2.1.

Adaptive Optics Full-Field Optical Coherence Tomography

The apparatus schematic diagram is shown in Fig. 1. The main part of the system is the typical FFOCT system based on a Linnik interferometer. An LED with $\lambda =660\mathrm{nm}$ center wavelength and 20-nm bandwidth (M660L4, Thorlabs) is used as the incoherent light source. The illumination beam is split into the reference arm and the sample arm at a ratio of $50:50$ with a nonpolarizing beamsplitter. Two Nikon 4X/0.2NA Plan APO objectives are used, one is in the sample arm to simulate the open pupil human eye, and the other is in the reference arm. A reference mirror supported by a piezoelectric transducer is placed at the focal plan of the objective in the reference arm while the imaging object is placed in the sample arm. The back-reflected beams from the reference mirror and the sample are recombined by the beamsplitter and imaged with an achromatic doublet lens onto a fast (150 fps) CMOS camera (MV-D1024E-160-CL-12, PhotonFocus). The camera has a resolution of $1024\times 1024\text{pixels}$ with $10.6\mu \mathrm{m}\times 10.6\mu \mathrm{m}$ pixel size, and the whole active optical area is used for imaging in experiments demonstrated here. The setup is aligned to ensure that the focusing of the two arms and their optical paths are matched. The piezoelectric transducer creates a four-phase modulation of the reference arm and an FFOCT image can be reconstructed with these four corresponding images.⁴ Usually several FFOCT images are averaged for improving the signal to noise ratio (SNR). Five images were used for the experiments described in this paper requiring about 150-ms acquisition time. The system has a field of view of $1.7\times 1.7{\mathrm{mm}}^2$, and the theoretical resolutions are $2\mu \mathrm{m}$ (transverse) and $7.7\mu \mathrm{m}$ (axial).

Fig. 1

Schematic of AO FFOCT system coupled with LCSLMs. BS, beamsplitter; LCSLM, liquid crystal spatial light modulator; PZT, piezoelectric transducer.

For conducting the wavefront correction, a transmissive LCSLM is installed in the sample arm at about 2.5 cm after the back aperture of the objective lens while another identical LCSLM is set in the reference arm for dispersion correction. A polarizer is inserted in the illumination path since the LCSLM works only with polarized light. By electronically varying the orientation of the molecules inside the pixels of the LCSLM, the refractive index of the pixels is changed independently from each other, resulting in variable retardance abilities to the polarized light passing through them.

2.2.

Resolution Almost Insensitive to Aberrations

Our recent work on quantifying the effect of geometrical aberrations on incoherent interferometry has shown that the width of the system PSF is almost insensitive to aberrations.^39,40 In a nutshell, if we consider the aberrated object channel wavefront corresponding to a single point scatter in the “best focus” plane of the sample, because of its partial overlap with the wavefront of the corresponding diffraction limited spot in the reference channel, the signal is damped. Nevertheless, the interferometric signal corresponding to a neighboring diffraction spot is much more damped. Indeed the shift to the neighboring spot in the reference channel is associated to a linear increase of $\pm 2\pi$ of the phase shift from one side of the pupil to the other. This supplementary phase shift increases the root-mean-square (RMS) wavefront error of the aberrated wavefront leading to a strong decrease of the Strehl ratio and of the signal. Thus, as demonstrated in Ref. [39], the system PSF is computed as a dot product of the object channel PSF with the reference channel PSF for spatially incoherent interferometry while it is computed as a convolution of the object channel PSF with the reference channel PSF for spatially coherent interferometry. So in FFOCT, if the object channel PSF is distorted (mostly broadened), its interference with the reference channel conserves the main feature of an unperturbed PSF with only a reduction in the signal level. Such behavior, which takes advantage of the spatial incoherence of the source, is not likely to happen with scanning OCT setups, which use spatially coherent sources.

With a negative USAF set at the best focus position of the sample arm of our AO-FFOCT system, we confirmed experimentally this specific merit of FFOCT system. Here, a random aberration [Fig. 2(g), $\text{Strehl ratio}=0.06$, corresponding to $\mathrm{RMS}=0.27\lambda$] was induced with the LCSLM in the sample arm by generating and applying random voltages within the adjusting range across the LCSLM pixels. According to the definition, the “best focus” signal intensity damping compared to the diffraction limited condition is given (for small aberrations) by the Strehl ratio that is proportional to the peak aberrated image intensity. So the Strehl ratio for LCSLM-induced random aberrations/corrections in our experiments with USAF resolution target is actually calculated by $\mathrm{s}={(I_a/I_o)}^2$ as amplitude instead of intensity is obtained for FFOCT signal, where $I_o$ is the mean intensity of the FFOCT image before aberration is induced and $I_a$ is the mean intensity of aberrated/corrected FFOCT image. Figure 2 shows the sample reflectance images and FFOCT images of the USAF resolution target before and after the random aberration was induced. The reflectance images were recorded by blocking the reference arm in FFOCT; thus, the system works as a wide-field microscope. The reflectance image is blurred after the aberration is added, while there is no obvious blurring of the line patterns in the FFOCT image but only a reduction of the image intensity. The normalized intensity of the selected line in the reflectance image shows a distortion after the aberration was added, while it shows a conservation of the shape for the FFOCT image. Note that the image contrast of scanning OCT using spatially coherent illumination would be close to the reflectance image from the sample arm.

