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Curr. Opt. Photon. 2023; 7(1): 73-82

Published online February 25, 2023 https://doi.org/10.3807/COPP.2023.7.1.73

## Partial Spectrum Detection and Super-Gaussian Window Function for Ultrahigh-resolution Spectral-domain Optical Coherence Tomography with a Linear-k Spectrometer

Hyun-Ji Lee1,2, Sang-Won Lee1,2

1Safety Measurement Institute, Korea Research Institute of Standards and Science, Daejeon 34113, Korea
2Department of Medical Physics, Korea University of Science and Technology, Daejeon 34113, Korea

Corresponding author: *swlee76@kriss.re.kr, ORCID 0000-0001-6952-6957

Received: September 30, 2022; Revised: December 15, 2022; Accepted: December 19, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this study, we demonstrate ultrahigh-resolution spectral-domain optical coherence tomography with a 200-kHz line rate using a superluminescent diode with a−3-dB bandwidth of 100 nm at 849 nm. To increase the line rate, a subset of the total number of camera pixels is used. In addition, a partial-spectrum detection method is used to obtain OCT images within an imaging depth of 2.1 mm while maintaining ultrahigh axial resolution. The partially detected spectrum has a flat-topped intensity profile, and side lobes occur after fast Fourier transformation. Consequently, we propose and apply the super-Gaussian window function as a new window function, to reduce the side lobes and obtain a result that is close to that of the axial-resolution condition with no window function applied. Upon application of the super-Gaussian window function, the result is close to the ultrahigh axial resolution of 4.2 μm in air, corresponding to 3.1 μm in tissue (n = 1.35).

Keywords: Spectral domain, Super-Gaussian window, Ultrahigh resolution optical coherence tomography

OCIS codes: (110.4500) Optical coherence tomography; (170.3880) Medical and biological imaging; (170.4500) Optical coherence tomography

### I. INTRODUCTION

Optical coherence tomography (OCT) has been extensively studied as a clinical and noninvasive imaging tool for biological tissues, because it provides high-resolution cross-sectional and three-dimensional volumetric images [1, 2]. Many OCT study groups have spent significant effort on trying to obtain higher axial resolutions, higher sensitivities, and increased acquisition speeds in various fields, including medical application studies [313]. Ultrahigh-resolution OCT (UHR-OCT) with an axial resolution of 3 μm or less can yield clear visualization of microstructured layers in tissues, close to the level of histology. The higher acquisition speed can minimize motion artifacts and facilitate quantitative analysis of three- and four-dimensional image data. Recently, Fourier-domain OCT (FD-OCT)—one type based on a wavelength-swept source (SS-OCT), and another on a spectral domain (SD-OCT)—has been actively used in high-sensitivity and high-acquisition-speed applications [911]. SS-OCT can provide an increased imaging depth of over 5 mm and a lower sensitivity roll-off. The acquisition speed of SS-OCT has increased substantially to line rates of a few hundred kilohertz and even up to a few megahertz, since wavelength-swept sources based on Fourier-domain mode locking (FDML) and high-speed polygon scanners were introduced [1215]. A wavelength-swept source with 100–200 kHz line rate has recently been commercialized [2]. However, for SS-OCT commercial wavelength-swept sources and data-acquisition boards with high sampling rates, on the order of 108–109 per second, are still very expensive. In SD-OCT, the acquisition speed can be increased up to 312 kHz by using a subset of the total number of camera pixels [16]. In addition, the acquisition speed of SD-OCT can be made to achieve a line rate of 500 kHz by using interlaced detection with two spectrometers and selecting only 800 out of 4,096 pixels in the camera, to increase the A-line rate [17]. However, SD-OCT has trade-offs among imaging depth range, sensitivity roll-off, axial resolution, and acquisition speed. SD-OCT has to sacrifice spectral resolution by using some of the camera pixels in the spectrometer to increase the acquisition speed. Consequently, the imaging-depth range is limited to below 2 mm in air, and the sensitivity roll-off decays rapidly. Further, SD-OCT cannot preserve axial resolutions below 10 μm in air to maintain long imaging-depth ranges over 2 mm, when the number of pixels in the region of interest (ROI) in the camera is reduced to facilitate high acquisition speeds [16, 17].

The axial resolution of OCT is inversely proportional to the full width at half maximum (FWHM) of the light source. Since UHR-OCT with 1-μm axial resolution by using an ultrashort femtosecond laser with FWHM of 260 nm at 800 nm was first introduced by Drexler et al. [3], a supercontinuum light source with a femtosecond laser coupled with a long optical fiber or a super-luminescent diode (SLD) combining several SLD modules has been used as a wide-bandwidth light source for UHR-OCT [48]. Most light sources with wide FWHM do not have Gaussian spectra, and the non-Gaussian spectral shape of the light results in the occurrence of side lobes. In conventional time-domain OCT (TD-OCT), spectral filtering, shaping of the source spectrum, and interactive deconvolution with the coherence envelope’s point-spread function (PSF) in the space domain have been used to digitally reduce side lobes [3, 4, 1820]. In addition, Akcay et al. [21] and Choi et al. [22] proposed using a programmable spectral processor and a fiber-based spectral filter for spectral shaping in TD-OCT. In SD-OCT, spectral reshaping by digital processing of the spectrum to approximate a Gaussian envelope before fast Fourier transformation (FFT) has been performed to reduce the height of the side lobes [6]. In addition, several window functions such as Hann, Hamming, and Gaussian window functions can significantly compress the side lobes. However, the PSF is broadened in such cases. In other words, the axial resolution is increased, compared to the axial resolution without multiplication by any window function.

