3-D Raman Imaging Using Time-Resolving CMOS SPAD Line Sensor and 2-D Mapping

The capability of Raman imaging to produce 2-D and 3-D chemical presentations of samples has gained a lot of interest in different application fields. In this article, we present a 3-D chemical image reconstruction based on 2-D scanning of a sample utilizing a time-resolved Raman spectrometer based on a complementary metal–oxide–semiconductor (CMOS) single-photon avalanche diode (SPAD) line sensor. The 2-D scanning data contain the lateral information (XY plane), whereas the time-of-arrival data of the Raman photons measured by the sensor carry the axial information (i.e., depth information, $Z$ -axis). The sensor is fabricated in 110-nm CMOS technology. It has 256-spectral channels, and each channel has its own 7-bit ON-chip time-to-digital converter (TDC) with an adjustable resolution from 25 to 65 ps. In addition to the 3-D chemical reconstruction of the scanned sample, we have shown the ability to retrieve depth profiling information of each scanned pixel, such as the boundaries and middle points of any selected layer over the depth range of the scanned object by means of a single measurement for each scanned pixel. In addition, we have discussed the system components and the postprocessing parameters that affect the depth profiling accuracy and the 3-D reconstruction operation the most. Results showed that the instrument response function (IRF) of the system and the time gate window width in a postprocessing phase are playing the most important role in determining the axial (depth) accuracy. We believe that our system will enable a whole new class of Raman applications that will allow simultaneous 3-D chemical geometric representation at the centimeter level during Raman operations.


3-D Raman Imaging Using Time-Resolving CMOS SPAD Line Sensor and 2-D Mapping
Belal Mostafa Amin , Jere Kekkonen , Tuomo Talala , and Ilkka Nissinen , Member, IEEE Abstract-The capability of Raman imaging to produce 2-D and 3-D chemical presentations of samples has gained a lot of interest in different application fields. In this article, we present a 3-D chemical image reconstruction based on 2-D scanning of a sample utilizing a time-resolved Raman spectrometer based on a complementary metal-oxide-semiconductor (CMOS) singlephoton avalanche diode (SPAD) line sensor. The 2-D scanning data contain the lateral information (XY plane), whereas the time-of-arrival data of the Raman photons measured by the sensor carry the axial information (i.e., depth information, Z-axis). The sensor is fabricated in 110-nm CMOS technology. It has 256-spectral channels, and each channel has its own 7-bit ON-chip time-to-digital converter (TDC) with an adjustable resolution from 25 to 65 ps. In addition to the 3-D chemical reconstruction of the scanned sample, we have shown the ability to retrieve depth profiling information of each scanned pixel, such as the boundaries and middle points of any selected layer over the depth range of the scanned object by means of a single measurement for each scanned pixel. In addition, we have discussed the system components and the postprocessing parameters that affect the depth profiling accuracy and the 3-D reconstruction operation the most. Results showed that the instrument response function (IRF) of the system and the time gate window width in a postprocessing phase are playing the most important role in determining the axial (depth) accuracy. We believe that our system will enable a whole new class of Raman applications that will allow simultaneous 3-D chemical geometric representation at the centimeter level during Raman operations.

I. INTRODUCTION
R AMAN spectroscopy is a nondestructive and noninvasive technique used to identify the chemical composition of a sample under measurement. It is widely used in various industries and fields, such as agricultural, food, oil, and pharmaceutical industries, medical diagnosis, disease monitoring, explosive detection, and mineral sample analysis [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Many applications also have a demand for 2-D imaging functionality to derive the Raman fingerprint, i.e., chemical, surface maps of the studied samples [11], [12], [13], [14]. Often, however, the surface information is not enough, which has led to the development of deep subsurface Raman spectroscopy techniques that aim at providing information on the chemical composition of a sample at its different layers (depths) with resolutions ranging from micrometers to millimeters. The depth profile adds the third dimension to the surface maps enabling the reconstruction of 3-D chemical images with the deep subsurface Raman techniques.
