Visual and Physiological Optics: introduction to the joint feature issue in Biomedical Optics Express and Journal of the Optical Society of America A.

This feature issue collects articles presented at the tenth Visual and Physiological Optics meeting (VPO2022), held August 29-31, 2022, in Cambridge, UK. This joint feature issue between Biomedical Optics Express and Journal of the Optical Society of America A includes articles that cover the broad range of topics addressed at the meeting and examples of the current state of research in the field.

Method to reduce undesired multiple fundus scattering effects in double-pass systems.

Double-pass systems rely on backscattering of light by the human ocular fundus to assess the optical quality of the eye. In this work, we present a method to reduce double-pass image degradation caused by undesired multiple scattering effects in the eye fundus. The reduction is based on combined data processing of simultaneous measurements using two different configurations: one symmetric with equal entrance and exit pupils and another asymmetric with unequal entrance and exit pupils. Under certain conditions, such scattering effects may be effectively suppressed. Measurements of human eyes show that, although multiple fundus scattering imposes a shift on the estimations, double-pass systems can be used to predict the optical quality of the eye within a population.

Hartmann-Shack wavefront sensing without a lenslet array using a digital micromirror device.

The common Hartmann-Shack wavefront sensor makes use of a lenslet array to sample in-parallel optical wavefronts. Here, we introduce a Hartmann-Shack wavefront sensor that employs a digital micromirror device in combination with a single lens for serial sampling by scanning. Sensing is analyzed numerically and validated experimentally using a deformable mirror operated in closed-loop adaptive optics with a conventional Hartmann-Shack wavefront sensor, as well as with a set of ophthalmic trial lenses, to generate controllable amounts of monochromatic aberrations. The new sensor is free of crosstalk and can potentially operate at kilohertz speed. It offers a reconfigurable aperture that can exclude unwanted parts of the wavefront.

Analysing the impact of myopia on the Stiles-Crawford effect of the first kind using a digital micromirror device.

PURPOSE: Photoreceptor light acceptance is closely tied to the Stiles-Crawford effect of the first kind (SCE-I). Whether the SCE-I plays a role in myopic development remains unclear although a reduction in directionality has been predicted for high myopia. The purpose of this study is to analyse the relationship between foveal SCE-I directionality, axial eye length, and defocus for emmetropic subjects wearing ophthalmic trial lenses during psychophysical measurements and for myopic subjects with their natural correction. METHOD: A novel uniaxial flicker system has been implemented making use of a Digital Micromirror Device (DMD) to flicker between a 2.3 visual degrees circular reference and a set of circular test patterns in a monocular Maxwellian view at 0.5 Hz. The brightness of the test is adjusted by the duty cycle of the projected light to an upper limit of 22 727 Hz. The wavelength and bandwidth are set by a tuneable liquid-crystal filter centred at 550 nm. A total of four measurement series for 11 pupil entrance points have been realized for the right eye of 6 emmetropic and 10 myopic subjects whose pupils were dilated with tropicamide. Five of the emmetropic subjects wore ophthalmic trial lenses in the range of -3 to +9 dioptres to mimic hyperopic to highly myopic vision and resulting visibility plots have been fitted to a Gaussian SCE-I function. In turn, the myopic subjects wore their natural correction during the analysis of the SCE-I. All subjects had their axial eye length determined with an ultrasound device. RESULTS: A SCE-I directionality parameter in the range of 0.03 to 0.06/mm2 was found for the emmetropic subjects with corrected vision in fair agreement to values in the literature. The results also revealed a marked reduction in directionality in the range from 16% to 30% with every 3 dioptre increase of simulated myopia, as well as a 10% increased directionality in simulated hyperopic eyes. For both emmetropic and myopic subjects, a decrease in directionality with increase in axial length was found in agreement with theoretical expectations. CONCLUSION: The study confirms a clear link between SCE-I directionality, uncorrected defocus, and axial eye length. This may play a role for emmetropization and thus myopic progression as cone photoreceptors capture light from a wider pupil area in elongated eyes due to a geometrical scaling.

Retina-simulating phantom produced by photolithography.

Cone photoreceptors have a narrow acceptance angle that is well matched to the size of the eye pupil and dampens the visual impact of aberrations and scattering. However, the structure of the human retina is not replicated in existing eye models used to test refractive designs or retinal implants that restore partial vision to the blind. Here, we report on an artificial waveguide-based retinal phantom manufactured by photolithography in photoresist film with dimensions and refractive index contrast similar to the retinal receptor layer. The optical performance of the waveguide array is analyzed in terms of angular coupling efficiency, and it is experimentally verified that the structure leads to improved resolution and contrast of optical images transmitted through the layer when defocus is present.