In this study, we demonstrate UHR SD-OCT with an acquisition speed (line rate) of 200 kHz. To achieve a 200-kHz line rate we use 1,152 pixels, a subset of the overall 4,096 pixels in the camera at 70 kHz line rate. A wide-band SLD combining two SLD modules is used for ultrahigh axial resolution. In addition, partial spectrum detection is used to obtain OCT images within an imaging depth of 2.1 mm, while maintaining ultrahigh axial resolution. Our SLD has the spectrum of a flat-topped intensity profile, resulting in the appearance of side lobes. Consequently, we apply the super-Gaussian function, which has been used to estimate the flat-topped intensity profile of laser beams in the field of optics [23, 24], and in the design of finite-impulse-response (FIR) filters in digital signal processing [25], as a new window function. We then calculate the frequency response of the super-Gaussian window function and compare the result to those of other popular window functions after application to partial spectrum detection.

A schematic of the SD-OCT system based on a linear wavenumber-domain (k-domain) spectrometer is depicted in Fig. 1. An SLD at 849 nm (BLM2-D-840-B-I-10; Superlum, Carrigtwohill, Ireland) has FWHM of 100 nm and optical power of 10 mW. We use the sample arm in Fig. 1(a) to measure the system performance and obtain images of skin tissue. The configuration of this system is described in detail in [26]. The linear k-domain spectrometer is slightly modified: We use a 90° off-axis parabolic mirror to make a collimated beam, instead of a collimation lens and a prism mirror between the pair of lenses and the camera, to reduce the physical size of the spectrometer, as shown in Fig. 1. We adjust the starting pixel and ROI in the camera to the 1,473rd and 1,152nd pixels respectively, to increase the acquisition speed from 128 to 200 kHz. The exposure time is set to 3.7 μs. For ophthalmic imaging, we change the split ratio of the optical-fiber coupler and the sample arm, as shown in Fig. 1(b). Light from the SLD is split into the reference (90%) and sample (10%) arms, to satisfy the American National Standards Institute (ANSI) safety requirements and increase detection efficiency. The sample arm consists of a two-dimensional galvanometer, an achromatic doublet lens (L3: f = 50 mm; Thorlabs Inc., NJ, USA), and a double aspheric ocular lens (L4: 20 D; Volk Optical Inc., OH, USA). We use a neutral-density (ND) filter in the reference arm to reduce the source-intensity noise [27].

Figure 1.Schematic of the SD-OCT based on a linear k-domain spectrometer. (a) The sample arm to measure the system performance and obtain the skin tissue’s image. (b) The sample arm to get the image of the retina. SD-OCT, spectral domain optical coherence tomography; PC, polarization controller; CL, collimation lens; OL, objective lens; DCB, dispersion compensation block; RM, reference mirror; RC, reflective collimator; G, grating; DP, dispersive prism; PM, prism mirror; L1 to L4, lenses.

Spectral data from the spectrometer are digitized using a frame grabber (PCIe-1433; National Instruments Corp., TX, USA). The digitized spectral data are then processed using a quad-core central processing unit (CPU) and a graphic processing unit (GPU) to accelerate numerical calculations and display real-time two-dimensional images. We develop the software in Microsoft Visual C++ with NVIDIA’s compute unified device architecture (CUDA10.0) technology [28, 29].

### 3.1. Partial Spectrum Detection Versus Axial Resolution

Figures 2(a)2(c) show the normalized spectrum of the SLD according to the sampling number. The original spectrum is acquired with 10,001 sampling points using an optical spectrum analyzer (AQ6317B; Ando Corp., CA, USA). The acquired original spectrum is then resampled with 2,048, 1,152, and 1,024 sampling points and converted to wavenumber (k-domain) with the same spectral resolution as our spectrometer. Figure 2(d) shows the point-spread functions (PSFs) of the coherence length according to changes in the number of sampling points, while maintaining the spectral resolution. When the sampling points are 2,048 and 1,152, the coherence length is calculated to be 3.1 μm and 3.3 μm respectively. In addition, the coherence length at 1,024 sampling points is broadened to 3.7 μm. We do not include the calculated result for 512 sampling points in Fig. 2(d), but we find that the coherence length is also broadened, to 7.6 μm. To obtain the smooth curves shown in Fig. 2(d), we employ zero-padding by including sufficient sampling points.

Figure 2.Resampled spectrum from the original spectrum with 10,001 sampling points, by means of the optical spectrum analyzer: (a) 2,048 sampling points, (b) 1,152 sampling points, and (c) 1,024 sampling points. (d) PSF of the coherence length for each spectrum, (a) to (c). PSF, point-spread function.

### 3.2. Comparison of the Frequency Responses of the Window Functions

The frequency response (or frequency spectrum) of a truncation window should ideally be a frequency-domain impulse, which should have a very narrow main lobe and no side lobes. However, in practice, windows with narrow main lobes tend to have large side lobes, and vice versa [30]. Large side lobes can obscure the weaker frequency peak after FFT, when the waveform comprises two adjacently frequencies. The Hann window, Hamming window, and Gaussian window are commonly used to reduce such side lobes. The Hann window and Hamming window are defined from generalized Hamming windows as follows [30]:

w[n]=ABcos2πnN1n= 0, 1, 2,,N1

when A = B = 0.5, w[n] is called a Hann window. Conversely, when A = 0.54 and B = 0.46, w[n] is called a Hamming window. In addition, the Gaussian window function can be defined as

w[n]=exp12 n(N1)/2 σ(N1)/22σ0.5

The graphs of the window functions plus the frequency response of each window function are shown in Fig. 3. In that figure, the rectangular window function is w[n] = 1, where n = 0, 1, 2, ..., N−1. For the Gaussian window function, we set σ = 0.5, which is the maximum value. As seen from Figs. 3(b)3(d), the Hann window function has the widest main lobe. Computations reveal that the main lobes of the Hann and Gaussian window functions are respectively 1.6 and 1.34 times as wide as the rectangular window function. The side lobes of the rectangular window function are the highest, compared to the other window functions. In addition, although the first side lobe of the frequency response of the Hann window function is similar to the second side lobe of the Gaussian window function, it can be seen from Figs. 3(c) and 3(d) that the side lobes of the Hann window function decay faster.

