It then translates to. Within the aperture the coherent amplitude transfer function only has a phase component,.
Outside the aperture, the amplitude transfer function is 0 as no light is transmitted Fig. Hence, the multiplication with in equation 2 effectively low-pass filters the image U img. Aberrations of the imaging system including defocus will only change the phase of , and consequently its effect on the image is completely reversed by multiplication of with the complex conjugate of , which corresponds to a deconvolution of Equation 1. Since the signal energy at all transmitted spatial frequencies is not attenuated, i.
The corresponding incoherent process illustrates the difference to a deconvolution in standard image processing. During incoherent imaging, defocus and aberrations only cause a loss in contrast for small structures Fig. However, the optical transfer function, i. Hence the effect of aberrations on image quality cannot be inverted without losing information or increasing noise. In this context, it is remarkable that a simple multiplication with the complex conjugate of inverts the coherent process, despite of speckle noise. Here, is a function of the spectral wavenumber k , and the Fourier conjugate to k is the depth.
Shape and width of are given by the spectrum of the light source, which also determines the axial PSF and thus the resolution. Similar to coherent aberrations, an additional phase term is introduced if reference and sample arm have a group velocity dispersion mismatch or, which is relevant for FF-SS-OCT, if the sample moves axially As for aberrations, these effects are corrected losslessly by multiplication of the spectra with the conjugated phase term, if it is known. One approach uses single points in the image data as guide stars 11 , 25 , which is the numerical equivalent to a direct aberration measurement with a wavefront sensor.
Although photoreceptors can be used as guide stars in not too severely aberrated retinal imaging 16 , a guide star is usually not available in other retinal layers or other tissue. A second approach cross-correlates low-resolution reconstructions of the aberrated image from different sub-apertures to estimate the phase front. However, these low-resolution images of scattering structures usually show independent speckle patterns, which carry no information about the aberrations and limit the precision of the phase front determination. Here, we iteratively optimized the image quality to obtain the correcting phase, which provided very good results.
Although it is computationally expensive, this idea was already applied to digital holography 28 , synthetic aperture radar SAR, refs 21 and 29 , and also scanning OCT to correct aberrations 10 and dispersion mismatch After an inverse Fourier transform a corrected image is obtained, which can be evaluated for image quality. The metric S needs to be minimal or maximal for the aberration-free and focused image, even in the presence of speckle noise. Finally, a robust optimization technique must find the global minimum of the metric without getting stuck in local minima.
As the number of free parameters increases with higher aberration order, the global optimization becomes more difficult and increasingly time consuming; the algorithm performance is therefore crucial. A variety of metrics and image-sharpness criteria have been used in previous research for coherent and incoherent imaging 8 , 21 , 29 , 31 , For a normalized complex image given by U mn at pixel m , n , a special class of metrics 8 only depends on the sum of transformed image intensities see also Methods :.
Here, we used the Shannon entropy ref. When these metrics reach a minimum we observed good image quality, despite of speckle dominated data.
Speckle reduction in double-pass retinal images
These are established in the description of optical aberrations including defocus, and their use gave good performance and results during optimization. Zernike polynomials up to 8 th radial degree were used, excluding piston, tip, and tilt, which results in 42 degrees of freedom.
To achieve this, we used a two-step approach. At first, a simplex-downhill algorithm was applied This algorithm follows the global trend of the metric function and is thereby rather insensitive to local minima, albeit there is no guarantee it does not converge to a local minimum. Once being close to the presumed global minimum, a gradient-based algorithm was used, which significantly boosted performance.
Here, we used the conjugate gradient method A useful property of metrics described by equation 5 is that their complete gradient with respect to the Zernike coefficients can be computed efficiently; it requires only a single additional Fourier transform see refs 8 and 21 and Methods. If aberrations were too strong and the degrees of freedom too large, we observed that resulting images did not always show the expected structures, i.
We therefore modified the approach and performed the optimization first with a computationally reduced numerical aperture see Methods. Afterwards, the optimization was repeated several times while increasing the NA. Using a smaller NA in the beginning gave more robust results since at low NA the aberrations are smaller and relatively sharp images are already obtained. Therefore, the optimization procedure detects structures it can use to converge. After increasing the NA, the optimization starts with already visible structures and converges more easily.
