An optical spectrometer, an instrument used to measure the wavelength-dependent intensity distribution of light, has a wide range of applications in biomedical imaging, astronomy, and biochemical analysis [1]. In spectral-domain optical coherence tomography (SD-OCT), a spectrometer is typically employed to detect spectral interferograms as a function of wavelength for depth-resolved imaging of a sample [2]. Although the information on the exact wavelength is not necessarily required in a typical SD-OCT system, optical configuration and alignment of the spectrometer directly affect the imaging performance and processing strategies. In multiple-spectrometer-based SD-OCT, cross-calibration between the spectrometers is crucial in addition to the calibration of an individual spectrometer to achieve maximum possible performance [3–5].

As the precise registration of interference signals across different spectrometers requires a high level of accuracy, hardware approaches to spectrometer alignment possess many practical challenges. While optical simulation tools provide idealized positioning of optical components in a spectrometer design, manufacturing variations, environmental factors, and structural integrities of the instrument can contribute to the alignment errors. However, cross-calibration of spectral alignment in two or more spectrometers can be performed using a computational approach once the data are acquired. Through mapping the corresponding pixels across spectrometers, cross-calibration can be achieved without the knowledge of the exact wavelength corresponding to each pixel. For example, a simple spectral matching approach acquires a set of calibration interference fringes and estimates the pixel shift between two spectra by cross correlation; unique features of the spectra such as zero-crossing points or amplitude variations can be correlated [3,6].

Recently, we developed an optimization-based spectral matching method [5], in which both shifting and nonlinear transformation (e.g., scaling) of the spectra from misalignment are considered. This technique iteratively applies polynomial feature transformation to the target spectra and searches for a set of coefficients that minimizes the square of the differences among spectra acquired from different spectrometers. Another interesting technique was recently demonstrated by Kho et al. [7] and Rubinoff et al. [8], where high excess photon noise of a supercontinuum source is used to estimate pixel-to-pixel correspondence between a set of spectrometers. Since temporal intensity changes of excess noise are wavelength-dependent, an accurate pixel mapping of two spectrometers can be obtained through correlation analysis of the recorded noise. Computational approaches simplify the spectrometer alignment processes while ensuring a high precision of coalignment. However, the spectral resolution of the individual spectrometer does not improve through a computational approach. In addition, numerical alignment cannot recover the non-overlapping part of the signals, resulting in reduced bandwidth. Finally, Kho et al. recently demonstrated a hybrid approach where the mechanical alignment of a spectrometer is guided proactively in real-time via metrics calculated from a computational approach [9]. The alignment metrics created from noise correlation, similar to those in [7], can accurately guide the spectrometer alignment and suppress common noise in visible-light OCT. However, this method is only applicable to light sources with high excess noise, at present.

In this Letter, we present a computational method for estimating the pixel-to-pixel correspondence in wavelength between the two spectrometers using OCT B-scan images. This approach requires no special calibration procedure and can be used to guide mechanical alignment as well as to perform a numerical alignment.

Figure 1 demonstrates the data acquisition and output of the proposed image-based cross-calibration. In the cross-calibration, a pair of OCT B-scan images were first acquired from a multiple-spectrometer-based OCT followed by the construction of a 2D correlation matrix (CM). By scanning the OCT beam across a sample, paired B-scans containing time-dependent spectral interferograms can be obtained. In this study, each B-scan contains 500 spectra. The main assumption of this technique is that the spectral interferograms in a spectrometer pair will have high cross correlation not only in spectral data but also in temporal data if they have an identical spectral alignment. Temporal correlation indicates the similarity of signal variations over a time course of a single B-scan $(x )$ while the data are acquired synchronously from the two spectrometers. While the optimization-based method [5] estimates spectral alignment by finding the highest correlation in the spectral data, this method performs correlation analysis on the wavelength-dependent variation of te temporal signal intensity. Note that while noise correlation gives a single quasi-diagonal correlation line [7], the image-based method can generate additional weaker correlation lines due to the nature of interference.