Figure 3.Graphs of three window functions and the frequency responses according to window functions. (a) Window functions, (b) the frequency response of the rectangular, (c) the frequency response of Hann, and (d) the frequency response of Gaussian window functions.

The super-Gaussian window function is expanded from the Gaussian window function, and is defined mathematically as [2325]

w[n]=exp12 n(N1)/2 σ(N1)/22MM= 1, 2, 3, 4,,

In the super-Gaussian window function, σ represents the width of the window. When the value of M increases, the window function rapidly decays, and becomes the rectangular function at M = ∞. Figure 4(a) presents the super-Gaussian window functions, according to varying σ and M. Figure 4(b) shows the frequency response of the super-Gaussian window function (σ = 0.62, M = 2) with those of the rectangular and Gaussian (σ = 0.5) window functions. In the frequency response, the main lobe of the super-Gaussian is narrower than that of the Gaussian window function. Although the first side lobe of the super-Gaussian is higher than that of the Gaussian window function, the side lobes decay faster. In addition, it is clear that the first side lobe of the super-Gaussian is lower (by approximately 6.2 dB) than that of the rectangular window function [Fig. 4(b)]. The wider the width (σ), the narrower the main lobe becomes; However, the first side lobe gets higher. In addition, we compare the frequency responses of the super-Gaussian window function according to changes in the parameters σ and M. As shown in Fig 4(c), the first side lobe increases when the window function rapidly decays (M increases). The wider the width (σ), the narrower the main lobe becomes, similar to the comparison of the Gaussian and super-Gaussian window functions in Fig. 4(b).

Figure 4.Examples of the super-Gaussian window function and frequency response of the super-Gaussian window function. (a) Graphs of the super-Gaussian window functions with [σ = 0.6, M = 2] and [σ = 0.7, M = 4], (b) frequency response of the super-Gaussian window function with [σ = 0.62, M = 2] compared to those of the rectangular and Gaussian window functions, and (c) frequency response of the super-Gaussian window function, according to changes in two parameters.

### 3.3. Simulated and Experimental Results

Figures 5(a) and 5(b) are the results obtained for the simulated effects of the window functions, using the spectrum with 1,152 sampling points in Fig. 2(b). In applying the Gaussian window function, we set the value of σ at 0.5. For the super-Gaussian window function, the values of σ and M are 0.75 and 2 respectively. From the PSF in Fig. 5(a), we find the coherence length after FFT by multiplication by the Hann, Gaussian, and super-Gaussian window functions to be 5.5, 4.5, and 3.9 μm respectively—compared to the 3.3-μm coherence length obtained without multiplication by any window function. As shown in Fig. 5(b), the side lobes in the PSF after application of the Hann window function are the lowest, as expected. The first side lobes after applying the Gaussian and super-Gaussian window functions are similar and approximately 7.6 dB lower than the first side lobe without any window function.

Figure 5.Images shown in (a), (b) are PSFs of the coherence length (or axial resolution) for the simulation, and (c), (d) are experiments using slide glass with a thickness of 1 mm. (a) and (c) are displayed with a linear scale. (b) and (d) are displayed with a log scale. PSF, point-spread function.

To compare the effects of the window functions in our system, we use a 1-mm slide glass as a sample. The mirror is positioned approximately 870 μm from zero optical-path difference (OPD). Figures 5(c) and 5(d) are the PSFs of the measured axial resolution from the slide glass. We measure the axial resolutions at 5.5, 4.8, and 4.2 μm in air after applying the Hann, Gaussian, and super-Gaussian window functions respectively, as shown in Fig. 5(c). These values correspond respectively to 4.1, 3.6, and 3.1 μm in tissue (n = 1.35). Without the use of the window-function multiplier, the measured axial resolution becomes 3.7 μm in air, corresponding to 2.7 μm in tissue. There are marginal differences between the axial resolution of the simulated results and the measured axial resolution, because the dispersion mismatches between reference and sample arms are not perfectly corrected, although a dispersion-compensation prism is used. In Fig. 5(d) the first side lobes with the super-Gaussian window function (green) are 6.3 dB (left of the main lobe) and 2.3 dB (right of the main lobe) higher than those with the Hann window function (red). However, the first side lobes with the super-Gaussian window function are 2.6 dB lower than those without any window function (black).

Figure 6 shows UHR FD/SD-OCT images of human finger skin after applying the Hann, Gaussian, and super-Gaussian window functions. The results of the experiments do not show large differences in the side lobes between window functions, as shown in Fig. 4(d), although the differences in the simulated results are clear. However, because OCT images, like most, are displayed with log-scaled intensity (or color map), small side lobes appear in the OCT image. As shown in Fig. 6(a), the edge of the skin surface is sharp, but side lobes are clearly displayed. In contrast, the edge of the skin surface in Figs. 6(b) and 6(c), to which the Hann and Gaussian window functions have been applied, are a bit thicker than that in Fig. 6(a); however, the side lobes have disappeared. Figure 6(d) shows the OCT image after applying the super-Gaussian window function. Here the edge of the skin surface is thicker than that in Fig. 6(a), but thinner than those in Figs. 6(b) and 6(c). The side lobes in Fig. 6(d) are weakly visible.

Figure 6.UHR FD/SD-OCT images of the skin on a human finger: (a) no window function, (b) Hann window function, (c) Gaussian window function, and (d) super-Gaussian window function applied. The image size is 576 pixels (depth) × 1,000 pixels (width). OCT, optical coherence tomography; UHR-OCT, ultrahighresolution OCT; FD-OCT, Fourier-domain OCT; SD-OCT, spectral domain OCT.

