Variations in optical coherence tomography resolution and uniformity : a multi-system performance comparison

Point spread function (PSF) phantoms based on unstructured distributions of sub-resolution particles in a transparent matrix have been demonstrated as a useful tool for evaluating resolution and its spatial variation across image volumes in optical coherence tomography (OCT) systems. Measurements based on PSF phantoms have the potential to become a standard test method for consistent, objective and quantitative inter-comparison of OCT system performance. Towards this end, we have evaluated three PSF phantoms and investigated their ability to compare the performance of four OCT systems. The phantoms are based on 260-nmdiameter gold nanoshells, 400-nm-diameter iron oxide particles and 1.5micron-diameter silica particles. The OCT systems included spectraldomain and swept source systems in free-beam geometries as well as a time-domain system in both free-beam and fiberoptic probe geometries. Results indicated that iron oxide particles and gold nanoshells were most effective for measuring spatial variations in the magnitude and shape of PSFs across the image volume. The intensity of individual particles was also used to evaluate spatial variations in signal intensity uniformity. Significant system-to-system differences in resolution and signal intensity and their spatial variation were readily quantified. The phantoms proved useful for identification and characterization of irregularities such as astigmatism. Our multi-system results provide evidence of the practical utility of PSF-phantom-based test methods for quantitative intercomparison of OCT system resolution and signal uniformity. ©2014 Optical Society of America OCIS codes: (170.4500) Optical coherence tomography; (110.3000) Image quality assessment; (110.4850) Optical transfer functions; (350.4800) Optical standards and testing. References and Links 1. P. H. Tomlins, P. Woolliams, M. Tedaldi, A. Beaumont, and C. Hart, “Measurement of the three-dimensional point-spread function in an optical coherence tomography imaging system,” Proc. SPIE 6847, 68472Q (2008). 2. A. Agrawal, T. J. Pfefer, N. Gilani, and R. Drezek, “Three-dimensional characterization of optical coherence tomography point spread functions with a nanoparticle-embedded phantom,” Opt. Lett. 35(13), 2269–2271 (2010). 3. G. Lamouche, B. F. Kennedy, K. M. Kennedy, C.-E. Bisaillon, A. Curatolo, G. Campbell, V. Pazos, and D. D. Sampson, “Review of tissue simulating phantoms with controllable optical, mechanical and structural properties for use in optical coherence tomography,” Biomed. Opt. Express 3(6), 1381–1398 (2012). 4. A. Curatolo, B. F. Kennedy, and D. D. Sampson, “Structured three-dimensional optical phantom for optical coherence tomography,” Opt. Express 19(20), 19480–19485 (2011). #205897 $15.00 USD Received 10 Mar 2014; revised 30 May 2014; accepted 30 May 2014; published 9 Jun 2014 (C) 2014 OSA 1 July 2014 | Vol. 5, No. 7 | DOI:10.1364/BOE.5.002066 | BIOMEDICAL OPTICS EXPRESS 2066 5. T. S. Rowe and R. J. Zawadzki, “New developments in eye models with retina tissue phantoms for ophthalmic optical coherence tomography,” Proc. SPIE 8229, 822913 (2012). 6. S. Tahara, H. G. Bezerra, M. Baibars, H. Kyono, W. Wang, S. Pokras, E. Mehanna, C. L. Petersen, and M. A. Costa, “In vitro validation of new fourier-domain optical coherence tomography,” EuroIntervention 6(7), 875– 882 (2011). 7. A. Agrawal, C.-W. Chen, J. Baxi, Y. Chen, and T. J. Pfefer, “Multilayer thin-film phantoms for axial contrast transfer function measurement in optical coherence tomography,” Biomed. Opt. Express 4(7), 1166–1175 (2013). 8. P. H. Tomlins, R. A. Ferguson, C. Hart, and P. D. Woolliams, “Point-spread function phantoms for optical coherence tomography,” (NPL Report OP 2, Teddington, Middlesex, UK, 2009). 9. T. J. Pfefer and A. Agrawal, “A review of consensus test methods for established medical imaging modalities and their implications for optical coherence tomography,” Proc. SPIE 8215, 82150D (2012). 10. E. A. Berns, R. E. Hendrick, and G. R. Cutter, “Performance comparison of full-field digital mammography to screen-film mammography in clinical practice,” Med. Phys. 29(5), 830–834 (2002). 11. C.-C. Chen, Y.-L. Wan, Y.-Y. Wai, and H.-L. Liu, “Quality assurance of clinical MRI scanners using ACR MRI phantom: Preliminary results,” J. Digit. Imaging 17(4), 279–284 (2004). 12. D. A. Jaffray and J. H. Siewerdsen, “Cone-beam computed tomography with a flat-panel imager: Initial performance characterization,” Med. Phys. 27(6), 1311–1323 (2000). 13. A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: A review of clinical development from bench to bedside,” J. Biomed. Opt. 12(5), 051403 (2007). 14. International Electrotechnical Commission, “Ultrasonics – pulse-echo scanners – part 1: Techniques for calibrating spatial measurement systems and measurement of system point-spread function response,” STD568116 (Swedish Standards Institute, Geneva, Switzerland, 2006). 15. G. J. Brakenhoff, H. T. M. van der Voort, E. A. van Spronsen, and N. Nanninga, “Three-dimensional imaging by confocal scanning fluorescence microscopy,” Ann. N. Y. Acad. Sci. 483(1 Recent Advanc), 405–415 (1986). 16. A. K. Dunn, V. P. Wallace, M. Coleno, M. W. Berns, and B. J. Tromberg, “Influence of optical properties on two-photon fluorescence imaging in turbid samples,” Appl. Opt. 39(7), 1194–1201 (2000). 17. S. Hell, “Increasing the resolution of far-field fluorescence light microscopy by point-spread-function engineering,” in Topics in Fluorescence Spectroscopy; volume 5: Nonlinear and Two-Photon-Induced Fluorescence, J. Lakowicz, ed. (Plenum Press, New York, 1997). 18. A. Agrawal, M. Connors, A. Beylin, C.-P. Liang, D. Barton, Y. Chen, R. A. Drezek, and T. J. Pfefer, “Characterizing the point spread function of retinal OCT devices with a model eye-based phantom,” Biomed. Opt. Express 3(5), 1116–1126 (2012). 19. P. D. Woolliams, R. A. Ferguson, C. Hart, A. Grimwood, and P. H. Tomlins, “Spatially deconvolved optical coherence tomography,” Appl. Opt. 49(11), 2014–2021 (2010). 20. P. D. Woolliams and P. H. Tomlins, “Estimating the resolution of a commercial optical coherence tomography system with limited spatial sampling,” Meas. Sci. Technol. 22(6), 065502 (2011). 21. E. F. Schubert, “Refractive index and extinction coefficient of materials” (2004), retrieved 11/1/2013, http://homepages.rpi.edu/~schubert/Educational-resources/Materials-Refractive-index-and-extinctioncoefficient.pdf. 22. P. Patnaik, Handbook of Inorganic Chemicals (The McGraw-Hill Companies, Inc., 2002). 23. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965). 24. Q. Li, M. L. Onozato, P. M. Andrews, C.-W. Chen, A. Paek, R. Naphas, S. Yuan, J. Jiang, A. Cable, and Y. Chen, “Automated quantification of microstructural dimensions of the human kidney using optical coherence tomography (oct),” Opt. Express 17(18), 16000–16016 (2009). 25. D. X. Hammer, N. V. Iftimia, R. D. Ferguson, C. E. Bigelow, T. E. Ustun, A. M. Barnaby, and A. B. Fulton, “Foveal fine structure in retinopathy of prematurity: An adaptive optics Fourier domain optical coherence tomography study,” Invest. Ophthalmol. Vis. Sci. 49(5), 2061–2070 (2008). 26. A. Agrawal, S. Huang, A. Wei Haw Lin, M. H. Lee, J. K. Barton, R. A. Drezek, and T. J. Pfefer, “Quantitative evaluation of optical coherence tomography signal enhancement with gold nanoshells,” J. Biomed. Opt. 11(4), 041121 (2006). 27. S. S. Rogers, T. A. Waigh, X. Zhao, and J. R. Lu, “Precise particle tracking against a complicated background: Polynomial fitting with Gaussian weight,” Phys. Biol. 4(3), 220–227 (2007). 28. S. Prahl, “Mie scattering calculator (web site)” (2012), retrieved 10/16/2013, http://omlc.ogi.edu/calc/mie_calc.html. 29. J. Pfefer, A. Fouad, C.-W. Chen, W. Gong, P. Tomlins, P. Woolliams, R. Drezek, A. Agrawal, and Y. Chen, “Multi-system comparison of optical coherence tomography performance with point spread function phantoms,” Proc. SPIE 8573, 85730C (2013). 30. B. Cense, N. Nassif, T. Chen, M. Pierce, S.-H. Yun, B. Park, B. Bouma, G. Tearney, and J. de Boer, “Ultrahighresolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12(11), 2435–2447 (2004). 31. S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, “Measurement of the 4pi‐confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994). #205897 $15.00 USD Received 10 Mar 2014; revised 30 May 2014; accepted 30 May 2014; published 9 Jun 2014 (C) 2014 OSA 1 July 2014 | Vol. 5, No. 7 | DOI:10.1364/BOE.5.002066 | BIOMEDICAL OPTICS EXPRESS 2067 32. A. C. Akcay, J. P. Rolland, and J. M. Eichenholz, “Spectral shaping to improve the point spread function in optical coherence tomography,” Opt. Lett. 28(20), 1921–1923 (2003).