The most common techniques to resolve the Raman depth profiles are confocal Raman spectroscopy, spatially offset Raman spectroscopy (SORS), and time-correlated Raman spectroscopy (TCRS) [15], [16], [17], [18]. A confocal Raman microscope is typically used, and often limited, for micrometer-scale depth scanning. Confocal microscopy requires 3-D scanning of the sample (either by moving the sample or the laser beam), in which the axial (depth) scanning is done by sweeping the focal point of the laser [15], [19]. The SORS is commonly used for turbid media with a depth range of several millimeters. The depth profiling in SORS is realized either by sweeping the offset between the source and the detector or by a more complex multisource/detector solution. The main challenge in SORS is that the depth profiling is strongly dependent on the optical properties (scattering and absorption) of the sample making the depth profiling more complicated, limiting the achievable depth range and resolution, and setting restrictions for the studied material and its physical dimensions [16], [17]. The depth profiling by using the TCRS is based on measuring the time-domain distribution of Raman photons that yields direct depth information. Therefore, depth profiling with TCRS techniques is not material dependent and can be both precise and cover deep probing depths. In addition, TCRS techniques enable the suppression of the background radiation (both fluorescence and ambient light) when short laser pulses (shorter than the fluorescence lifetime) are used for illumination and a time-gated detector is synchronized to collect photons only during the laser pulse [10], [20], [21], [22], [23]. The basic principle of depth profiling in TCRS is shown in Fig. 1. Raman photons from layer A (red) are arriving earlier at the detector than those from layer B (blue). Thus, the time difference (450 ps) between the time-domain (TD) Raman intensity peaks of the two layers corresponds to the timeof-flight (ToF) difference of photons from these two layers. Therefore, the depth difference between layers A and B can This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Basic principle of the depth profiling in TCRS. Red and blue distributions represent two Raman signals from two different layers A and B separated by 450-ps peak-to-peak. The peak-to-peak time difference corresponds to 56.25 mm with an n of 1.2.
be derived as where c is the speed of light in air, t is the time difference between the TD Raman intensity peaks, and n is the refractive index of the medium. This operation principle is similar to that used in pulsed 3-D ToF imagers, in which a short laser pulse is needed for the accurate detection of adjacent surfaces of an object [24], [25], [26]. If there are multiple layers of different materials, the average refractive index n average can be calculated as where k is the total number of different layers encountered until the depth of interest, d i is the distance the laser pulse will travel inside the specific layer, and n i is the refractive index of that specific layer. Now, the time difference of 450 ps converts with (1) to the depth difference of 56.25 mm between layers A and B with the n of 1.2, as depicted in Fig. 1. In the case that the refractive indices are unknown, two approaches can be employed: estimating the average refractive index using TD Raman data when the outer dimensions of a multilayered object are known or analyzing Raman spectra to identify the layers and obtain the refractive indices of the layers from databases or literature. The challenge with TCRS has been the complexity of the devices and the synchronization of the detector with the laser pulses. During the last ten years, time-resolved single-photon avalanche diode (SPAD) sensors fabricated with standard complementary metal-oxide-semiconductor (CMOS) technology have been used and developed to downsize and simplify the TCRS implementation [27], [28]. CMOS SPADs have the advantage of detecting even a single photon with better than 50-ps time precision. In addition, the time-correlated single-photon counting (TCSPC) electronics as well as the SPAD array itself can be integrated on the same silicon die enabling a high-throughput full spectral acquisition with less complex overall electronics [29], [30], [31], [32], [33], [34], [35], [36] compared to, for example, a time-gated intensified charge-coupled device (ICCD).
We have recently shown that CMOS SPAD-based spectrometer can resolve depth information of target samples embedded in a centimeter-scale semi-transparent medium and suppress the fluorescence of embedded samples during normal Raman depth profiling operation [37]. The proposed system incorporated a time-gated CMOS SPAD line sensor with an OFF-chip delay unit that was used to sweep the time-gate position of the sensor with a small time 19 steps of 34 ps to realize the depth probing. We have also shown the ability to obtain the Raman depth profiling without the need for an OFFchip delay unit and time-consuming time-gate sweeping (or any other scanning method) since the time-of-arrivals (ToAs) of Raman photons were measured by the integrated timeto-digital converters (TDCs) of the sensor making the system even more compact and the measurement much faster [38]. However, the depth-resolving accuracy of that earlier sensor was quite low because of the timing skew of the sensor and the low temporal resolution of the ToA measurement units.