Figure 7 shows cross-sectional OCT images of the human retina. Whereas Fig. 6 compared images to which window functions multipliers were applied in the interface between air and tissue, Fig. 7 shows the differences in the inner layers of the retina. As shown in the red area of Fig. 7(a), the interfaces between photoreceptor inner-segment/outer-segment junction (IS/OS, upper blue arrow), photoreceptor outer segments (PR OS, middle blue arrow), and retinal pigmentation epithelium (RPE, lower blue arrow) are ambiguous due to the effect of side lobes, compared to those in Figs. 7(b)7(d). The side lobes appear in the IS/OS and PR OS layers in a similar fashion to the blue boxed area of Fig. 7(a). In Figs. 7(c) and 7(d), to which the Gaussian and super-Gaussian window functions have been applied, the IS/OS, PR OS, and RPE layers are clearly distinguished. In addition, the layers in Fig. 7(d) are sharper than those in Fig. 7(c). A windowing process causes some power loss for the overall OCT signal, as shown in Fig. 3(a). However, in this study we have assumed that the power loss after the windowing process would not make a significant difference to the OCT images, because the OCT signals were represented as images with log scale or exponential scale. In Figs. 6 and 7, as assumed, no significant differences are seen between OCT images according to their window functions. To obtain Figs. 6 and 7, the fast-axis galvanometer is scanned using a sawtooth signal with 80% duty cycle. Consequently, we obtain a skin image with an acquisition time of 6.25 ms (160 fps), and a retina image with an acquisition time of 9.4 ms (106.7 fps), by using multithread CPU processing and parallel GPU computation processing.

Figure 7.UHR FD/SD-OCT images of the human retina: (a) no window function, (b) Hann window function, (c) Gaussian window function, and (d) super-Gaussian window function applied. The image size is 576 pixels (depth) × 1,500 pixels (width). IS/OS, photoreceptor inner-segment/outer-segment junction; PR OS, photoreceptor outer segments; RPE, retinal pigment epithelium. OCT, optical coherence tomography; UHR-OCT, ultrahighresolution OCT; FD-OCT, Fourier-domain OCT; SD-OCT, spectral domain OCT.

The super-Gaussian window function is an expanded Gaussian window function, and has the advantage of its width and slope being adjustable. In both simulation and experiment, although the super-Gaussian window function does not significantly enhance the axial resolution, the axial resolution at the PSF following application of the super-Gaussian window function is closer to that at the PSF without the window function applied than is the case with the Hann or Gaussian window function. In addition, the super-Gaussian window function has the effect of reducing the side lobes. The window function should be used while considering factors such as spectrum shape and bandwidth of the light source. Even if the super-Gaussian window function is not always used for all light sources, for spectra with flat-topped intensity profiles it is a good function to help reduce side lobes and obtain results close to the theoretical axial resolution. In this study, the width of the window σ and decay parameter M are found manually from the obtained PSF after FFT. It is necessary to develop an algorithm to automatically find parameter values, in a further study.

### IV. CONCLUSION

We have demonstrated UHR SD-OCT at 200-kHz line rate, using a wideband SLD of 100 nm at 849 nm and a subset of the total number of camera pixels. In addition, partial spectrum detection was used to obtain OCT images within an imaging depth of 2.1 mm while maintaining ultrahigh axial resolution. The full spectrum of the SLD used in this study and the partially detected spectrum had flat-topped intensity profiles. These intensity profiles resulted in the occurrence of side lobes after FFT. Consequently, we proposed and applied the super-Gaussian function as a new window function to reduce the side lobes and obtain results that were closer to that of the axial resolution when no window function was applied. The side lobes at PSF following application of the super-Gaussian window function were higher than those at PSF following application of the Hann or Gaussian window function, but lower than those at PSF with no window function applied. In addition, the application of the super-Gaussian window function gave results close to the ultrahigh axial resolution of 4.2 μm in air, corresponding to 3.1 μm in tissue (n = 1.35).

The authors declare no conflicts of interest.

### DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

Development of Measurement Standards and Technology for Biomaterials and Medical Convergence, funded by the Korea Research Institute of Standards and Science (KRISS-GP2022-0006); Creative Materials Discovery Program (2018M3D1A1058814); Korea Medical Device Development Fund grants, funded by the Korean government (Ministry of Science and ICT, Ministry of Trade, Industry and Energy, Ministry of Health & Welfare, Ministry of Food and Drug Safety) (Project Number: KMDF_PR_20200901_0024 and KMDF_PR_20200901 _0026).

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### Article

#### Article

Curr. Opt. Photon. 2023; 7(1): 73-82

Published online February 25, 2023 https://doi.org/10.3807/COPP.2023.7.1.73

## Partial Spectrum Detection and Super-Gaussian Window Function for Ultrahigh-resolution Spectral-domain Optical Coherence Tomography with a Linear-k Spectrometer

Hyun-Ji Lee1,2, Sang-Won Lee1,2

1Safety Measurement Institute, Korea Research Institute of Standards and Science, Daejeon 34113, Korea
2Department of Medical Physics, Korea University of Science and Technology, Daejeon 34113, Korea

Correspondence to:*swlee76@kriss.re.kr, ORCID 0000-0001-6952-6957

Received: September 30, 2022; Revised: December 15, 2022; Accepted: December 19, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

In this study, we demonstrate ultrahigh-resolution spectral-domain optical coherence tomography with a 200-kHz line rate using a superluminescent diode with a−3-dB bandwidth of 100 nm at 849 nm. To increase the line rate, a subset of the total number of camera pixels is used. In addition, a partial-spectrum detection method is used to obtain OCT images within an imaging depth of 2.1 mm while maintaining ultrahigh axial resolution. The partially detected spectrum has a flat-topped intensity profile, and side lobes occur after fast Fourier transformation. Consequently, we propose and apply the super-Gaussian window function as a new window function, to reduce the side lobes and obtain a result that is close to that of the axial-resolution condition with no window function applied. Upon application of the super-Gaussian window function, the result is close to the ultrahigh axial resolution of 4.2 μm in air, corresponding to 3.1 μm in tissue (n = 1.35).