Introduction
Advances in optical coherence tomography (OCT) technology over the past 20 years have led to its widespread clinical acceptance for retinal imaging as well as its emergence for other indications such as intravascular and endoscopic imaging.Despite the success of this field and the increasing variety of OCT-based techniques, relatively little progress has been made in developing standardized test methods for evaluation of OCT systems.These approaches are important for a variety of reasons, including system development and optimization, calibration, and quality control during manufacturing and clinical use, including human trials.Evaluation of OCT system resolution has commonly involved either a very simple quantitative benchtop approach -measurement of a specular surface -or subjective visualization of in vivo or ex vivo tissue images.In recent years, there has been a movement towards development of phantom-based techniques for OCT system resolution and other image quality parameters [1][2][3][4][5][6][7][8].These approaches parallel those found in international consensus performance standards for established imaging modalities such as X-ray computed tomography, magnetic resonance imaging and ultrasound [9].In these standards, phantoms with well-defined structures and material properties form the basis of test methods used to quantify device performance prior to device acceptance into clinical use and during periodic quality assurance evaluations, or even to compare the performance of different systems [10][11][12][13].While the list of performance characteristics varies greatly from document to document, the most widely referenced parameter is spatial resolution.Two of the most common methods for evaluating resolution involve the use of periodic structures in a phantom at a range of separation distances, as in the 1951 USAF resolution test chart, and small, high-contrast inclusions such as beads or filaments to determine point and line spread functions [14].
The concept of point spread function (PSF) phantoms incorporating sub-resolution particles for evaluation of spatial resolution has been utilized for other types of optical imaging systems, including confocal microscopy [15] and two-photon fluorescence microscopy [16].In addition to determining resolution in terms of individual values (e.g., full-width-half-maximum (FWHM) in 3D Cartesian coordinates), these phantoms have been used for point spread function engineering.This approach involves characterizing the shape of a point spread function (typically an irregular one) and then modifying system characteristics to optimize the shape of the PSF, thus improving system resolution [17].The use of highly scattering dispersed particles for OCT system resolution evaluation has been studied by several groups [1,2,[18][19][20].In these studies, randomly distributed particles are used to evaluate and quantify the PSF along all three spatial axes.Variations in PSF throughout the image volume can then be used to identify regions of optimal and sub-optimal resolution.Prior studies have provided quantitative validation of this approach against standard techniques such as specular surface measurements and beam profiling and studied its viability for evaluating retinal OCT systems using a model eye [2,18].To date, there has been minimal data providing a comparison of materials for PSF phantom fabrication.Furthermore, the ability of PSF phantoms to provide quantitative, objective inter-comparisons of image quality between OCT systems has not yet been established.
The purpose of the current study was to advance the understanding of PSF phantoms towards standardization of performance testing as well as to provide novel, quantitative insights into system-to-system variations.Specifically, our goals were to perform resolution and intensity measurements with PSF phantoms based on three different high-contrast particles using four OCT system formats incorporating different technologies and designs, including free-beam and catheter-based delivery systems.The results from these measurements were then analyzed to evaluate the phantoms and the ability of this approach to characterize OCT system performance.