In this way even high-order aberrations, up to 42 degrees of freedom, could be corrected for. Performance of the algorithm was judged by visually analyzing the corrected images for well known anatomical structures, such as photoreceptors, blood vessels, and nerve fiber bundles.
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In general the assumption of a laterally invariant PSF is not valid, and equation 1 only holds for small volumes. The entire data were therefore divided into sufficiently small sub-regions see Methods , which were then corrected independently. By stitching these, aberration-free data for the complete recorded volume were obtained. To demonstrate the accuracy of the algorithms, we first imaged lens tissue MC-5, Thorlabs with a simple achromatic lens at an NA of 0. Before correction en face images were severely blurred Fig. Since the aberrations were not translation invariant, different sub-images were corrected independently Fig.
Scale bars are 0. Wavefront and PSF resulting from the aberration determination of Fig. The obtained wavefront was compared to a raytracing simulation Zemax, Fig.
A slight lateral misalignment of the imaging optics explains remaining differences. We then imaged the retina of a young healthy volunteer in vivo. Without the aberration correction the volumes were laterally blurred in all layers of the retina with image degradation being significantly stronger in the high NA data, where hardly any lateral structures were visible at first. Several of the layers were aberration corrected, including the nerve fiber layer NFL, Figs 4c and 5b , small capillaries Fig.
The optimization algorithm improved image quality nearly to diffraction limit, showing otherwise invisible structures.
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In particular, the structure of the nerve fiber layer and small capillaries became visible and single photoreceptor cells were identified. In the choroid of the imaged retina, barely any structures are visible, which is caused by multiple scattered photons 35 , In addition, artifacts in the larger vessels, caused by the Doppler effect, decrease overall image quality. Thereby, the artifacts induced by the Doppler effect, and multiple scattering did not disturb the optimization. For the measurements we performed, we observed that if structures were expected to be visible in an aberration-free imaging, the optimization was able to restore them.
The computation time with the current implementation depends on the size of the region for which aberrations are corrected. A significant further speed-up is expected by tweaking the reconstruction parameters, by optimizing the code, or by implementing the algorithms on a graphics processing unit GPU. For the first time, completely phase-stable volumetric data of human retina were acquired in vivo.
In contrast to scanning OCT, all lateral points are acquired simultaneously, thereby preventing sample motion from causing phase changes between A-scans. Additionally, only one single laser sweep is required to obtain a volume, which removes effects from irreproducible laser sweeps. Lateral phase stability is therefore inherent to the areal data acquisition. Axial phase stability was restored by computational phase correction, resulting in axial resolution at the theoretical limit.
The effective phases within a single volume were therefore only given by the tissue morphology, and phase changes between volumes consequently reflect changes thereof. The phase-stable data allowed us to correct aberrations and to remove the effects of limited focal depth. The demonstrated image quality optimization was able to correct images of the nerve fiber layer, small capillaries, and photoreceptor cells.
It is largely independent of the imaged structures. The chosen optimization strategy turned out to be quite robust without being overly sensitive to local minima. Having said this, there is currently no obvious way to check that the optimization found the global optimum, or that the global optimum actually corresponds to the aberration-free image.
Still, the optimization was able to recover otherwise invisible or blurred structures. Only specular reflections not filling the aperture, or the absence of signals disturbed the correction.
Aberration-free volumetric high-speed imaging of in vivo retina | Scientific Reports
This way, in only one measurement, images of all retinal layers were obtained with near diffraction limited resolution. Currently, the pixel number of the camera that can be used at the required acquisition rate, and the tuning range of the laser limit the system capabilities. However, we expect that both limitations could be overcome by future technological advances.
However, the effect was not as severe as we anticipated and high-quality images of the neuronal retina could be acquired. Furthermore, the flexibility of the system with respect to the field of view and lateral resolution is reduced, as the sampled area is bound to the camera chip, and numerical aperture and lateral sampling distance cannot be selected independently. Sensitivity of our system is lower compared to currently used scanning systems due to the higher acquisition speed.