Keywords: Spectral domain, Super-Gaussian window, Ultrahigh resolution optical coherence tomography

### I. INTRODUCTION

Optical coherence tomography (OCT) has been extensively studied as a clinical and noninvasive imaging tool for biological tissues, because it provides high-resolution cross-sectional and three-dimensional volumetric images [1, 2]. Many OCT study groups have spent significant effort on trying to obtain higher axial resolutions, higher sensitivities, and increased acquisition speeds in various fields, including medical application studies [313]. Ultrahigh-resolution OCT (UHR-OCT) with an axial resolution of 3 μm or less can yield clear visualization of microstructured layers in tissues, close to the level of histology. The higher acquisition speed can minimize motion artifacts and facilitate quantitative analysis of three- and four-dimensional image data. Recently, Fourier-domain OCT (FD-OCT)—one type based on a wavelength-swept source (SS-OCT), and another on a spectral domain (SD-OCT)—has been actively used in high-sensitivity and high-acquisition-speed applications [911]. SS-OCT can provide an increased imaging depth of over 5 mm and a lower sensitivity roll-off. The acquisition speed of SS-OCT has increased substantially to line rates of a few hundred kilohertz and even up to a few megahertz, since wavelength-swept sources based on Fourier-domain mode locking (FDML) and high-speed polygon scanners were introduced [1215]. A wavelength-swept source with 100–200 kHz line rate has recently been commercialized [2]. However, for SS-OCT commercial wavelength-swept sources and data-acquisition boards with high sampling rates, on the order of 108–109 per second, are still very expensive. In SD-OCT, the acquisition speed can be increased up to 312 kHz by using a subset of the total number of camera pixels [16]. In addition, the acquisition speed of SD-OCT can be made to achieve a line rate of 500 kHz by using interlaced detection with two spectrometers and selecting only 800 out of 4,096 pixels in the camera, to increase the A-line rate [17]. However, SD-OCT has trade-offs among imaging depth range, sensitivity roll-off, axial resolution, and acquisition speed. SD-OCT has to sacrifice spectral resolution by using some of the camera pixels in the spectrometer to increase the acquisition speed. Consequently, the imaging-depth range is limited to below 2 mm in air, and the sensitivity roll-off decays rapidly. Further, SD-OCT cannot preserve axial resolutions below 10 μm in air to maintain long imaging-depth ranges over 2 mm, when the number of pixels in the region of interest (ROI) in the camera is reduced to facilitate high acquisition speeds [16, 17].

The axial resolution of OCT is inversely proportional to the full width at half maximum (FWHM) of the light source. Since UHR-OCT with 1-μm axial resolution by using an ultrashort femtosecond laser with FWHM of 260 nm at 800 nm was first introduced by Drexler et al. [3], a supercontinuum light source with a femtosecond laser coupled with a long optical fiber or a super-luminescent diode (SLD) combining several SLD modules has been used as a wide-bandwidth light source for UHR-OCT [48]. Most light sources with wide FWHM do not have Gaussian spectra, and the non-Gaussian spectral shape of the light results in the occurrence of side lobes. In conventional time-domain OCT (TD-OCT), spectral filtering, shaping of the source spectrum, and interactive deconvolution with the coherence envelope’s point-spread function (PSF) in the space domain have been used to digitally reduce side lobes [3, 4, 1820]. In addition, Akcay et al. [21] and Choi et al. [22] proposed using a programmable spectral processor and a fiber-based spectral filter for spectral shaping in TD-OCT. In SD-OCT, spectral reshaping by digital processing of the spectrum to approximate a Gaussian envelope before fast Fourier transformation (FFT) has been performed to reduce the height of the side lobes [6]. In addition, several window functions such as Hann, Hamming, and Gaussian window functions can significantly compress the side lobes. However, the PSF is broadened in such cases. In other words, the axial resolution is increased, compared to the axial resolution without multiplication by any window function.

In this study, we demonstrate UHR SD-OCT with an acquisition speed (line rate) of 200 kHz. To achieve a 200-kHz line rate we use 1,152 pixels, a subset of the overall 4,096 pixels in the camera at 70 kHz line rate. A wide-band SLD combining two SLD modules is used for ultrahigh axial resolution. In addition, partial spectrum detection is used to obtain OCT images within an imaging depth of 2.1 mm, while maintaining ultrahigh axial resolution. Our SLD has the spectrum of a flat-topped intensity profile, resulting in the appearance of side lobes. Consequently, we apply the super-Gaussian function, which has been used to estimate the flat-topped intensity profile of laser beams in the field of optics [23, 24], and in the design of finite-impulse-response (FIR) filters in digital signal processing [25], as a new window function. We then calculate the frequency response of the super-Gaussian window function and compare the result to those of other popular window functions after application to partial spectrum detection.

### II. METHOD

A schematic of the SD-OCT system based on a linear wavenumber-domain (k-domain) spectrometer is depicted in Fig. 1. An SLD at 849 nm (BLM2-D-840-B-I-10; Superlum, Carrigtwohill, Ireland) has FWHM of 100 nm and optical power of 10 mW. We use the sample arm in Fig. 1(a) to measure the system performance and obtain images of skin tissue. The configuration of this system is described in detail in [26]. The linear k-domain spectrometer is slightly modified: We use a 90° off-axis parabolic mirror to make a collimated beam, instead of a collimation lens and a prism mirror between the pair of lenses and the camera, to reduce the physical size of the spectrometer, as shown in Fig. 1. We adjust the starting pixel and ROI in the camera to the 1,473rd and 1,152nd pixels respectively, to increase the acquisition speed from 128 to 200 kHz. The exposure time is set to 3.7 μs. For ophthalmic imaging, we change the split ratio of the optical-fiber coupler and the sample arm, as shown in Fig. 1(b). Light from the SLD is split into the reference (90%) and sample (10%) arms, to satisfy the American National Standards Institute (ANSI) safety requirements and increase detection efficiency. The sample arm consists of a two-dimensional galvanometer, an achromatic doublet lens (L3: f = 50 mm; Thorlabs Inc., NJ, USA), and a double aspheric ocular lens (L4: 20 D; Volk Optical Inc., OH, USA). We use a neutral-density (ND) filter in the reference arm to reduce the source-intensity noise [27].

