Three-dimensional surface phase imaging based on integrated thermo-optic swept laser

We developed an optical frequency domain imaging (OFDI) system based on an integrated thermo-optic swept laser to achieve three-dimensional surface imaging. The wavelength was swept by applying a heating signal to a thermo-optic polymeric waveguide. The sub-micrometer surface profile was converted from the three-dimensional phase information of the OFDI system on various samples used as resolution targets with a step height of 120 nm.


Introduction
With the rapid growth of the small-component industry, there has been increased demand for cost-effective, noncontact, high-speed, high-accuracy three-dimensional (3D) surface inspection technology. Considering the build-up cost, inspection speed, submicron measurement and availability of multifunctional inspection equipment, optical surface imaging systems can provide a powerful tool for the precision components industry. There are various optical approaches to imaging 3D surface profiles. Mechanical displacements of an axial scanner can record the phase variance on a sample surface in an optical interferometer [1][2][3]. However, those approaches using a mechanical movement could suffer hysteresis of the mechanical translator, making them unsuitable for the increasing degree of integration of imaging systems. The alternative of employing a tunable laser source to build non-mechanical movement optical imaging systems has been extensively studied [4][5][6]. For the last decades, optical 5 Author to whom any correspondence should be addressed. frequency domain imaging (OFDI), also known as sweptsource optical coherence tomography, has been studied not only to avoid mechanical movement in axial scanning, but also to enhance the signal-to-noise ratio (SNR) compared to traditional optical imaging systems using a white-lightsource-based time-domain process [7,8]. OFDI is a frequencydomain-based image technique that uses a swept source and an optical interferometer. Once the swept source changes its wavelength within the designed spectral bandwidth, an OFDI system acquires spectrally resolved interference signals, which are processed by frequency domain analysis [9]. More importantly, the area-beam-type OFDI approach can be suitable for 3D surface phase imaging without any mechanical movement [10]. One of the most important issues for increasing the degree of integration of the OFDI system has to do with the swept source. Recently, a number of integrated swept sources have been demonstrated for OFDI using a resonant-mirror-based swept laser [11] and an optically pumped swept vertical-cavity surface-emitting laser [12].
However, most of these costly swept sources are intended to work at high speeds of more than 10 kHz and to acquire a depth image of a multilayer structure [13]. In this study, we present an alternative novel cost-effective approach for an integrated thermo-optic swept laser to implement an integrated OFDI system for 3D surface phase imaging. This study, which employs polymeric waveguide technology, demonstrates the significant advantages of matured fabrication technology, reliable polymer material in a 1.5 μm spectral window and cost-effectiveness. However, there is still a critical disadvantage of slow response time due to the thermo-optic effect [14][15][16]. Nevertheless, this integrated thermo-optic swept laser can be a good choice when combined with a line-beam-type OFDI application because the line-beamtype OFDI system does not require a high repetition rate compared to the conventional point-beam-type OFDI system. The limiting factor of data acquisition in the line-beam-type OFDI is the frame rate of an array detector, such as a chargecoupled device (CCD) and a complementary metal-oxidesemiconductor (CMOS) camera (roughly a few kHz). If 1024 frames are required for 2D depth profiles, a slow repetition rate of a few Hz for the swept source can be sufficient to reconstruct the cross-sectional surface phase imaging from the array detector with thousands of pixels used in parallel. Moreover, the integrated thermo-optic swept laser can increase the degree of integration of the OFDI system. For the ultimate integration of the OFDI system on an all-in-one-chip, it can be easily expanded to integrate other polymer-waveguide-based optical components, such as the main optical interferometer, auxiliary k-resampling interferometer and interconnection to the optical fiber [14].