In this article, we present an advanced utilization of the depth-resolving concept proposed in [38]. We present a 3-D Raman image reconstitution of 2-D mapping data measured by a time-resolved Raman spectrometer based on a CMOS single-photon SPAD line sensor. The 2-D scanning data contain the lateral information (XY plane), whereas the ToAs of the Raman photons measured by the sensor with its 256 integrated 7-bit TDCs (256 spectral channels) carry simultaneously the axial information (i.e., depth information, Z -axis). The method is inherently faster compared to methods that also need some sort of scanning to obtain the axial information. We have demonstrated 3-D Raman image reconstruction with lateral image area and resolution of 39.5 × 24.5 mm and 0.5 mm, respectively, and 121-mm axial (depth) range and mm-range resolution. In other words, the 3-D Raman image of 512 000 points is reconstructed by the lateral scanning (XY) of 50 × 80 pixels because of simultaneous ToA measurement of Raman photons of 128 time bins (50 × 80 × 128). In addition, the capability of the device to derive the depths and thicknesses of chemically different layers in multilayered samples is studied in more detail with separate single-point measurements. Section II will present the system setup, Section III will present the different measurement results with discussion, and finally, Section IV will conclude this article.

II. SYSTEM SETUP
A simplified block diagram of the system setup used to conduct the measurements in this article is shown in Fig. 2. The system consists of a 532-nm pulsed laser (Teem Photonics ANG-500P-CHS) with a 280-kHz pulse rate, a full-width at half-maximum (FWHM) pulsewidth of 140 ps, and an average power of 150 mW. The median FWHM instrument response function (IRF) of the entire system is 181 ps. Over the sensor array, the standard deviation for the IRF peak position is 3.4 ps and the standard deviation for the IRF FWHM width is 2.1 ps [39]. The pulsed laser shoots a laser pulse to the sample. A beam splitter is used to guide a small share (2% of the pulse energy) of a pulse to a light detector that triggers an electrical pulse that synchronizes the CMOS SPAD sensor with the laser pulse. The rest of the pulse energy is directed to the sample as a collimated beam with a radius of ∼3 mm. The Raman photons backscattered from the sample (180 • excitation/collection scheme) are directed through a dichroic (Semrock LPD01-532RU-25 × 36 × 1.1) mirror to a holographic grating (custom made from Wasatch-1800 mm −1 groove density) that diffracts collected Raman photons at different angles based on their wavelengths, so that each wavelength is directed to a specific point in the line sensor. The ToAs of the photons at each wavelength recorded by the integrated TDCs of the sensor are sent to a computer through an FPGA board (Opal Kelly XEM7310-A200), which handles the data readout and controlling of the sensor. The basic principle is similar to in any other TCSPC system, and after hundreds of thousands or millions of laser pulses, the Raman spectra as a function of time can be derived.
The detector of the spectrometer is a 256-channel SPAD line sensor manufactured in 110-nm CMOS technology. Each of the 256 spectral channels includes eight 27.7 × 27.2 µm SPADs, a SPAD controlling block, and a 7-bit (128 time bins) TDC. The pitch and fill-factor of the 256 × 8 SPAD array are 32.9 µm and 37.9%, respectively. The spectral resolution is approximately 6 cm −1 with a spectral range of 1531 cm −1 . The temporal resolution and range of TDCs can be adjusted with an external reference clock signal in the range of 25.6-65 ps and 3.2-8.2 ns, respectively. In our measurements, the temporal resolution was set to 30 ps (time bin = 30 ps) resulting in the temporal range of 3.8 ns. Data are read from the sensor to the FPGA board through four 7-bit buses using 150-MHz clock frequency, resulting in an output data rate of 4200 Mbps and a maximum excitation pulse rate of 2.0 MHz. More detailed and technical specifications of the sensor used can be found in [39].

A. Three-Dimensional Raman Image Reconstruction
The main goal of this section is to show the capability of the time-resolving Raman spectrometer based on the CMOS SPAD sensor to reconstruct a 3-D chemical image of an object that is placed inside a transparent plastic [polystyrene (PS)] water container. The sample is scanned only in the 2-D lateral plane (XY plane) and the axial (Z -axis, depth), and information is obtained from the ToAs of Raman photons measured simultaneously by the ON-chip TDCs. The imaged object is an irregularly shaped block of transparent polymethyl methacrylate (PMMA), as shown in Fig. 3(a) and (b). The shape of the PMMA block was designed to enable a comprehensive study of the 3-D Raman image reconstruction capability of the spectrometer setup, as detailed in the following.