Methods
This study involved experimental methods for phantom fabrication and measurement with OCT systems as well as the analytical methods for converting image files into quantitative metrics for assessment of image quality.

PSF phantom development
The first phantom (labeled "Nano") was fabricated at the Food and Drug Administration and is similar to those described in our prior studies [2,18].The nanoshells used in this phantom were fabricated at Rice University, and were comprised of a silica core of 224 nm diameter and 18-nm-thick gold shell.The matrix consisted of a UV-curing epoxy (Light Weld 4-20577, DYMAX Corp., Torrington, CT).The remaining two PSF phantoms were prepared at the National Physical Laboratory in the UK.The second phantom (labeled "FeO") incorporated red iron (III) oxide spheroidal nanoparticles (07674, Polysciences, Inc., USA) in a matrix of two-part polyurethane resin (DR006, Atlas Polymers, UK).The FeO particles have a diameter of 300-800 nm.Further description of this phantom and its fabrication is provided in a prior article [19].The third phantom (labeled "Silica") incorporated silica microspheres (1.5 μm mean diameter, MSS001a, Whitehouse Scientific, Ltd., UK) embedded in an epoxy matrix (Araldite DBF resin + Araldite HY951 hardener, Huntsman International, LLC).Assembly of each phantom from raw components was completed in under two days.
The designed concentration of nanoshells in the Nano phantom was 10 7 particles per ml, which corresponds to each particle occupying, on average, a cubic volume of size 56 3 μm 3 .The FeO phantom was denser, with particles designed to occupy a cube of matrix with side length between 25 and 50 μm.The Silica phantom was not designed for a specific density, but was later found to be much less sparsely packed than the other two phantoms.A summary of these phantoms and the indices of refraction for each of their matrix and particle components is presented in Table 1.Typical B-scan images from each phantom are shown in Fig. 1.Particle concentration is not designed to vary in X, Y or Z. Particle densities of all three phantoms as estimated from OCT imaging are shown in Table 2.These approximations were determined by measuring the number of PSFs found in a volume ± 100 µm from the apparent focal plane in TDOCT images.The TDOCT system was used for this measurement because it has the smallest axial pixel spacing, and accordingly, its PSFs were least likely to be excluded due to clustering or other quality checks (a description of our PSF filters follows in section 2.3.2).On average, these values correspond with each nanoshell, iron oxide particle or silica particle occupying a volumetric cube measuring 58, 51 or 102 μm per side, respectively.

OCT systems
Four OCT system/geometry combinations were studied: a time-domain OCT system with sample/collection arm in free beam (TDOCT) and intravascular fiberoptic probe (IV-TDOCT) configurations, a spectral domain OCT system in free-beam format (SDOCT) and a swept-source system in free-beam format (SSOCT).Key specifications of each system are provided in Table 3.The TDOCT system is a fiberoptic common-path interferometer.The IV-TDOCT variant used the same light source and sample scanning mechanism, but incorporated the commercially available fiberoptic probe with unknown optics.We include this setup as an example of an optical "black box" system with behavior that can be revealed with PSF measurements.Instead of using a common path interferometry approach, a reference arm was constructed and the fiberoptic probe was immersed in water to minimize the first-surface specular reflection.Lateral scans were performed as for TDOCT.Images were corrected for micron-scale catheter vibration before post-processing.Using an automatic algorithm, the interface between the probe and the water in each A-scan (Z data) was detected and the entire vector was shifted axially until this interface appeared at the same axial position in each Ascan.