Figure 1. Schematic of the SD-OCT based on a linear k-domain spectrometer. (a) The sample arm to measure the system performance and obtain the skin tissue’s image. (b) The sample arm to get the image of the retina. SD-OCT, spectral domain optical coherence tomography; PC, polarization controller; CL, collimation lens; OL, objective lens; DCB, dispersion compensation block; RM, reference mirror; RC, reflective collimator; G, grating; DP, dispersive prism; PM, prism mirror; L1 to L4, lenses.

Spectral data from the spectrometer are digitized using a frame grabber (PCIe-1433; National Instruments Corp., TX, USA). The digitized spectral data are then processed using a quad-core central processing unit (CPU) and a graphic processing unit (GPU) to accelerate numerical calculations and display real-time two-dimensional images. We develop the software in Microsoft Visual C++ with NVIDIA’s compute unified device architecture (CUDA10.0) technology [28, 29].

### 3.1. Partial Spectrum Detection Versus Axial Resolution

Figures 2(a)2(c) show the normalized spectrum of the SLD according to the sampling number. The original spectrum is acquired with 10,001 sampling points using an optical spectrum analyzer (AQ6317B; Ando Corp., CA, USA). The acquired original spectrum is then resampled with 2,048, 1,152, and 1,024 sampling points and converted to wavenumber (k-domain) with the same spectral resolution as our spectrometer. Figure 2(d) shows the point-spread functions (PSFs) of the coherence length according to changes in the number of sampling points, while maintaining the spectral resolution. When the sampling points are 2,048 and 1,152, the coherence length is calculated to be 3.1 μm and 3.3 μm respectively. In addition, the coherence length at 1,024 sampling points is broadened to 3.7 μm. We do not include the calculated result for 512 sampling points in Fig. 2(d), but we find that the coherence length is also broadened, to 7.6 μm. To obtain the smooth curves shown in Fig. 2(d), we employ zero-padding by including sufficient sampling points.

Figure 2. Resampled spectrum from the original spectrum with 10,001 sampling points, by means of the optical spectrum analyzer: (a) 2,048 sampling points, (b) 1,152 sampling points, and (c) 1,024 sampling points. (d) PSF of the coherence length for each spectrum, (a) to (c). PSF, point-spread function.

### 3.2. Comparison of the Frequency Responses of the Window Functions

The frequency response (or frequency spectrum) of a truncation window should ideally be a frequency-domain impulse, which should have a very narrow main lobe and no side lobes. However, in practice, windows with narrow main lobes tend to have large side lobes, and vice versa [30]. Large side lobes can obscure the weaker frequency peak after FFT, when the waveform comprises two adjacently frequencies. The Hann window, Hamming window, and Gaussian window are commonly used to reduce such side lobes. The Hann window and Hamming window are defined from generalized Hamming windows as follows [30]:

when A = B = 0.5, w[n] is called a Hann window. Conversely, when A = 0.54 and B = 0.46, w[n] is called a Hamming window. In addition, the Gaussian window function can be defined as

$w[n]=exp−12 n−(N−1)/2 σ(N−1)/22 σ≤0.5$

The graphs of the window functions plus the frequency response of each window function are shown in Fig. 3. In that figure, the rectangular window function is w[n] = 1, where n = 0, 1, 2, ..., N−1. For the Gaussian window function, we set σ = 0.5, which is the maximum value. As seen from Figs. 3(b)3(d), the Hann window function has the widest main lobe. Computations reveal that the main lobes of the Hann and Gaussian window functions are respectively 1.6 and 1.34 times as wide as the rectangular window function. The side lobes of the rectangular window function are the highest, compared to the other window functions. In addition, although the first side lobe of the frequency response of the Hann window function is similar to the second side lobe of the Gaussian window function, it can be seen from Figs. 3(c) and 3(d) that the side lobes of the Hann window function decay faster.

Figure 3. Graphs of three window functions and the frequency responses according to window functions. (a) Window functions, (b) the frequency response of the rectangular, (c) the frequency response of Hann, and (d) the frequency response of Gaussian window functions.

The super-Gaussian window function is expanded from the Gaussian window function, and is defined mathematically as [2325]

In the super-Gaussian window function, σ represents the width of the window. When the value of M increases, the window function rapidly decays, and becomes the rectangular function at M = ∞. Figure 4(a) presents the super-Gaussian window functions, according to varying σ and M. Figure 4(b) shows the frequency response of the super-Gaussian window function (σ = 0.62, M = 2) with those of the rectangular and Gaussian (σ = 0.5) window functions. In the frequency response, the main lobe of the super-Gaussian is narrower than that of the Gaussian window function. Although the first side lobe of the super-Gaussian is higher than that of the Gaussian window function, the side lobes decay faster. In addition, it is clear that the first side lobe of the super-Gaussian is lower (by approximately 6.2 dB) than that of the rectangular window function [Fig. 4(b)]. The wider the width (σ), the narrower the main lobe becomes; However, the first side lobe gets higher. In addition, we compare the frequency responses of the super-Gaussian window function according to changes in the parameters σ and M. As shown in Fig 4(c), the first side lobe increases when the window function rapidly decays (M increases). The wider the width (σ), the narrower the main lobe becomes, similar to the comparison of the Gaussian and super-Gaussian window functions in Fig. 4(b).

Figure 4. Examples of the super-Gaussian window function and frequency response of the super-Gaussian window function. (a) Graphs of the super-Gaussian window functions with [σ = 0.6, M = 2] and [σ = 0.7, M = 4], (b) frequency response of the super-Gaussian window function with [σ = 0.62, M = 2] compared to those of the rectangular and Gaussian window functions, and (c) frequency response of the super-Gaussian window function, according to changes in two parameters.

