2.1.

Calibration Object

Figure 1 shows a diagram of the cross-section of the circular calibration object, which combines two distinct technologies: single-point diamond turning to create surfaces with optical precision and a polyurethane-titanium dioxide solid setting liquid used as tissue-mimicking phantom material. The base is composed of a 2-in. diameter and $\sim 1$-in. high cylinder made of aluminum: an inexpensive, stable material easily machined to optical quality surface roughness. A well is machined on top of the cylinder, which is then filled with an imaging phantom material developed to mimic biological tissues.

Fig. 1

Cross-section of the calibration object. (a) The cross-section of the target, with the well cut into the top of an aluminum cylinder, which is then filled with a tissue-mimicking material. A close-up of the rectangular region can be found in (b), where the step profile is described.

2.1.1.

Aluminum well fabrication

The aluminum cylinder, which forms the base, was machined into a well using single-point diamond-turning on a Nanotech 250UPL diamond-turning lathe (Moore Nanotechnology Systems, Keene, New Hampshire). With the ability to create large optical free-form surfaces in a reasonable time frame with a shape precision better than $1\mu \mathrm{m}$, diamond-turning has the ability to create high quality and durable calibration objects. The $0.1\mu \mathrm{m}$ accuracy of this lathe is more than adequate for the creation of calibration objects for the OCT systems.

The circular symmetry of the lathe is exploited to create mirror rings as the machine cuts along one linear axis during the rotation of the metal base. The well base is composed of concentric rings of 1.000-mm wide mirror surfaces, each ring descending by 100.0 microns toward the center. In order to ensure a smooth machining process, 0.800-mm wide sloping transition zones between the flat rings were included in the design. Ten steps were cut, for a total well depth from top to bottom of 1.000 mm. The surface was cut by a single diamond tool (K&Y Diamond, Montreal, Canada) having a radius of curvature of 0.536 mm. Fifty machining steps using 25-micron deep cuts were necessary to create the well. The final surface was produced by performing a last 2.5-micron cut with mineral spirits spray for lubrication, a feed rate of $5\mathrm{mm}/\min$, and a spindle speed of $2000\text{rotation}/\min$. Figure 2(a) shows the base after machining before being filled with the phantom material. Measurements of the well with an optical profilometer (Micromesure, STIL SA, France) show that the actual axial and lateral positions of the step edges vary less than 0.3% from the specified values and that each mirror plateau has a flatness better than 200 nm.

Fig. 2

The calibration object (a) before and (b) after being filled with phantom material. In (b), after it has been filled with phantom material, the top surface was machined to produce a smooth, flat interface parallel to the object bottom surface.

2.2.

Automatic Analysis

The algorithm that was developed for the automatic analysis as well as a calibration data set is discussed in Ref. 13,14. The software was written using Python, and the main algorithm steps are given in Fig. 3.

Fig. 3

Automated optical coherence tomography (OCT) benchmarking algorithm. Orange, yellow, and blue boxes represent the inputs, processing steps, and outputs, respectively.

For input, the algorithm uses a stack of B-scans of the calibration object plotted in dB and saved as individual 8-bit grayscale image files. When acquiring and saving a stack of B-scans, the user should set the acquisition parameters and image dynamic range to maximize the 8-bit scale use while preventing saturation and setting the noise floor above zero in the 8-bit image scale. The imaged area should encompass a maximum number of well plateaus, including the deepest one. The sampling pitch in all dimensions should be better than $10\mu \mathrm{m}$, and the image volume should be larger than $8\mathrm{mm}\times 8\mathrm{mm}$ laterally and 3.5 mm axially. An example of such a dataset is presented in Fig. 4. In addition to the OCT images, the user must manually select the region of interest (ROI) where the steps of the well are located [see Fig. 4(b)] as well as the corresponding dynamic range in decibel.

Fig. 4

(a) Three-dimensional view of a C-scan of the calibration object ($1075\times 1075$ A-lines)—fast ($x$), slow ($y$), and optical ($z$) axes shown in blue. (b) Typical B-scan showing the limits of the user-selected region of interest (ROI) (solid blue lines) encompassing the second interface. (c) Typical A-line (after binning) showing interfaces detected by the algorithm (dashed red lines). Orange-highlighted area corresponds to the user-selected ROI. Insets show normalized reflectance for each interface in linear scale, used to automatically compute the full width at half maximum (FWHM)—dashed red lines.

All operations described henceforth are performed automatically. The first operation converts each A-line back to a linear scale and bins 49 adjacent A-lines (seven consecutive A-lines from seven consecutive B-scans) to improve the SNR. Each binned A-line is then analyzed to measure the properties (intensity and coordinates) of two reflectivity peaks related to the air-phantom interface and the phantom-aluminum interface. Detection of each interface is performed by finding the maximum reflectivity inside and outside the ROIs defined by the user [see Fig. 4(c)].