OCT imaging
In all phantom imaging data presented here, an X, Y, Z spatial convention was used where Z represents the axial direction and an XZ plane denotes a B-scan.During experiments, we attempted to set the focal plane of each system 300-1000 μm below the surface of each sample in order to capture the focusing effect.Except when precluded by system limitations, the pixel size of each system in the X, Y and Z directions was set < 3µm, which allows sampling of 5-15 pixels per PSF in each direction.Exceptions were made for the Z-direction on SSOCT (5.0 µm, fixed) and the X and Y directions on IV-TDOCT (4.0 µm, chosen to capture a large number of PSFs)."Narrow scans" were < 1 mm 2 in area; "wide scans" totaled 8.3 by 6.7 mm (SSOCT) and 2.4 by 0.5 mm (SDOCT).Narrow scans were located at the center of the wide scans.For the SSOCT and SDOCT systems, 8-10 3D scans were recorded serially and averaged to reduce random noise.For the TDOCT and IV-TDOCT systems, 5 Ascans at each lateral position were averaged.All OCT signal intensity data was converted to linear format before FWHM calculations.In order to maintain pixel sizes of <3 µm, the SSOCT wide scan data consisted of 21 (7x3) narrow scans of adjacent locations stitched together before post-processing.Because of the quantity of data collected, each of these 21 narrow scans was imaged serially only 4 times for averaging.

Post-processing algorithm
Matlab (Mathworks, Natick, MA) code was developed for post-processing tasks.First, a portion of a freely available algorithm [27] was adopted to automatically locate maxima in the 3D data set.PSFs were extracted as the center of a small data cube surrounding each maximum (generally 21 by 21 by 21 voxels in size), but excluded from consideration if the cube contained multiple maxima, or was located above or below the apparent depth range of PSFs.For tightly packed particles such as those within the FeO phantom, the former constraint supports the condition that any analyzed volume contains a single PSF.The peak intensity and FWHM size (X, Y and Z) of each PSF was measured, the latter using three 1D Gaussian fits to minimize sampling errors [2,18].Axial side lobes were excluded from the fit for the SDOCT by fitting only between the two minima immediately surrounding the peak.Candidate PSFs were also discarded if they had poor Gaussian fits (r 2 <0.85) in the X or Y directions.
Finally, PSFs were grouped by depth into bins of size 100 µm in the Z direction, and outliers (such as falsely identified noise or scatterers composed of multiple particles) with FWHM or intensity values greater than ± 1.5 standard deviations from the mean value in each bin were removed.This simplistic deletion rule was compared against a more rigorous Thompson analysis of outliers on the SSOCT system and found to be more permissive and yield mean FWHM-vs-depth curves within 0.09 µm (mean difference) of curves obtained using a Thompson deletion rule (data not shown).
Data visualization was also performed with Matlab, and included plots of FWHM and intensity versus 3D position.We have made our code (including relevant functions adapted from other groups, with attribution) and documentation available for download at the following web address: http://terpconnect.umd.edu/~yuchen/PSF2.zip.

PSF phantom comparison
A comparison of results from all three phantoms based on SSOCT system measurements is provided in Fig. 2.These data enable a direct quantitative comparison of each parameter studied.Excellent agreement in X-, Y-and Z-FWHM values (Fig. 2(a), 2(b), 2(c) respectively) as a function of depth is evident for FeO and Nano phantoms.Even the largest (~1µm) difference between the Y-FWHMs of the FeO and Nano phantoms lies well within the combined variabilities of each measurement, and a mean difference (MD) of 0.55 µm exists between the curves.The agreement between X-FWHMs (SSOCT B-scan) is even stronger, with a MD of 0.046 µm.For Z-FWHMs, the Silica phantom yielded slightly higher sizes than the FeO and Nano phantoms, with MD values of 0.72 µm against Nano and 1.7 µm against FeO.Corresponding measurements of Z-FWHM from a specular surface indicated an axial FWHM of 9.7 µm, which is closest to the axial result from FeO.
As shown in the intensity overlay plot (Fig. 2(d)), the FeO and Nano phantoms provided evidence of an intensity maximum ~600 µm below the phantom surface, while the silica phantom generally produced weaker PSFs with a depth trend that was less certain.Beginning around Z = 1200 µm, rolloff dramatically accelerates the signal decay, although it never reaches a noise floor within the recordable depth window.