The PS water container with the PMMA object inside was placed on a motorized 2-D scanning stage shown above in Fig. 3. The sample was scanned over an area of 39.5 × 24.5 mm with a step size of 0.5 mm resulting in an 80 × 50 pixel 2-D image plane (XY plane), as illustrated in Fig. 3(b). At each pixel, one million laser pulses were shot to the sample with the repetition rate of 280 kHz that results in a single-pixel acquisition time of 3.6 s and a total imaging time of ∼4 h. Due to the limited range of the motorized sample stage, part of the other leg of the PMMA object was cropped out from the image.
In this proof-of-concept paper, we have used only single Raman peaks to recognize different materials in 3-D chemical imaging. The Raman peaks to identify PMMA (the actual imaged object) and PS (the plastic water container) were 1001 and 885 cm −1 , respectively, as indicated in Fig. 4, which shows the Raman spectra of the different plastics used in this work. Fig. 5 shows an example of TD spectral data measured at each of the 2-D image pixels [point 1 in Fig. 3(a)].  In the TD spectral data, the signal intensity (photon count divided by the actual bin widths of the TDCs, which gives the intensity in the unit of hits/ps) is presented as a function of time (i.e., the data represent the spectrally resolved ToAs of the detected photons). The TD spectral data are postprocessed from the raw data by performing timing skew, dark count, photon detection efficiency, baseline compensations, and fluorescence suppression as explained in more detail in [37] and [39]. As has been mentioned, the ToAs of (Raman) photons are directly proportional to the path length of the photons, and thus, the ToAs, i.e., the time axis in the TD spectral data, can be translated to depth information with (1). For example, from the TD spectral data in Fig. 5 can be seen two Raman intensity peaks at 1001 cm −1 with a time difference of 1077 ps, indicating that two PS layers exist with a depth difference of ∼121 mm (n water = 1.33). This exactly matches the distance between the front and back edges of the PS water container used (note that the pixel concerned was outside the PMMA object, and thus, no PMMA Raman signal is observed in this specific TD spectral data).
Figs. 6 and 7 show the TD spectral data from two other example pixels of the 2-D scanning [points 2 and 3, respectively, in Fig. 3(a)]. From these TD spectral data can also be observed the Raman signatures of the PMMA object. It is clearly seen in both Figs. 6 and 7 that the PMMA signal increases later than the PS signal from the front edge of the PS container indicating that the PMMA object is inside the container. The depth difference between the front edge of a Fig. 6. TD spectral data of all detected layers through the path of line 2 in Fig. 3(a). container and the middle point of a PMMA object can be estimated to be ∼35 mm based on the time difference of 2497-2184 ps in Fig. 6 having an error of 2.5 mm to the actual separating distance.
In addition, the PMMA signal in Fig. 7 [point 3 in Fig. 3(a)] starts to increase earlier and lasts longer (i.e., the time response is wider) compared to the PMMA signal in Fig. 6 (point 2). This is explained by that point 3 (Fig. 7) represents the 60 mm long part of the PMMA object and point 2 represents the 10-mm shoulder piece of the object, which is located 10 mm after the front edge of the 60-mm-long backbone of the object.
This shows that the ToAs of the Raman photons do not only give information on the depth location of the material but also on the thickness of the material. For example, the thickness of the backbone of the PMMA object [point 3 in Fig. 3(a)] can be derived by estimating the FWHM width of the time-domain distribution at the wavenumber of 812 cm −1 resulting in ∼ 632 ps and thus the thickness of 63.7 mm (n PMMA = 1.49) with an error of 3.7 mm compared to the actual value. Fig. 8 provides an overview of how to construct a 3-D matrix that represents the chemical composition of each pixel. The starting point is the TD spectral data of each scanned pixel, as shown in Fig. 8(a).