Setup for integrated thermo-optic swept laser
As shown in figure 1, the integrated thermo-optic swept laser consists of a superluminescent laser diode, an aspherical lens, Bragg grating made in a fluorinated polymer waveguide and a heating electrode on the top surface of the upper cladding. The Bragg grating waveguide was fabricated by photolithography and dry etching process. More detailed description of the fabrication process can be found in the previous paper [15]. All the components are aligned actively with a transistor outline can-type package to increase the coupling efficiency of the module and the fabrication yield. To accomplish a continuous and constant wavelength change in the swept laser output, we applied linearized power tuning to the Ti-Au heating electrode using an arbitrary function generator. To ensure stable heat distribution in the external laser cavity for a rapidwavelength-swept output, the shape of the Ti-Au heating electrode was optimized with a polymeric tunable Bragg grating under an embedded thermoelectric cooler. Unlike the discrete tuning of the wavelength output used in wavelength division multiplexing passive optical network applications, the OFDI system requires continuous sweeping of the wavelength from the swept laser. Since the generated Joule heating energy Q is proportional to the square of the applied voltage, it gives rise to Q(V ) = σV 2 , where σ is the electric conductivity of the heating electrode and V is the waveform voltage. To secure a constant wavelength change in the time domain, we applied a programmed waveform V(t) that is proportional to the square root of the time as given by the following equation: where A indicates the amplitude of the electric potential, p is the period of the linearized power tuning and t is the time lapse. We have developed a thermo-optic polymer material (Exguide TM LFR, Chemoptics Inc.) that has a negative thermooptic coefficient; the launched wavelength of the laser output decreased linearly, as shown in the following equation: where λ B is the range of the wavelength sweep, g is the period of the Bragg grating, m is the order of the Bragg grating, ∂n/∂T is the thermo-optic coefficient and T is the range of the temperature change. Figure 2(a) shows that the output power spectra were flattened across the entire swept range of around 0 dBm, and the side-mode suppression ratio ranged from 45 to 50 dB. The maximum operating laser power was 5 mW at the center wavelength. The instantaneous linewidth was 0.06 nm, which was similar to the spectral resolution of an optical spectrum analyzer. Figure 2(b) shows the wavelength traces obtained by continuous tuning of the heating power and voltage, respectively. As indicated in figure 2(b), the wavelength tuning slope obtained by using the linearized voltage is nonlinearly curved compared to the counterpart driven by the linearized heating power tuning. Thus, continuous and linearized wavelength sweeping should be generated according to the square of the applied voltage into this integrated thermo-optic swept laser.

Setup for the OFDI system
As shown in figure 3, the integrated thermo-optic swept laser was coupled to two types of interferometers, the pointbeam type and line-beam type, in the OFDI system. These interferometers were based on a Fizeau scheme in which a common path was shared between the reference and sample arms [17][18][19][20]. This scheme shows a highly polarizationstabilized interferogram because the signal reflected from the sample and that from the partial reflector each propagate back through a common optical path [21]. Interference signals from the point-beam and line-beam common-path interferometers were received by an adjustable gain photodetector (2053-FC, New Focus, USA) and a line-scan CCD camera (SU-LDH-1.7, Goodrich Co., USA), respectively. For the point-beam type, lateral scans in the x-and y-directions were performed by two linear transverse scanning stages (M-562, Newport Co., USA). Each A-scan was performed at a repetition rate of 20 Hz, which is analogous to the rate of change of the wavelength of the swept laser. For the line-beam type, a cylindrical lens was used after the expanding lens to shape a linear beam, which removed the need for a lateral scan in the x-direction. The length and width of line-beam on the cylindrical lens focus were 6.993 mm and 23.96 μm, respectively. Because each of the 1024 pixels of the line-scan CCD camera acted as a photodetector, we could remove the B-scan from the imaging system. Only one lateral scan in the y-direction must be performed by a linear transverse scanning stage (T-LSM200B-S, Zaber Tech., USA). The A-scan of each pixel of the line-scan CCD camera was simultaneously performed at a repetition rate of 8.736 Hz, which was determined from the rate of change of the wavelength of the swept laser and the line rate of the line-scan CCD camera. In both types of OFDI systems, the overall system operation and visualization of sampled data were performed by a customized program code written by National Instrument Co. called LabView R .

Image processing
To optimize the performance of the thermo-optic swept laser for OFDI system application, we maintained a constant rate of change of the laser wavelength in the time domain. However, the interference signal was a linearized function of the wavenumber k. To avoid coherence gate broadening in the frequency domain, a low-pass-filtered photodetector output signal was k-resampled using a non-uniform resampling method. Once the k-resampled signal was converted to the frequency domain by applying a fast Fourier transform algorithm, the phase information at a coherence gate was recorded as an A-scan point of a 3D surface imaging data set. The time domain interference signal i(k) can be written as follows: where k is the wavenumber, s(k) is the spectral power function of the swept bandwidth, E 0 is a reference electric field, E 1 is the sample electric field. n is an average group velocity index and l is the optical path distance (OPD) between the reference and the sample paths. The factor of 2 indicates a round trip in the reflection geometry and φ is the phase term of the interference signal. OFDI surface phase imaging can reduce the 2π ambiguity by using the coherence gate information. According to the Wiener-Khinchin theorem, the spectral power function of the swept bandwidth of the laser was transformed into the coherence gate function in the frequency domain. The Fourier-transformed interference signal i(z) can be written as where z is a depth variable, S(z) is the coherence gate function, δ is the Dirac delta function and j is the imaginary unit. At a certain peak of the coherence gate, the phase term φ contains the smaller height information, δh, for surface information within the above coherence gate: where λ 0 is the center wavelength of the swept bandwidth, δφ is the phase difference of two points and ε(t) is the phase error in the time domain. For the point-beam-type OFDI system, the 3D image consisted of 256 × 256 A-scans. For the linebeam one, the 3D image was n × N in size, where n is the pixel number of the line-scan CCD camera (1024) and N is the movement number for the C-scans.