Resolution as a function of depth
Due to their relative consistency and high PSF densities, the Nano and FeO phantoms were used to compare the performance of the four OCT systems.The PSF FWHM results of each system investigated are shown side-by-side in Fig. 3.Each plot shows FWHM (X, Y and Z) as a function of optical depth within the Nano phantom, and the minimum FWHM values for each direction and system are specified in Table 4.For the SSOCT system (Fig. 3(a)), lateral resolution data show a relatively large depth of field and small lateral variation.For the SDOCT system (Fig. 3(b)), the X-FWHM values decrease to a minimum while the Y-FWHM monotonically increases.No discernible focus position is evident.The TDOCT system (Fig. 3(c)) displayed a well-matched decrease and increase in FWHM values in X and Y, indicating an optimal focus position at Z ~0.6 mm.While all of the other systems show minimal change in the variability of resolution data with depth, the TDOCT exhibits a reduction in data variability within a few hundred microns of the optimal focus, the region of maximal SNR.In contrast, astigmatism and higher FWHM variability were observed when switching to the IV-TDOCT setup (Fig. 3(d)).Uniformity data for the SSOCT system (Fig. 4(a)) show a small intensity maximum about 600 µm below the surface, and an increasingly rapid decay with depth after that point.PSF intensities measured from the SDOCT system (Fig. 4(b)) showed a monotonic decay with depth, with no evidence of a subsurface maximum.As with the resolution measurements in Fig. 3, usable PSFs became sparse after 1.1 mm.The TDOCT system showed the clearest subsurface intensity maximum (Fig. 4(c)), with values falling quickly with distance in either direction from Z = 650 µm.This maximum correlates with the lateral FWHM minimum in Fig. 3(c).IV-TDOCT intensity data presented the least depth dependence (Fig. 4  Mean data from Figs. 3 and 4 are re-organized and overlaid for direct inter-system comparison of each key parameter in Fig. 5.It is particularly evident that the SDOCT and TDOCT had the lowest minimum lateral resolution levels (Fig. 5(a), 5(b)) while the SSOCT and SDOCT had the lowest minimum axial resolution levels (Fig. 5(c)).Figure 5(c) also highlights the fact that the TDOCT system was the only one to show a non-monotonically depth-dependent axial FWHM (discussed in greater detail in section 4.3.4); the SDOCT axial resolution increased slightly with depth before becoming unstable at depths > 1 mm.The intensity overlay (Fig. 5(d)) indicates depth dependence on all systems.
Representative individual PSFs from each system are shown in Fig. 6, which can be understood more clearly using the corresponding video animations (Media 1).Rows signify the relative depth order of PSFs within the phantom.For the SSOCT (Fig. 6(a)-6(c)), ideally spherical PSFs were only observed near the center of the depth range, corresponding to the minimum X-and Y-FWHM values in Fig. 3(a).At other depths, a progression in the elongated axis is evident, with the elongation near the surface (Fig. 6(a)) being perpendicular to elongation near the depth limit (Fig. 6(c)).The absence of this astigmatism from Fig. 3(a   Many PSFs from SDOCT images (Fig. 6(d)-6(f)) showed side lobes in the axial direction, especially with the FeO phantom.SDOCT results also showed a progression of astigmatic changes in X and Y resolution as a function of depth, with a spherical PSF occurring only at the central location (Fig. 6(e)).The TDOCT did not exhibit astigmatism (Fig. 6(g)-6(i)); its XY cross section was always approximately circular.IV-TDOCT PSFs (Fig. 6(j)-6(l)) were large, with a non-ideal shape.IV-TDOCT images were pixelated in the X and Y directions due to the 4 µm pixel size used.

Resolution across 3D space
A defining advantage of PSF phantoms is their ability to quantify resolution as a function of 3D space.Data in the previous section illustrated resolution as a function of depth.In this section we present resolution (X, Y and Z) and PSF intensity as a function of 3D position within the phantom.Figure 7 presents results for the SSOCT system.The first row of maps in Fig. 7 (corresponding to Media 2, Media 3, Media 4, and Media 5) displays the trend in each parameter (X, Y or Z FWHM, or intensity) across the X and Y directions.Each map was formed by flattening (taking the mean of) data in the Z direction, while preserving X and Y position information.Likewise, the second row (Media 6, Media 7, Media 8, and Media 9) displays resolution trends across a flattened XZ plane, which was averaged in the Y direction.Data is linearly interpolated to provide spatial continuity, where needed.Narrow scan results presented in previous sections were obtained near the lateral center of these maps.The only parameter to remain approximately constant across the entire imaging volume was the axial (Z) resolution.Lateral and axial dependency were observed for both X-and Y-FWHM results, which showed areas of suboptimal resolution towards the extremeties of the volume.PSF intensity decreased radially from a point near the corner (X,Y) = (8000, 6000) µm.
A similar analysis for the SDOCT system is presented in Fig. 8, which is a static representation of Media 10, Media 11, Media 12, Media 13, Media 14, Media 15, Media 16, and Media 17.The SDOCT system shows the same XY astigmatism as the narrow scan data, but reveals that the focusing effects for this system do not truly align with the Z direction.Instead, values of the X-and Y-FWHMs change along a tilted axis in the XZ plane, causing the FWHM values to be X-dependent but not Y-dependent.The maximal X-FWHM value, and minimal Y-FWHM values, occur in the corner of the data cube where X > 2200 µm.Intensity data was locally variable, but generally showed a monotonic decrease that was not clearly tilted in the same way as the FWHM trends.Wide scans were not obtained for the time-domain systems since they relied on sample scanning instead of beam scanning.