Next, the TD spectral data of each pixel is converted to a 1-D array by removing the intensities of irrelevant Raman wavenumbers and summing the intensities of relevant (Raman) Fig. 8. Processing steps involved in constructing the overall 3-D intensity matrix used for sample structure reconstruction from the raw TD Raman spectra of each scanned pixel. wavenumbers for each time bin, as illustrated in Fig. 8(b). To illustrate the process, we are interested in detecting only the PMMA and PS layers at specific wavenumbers, 812 and 1001 cm −1 , respectively. In this case, we only consider the vectors that represent these wavenumbers and sum their intensities [the wavenumber of 1001 cm −1 is highlighted by red color in Fig. 8(a) showing the wavenumber range, which is converted to a 1-D array shown in Fig. 8 This results in a 1-D array with 128 elements (time bins), representing the Raman intensities of the materials of interest for a single pixel, as shown in Fig. 8(b). In this array, each time bin corresponds to the sum of the intensities of the specific wavenumbers that are relevant to that time bin.
By repeating this process for each pixel, as shown in Fig. 8(c), the 3-D Raman intensity representation of the object under measurement can be fully developed. Fig. 8(d) shows the resulting volume representation of the intensity matrix using the maximum intensity projection algorithm in the MATLAB volume viewer app. Fig. 9 shows how the intensity projections of the PS container with the PMMA sample inside it are obtained using the method explained earlier. However, this method can present some practical limitations due to variations in object thicknesses. For instance, the PMMA sample is much thicker than the PS container sides, leading to higher Raman signals for the PMMA compared to the PS. Consequently, when visualizing the matrix based on intensity projection, lower PS intensities may appear nearly invisible compared to higher PS or PMMA intensities (blue represents the low intensity and dark red represents the high intensity). Nevertheless, Fig. 9 illustrates that this method can effectively visually distinguish the front and back edges of the PS container and the PMMA object.
An isosurface representation, which is another way to produce the chemically specific 3-D image, of the PMMA object inside the container is shown in Fig. 10(a) and (b). To create this isosurface presentation, the TD spectral data have been postprocessed to enhance the SNR. This is done by merging three adjacent time bins by summing the Raman intensities of the time bins as follows: I t = (I t + I t+1 + I t+2 ), where I t represents the Raman intensity at a given time bin t. Since the IRF of the system is 181 ps and thus Raman photons are scattered within that period, it is better to use more than one time bin (30 ps) to collect Raman photons. Therefore, to collect more Raman photons for a specific time stamp, three time bins were used. Normally, the raw TD spectral data correspond to intensities recorded within one time bin. By increasing that time window through bin merging, the Raman SNR is improved, leading to a clearer isosurface representation. Then, the TD spectral data are processed by the steps presented in Fig. 8. After that, MATLAB (MathWorks, USA) Image Processing Toolbox Application Volume Viewer (Image Processing Toolbox) was used to reconstruct the chemically specific 3-D representations shown in Fig. 10(a) and (b).
The accuracy of depth profiling is affected by the choice of the time window. A wider time window can lead to the merging of details and loss of accuracy in the reconstructed 3-D image. For instance, in Fig. 10(d), the TD spectral data were formed using a time window of five time bins (150 ps), resulting in the merging of parts of the object such as the legs. This issue is discussed in more detail in Section III-B and [37].
The isosurface representations in Fig. 10(a) and (b) represent the 3-D structure of the PMMA object shown in Fig. 3. Using the same MATLAB Volume Viewer application, it is also possible to show a labeled 3-D representation of the object, as shown in Fig. 10(c). The different colors in the labeled presentation depict the chemically different materials detected from the TD spectral data (orange for PS and violet for PMMA). The detection of the materials for the labeling is done by comparing the Raman intensities at the material-specific wavenumbers (see Fig. 4) to the threshold value. The advantage of this kind of representation is that it clearly shows the different materials or chemical compounds that exist in the scanned sample, unlike the plain intensity projection (Fig. 9) or isosurface representation (Fig. 10), which are only material-agnostic representations.
The proportions in the 3-D reconstructed images shown in Figs. 9 and 10 are accurate for the xand y-axes, but the depth axis seems too short. The reason for this is that in the MATLAB Volume Viewer app, which is not originally designed for this purpose, it is difficult to compensate for the varying refractive indices of the imaged sample and to set all the necessary intensity thresholds for every pixel (e.g., for resolving the FWHM width from the TD spectral data intensity peak that can be used to define the length of an object as discussed above in Fig. 7) needed for accurate depth analysis from the TD spectral data. Nevertheless, the Volume Viewer app provided an easy-to-use and immediately available solution with good enough 3-D reconstruction capabilities to prove the main claim of the study: chemically specific 3-D images can be reconstructed from 2-D scanning data. For more accurate 3-D reconstruction, custom-made software exclusively designed for this purpose should be developed, which is out of the scope of this study and a topic for later research. The next section will discuss the depth profile reconstruction from the TD spectral data with multilayered samples in more detail, thus giving an insight into the requirements of more sophisticated software to be developed.