Fortunately, this lower sensitivity is partially compensated by the areal illumination, which circumvents the limitations imposed by the maximum permissible exposure of a focused beam. Additionally, incoherent background light from reflections and undesired scattering within the eye increase shot noise and reduce the achieved signal-to-noise ratio, since this light is not filtered by a confocal gating in full-field imaging.
Finally, scanning OCT systems do not suffer from significant Doppler artefacts, which were visible with the proposed full-field approach. A general assessment on the advantages and disadvantages of FF-SS-OCT is difficult, since the performance depends on the imaging parameters and on the application. Computational cost of the presented approach is not negligible. Time to completely reconstruct an entire dataset 50 volumes and to obtain a single aberration-free layer of these volumes was more than an hour.
However, starting from there, other layers can be reconstructed more easily by removing the remaining defocus. No moving parts are involved. Our setup benefits from a recently available high-speed CMOS camera, which is its most advanced and expensive component and currently costs about , USD. As the technology matures, availability of suitable cameras might increase at decreasing costs. This mentioned complexity is still a significant hurdle for AO-OCT to find wide spread use in clinical diagnostics and research.
Fully coherent high-speed tomography does not only visualize dynamic processes with near diffraction limited resolution, but will also provide new contrast mechanisms that rely on fast but very small changes of scattering properties or optical pathlengths. Light from a tunable light source was split by a fiber coupler into reference and sample arm.
The light in the reference arm was collimated and brought onto the camera via a beam splitter cube. Light from the sample arm illuminated the retina through the same beam splitter cube and the imaging optics with a parallel beam. The backscattered light from the retina was imaged onto the camera with numerical apertures NA ranging from 0.
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The illuminated area on the retina was imaged onto the area-of-interest of the camera, maximizing light efficiency. Polarizations of both arms were matched to enhance interference contrast and sensitivity. The laser sweep was sufficiently reproducible due to an electronically driven optoacoustic filter, and no k -clock was needed. For each volume images were acquired, each at a different wavenumber in the tuning range of the light source. The acquisition speed is thus equivalent to For each measurement 50 volumes were imaged. For optimum imaging of an in vivo retina, a fixation target illuminated by a green LED was used to adjust the field-of-view on the retina.
The necessary steady and repeatable head position was assured by a custom fit plastic face mask, originally used in radiotherapy. All investigations were done with healthy volunteers; written informed consent was obtained from all subjects. Compliance with the maximum permissible exposure MPE of the retina and all relevant safety rules was confirmed by the responsible safety officer. All experiments were performed in accordance with relevant guidelines and regulations.
According to the ANSI standards, allowed radiant flux scales linearly with the size of the irradiated area To start off, a coherent average of the 50 acquired volumes was computed and the result was subtracted from all volumes. This removed fixed and phase stable artifacts in the images, while leaving the signals of the moving retina intact, since these changed from volume to volume due to eye motion.
Following this, similar to FD-OCT signal processing, the OCT volumes were reconstructed by Fourier transforming the acquired images along the wavenumber axis giving the depth information at each pixel of the image Reconstruction in Table 1. The data was then corrected for group velocity dispersion GVD mismatch in reference and sample arm and slight axial bulk motion during the wavelength sweep.
Since such axial phase errors are both, of low polynomial order and equal in all A-scans of a volume, they can effectively be estimated and corrected by using the same optimization approach that facilitates the aberration correction. This ensured that the layers of the retina were at identical depth positions and made selection of the input regions for the aberration correction easier. Get Citation Citation. Get Permissions. Permission to republish any abstract or part of an abstract in any form must be obtained in writing from the ARVO Office prior to publication.
View Metrics. Forgot password? To View More Create an Account or Subscribe Now. Comparison of optical quality after implantable collamer lens implantation and wavefront-guided laser in situ keratomileusis. References Publications referenced by this paper. Off-axis image quality in the human eye Jessica A. Jennings , W. Double-pass and interferometric measures of the optical quality of the eye.
David R. Williams , David H. Brainard , M. McMahon , Rafael Navarro. Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor. Goelz , Josef F. The effect of decentered small pupils on optical modulation transfer and contrast sensitivity,. Marcos , P. Artal , D. Effects of aging in retinal image quality.