Results
The coherence length (l c ) in the frequency domain indicates the minimum depth resolution of OPD in OFDI image, whereas the phase information at a certain OPD contains the smaller height information within sub-coherence length. The coherence length is determined by the light source. It can be written as where λ and λ 0 are the spectral bandwidth and center wavelength of the light source, respectively. If δh is smaller than the coherence length, the phase readout at the OPD can be converted to relative height information of a target surface. In other words, we can reduce the 2π ambiguity of phase imaging in a coherence gate. Figure 4 illustrates the phase sensitivity of the OFDI system. The temporal phase variation was measured at an arbitrary point of the coverslip in subsequent acquisition time of more than 2000 ms. The sensitivity of the OFDI system can be characterized by the standard deviation of the phase [22]. The phase standard deviations, which are the imaging sensitivity of this system, for the point-beam-and line-beamtype systems were 0.513 nm and 1.74 nm, respectively. The phase error comes from both the thermo-optic laser itself and the common-path interferometer disturbance. The reason that the line-beam-type system was three times less stable than the point-beam type is that the free-space optical system is more sensitive to external vibration than the fiber-type optical system. Figure 5 shows quantitative 3D surface images ((a), (c)) and 2D cross-sectional profiles along the lateral axis ((b), (d)). A USAF-1951 resolution target (Applied Image Inc. T-20) was visualized in the surface phase image using the developed OFDI system in figure 3. In the point-beam-type OFDI system, the region of interest (ROI) of the target was selected as group 6, elements 2 and 3, which have 6.96 μm and 6.20 μm spacing per line pair, respectively. The lateral resolution (∼2.7 μm) of the point-beam-type OFDI system is determined by the laser beam spot size, which is related to the numerical aperture of the objective lens. A 3D surface image on the ROI is shown in figure 5(a). The 3D image size is 200 μm × 200 μm. Figure 5(b) shows the 2D result of a selected B-scan, which shows good conformity with the line spacing and height (∼120 nm) information of the resolution target sample. The total data acquisition time was the product of the number of transverse pixels and the wavelength sweeping time, which comes to 54.6 min.
In the line-beam-type system, the ROI of the target was all elements of group 5, which have a spacing per line pair of at least 8.77 μm. A 3D surface image of the ROI is shown in figure 5(c). Because of the Gaussian intensity distribution of the line beam, 110 lateral pixels of the line-scan CCD camera were selected for acquiring the x-direction information. For y-directional imaging, a linear stage was moved for the C-scan along a distance of 476.25 μm with velocity 4.16 μm s −1 . By combining many 2D images, we could build a 3D surface phase profile with a size of 312.4 μm × 476.25 μm. Figure 5(d) is the 2D profile of a selected B-scan (dashed line in figure 5(c)). In this system, the observed x-direction and y-direction resolutions were 4.87 μm and 24.98 μm, respectively [23]. As calculated in the previous section, the xdirection resolution (3.125 μm) was determined by the relation between each pixel width of the line-scan CCD camera and the magnification of the optical system. On the other hand, the ydirection resolution (23.69 μm) was determined by the optical waist of the line beam, which is related to the focal length of the cylindrical lens and the size of the beam input to the cylindrical lens. Figure 5(d) shows a selected B-scanned profile, which shows that the smallest bar on group 5 was clearly resolved according to the height information (∼25 nm) of the resolution target. The total data acquisition time was the product of the number of C-scan steps and the wavelength-sweeping time, which is 28.2 s. In both results, the B-scan and C-scan errors in each system were the result of the uneven group index and thickness of the partial reflector, scanning artifacts induced by a step-motor-based lateral scanning stage, and particles on the surface.

Conclusion
We developed an OFDI system based on an integrated thermooptic swept laser for 3D surface phase imaging with both pointbeam-and line-beam-type setups. To optimize the thermooptic swept laser for OFDI system applications, a linearized constant rate of wavelength sweeping is achieved by applying an arbitrary waveform to the heating electrode. The pointbeam-type OFDI system showed the stability of the height measurements with the standard deviation of 0.513 nm, while the line-beam-type OFDI system enabled 116.2-fold faster data acquisition time at 2.4-fold slower laser sweeping rate than the point-beam-type OFDI system.
Even though the thermo-optic swept laser we developed has limitations on swept-bandwidth and repetition rate compared to other swept laser technologies on the shelf, those will be improved through optimized thermo-dynamic designs and polymeric waveguide fabrication techniques. The strength of the integrated thermo-optic swept laser lies in its compactness, cost-effectiveness and highly stable feature of the phase. This work will have significant impact on lowcost and compact high-precision imaging device development. Due to the stability of the phase, the thermo-optic swept laser can also be incorporated into phase-contrast microscopic applications and point-of-care biomedical imaging devices as well. In future work, the thermo-optic swept laser will be incorporated into a phase-contrast microscopic application to assess quantitative cell dynamics and subcellular microstructure with transparent cell lines.