B. Single-Pixel Raman Depth Profile Reconstruction of Multilayer Structures
The aim of these measurements is to answer the following questions: 1) How the TD spectral data can be used to reconstruct the depth profile of a single image pixel? 2) What are the main limitations degrading the accuracy of the depth profile?
1) Depth-Resolving Raman Results of a Two-Layer Sample With Separation: Two different sample configurations were used, as shown in Fig. 11(a) and (b), and the direction of the collimated laser beam was from left to right. We used two materials for this measurement, which are transparent PMMA and transparent polycarbonate (PC).
The first sample configuration is shown in Fig. 11(a), where the distance between a PMMA layer (thickness of 30 mm) and a PC layer (thickness of 4 mm) was 11 mm. The distance between the middle points of these pieces was 28 mm. The second setup is shown in Fig. 11(b) having PMMA and PC layers with thicknesses of 3 and 4 mm, respectively. The distance between layers was 24.5 mm, and thus, the distance between middle points was 28 mm too. One million laser pulses were shot through the sample configuration in both cases to collect backscattered Raman photons from the samples, and thus, the intensity of Raman photons as a function of time could be derived similarly as shown earlier in the article. The wavenumbers of 812 and 885 cm −1 were used to distinguish the PMMA and PC pieces from the spectra, as shown in Fig. 4. The raw results were then postprocessed by using MATLAB with a window size of two time bins.
The postprocessed (window size of two time bins) timedomain distributions of Raman photons of the wavenumber 812 cm −1 (PMMA, red solid color) and 885 cm −1 (PC, blue color) for the sample configuration shown in Fig. 11(a) are presented in Fig. 11(c). As shown in Fig. 11(c), the peak intensity of PMMA is much higher than the peak intensity of the PC even if the Raman scattering probability of PC is higher than that of PMMA (see Fig. 4). In addition, the time-domain response of PMMA is wider in the time domain than that of a PC piece. These differences between the time-domain responses of a PMMA piece and a PC piece are caused by the larger thickness of a PMMA piece, in which case Raman photons are scattered for a longer time compared to the case of a PC piece. The FWHM of the pulse of the laser was approximately 150 ps corresponding to a depth width of 30 mm in PMMA, and thus, the whole pulse fits inside a thicker PMMA piece resulting in higher intensity (when the pulse is at the middle of the sample) and wider time response.
The distance between the middle points of the PMMA and the PC in Fig. 11(a) can be calculated to be 24.4 mm based on (1) with the time difference of PMMA and PC peaks of 212 ps [1890-1678 ps shown in Fig. 11(c)] resulting in an error of 3.6 mm (a real separation is 28 mm). The average refractive index n was calculated by using (2) giving the n of ∼ 1.304. In addition, it is possible to get the approximated value of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  In Fig. 11(c), the time-domain distribution of a PMMA piece exhibits some artifacts (shoulders) even though the falling and rising edges should follow more or less the Gaussian laser pulse shape. The shoulder at 2000 ps is likely caused by the PMMA Raman photons reflected from the PC piece, which widens the pulsewidth and explains the larger error in the estimation of the PMMA piece's width. To address this, we used the MATLAB fitting tool to perform Gaussian fitting of the PMMA response, resulting in the black curve in Fig. 11(c). Recalculated values of the peak-to-peak distance (p-to-p in Table I) and the width of a PMMA piece with error values are shown in Table I On the other hand, when determining the width of the PC shown in Fig. 11(a) and (c) by calculating the FWHM of the time response of the PC (without Gaussian fitting), the error is 9 mm. The main reason for the high error is the thickness of the scanned object compared to the FWHM of a laser pulse. The Raman response of any scanned object cannot have an FWHM that is smaller than the FWHM of the used laser pulse (since it is the dominating component in the FWHM of the impulse response function of the whole system). Therefore, if the thickness of the scanned object is smaller than the FWHM of the laser pulse used, the calculated thickness will be wider than the actual thickness. The second contributor to the accuracy of the calculated thickness of the scanned object is the postprocessing parameter, window size. The bigger the window size, the wider the Raman response will be, which means an extra error in the thickness calculation. This will be presented in the next section in more detail.