Fig. 2

Comparison of (b, c) the reflectance and (e, f) FFOCT images of a negative USAF resolution target (b, e) before and (c, f) after adding a defocus aberration. (a,d) The comparison of the normalized reflectance intensity and FFOCT signal of the selected line without (blue) and with (red) aberration added. The plot of the random aberration pattern is shown in (g), $\text{Strehl ratio}=0.06$. Scale bar: $100\mu \mathrm{m}$.

2.3.

Aberration Correction Algorithm

Since aberrations affect only the signal level without reducing the image resolution in FFOCT, we naturally decide to apply a wavefront sensorless approach for aberration correction based on the FFOCT signal level. The wavefront sensorless method consists of the sequential adjustment of the coefficients of low-order orthogonal Zernike polynomial functions applied to the LCSLM to optimize the metric function. In our experiment, the mean intensity of FFOCT image was used as the metric function for LCSLM-induced aberration correction with USAF resolution target as the sample. For in-depth sample-induced aberration correction, the average intensity of the 300 pixels with maximum intensity values in the FFOCT image was used as the metric function because the mean intensity of the overall image would be less sensitive to the AO process since most parts of the FFOCT image has very low or even no signal. Of course we could also restrict to specific region of interest for the optimization process. Indeed anisoplanatism shows up as shown in Fig. 4, but the experiment results we acquired show acceptable correction with this simple AO algorithm. No phase wrapping was used for experiments in this paper because the magnitude of the wavefront distortions to be compensated was within the dynamical range of our SLM. Coefficients were indeed selected within the adjusting range of the LCSLM. The orthogonality of different Zernike modes ensures that the coefficient of each mode for optimal correction is determined independently.^43,44 This algorithm has been proposed and used by many groups with different wavefront shaping methods and optimization metrics in specific applications.^22,45,46 For the aberration correction experiments mentioned in this paper, only Zernike modes three to eight were optimized just to demonstrate the feasibility of our system and method. For each mode, FFOCT images were taken for seven different coefficients within the adjusting range. With the extracted metric function values, B-spline interpolations were done and the coefficient that produced the highest metric function was chosen as the correction value. As a result, the entire optimization process could be done in about 6.3 s.

3.1.

Liquid Crystal Spatial Light Modulator-Induced Aberration Correction

To test the performances of our AO-FFOCT system with no well-defined conjugation and wavefront sensorless algorithm, experiments of LCSLM-induced aberration correction were first conducted by imaging a negative USAF resolution target. As shown in Fig. 3, in this experiment we inserted LCSLM2 into the sample arm for aberration introduction at about 5 cm after the original LCSLM1, which was used for aberration correction, thus there is no well-defined conjugation between the aberration introduction plane and the correction plane. A glass slide was inserted into the reference arm for dispersion compensation.

Fig. 3

Schematic of AO FFOCT system for LCSLM-induced aberration correction. LCSLM2 was inserted at 50 mm after LCSLM1. LCSLM2 was used for aberration introduction while LCSLM1 was used for aberration correction.

The USAF target was set at the best focus position in the sample arm and a random aberration mask ($\mathrm{RMS}=0.23\lambda$, $\text{Strehl ratio}=0.12$) was generated and applied to the LCSLM2. Figure 4(a) shows the original FFOCT image with the added aberration. By using the wavefront correction algorithm and applying the correction phase mask onto LCSLM1, defocus, astigmatism, coma, and spherical aberration were corrected sequentially. Figures 4(b)–4(g) show the images after each correction with a clearly visible improvement of image quality after each optimization process. The black curve in Fig. 4(h) shows the increase of the metric function and the red, blue, and green dashed curves display the mean intensity changes of the corresponding selected regions indicated with the same colors in Figs. 4(a) and 4(g). The fact that different levels of improvement were achieved for different regions with the same correction phase mask for each Zernike mode implies the existence of anisoplanatism in our experiment. Nevertheless, the mean intensity of the FFOCT image got an increase of 135% after the overall correction, reaching 80.0% of the nonaberrated FFOCT image while having diffraction-limited resolution. The RMS wavefront distortion was reduced by a factor of $2.2$ to $0.11\lambda$, and the Strehl ratio was increased by a factor of 5.3 to a value of 0.64. This experiment was repeated three times in the same condition with different random aberration phase masks added to LCSLM2, and the corrections result in an average increase of the mean intensity to $78.0\%\pm 2.2\%$ of the nonaberrated FFOCT image, corresponding to a Strehl of $0.61\pm 0.035$.