### 3.3. Simulated and Experimental Results

Figures 5(a) and 5(b) are the results obtained for the simulated effects of the window functions, using the spectrum with 1,152 sampling points in Fig. 2(b). In applying the Gaussian window function, we set the value of σ at 0.5. For the super-Gaussian window function, the values of σ and M are 0.75 and 2 respectively. From the PSF in Fig. 5(a), we find the coherence length after FFT by multiplication by the Hann, Gaussian, and super-Gaussian window functions to be 5.5, 4.5, and 3.9 μm respectively—compared to the 3.3-μm coherence length obtained without multiplication by any window function. As shown in Fig. 5(b), the side lobes in the PSF after application of the Hann window function are the lowest, as expected. The first side lobes after applying the Gaussian and super-Gaussian window functions are similar and approximately 7.6 dB lower than the first side lobe without any window function.

Figure 5. Images shown in (a), (b) are PSFs of the coherence length (or axial resolution) for the simulation, and (c), (d) are experiments using slide glass with a thickness of 1 mm. (a) and (c) are displayed with a linear scale. (b) and (d) are displayed with a log scale. PSF, point-spread function.

To compare the effects of the window functions in our system, we use a 1-mm slide glass as a sample. The mirror is positioned approximately 870 μm from zero optical-path difference (OPD). Figures 5(c) and 5(d) are the PSFs of the measured axial resolution from the slide glass. We measure the axial resolutions at 5.5, 4.8, and 4.2 μm in air after applying the Hann, Gaussian, and super-Gaussian window functions respectively, as shown in Fig. 5(c). These values correspond respectively to 4.1, 3.6, and 3.1 μm in tissue (n = 1.35). Without the use of the window-function multiplier, the measured axial resolution becomes 3.7 μm in air, corresponding to 2.7 μm in tissue. There are marginal differences between the axial resolution of the simulated results and the measured axial resolution, because the dispersion mismatches between reference and sample arms are not perfectly corrected, although a dispersion-compensation prism is used. In Fig. 5(d) the first side lobes with the super-Gaussian window function (green) are 6.3 dB (left of the main lobe) and 2.3 dB (right of the main lobe) higher than those with the Hann window function (red). However, the first side lobes with the super-Gaussian window function are 2.6 dB lower than those without any window function (black).

Figure 6 shows UHR FD/SD-OCT images of human finger skin after applying the Hann, Gaussian, and super-Gaussian window functions. The results of the experiments do not show large differences in the side lobes between window functions, as shown in Fig. 4(d), although the differences in the simulated results are clear. However, because OCT images, like most, are displayed with log-scaled intensity (or color map), small side lobes appear in the OCT image. As shown in Fig. 6(a), the edge of the skin surface is sharp, but side lobes are clearly displayed. In contrast, the edge of the skin surface in Figs. 6(b) and 6(c), to which the Hann and Gaussian window functions have been applied, are a bit thicker than that in Fig. 6(a); however, the side lobes have disappeared. Figure 6(d) shows the OCT image after applying the super-Gaussian window function. Here the edge of the skin surface is thicker than that in Fig. 6(a), but thinner than those in Figs. 6(b) and 6(c). The side lobes in Fig. 6(d) are weakly visible.

Figure 6. UHR FD/SD-OCT images of the skin on a human finger: (a) no window function, (b) Hann window function, (c) Gaussian window function, and (d) super-Gaussian window function applied. The image size is 576 pixels (depth) × 1,000 pixels (width). OCT, optical coherence tomography; UHR-OCT, ultrahighresolution OCT; FD-OCT, Fourier-domain OCT; SD-OCT, spectral domain OCT.

Figure 7 shows cross-sectional OCT images of the human retina. Whereas Fig. 6 compared images to which window functions multipliers were applied in the interface between air and tissue, Fig. 7 shows the differences in the inner layers of the retina. As shown in the red area of Fig. 7(a), the interfaces between photoreceptor inner-segment/outer-segment junction (IS/OS, upper blue arrow), photoreceptor outer segments (PR OS, middle blue arrow), and retinal pigmentation epithelium (RPE, lower blue arrow) are ambiguous due to the effect of side lobes, compared to those in Figs. 7(b)7(d). The side lobes appear in the IS/OS and PR OS layers in a similar fashion to the blue boxed area of Fig. 7(a). In Figs. 7(c) and 7(d), to which the Gaussian and super-Gaussian window functions have been applied, the IS/OS, PR OS, and RPE layers are clearly distinguished. In addition, the layers in Fig. 7(d) are sharper than those in Fig. 7(c). A windowing process causes some power loss for the overall OCT signal, as shown in Fig. 3(a). However, in this study we have assumed that the power loss after the windowing process would not make a significant difference to the OCT images, because the OCT signals were represented as images with log scale or exponential scale. In Figs. 6 and 7, as assumed, no significant differences are seen between OCT images according to their window functions. To obtain Figs. 6 and 7, the fast-axis galvanometer is scanned using a sawtooth signal with 80% duty cycle. Consequently, we obtain a skin image with an acquisition time of 6.25 ms (160 fps), and a retina image with an acquisition time of 9.4 ms (106.7 fps), by using multithread CPU processing and parallel GPU computation processing.

Figure 7. UHR FD/SD-OCT images of the human retina: (a) no window function, (b) Hann window function, (c) Gaussian window function, and (d) super-Gaussian window function applied. The image size is 576 pixels (depth) × 1,500 pixels (width). IS/OS, photoreceptor inner-segment/outer-segment junction; PR OS, photoreceptor outer segments; RPE, retinal pigment epithelium. OCT, optical coherence tomography; UHR-OCT, ultrahighresolution OCT; FD-OCT, Fourier-domain OCT; SD-OCT, spectral domain OCT.