As we derived the widths and the distance between the middle points of the PMMA and PC pieces, we can deduce the depth profile of the sample configuration shown in Fig. 11(a). Setting the front edge of the PMMA piece at the zero, the rear edge of that piece locates at 32.9 mm (measured width of PMMA through the Gaussian-fitted curve) with the middle point at 16.45 mm, as shown in Fig. 11(c). The gap between the PMMA piece and the PC piece can be calculated to be 4.65 mm having an error of 6.35 mm, which is mainly caused by the wide FWHM of the laser (in depth) compared to the thickness of the PC piece.
The depth profile of the sample configuration shown in Fig. 11(b) and (d) can be performed similarly. Setting the front edge of the PMMA piece at the zero, the rear edge of that piece locates at the 14.2 mm with the middle point at 7.1 mm, as shown in Fig. 11(d). It is clear from Fig. 11(d) that the peak is not visually located in the middle. However, the Gaussian fitting was not used in this case because the Raman response is as wide as the laser pulse itself and we cannot accurately derive the thicknesses of plastic pieces. The derived values with errors are shown in Table I [ labeled (b)]. The gap between the rear edge of the PMMA piece and the front edge of the PC piece can be derived to be 16.95 mm instead of 24.5 mm, resulting in an error of 7.55 mm.
As can be seen from Table I, the depth difference between the middle points of plastic pieces can be derived quite accurately, but the estimation of the widths of the plastic pieces is dramatically degraded by the limited pulsewidth of the laser. Therefore, the procedure for the thickness estimation must be limited to results showing a wide enough time response compared to width of the laser pulse. In addition, note that we can see the second peak of the PMMA piece caused by the reflection of the Raman photons from the PC piece at approximately 1775 ps, as shown in Fig. 11(d).
2) Depth-Resolving Raman Results of Multilayer and Embedded Samples: The sample configuration is shown in Fig. 12(a). We used two PMMA pieces with different thicknesses of 30 and 3 mm, as well as two pieces of PC with thicknesses of 10 and 4 mm, as shown in Fig. 12(a). Ten million laser pulses were shot through the sample from left to right to collect backscattered photons from the samples, and thus, the intensity of Raman photons as a function of time could be derived similar to in the previous measurements.
The time-domain distributions of backscattered Raman photons at wavenumbers of 812 cm −1 (PMMA, solid red line) and 886 cm −1 (PC, blue solid line) postprocessed by using the window size of two time bins are shown in Fig. 12(b). As shown in Fig. 12(b), the PMMA has a double peak [points (1) and (2)], which corresponds to the 30-mm PMMA piece and the 3-mm PMMA behind a 10-mm PC piece, as shown in Fig. 12(a). On the other hand, the PC has only a single peak [point (5)] instead of two peaks, which would be expected by the two PC pieces. The reason for this issue will be discussed later in this section. Still note that the peak of the time-domain distribution of PC is located earlier than the second peak of PMMA, indicating that the PC is between two PMMA pieces.
Initially, we will analyze the depth information for the PMMA. As discussed earlier, the peaks [points (1) and (2) in Fig. 12(b)] should represent the middle points of the PMMA pieces. The time-domain distribution of each PMMA piece should follow more or less the Gaussian shape. However, as shown in Fig. 12(b), the time-domain distributions PMMA pieces are overlapping causing the deteriorated time-domain distribution. Therefore, we used Gaussian fitting comprising the sum of two Gaussian functions resulting in the fitted distribution shown in Fig. 12(b) (black solid line). Based on (1), the distance between the two peaks (points 3 and 4 with n = 1.52) is calculated to be 23.5 mm instead of 26.5 mm resulting in an error of 3 mm. Without Gaussian fitting, the error would be 9.3 mm.
The first assumption for the PC piece is that only a single PC piece is between two PMMA pieces as we can see only one peak in the time-domain distribution of a PC between PMMA peaks. Thus, the separation of the middle points of the first PMMA and PC can be calculated to be 19.67 mm (actual distance = 20 mm), assuming that the peak at point 5 represents the middle point of the 10 mm PC (2286-2088 ps with n ∼1.5).