Fig. 4

FFOCT images of a negative USAF resolution target during the nonconjugate AO correction process of a random aberration. (a) Original image with a random aberration added, (b–g) images after defocus, astigmatism 45, astigmatism 0, coma 90, coma 0, and spherical aberration were corrected, respectively, (h) graph of the metric function (black curve) increase after each correction step and mean intensity changes (red, blue, and green dashed curves) of the corresponding selected regions indicated in (a, g). Scale bar: $350\mu \mathrm{m}$.

Note that in conjugate AO, the aberration corrector is conjugated with the plane where aberrations dominate. For simplification and avoiding modification of the system, a simulation of conjugate AO experiment by using the same LCSLM for aberration introduction and correction was conducted to correct low-order aberrations for comparison with our nonconjugate AO experiments. Again an USAF resolution target was first set at the focal plane in the sample arm. With the same random aberrations induced by LCSLM2 for nonconjugate AO experiments, we demonstrate the aberrations corrections here also on LCSLM2. Indeed the net wavefront of the original aberration phase mask plus the correction phase mask was applied to the LCSLM2 during the correction process. With the same algorithm based on the mean intensity increase, Zernike modes three to eight were blindly corrected. Figure 5 shows the correction of the same random aberration corresponding to the results displayed in Fig. 4, the whole correction result in the mean intensity of the FFOCT image reaching 86.0% of the nonaberrated FFOCT image. The RMS wavefront distortion was reduced by a factor of 2.6 to $0.09\lambda$, and the Strehl ratio was increased by a factor of 6.2 to a value of 0.74. The three repeated experiments result in an average increase of the mean intensity to $84.3\%\pm 2.1\%$ of the nonaberrated FFOCT image, corresponding to a Strehl of $0.71\pm 0.036$.

Fig. 5

FFOCT images of a negative USAF resolution target before and after the conjugate AO correction process of a random aberration. (a) Original image with a random aberration added and (b) image after defocus, astigmatism 45, astigmatism 0, coma 90, coma 0, and spherical aberration were corrected. Scale bar: $350\mu \mathrm{m}$.

3.2.

Sample-Induced Aberrations Correction

Due to the spatial variations of refractive index within biological samples and surface topography, aberration distortion is severe when imaging into the sample volume. In order to further demonstrate the feasibility of our system and method even for weak aberration correction, experiments of sample-induced aberration corrections were done with a ficus leaf. The system setup described in Fig. 1 was used here. By imaging at a depth of $75\mu \mathrm{m}$ under the leaf surface, only weak aberrations are induced and we can, thus, check the sensitivity of our correction approach; the low-order contents of the self-induced sample aberrations were corrected step-by-step with the aforementioned methods. As showed in Fig. 6, the optimized image [Fig. 6(b)] shows an intensity increase compared with the original image [Fig. 6(a)] and from the zoomed in images, more structured information appears. This is due to the fact that the correction process increased the SNR and more signals that were buried by the noise before appear after the AO correction. The graph of the metric function while adjusting the coefficients of each Zernike mode is displayed in Fig. 6(c). The highest positions of each curve correspond to the coefficients used for the optimal correction of each mode. Figure 6(d) shows the increase of metric function. The whole correction process results in 13.3% improvement of the metric function. As expected the metric function improvement increases to 35.5% when imaging deeper at $120\mu \mathrm{m}$ under the leaf surface in another experiment (not shown here).

Fig. 6

Comparison of FFOCT images of a ficus leaf (a) before and (b) after sample self-induced aberration was corrected when imaging at a depth of $75\mu \mathrm{m}$. (c) Graph of the metric function during the optimization process and (d) graph of the metric function increase after each correction step. Scale bar: $500\mu \mathrm{m}$, Zoomed in area: $425\times 425\mu \mathrm{m}$.

After showing the ability of our approach to optimize the signal even with a low level of aberration, we checked another biological tissue of relevance that suffers from strong scattering and stronger aberrations is brain tissue, where FFOCT signal is usually strongly reduced when imaging deep in the sample. We have also conducted experiments with a fixed mouse brain tissue slice to correct the wavefront distortion. Imaging was performed at $50\mu \mathrm{m}$ under the brain tissue surface without liquid matching fluid, and the results are shown in Fig. 7. The high-signal fiber-like myelin fiber structures appeared much more clearly after the whole correction process because of the increased SNR; indeed the metric function was increased by 121%.

Fig. 7

Comparison of FFOCT images of fixed mouse brain tissue slice (a) before and (b) after sample self-induced aberration was corrected when imaging at a depth of $50\mu \mathrm{m}$. Scale bar: $500\mu \mathrm{m}$.