Discussion
Objective and quantitative methods for standardized evaluation of OCT system performance are needed to enhance device development and optimize clinical implementation.Phantombased approaches for assessment of key image quality characteristics such as spatial resolution and uniformity can help fill this role.In this study we have evaluated three PSF phantoms and implemented them to compare the performance of four OCT systems.The results presented here provide novel insights into phantom optimization and illustrate the broad utility of PSF phantoms in characterizing image quality and identifying system flaws.

PSF phantom evaluation
In general, results indicated that the Nano and FeO phantoms provided data that were well correlated and of high quality (Fig. 2), whereas poorer results were obtained from the silica microsphere phantom.While the phantom comparison data shown here was based on SSOCT images, a comparable level of agreement between the FWHM results of the Nano and FeO phantoms was observed for the other systems (not shown).The most consistent, though minor, discordance between the phantoms was seen for axial resolution.The predicted axial coherence length is 7.7 µm, but specular surface measurements confirmed an axial resolution of just below 10 µm. Figure 2(c) indicates that FeO results were closest to the specular surface value, followed closely by Nano.The accuracy of axial PSFs acquired with the SSOCT system is compromised by the fixed axial sampling distance of 5 µm.The increased size of the axial PSFs measured with the Silica phantom may indicate that these particles were not sufficiently small to act as point sources when used with the SSOCT system.
The particle intensity order shown in Fig. 2(d) (FeO > Nano > Silica) is not in full agreement with Mie theory backscattering cross section values estimated in part by [28], indicating that some other variable factors, especially reflectance/signal loss at the phantom surfaces, also affect the observed intensities of PSFs.However, the general observation can be made that the best results were obtained from phantoms for which the refractive indices of the particles were substantially different from those of the surrounding matrix (See Table 1).This condition, which should lead to the greatest backscattering at each particle surface, was true for the FeO and Nano designs, but not for the Silica phantom.Even the large (1.5-1.6 µm) particle size failed to compensate for the limited backscattering of the particles in the Silica construct.
Moreover, the Silica phantom contained far fewer particles to sample than the FeO and Nano phantoms (Table 2), leading to more uncertainty and noise in the data.This is especially evident for the Silica intensity data in Fig. 2(d), which does not show clear evidence of the intensity maximum expected due to beam focusing.While a thorough investigation of the particle concentration required for adequate measurements was not performed, the lowest concentration level that provided adequate signal levels in this study was 5100 per mm 3 .

Validation of near-ideal optical behavior
When using PSF phantoms as a system evaluation tool, results typically either confirm nearideal behavior, or provide data on the type and magnitude of imperfections in image quality.We documented several cases of near-ideal behavior in our systems.
The TDOCT system shows minimal astigmatism and performance characteristics dominated by a strong focusing effect.Lateral resolution parameters (X-and Y-FWHMs) are nearly indistinguishable and show a variation from about 14 µm to less than 8 µm and back to 15 µm through the best focus position of Z = 0.65 mm.This trend is also visible in individual PSFs in Fig. 6(g)-6(i).Astigmatism was likely absent from these results because the sample was scanned and the beam never moved relative to the center of the objective.The TDOCT system was predicted to have a beam waist of 6.6 µm, which lies within 1 µm of the minimum average lateral FWHM, 7.4 µm.This depth region of optimal resolution was also accompanied by a reduction in the variability of these parameters.
In contrast to the focusing trends expected in the XY plane, axial resolution is expected to remain constant with depth as it depends on the coherence length of the light source, not on the focusing optics.The SSOCT (and IV-TDOCT) Z-FWHM results exemplify this fact (Fig. 5(c)), never varying by more than 1 μm over the entire recorded depth range.The minimum SSOCT axial resolution of 9.6 µm is larger than the theoretical coherence length of 7.7 µm, but confirmed by the 9.7 µm specular surface measurement; the 5 μm axial sampling size imposes a separate limitation on the resolution of this system.
Signal intensity approaching the focal plane (if present) was expected to increase due to the shrinking cross sectional profile of the beam, and decrease at depths beyond this plane.Accordingly, SSOCT signal intensity reached a small peak around 1 mm below the phantom surface (Fig. 4(a)) as the spot size of the beam decreased, but this trend was quickly reversed by signal loss with depth.Similarly, TDOCT signal intensity and depth limitations (Fig. 4(c)) were dominated by the strong focusing effect of this system, with signal rapidly decaying above and below the focal point ~650 µm below the phantom surface.

Characterization of deviations from ideal optical behavior
The PSF phantoms are most useful for rapidly identifying and characterizing non-ideal OCT image quality.We used the FeO and Nano phantoms to identify optical aberrations across all four systems, including astigmatism, side lobes, non-uniform intensity, and axial FWHM variations.Some of these flaws were highly unexpected and would likely have gone undetected with standard OCT assessment methods.