 

Fig. 1. (a) Paired B-scans in multiple-spectrometer-based OCT are used to construct (b) a correlation matrix, where the quasi-diagonal contour can guide spectrometer cross-calibration.

Download Full Size | PDF

Let ${a_i}$ and ${b_j}$ be the 1D data of signal intensity values recorded from camera pixel position i and j in spectrometer A and B, respectively, over the time course of a B-scan, $\tau = 1\ldots T$. Cross correlation estimates the correlation between the time-series data of a certain pixel in one spectrometer and another pixel in the other spectrometer. Now, we calculate normalized cross correlation as follows:

In this study, additional signal filtering steps were implemented to clearly distinguish the highest correlation values in CM. The signal processing pipeline consists of the following three steps.

Step 1. DC subtraction: The source spectrum is subtracted from each A-line to suppress DC contribution. The source spectrum is estimated by taking the median of A-line spectra along the B-scan.

Step 2. Matrix multiplication: The correlation matrix is derived from a variance-covariance matrix of a B-scan pair ($A,B$) as

Step 3. Spatial filtering: After the previous step, the correlation matrix contains quasi-diagonal lines as well as vertical and horizontal striations, artifacts from the residual DC components in the A-line spectra. These artifacts are removed by calculating a 2D fast Fourier transformation (FFT) of the resulting CM and applying a crossline mask to the power spectrum. Then, the noise-suppressed CM is obtained by calculating the inverse FFT.

Figure 2 shows representative correlation matrices constructed from a single B-scan retinal OCT image after signal processing. We estimated the alignments from the two sets of spectrometer pairs: custom-built and commercial spectrometers (Cobra-S 800-840/120, Wasatch Photonics Inc., USA), both operating at 250-kHz line-rate and covering the 780–900-nm wavelength range. In the custom spectrometers, proactive spectrometer alignment is performed based on the CM. If the two spectrometers do not have perfect coalignment, the quasi-diagonal contour deviates from the diagonal element of the CM (white dotted lines in Fig. 2). The amount of deviation in the quasi-diagonal contour directly relates to the error in the spectrometer coalignment, and therefore, can be used to guide the mechanical alignment. Furthermore, the degree of spectrometer coalignment can be more precisely assessed by a line segmentation of contour. In this study, we find the centerline of the contour by manually extracting the two coordinates along the contour and fitting them to the first-order polynomial curve. Here, the zeroth coefficient ($\alpha $) corresponds to the zero-crossing point of the line segmentation and the first polynomial coefficient ($\beta $) corresponds to the slope, which is then used to estimate the alignment error. To convert the coefficients into pixel values, we further define the spectrometer offset (${c_0}$) and tilt (${c_1}$) index as

 

Fig. 2. Correlation matrix in two types of spectrometers. White dotted lines indicate diagonal elements.

Download Full Size | PDF

The accuracy of the alignment estimation in image-based cross-calibration was compared to the optimization-based spectral remapping [5]. For the optimization-based method, a set of calibration interferogram signals were acquired from a mirror using the same system setups. Table 1 shows the comparison of the coefficients using two different calibration approaches. In both spectrometer cases, pixel correspondence estimation from the CM method shows good correspondence with the optimization-based approach. Moreover, the CM method has the advantages of less computational load and convenience without the need to acquire calibration mirror data. In our case, the mean processing time of the optimization and the CM method are 52 seconds and 0.38 seconds, respectively. The custom spectrometer pair achieved a higher degree of coalignment compared to the commercial spectrometer pair through the guidance of the mechanical alignment based on the CM method.

Table 1. Coalignment in Spectrometer Pairs

View Table | View all tables in this article

Aside from guiding the mechanical alignment, a numerical spectrometer calibration can be performed. In spectral remapping, one of the spectrometer’s data are interpolated based on a remap look-up-table (rLUT) to computationally match the target spectrometer data to the reference spectrometer data. The rLUT is defined as

 

Fig. 3. Degree of coalignment evaluated thorough mirror measurements. (a) Comparison of signal amplitude roll-off and (b) noise background.