The super-Gaussian window function is an expanded Gaussian window function, and has the advantage of its width and slope being adjustable. In both simulation and experiment, although the super-Gaussian window function does not significantly enhance the axial resolution, the axial resolution at the PSF following application of the super-Gaussian window function is closer to that at the PSF without the window function applied than is the case with the Hann or Gaussian window function. In addition, the super-Gaussian window function has the effect of reducing the side lobes. The window function should be used while considering factors such as spectrum shape and bandwidth of the light source. Even if the super-Gaussian window function is not always used for all light sources, for spectra with flat-topped intensity profiles it is a good function to help reduce side lobes and obtain results close to the theoretical axial resolution. In this study, the width of the window σ and decay parameter M are found manually from the obtained PSF after FFT. It is necessary to develop an algorithm to automatically find parameter values, in a further study.

### IV. CONCLUSION

We have demonstrated UHR SD-OCT at 200-kHz line rate, using a wideband SLD of 100 nm at 849 nm and a subset of the total number of camera pixels. In addition, partial spectrum detection was used to obtain OCT images within an imaging depth of 2.1 mm while maintaining ultrahigh axial resolution. The full spectrum of the SLD used in this study and the partially detected spectrum had flat-topped intensity profiles. These intensity profiles resulted in the occurrence of side lobes after FFT. Consequently, we proposed and applied the super-Gaussian function as a new window function to reduce the side lobes and obtain results that were closer to that of the axial resolution when no window function was applied. The side lobes at PSF following application of the super-Gaussian window function were higher than those at PSF following application of the Hann or Gaussian window function, but lower than those at PSF with no window function applied. In addition, the application of the super-Gaussian window function gave results close to the ultrahigh axial resolution of 4.2 μm in air, corresponding to 3.1 μm in tissue (n = 1.35).

### DISCLOSURES

The authors declare no conflicts of interest.

### DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

### FUNDING

Development of Measurement Standards and Technology for Biomaterials and Medical Convergence, funded by the Korea Research Institute of Standards and Science (KRISS-GP2022-0006); Creative Materials Discovery Program (2018M3D1A1058814); Korea Medical Device Development Fund grants, funded by the Korean government (Ministry of Science and ICT, Ministry of Trade, Industry and Energy, Ministry of Health & Welfare, Ministry of Food and Drug Safety) (Project Number: KMDF_PR_20200901_0024 and KMDF_PR_20200901 _0026).

### Fig 1.

Figure 1.Schematic of the SD-OCT based on a linear k-domain spectrometer. (a) The sample arm to measure the system performance and obtain the skin tissue’s image. (b) The sample arm to get the image of the retina. SD-OCT, spectral domain optical coherence tomography; PC, polarization controller; CL, collimation lens; OL, objective lens; DCB, dispersion compensation block; RM, reference mirror; RC, reflective collimator; G, grating; DP, dispersive prism; PM, prism mirror; L1 to L4, lenses.
Current Optics and Photonics 2023; 7: 73-82https://doi.org/10.3807/COPP.2023.7.1.73

### Fig 2.

Figure 2.Resampled spectrum from the original spectrum with 10,001 sampling points, by means of the optical spectrum analyzer: (a) 2,048 sampling points, (b) 1,152 sampling points, and (c) 1,024 sampling points. (d) PSF of the coherence length for each spectrum, (a) to (c). PSF, point-spread function.
Current Optics and Photonics 2023; 7: 73-82https://doi.org/10.3807/COPP.2023.7.1.73

### Fig 3.

Figure 3.Graphs of three window functions and the frequency responses according to window functions. (a) Window functions, (b) the frequency response of the rectangular, (c) the frequency response of Hann, and (d) the frequency response of Gaussian window functions.
Current Optics and Photonics 2023; 7: 73-82https://doi.org/10.3807/COPP.2023.7.1.73

### Fig 4.

Figure 4.Examples of the super-Gaussian window function and frequency response of the super-Gaussian window function. (a) Graphs of the super-Gaussian window functions with [σ = 0.6, M = 2] and [σ = 0.7, M = 4], (b) frequency response of the super-Gaussian window function with [σ = 0.62, M = 2] compared to those of the rectangular and Gaussian window functions, and (c) frequency response of the super-Gaussian window function, according to changes in two parameters.
Current Optics and Photonics 2023; 7: 73-82https://doi.org/10.3807/COPP.2023.7.1.73

### Fig 5.

Figure 5.Images shown in (a), (b) are PSFs of the coherence length (or axial resolution) for the simulation, and (c), (d) are experiments using slide glass with a thickness of 1 mm. (a) and (c) are displayed with a linear scale. (b) and (d) are displayed with a log scale. PSF, point-spread function.
Current Optics and Photonics 2023; 7: 73-82https://doi.org/10.3807/COPP.2023.7.1.73

### Fig 6.

Figure 6.UHR FD/SD-OCT images of the skin on a human finger: (a) no window function, (b) Hann window function, (c) Gaussian window function, and (d) super-Gaussian window function applied. The image size is 576 pixels (depth) × 1,000 pixels (width). OCT, optical coherence tomography; UHR-OCT, ultrahighresolution OCT; FD-OCT, Fourier-domain OCT; SD-OCT, spectral domain OCT.
Current Optics and Photonics 2023; 7: 73-82https://doi.org/10.3807/COPP.2023.7.1.73

### Fig 7.

Figure 7.UHR FD/SD-OCT images of the human retina: (a) no window function, (b) Hann window function, (c) Gaussian window function, and (d) super-Gaussian window function applied. The image size is 576 pixels (depth) × 1,500 pixels (width). IS/OS, photoreceptor inner-segment/outer-segment junction; PR OS, photoreceptor outer segments; RPE, retinal pigment epithelium. OCT, optical coherence tomography; UHR-OCT, ultrahighresolution OCT; FD-OCT, Fourier-domain OCT; SD-OCT, spectral domain OCT.
Current Optics and Photonics 2023; 7: 73-82https://doi.org/10.3807/COPP.2023.7.1.73

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Wonshik Choi,
Editor-in-chief