Astigmatism
Three out of the four systems studied showed astigmatism.In the case of the SSOCT system, astigmatism was visible in individual PSFs (Fig. 6(a), 6(c)) but absent from quantitative measures of lateral PSF FWHM (Fig. 3(a)).This was because the axis of elongation did not align with the X or Y axes (Fig. 9(a)), and therefore was not quantified when comparing Xand Y-FWHMs.When FWHM values were measured in the E and E′ directions, offset by 45º from X and Y, the maximal magnitude of the astigmatism was found to be approximately 3 µm (Fig. 9(b)).The SSOCT scanning galvanometer was damaged and replaced just before these measurements were taken.PSFs that were measured before the replacement showed a maximum astigmatism of approximately 11 µm with elongation that aligned closely with the X axis; FWHM values in the X and Y directions near the surface of the Nano phantom, respectively, were 23 and 12 microns (Fig. 9(c) and [29]).The reduction in the magnitude of astigmatism and ~45° rotation in its axis of elongation indicates the extent to which OCT astigmatism is dependent on the placement of the main scanning galvanometer.Furthermore, this improvement provides an example of the utility of volumetric PSF visualization in assessing the effect of instrumentation changes on imaging performance.
Compared to the SSOCT system, the SDOCT system showed a large degree of astigmatism.Given that the SDOCT was designed primarily for retinal imaging -but with flexibility to perform limited measurements on flat samples -these limitations are not unexpected.The minimum average lateral resolution measured on SDOCT was 7.3 ± 0.58 µm, a value smaller than, and just outside 1 standard deviation of, the predicted lateral resolution of 7.9 µm.This is likely due to the severity of the astigmatism, which has been previously characterized for this system by multiple methods [18].Moreover, the illumination angle of the sample on this system was oblique; this causes the X-dependency of the astigmatism in Fig. 8.
Finally, the astigmatism exhibited by the IV-TDOCT system consisted of very gradual focusing in the X-direction (with a focal depth of about 1.3 mm) and a much more rapid focusing in the Y-direction (Figs. 3(d) and 5).This irregularity is also visible in individual PSFs from the IV-TDOCT system, which illustrate an unequal progression in lateral FWHM sizes with depth (Fig. 6(j)-6(l)).Fig. 9. Isolated PSFs from the SSOCT system using the Nano phantom in the present study (a), with FWHMs quantified along the E and E′ axes (b), and (c) before we replaced the scanning galvinometer [29].The B scan direction (X) is the same in both cases.The E axis is offset from X by 45 degrees.The PSFs are 3D objects viewed axially.Scale bars are 10 µm.

Axial side-lobes
The PSF phantoms readily revealed axial side-lobes in SDOCT PSFs (Fig. 6(d), 6(f)), which were dispersed throughout the images without obvious dependence on lateral or axial position.The FWHM correction that was applied to SDOCT axial resolution (fitting the Gaussian only between the minima immediately surrounding the peak) was intended only to remove the influence of the side lobes on the Gaussian fit, to more accurately represent the theoretical FWHM.The true effect of side lobes on the axial FWHM may require an MTF approach to quantify [7].Axial side lobes arise from the non-Gaussian SLD spectrum, and are common in ultrahigh resolution OCT [30] and other optical imaging modalities [31].While we did not study these features quantitatively, our results show that PSF phantoms are useful for identifying side lobes and potentially for evaluating the effectiveness of correction approaches.

Signal intensity non-uniformity
Beyond the intensity trends discussed in section 4.2.2, multiple unexpected nonuniformities were readily characterized using the PSF phantoms, and especially by 3D mapping of the intensity (Figs. 7 and 8).
The SSOCT 3D map (Fig. 7) displayed an intensity peak near (X, Y) = (8000, 6000) µm with values decaying radially from this point.This was highly unexpected, since the default position of the laser is at the center of this map.It is therefore possible that the position of the peak was caused by misalignment of the beam relative to the center of the main objective lens.
The SDOCT system (Fig. 8) exhibited substantially greater local non-uniformity than the SSOCT system.The only clear trend is a decay in intensity with depth, as is expected.In spite of the fact that the oblique illumination angle of the SDOCT system beam caused an Xdependence in lateral FWHM sizes, a similar tilting was not observed for the SDOCT uniformity maps.This is likely a result of the astigmatism between X and Y axes not coming to a concurrent intensity maximum.The monotonic drop in signal intensiy due to spectral domain rolloff limited the maximum penetration depth of this system to about 1.2 mm.
In the IV-TDOCT image, PSF intensity remained at a nearly constant, though low, value of about 2 dB above noise throughout the recorded depth span.As a result of its lacking a clear rolloff trend, the IV-TDOCT probe provided the greatest depth penetration of any of the four systems (Fig. 5).Further explanation of the performance characteristics of this system in relation to its design is limited due to the proprietary nature of the catheter probe.
Although wide maps of the PSF were not obtained for either time-domain system studied, we do not expect them to vary substantially because, unlike the SSOCT and SDOCT, sample scanning was used while the beam remained fixed.