Download Full Size | PDF

Next, the improvement in OCT and optical coherence tomography angiography (OCTA) image quality in dual-balanced detection SD-OCT was evaluated qualitatively by using retinal data acquired from a healthy adult volunteer. The data were acquired using a 3-BM step bidirectional scan protocol [10], where three repeated B-scans are acquired in a single location. A total of 1500 B-scans were acquired with each B-scan consisting of 500 A-lines from each spectrometer and at 250-kHz A-line rates. Then, the OCTA data were processed with a complex variance algorithm [11].

Figure 4 shows representative B-scan OCT images before and after applying different spectral remapping approaches. To enhance the visibility of the retinal structures and to emphasize the effects of calibration, all the representative OCT B-scan images were constructed by performing magnitude averaging of five neighboring B-scans. Before the calibration, certain fine retinal features such as external limiting membrane (ELM), photoreceptors, and retinal pigmented epithelium (RPE) are blurred due to the ineffective spectral summation. This is because the misalignment causes the interference fringes of two different frequencies to be subtracted, leading to degradation of axial resolution and doubling of image features. In addition, the signal intensity of the inner retina is drastically reduced. Above the retinal surface, an inconsistent noise floor can be seen near DC, similar to what was observed in the mirror testing. After the spectral calibration, the overall image contrast is substantially improved. Furthermore, outer retinal layers are clearly visible in the B-scan images, indicating the improvement in the axial resolution. Interestingly, no noticeable difference was observed in the image contrast between the two numerical remapping approaches.

 

Fig. 4. Qualitative comparison of averaged B-scan retinal image quality. Green boxes indicate areas of enlarged view. Yellow and white boxes indicate selected signal and background portions for CNR estimation. Scale, 250 µm.

Download Full Size | PDF

Figure 5 shows OCTA projections of the retina centered at the fovea. To visualize superficial vessels and deep vessels separately, the data were further segmented in a superficial and deep retinal layer, respectively, using a deep learning algorithm [12]. The same segmentation lines were applied to both no-calibration data and calibrated data. Similar to OCT contrast, noise is noticeably suppressed, and vessel boundaries are visualized more distinctively once the spectrometers are numerically aligned. In the superficial retinal layer, capillary networks interconnecting large vessels and venules are obscured without calibration, as indicated by white arrows. After numerical alignment that is based on the optimization and CM, the visibility of capillary networks is noticeably improved. The improvement in the vascular visibility can be appreciated even more in the deep retinal layer that consists of a dense capillary network. Furthermore, the avascular zone can be better distinguished once the spectrometer is calibrated, as shown by the yellow arrows. Again, no apparent differences in the image quality were found between the two calibration methods.

 

Fig. 5. Qualitative comparison of OCTA images of (top) superficial and (bottom) deep vascular plexus. Scale, 500 µm.

Download Full Size | PDF

For quantitative comparison, two image quality metrics were evaluated: peak signal-to-noise ratio (PSNR) and contrast-to-noise ratio (CNR) [13,14]. The PSNR is defined as

Table 2 describes the image quality metrics estimated based on the retinal OCT data shown in Fig. 4. For PSNR, the ROI for noise estimation was set as the background area below the choroid. PSNR is calculated from all 500 B-scans, and the mean values and standard deviation are compared among different calibration methods. B-scans without numerical calibration have more than 5 dB lower PSNR compared to both calibration methods, while the PSNR values between optimization and CM methods are comparable. For CNR, the signal portions are set as 20 ${\times} $ 40 pixel areas within the inner plexiform layer (IPL) and RPE layer of the retina, marked as yellow boxes, and background portions for CNR are above the retinal surface, depicted as white boxes in Fig. 4. In both IPL and RPE areas, CNR is significantly improved after calibration.

Table 2. Image Quality Metrics

View Table | View all tables in this article

In conclusion, we demonstrated that spectrometer cross-calibration can be performed using a pair of OCT B-scan images acquired with a dual spectrometer configuration. The accuracy of alignment is comparable to the optimization-based calibration with little to no differences in the resulting image quality between the two methods. This technique could be applied to any multi-spectrometer-based OCT system, including polarization-sensitive OCT, making it a simple and robust calibration method.