For each peak, the algorithm records its axial position, its full width at half maximum (FWHM), and its SNR, defined as the ratio between the peak amplitude and the noise standard deviation. To calculate the noise floor and its standard deviation, a portion of the binned A-line where no reflectors are present is used. This region is located just after the second interface (metallic) and is one-tenth of the A-line long. We also fit the attenuation length and amplitude of the signal from the phantom between both interfaces. This fit is used to calculate the signal-to-background ratio (SBR) for each interface—the amplitude ratio between the interface reflection and the phantom signal. An example of extracted features for the two surfaces is shown in Fig. 5. At this point, all coordinates are measured in pixel units.

Fig. 5

En face views and corresponding lookup table showing the parameters extracted from each set of averaged A-lines. (a)–(c) show features related to the first (air-phantom) interface, whereas (d)–(g) are related to the second (phantom-aluminum) interface: (a) and (d) signal-to-noise ratio, (b) and (e) axial position, (c) and (f) axial FWHM, and (g) computed ROIs used to calculate the system properties at each mirror step.

In the next operation, the position of the second surface is subtracted from the position of the first surface to obtain a two-dimensional (2-D) map of the phantom thickness. Using the phantom thickness instead of the second interface coordinate directly removes most of the distortion and tilt and allows fitting of the theoretical well shape more easily. This fit uses six degrees of freedom: three for position and three for scaling. After completion, the scale factors that minimize the fit error give the pixel-to-micron conversion factor for each dimension. At this point, all pixel measurements can be transformed into physical distances. Moreover, the knowledge of the object position allows creating ROIs specific to each well step, as represented in Fig. 5(g). In each ROI, the algorithm extracted statistics for: mean, median, minimum and maximum signal; standard deviation of its axial position; axial response FWHM; and SNR. The FWHM of the axial response was calculated only for points where both SNR and SBR were higher than 10 to avoid artificial broadening of the axial response. Finally, a fit of the first-interface coordinate image with a biconic function was performed to assess the en face OCT image curvature.

2.3.

Optical Coherence Tomography System Benchmarking

The proposed method was applied to a commercial OCT system whose specifications are listed in Table 1. The calibration object was placed under the OCT objective lens so as to maximize the number of mirror segments—including the bottom of the well—visible within the image FOV. An OCT volume was acquired and exported as a stack of 2-D cross-sectional images. After opening the 3-D stack with an image stack viewer such as Fiji,¹⁵ the ROI where the well steps were located was defined. The ROI selection is performed by looking at the whole 3-D scan, considering some mirror steps may not be visible in every frame. This ROI, along with the directory of the image stack and the dB range of the acquisition (the absolute values of the range limit are not necessary, only the range), were fed to the calibration software. The software automatically saves calibration results (images and text report). The whole procedure takes less than 10 min from placing the calibration object to generating the report. From those 10 min, only 2 min are used to run the algorithm on a conventional office computer.

Table 1

Optical coherence tomography system specifications

3.1.

Geometric Calibration

An OCT acquisition can be seen as a collection of reflectance measurements taken at different positions in 3-D in a sample. The knowledge of the position of these samples is necessary to form an image or to do any geometrical measurement. In many cases, it is assumed that the sample points follow a rectangular grid with a constant spacing in any given direction. In practical implementations, this is never the case. For example, the OCT system used for this study relies on two dual-axis galvanometer mounted mirrors to scan the beam over the sample. As illustrated in Fig. 7, in a perfect image-space telecentric system, every output beam is parallel to the optical axis. In such a case, the OCT data geometry matches the Cartesian geometry of the reference frame of the laboratory. However, when the pupil position is not exactly placed at the back focal plane of the objective lens, OCT data are acquired with a spherical geometry. In the case of dual-axis galvanometer systems, only one scanning mirror can be placed at the objective pupil position. Hence, these systems cannot be telecentric in both dimensions. Nonlinear beam scanning, pupil aberration, and propagation in a nonhomogeneous medium can also alter the OCT data geometry. It is therefore necessary to measure the OCT data geometry before performing any geometric measurements.

Fig. 7

Illustration of (a) telecentric and (c) nontelecentric scanning mechanisms. P, P’, F, and F’ are the pupil plan, the image of the pupil plane, and the front and back focal planes, respectively. Ref planes traced in blue illustrate the virtual image of the OCT reference plane. In an object-telecentric setup, the pupil plane and the focal plane are collocated. (b) and (d) The resulting B-scan geometry of (a) and (c), respectively. ($x$, $y$, $z$) is a Cartesian system associated with the laboratory, where $z$ matches the optical system axis. The red-highlighted zone corresponds to a single A-line. ISP (image of the scanning point) is plotted.

The geometric calibration is performed in two steps. The first step seeks the Cartesian system that best matches the data set. The second step aims at measuring the volume distortion from the perfect grid found in the first step.