Axial PSF variation
The PSF phantoms revealed unexpected axial resolution results for the TDOCT system in both free-beam and IV probe-based delivery modes.The TDOCT was the only system that exhibited axial resolution that was a non-monotonic function of depth, instead showing a subsurface minima near 0.65 mm similar to lateral resolution results.Further analysis of variation in axial PSF with signal intensity on this system was performed by measuring a specular surface for which the signal was progressively dampened by neutral density filters to generate attenuation levels of 20 to 40 dB (Fig. 10).At lower intensities, the axial PSF was asymmetric, with a distinctive "raised tail" that increased the axial FWHM.At the highest intensities, this tail diminished, resulting in a more symmetric PSF with a smaller FWHM.The intensity dependence of the axial FWHM is thought to be caused by the analog filtering scheme of the system electronics.Therefore, the minimum in measured TDOCT axial resolution (14 µm, which agrees with the known coherence length) is the true axial resolution of the system.We are not aware of any prior study which has identified this type of OCT system behavior, and it is unlikely that this is a common problem with OCT.Nonetheless, the PSF approach provided a unique tool for identifying this effect, which may otherwise have gone unnoticed.
Lastly, despite using the same light source, the IV-TDOCT system had a broader axial PSF than the TDOCT system (18 μm vs. 14 μm) because it relied upon a custom built reference arm with dissimilar dispersion properties to the sample arm, a difference from the common path design.

Conclusions
This study evaluated and compared three OCT PSF phantom designs and demonstrated the utility of PSF phantoms in objectively assessing and comparing image quality across four OCT systems.Two of these phantoms consistently gave high quality and theoretically justifiable results: silica-gold nanoshells embedded in epoxy, with a particle density of ~5000 per mm 3 and iron oxide particles embedded in polyurethane, with a density of ~7500 per mm 3 .By contrast, the silica phantom (1.5 μm diameter silica particles in epoxy) suffered from low particle backscattering cross section and low particle concentration (<1000 particles/mm 3 ).
Our results indicate that a new characteristic can also be evaluated with PSF phantomssignal uniformity.This is a key image quality parameter that is commonly addressed in international standards for established medical imaging modalities such as ultrasound.While the variation in signal intensity was often higher than that seen for resolution results, mean signal intensity findings corresponded well with expected trends, including signal intensity maxima near depths where the beam width was smallest, as seen for the SSOCT and freebeam TDOCT geometries.
The advancement of this technique towards widespread implementation should greatly improve the ability to develop optimized OCT systems and compare performance of devices in an objective and quantitative manner.However, since the computational analysis might introduce measurement uncertainty, widespread implementation of PSF phantoms in assessing OCT performance would require some standardization of the analysis methods as well.
By analyzing 3D spatial variations in PSF intensity and FWHM in the axial and lateral directions in combination with volumetric representations of individual PSFs, it is possible to rapidly characterize OCT system performance and identify performance flaws such as astigmatism, side lobes, and signal intensity nonuniformity.Therefore, this approach has significant promise as a standardized method for objective, quantitative evaluation of OCT systems performance, or as a method for improving OCT image quality through PSF deconvolution [19] or by facilitating PSF engineering [32].

Fig. 1 .
Fig. 1.Representative B-scans from the SSOCT system for (a) Nano, (b) FeO and (c) Silica phantoms.Color scale represents recorded intensity in dB.

Fig. 2 .
Fig. 2. Comparison of all three PSF phantoms using narrow 3D scans from the SSOCT system.Data represents the mean value within ± 50 µm from the depth (Z) of each point.FWHM error bars shown for the Nano phantom are based on the standard deviation of particles in each depth bin, and are representative of the errors from other phantoms.

Fig. 3 .
Fig. 3. Resolution (X, Y and Z FWHM) of all four systems investigated as a function of depth below the Nano phantom surface in narrow scans.Black lines are the mean within depth bins identical to those in Fig. 2. Presented are: (a) SSOCT, (b) SDOCT, (c) TDOCT and (d) IV-TDOCT.

Fig. 4 .
Fig. 4. PSF intensity profile for all four systems as a function of optical depth below the surface of the Nano phantom, from the same data set as Fig. 3. Presented are: (a) SSOCT, (b) SDOCT, (c) TDOCT and (d) IV-TDOCT.Note the difference intensity scales between a-d.

Fig. 5 .
Fig. 5. Comparison of spatial resolution (a-c) and signal intensity uniformity (d) in all four systems with the Nano phantom.Data represents the mean value within ± 50 µm from the depth (Z) of each point.Each mean intensity curve is rescaled to fall between 0 and 1.

Fig. 6 .
Fig. 6.Isolated example PSFs from each system using the FeO phantom.The color scale encodes the relative, normalized intensity of each pixel within a PSF.Numerical labels indicate depth below the surface in mm.Rotating animations (Media 1) are presented for clarity.

Fig. 7 .
Fig. 7. 3D mapping of PSF FWHM (µm) and intensity (dB) performance using the FeO phantom on the SSOCT system.Columns: PSF parameter.Top row: XY mean projections of each parameter (averaged along the Z direction).Bottom row: XZ mean projections (averaged along the Y direction).Corresponding fly-through movies for each of the eight panes (Media 2-9) are available online.White areas indicate regions where no PSFs were found.Narrow scans discussed before were taken near the lateral center of these maps.

Fig. 8 .
Fig. 8. 3D mapping of PSF FWHM (µm) and intensity (dB) performance using the FeO phantom on the SDOCT system.Corresponding fly-through movies for each of the eight panes (Media 10-17) are available online.

Fig. 10 .
Fig.10.TDOCT A-scans in the axial (Z) direction.Data is shown from a specular surface (SS) that has been progressively attenuated by the neutral density filters indicated to reveal the intensity dependence of the "raised tail".Two PSFs from the nanoshell phantom, in focused (high intensity) and defocused (low intensity) regions, are shown as an example of this effect on phantom measurements.