From Fig. 12(b), the depth profile of the sample configuration can be estimated similar to the previous section. We can set the 50% rising edge of the time-domain distribution of PMMA to zero, and thus, the middle point of the first PMMA piece is located at the 16.42 mm, which means that the rear edge of the 30-mm PMMA layer should be at 16.42 × 2 = 32.84 mm. However, the location of point 9 [ Fig. 12(b)], which is assumed to be the front edge of the 10-mm PC layer, was derived to be 27.2 mm. Thus, the boundary between the first PMMA piece and the first PC piece is between 27.2 and 32.84 mm. Now, the middle point of the PC piece is at 36.2 mm [real value of 35 mm from Fig. 12(a)] and the middle point of the second PMMA piece is at 40.83 mm [the real value of 41.5 mm from Fig. 12(a)]. The FWHM of the time domain distribution of PC piece indicates a width of 21.53 mm (distance between points 9 and 10), but this cannot be true when the peak locations are considered to give the middle points of the pieces. The middle point of the second PMMA piece locates earlier than point 10, which is the rear edge of the PC layer. This means that the middle point of the second 3-mm PMMA piece is between two PC layers. The last 50% falling edge (point 10) is located 2413 ps after the middle point of the second 3-mm PMMA, and thus, the last piece is PC having the rear edge at the location of 48.73 mm.
There are two explanations for a single peak related to PC piece: 1) the pulsewidth of a laser is wide compared to the separating distance between PC layers causing the merged responses. In addition, as explained previously, the time-domain distributions of Raman photons of layers thinner than a laser pulsewidth (10-and 4-mm PC) are showing the response dominated by the pulsewidth of a laser and 2) the window size of two time bins used in postprocessing has also effect on the time-domain distributions merging these two layers to a single smooth distribution representing both layers.
Even if the limited pulsewidth of a laser and window size are degrading the depth-resolving capability of thin layers, the order of the pieces can be still resolved. It is worth mentioning that all this information was gathered through a single-point measurement by utilizing the ToA data and no additional sweeping in-depth domain is needed. In addition, a proper time window size can be selected in the postprocessing phase to increase the SNR or depth resolving accuracy depending on the sample configuration.
Finally, to further explain the effect of window sizing on the accuracy of interpreted depth information based on the time-domain distribution of Raman photons, we can consider the dashed red Raman response in Fig. 12(b). It shows the time-domain distribution of Raman photons of the PMMA layers when the raw data are postprocessed by a window size of five time bins. The SNR has been improved, however, at the cost of the depth information accuracy. We can see that both the 30-and 3-mm PMMA pieces have merged into a single piece.

IV. CONCLUSION
In this article, 3-D Raman imaging spectroscopy based on a 256-channel SPAD line sensor manufactured in 110-nm CMOS technology is presented. The detector employs 256-channel ON-chip TDC with an adjustable resolution of 25.5-65 ps and range of 3.2-8.2 ns that enables the simultaneous recording of the depth profile of samples during two dimensions x and y scanning. As the results of the measurements are suggesting, to achieve the desired accuracy in determining the thickness of different layers based on the FWHM of the Raman response, it is essential to utilize a laser pulse with a narrower FWHM. If the FWHM of the pulse of a laser is wider than the targeted layer, then the error in determining the thickness of layers will increase because the time-domain distribution of Raman photons is following the response of a pulsewidth of a laser. However, the middle points of different layers can be determined with the millimeter accuracy with the laser pulsewidth of 150 ps. On the other hand, even though shorter laser pulses (narrower IRF) can enhance the axial resolution, there is a tradeoff between the axial and the spectral resolution when short enough laser pulses (in the scale of a few picoseconds or less) are considered. When the laser pulse is shortened to a few picoseconds or under, the spectral linewidth of a bandwidth-limited pulse starts to degrade the spectral resolution of the whole system, making it more challenging to distinguish and identify spectral features. In addition, data postprocessing has an important role in making depth profiling usable. It is important that the used time window size in depth resolving is short enough to maintain important information about the layered structure of the sample but not too short to degrade the SNR. Threedimensional reconstructed images shown in this study were based on the MATLAB volume viewer, which cannot be used to form very accurate images. However, the results showed that single-pixel data collected can be utilized for more accurate 3-D images by developing more advanced MATLAB software. We believe that our system will enable a whole new class of Raman applications that will allow simultaneous 3-D chemical geometric representation at the centimeter-level during normal Raman operations.