of cells should be measured to achieve effective analysis with high statistical accuracy, which would be is our on-going work.
Fig. 7 (a), (c) Light microscope image of the nasopharyngeal carcinoma cells without and with tumor suppressor drugs. (b), (d) High speed time stretch image on the same region of (a) and (c) respectively. (a)-(d) has the same size of 230 × 400 um and the same plotting scale.
5. Conclusion
We have demonstrated an ultrafast quantitative phase imaging using an optical digital coherent receiver. It enables an imaging with 100 MHz line-scan rate and no averaging was needed. Quantitative phase imaging of silicon chip and fixed cells were performed with ~2 μm resolution and good imaging quality was present at ultrahigh imaging speed.
Funding
We acknowledge the funding support from the National Science Foundation of China (NSFC: 61525502, 61435006, 11174019, 61322509, 61505070, 81372382, 51522201 and 11121091), and National High Technology 863 Research and Development Program of China (No. 2015AA015502).
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