The first step uses the overall shape of the well obtained by the OCT 3-D acquisition to find the pixel-to-micrometer scale ratio that fits the theoretical shape of the well. The measured scale factors for each experiment are presented in Fig. 6(c), as well as the system’s specified values. By averaging results from the five tests, $x$-, $y$-, and $z$-axes scale ratio of $9.78\pm 0.06$, $9.92\pm 0.03$, and $9.29\pm 0.02\mu \mathrm{m}/\text{pixel}$ are measured, respectively. The 1% error between experiments shows the robustness of the proposed method. Moreover, the results are consistent with the values given by the system specifications ($x$: $9.77\mu \mathrm{m}/\text{pixel}$, $y$: $9.77\mu \mathrm{m}/\text{pixel}$, and $z$: $9.30\mu \mathrm{m}/\text{pixel}$). In the axial dimension, the ratio uncertainty does not only depend on the 3-D fitting error but also on the uncertainty of the refractive index of the phantom material, as OCT measures optical path differences. An additional uncertainty due to refractive index has to be added to the measured $z$-axis scale, hence a $z$-scale factor of $9.29\pm 0.13\mu \mathrm{m}/\text{pixel}$. Overall, the method provides volume size with 2% accuracy in all axes.

For the second step, the curvature of the air-phantom interface in the acquired volume is measured using a biconical fit that models defocusing. The curvatures for each test in each axis are shown in Fig. 6(d). The mean curvatures are zero in the $xz$-plane and $3.2\pm 0.1{\mathrm{m}}^{-1}$ in the $yz$-plane. Any curvature is due to an error in the pupil position or to pupil imaging aberrations and could be increased by any nonlinearity of the galvanometer scan. If the pupil position error is considered as the principal source of distortion, the measurement of this curvature is sufficient to correct the whole volume distortion. Indeed, from this curvature, it is possible to deduce the position of the image of the scanning point (ISP), and a spherical-to-Cartesian coordinates transformation can then be used to correct the volume geometry, as shown in Fang et al.¹⁶

3.2.

Axial Resolution

The axial resolution is obtained by measuring the FWHM of a signal peak due to the reflection from an interface. Figure 6(e) plots the mean and standard deviation axial response FWHM of each mirror segment for each test as well as for the first interface. The smallest and largest measured FWHM are 18.1 and $21.1\mu \mathrm{m}$, respectively. The maximum standard deviation for all those individual measurements is $2\mu \mathrm{m}$. FHWM decreases with depth within the phantom but not with absolute position with respect to the reference mirror. This suggests that the effect is due to the lower SNR at greater depth as opposed to nonlinear $k$-space sampling, a mechanism that would otherwise cause the FWHM to increase with distance from the reference plane. Overall, the measured axial FWHM is $20\pm 2\mu \mathrm{m}$ independently of the depth where it was measured. To validate our method, the axial response was also measured with the conventional procedure, which relies on scanning a mirror across the axial FOV. The mirror-scanning method yielded an FWHM of $21\pm 1\mu \mathrm{m}$. Both measurements are within 5% of each other, but differ from the specified resolution ($16\mu \mathrm{m}$). This may come from variation in the laser spectrum since its purchase. This shows the importance monitoring a system’s performance over time.

3.3.

Intensity Response Calibration

Calibration and benchmarking of OCT system signal intensity are mainly done using two parameters. The first is the system depth-dependent ability to detect a reflector, known as system fall-off or roll-off. The second is the system sensitivity, which corresponds to the reflectance level required to produce an SNR of 1 (or 0 dB).

Fall-off measurements are usually performed by axially translating a mirror. As the mirror reflectivity is constant, any detected signal variation is due to the system. Sensitivity (linear ratio) is obtained by dividing the SNR measured for a known reflector by its reflection coefficient.

The calibration object was first designed to allow measuring sensitivity and roll-off. Indeed, the combined knowledge of the phantom’s attenuation coefficient, its thickness above a particular mirror segment, and the absolute reflectivity of each mirror segment should have allowed for sensitivity measurements. Additionally, the multiple mirror segments positioned at increasing depth should have enabled system fall-off measurements. In practice, however, without controlling the tilt of the calibration object, and, moreover, with the system’s optics causing distortion, the variation in incidence angle and consecutively in collected specular reflection (with lateral position and in between tests) adds too much uncertainty to obtain an absolute reflectivity measurement.

As shown in Fig. 5(a), collected specular reflection varies by up to 30 dB from the first interface signal intensity. It is also shown in Fig. 6(f), which plots the attenuation slope in the mirror step regions. These values are obtained from the variation of median reflectivity for each step as a function of depth. The attenuation slope ranges from $-11$ to $-19\mathrm{dB}/\mathrm{mm}$ for tests 1 and 2, respectively. Overall, such uncertainties prevent any sensitivity or fall-off characterization and will be addressed in a future iteration.