Volumetric integration model of the Stiles-Crawford effect of the first kind and its experimental verification.

The integrated Stiles-Crawford function is commonly used as apodization model for vision through the natural eye pupil. However, this method does not account for possible effects related to the retinal thickness, the large length-to-diameter aspect ratio of the photoreceptors, or the use of nonMaxwellian illumination. Here, we introduce a geometrical optics model to calculate the fraction of overlap between light at the retina and the photoreceptor outer segments where absorption triggers vision. The model, which does not account for photoreceptor waveguiding, is discussed for both Maxwellian and nonMaxwellian illumination. The integrated Stiles-Crawford effect is analyzed experimentally with a uniaxial pupil-size flicker methodology and we find that the psychophysical measurements match better to the geometrical optics predictions than direct integration of a Stiles-Crawford function.

Virtual pyramid wavefront sensor for phase unwrapping.

Noise affects wavefront reconstruction from wrapped phase data. A novel method of phase unwrapping is proposed with the help of a virtual pyramid wavefront sensor. The method was tested on noisy wrapped phase images obtained experimentally with a digital phase-shifting point diffraction interferometer. The virtuality of the pyramid wavefront sensor allows easy tuning of the pyramid apex angle and modulation amplitude. It is shown that an optimal modulation amplitude obtained by monitoring the Strehl ratio helps in achieving better accuracy. Through simulation studies and iterative estimation, it is shown that the virtual pyramid wavefront sensor is robust to random noise.

Wavefront sensing using a liquid-filled photonic crystal fiber.

A novel wavefront sensor based on a microstructural array of waveguides is proposed. The method is based on the sensitivity in light-coupling efficiency to the wavefront gradient present at the entrance aperture of each waveguide in an array, and hence the amount of incident light that couples is influenced by wavefront aberrations. The concept is illustrated with wavefront measurements that have been performed using a liquid-filled photonic crystal fiber (LF-PCF) working as a coherent fiber bundle. The pros and cons of the LF-PCF based sensor are discussed.

Phase unwrapping with a virtual Hartmann-Shack wavefront sensor.

The use of a spatial light modulator for implementing a digital phase-shifting (PS) point diffraction interferometer (PDI) allows tunability in fringe spacing and in achieving PS without the need for mechanically moving parts. However, a small amount of detector or scatter noise could affect the accuracy of wavefront sensing. Here, a novel method of wavefront reconstruction incorporating a virtual Hartmann-Shack (HS) wavefront sensor is proposed that allows easy tuning of several wavefront sensor parameters. The proposed method was tested and compared with a Fourier unwrapping method implemented on a digital PS PDI. The rewrapping of the Fourier reconstructed wavefronts resulted in phase maps that matched well the original wrapped phase and the performance was found to be more stable and accurate than conventional methods. Through simulation studies, the superiority of the proposed virtual HS phase unwrapping method is shown in comparison with the Fourier unwrapping method in the presence of noise. Further, combining the two methods could improve accuracy when the signal-to-noise ratio is sufficiently high.

Digital phase-shifting point diffraction interferometer.

A digital phase-shifting (PS) point diffraction interferometer is demonstrated with a transmitting liquid crystal spatial light modulator. This novel wavefront sensor allows tunability in the choice of pinhole size and eliminates the need for mechanically moving parts to achieve PS. It is shown that this wavefront sensor is capable of sensing Zernike aberrations introduced with a deformable mirror. The results obtained are compared with those of a commercial Hartmann-Shack wavefront sensor.

Digital pyramid wavefront sensor with tunable modulation.

The pyramid wavefront sensor is known for its high sensitivity and dynamic range that can be tuned by mechanically altering its modulation amplitude. Here, a novel modulating digital scheme employing a reflecting phase only spatial light modulator is demonstrated. The use of the modulator allows an easy reconfigurable pyramid with digital control of the apex angle and modulation geometry without the need of any mechanically moving parts. Aberrations introduced by a 140-actuator deformable mirror were simultaneously sensed with the help of a commercial Hartmann-Shack wavefront sensor. The wavefronts reconstructed using the digital pyramid wavefront sensor matched very closely with those sensed by the Hartmann-Shack. It is noted that a tunable modulation is necessary to operate the wavefront sensor in the linear regime and to accurately sense aberrations. Through simulations, it is shown that the wavefront sensor can be extended to astronomical applications as well. This novel digital pyramid wavefront sensor has the potential to become an attractive option in both open and closed loop adaptive optics systems.

Exploring the Stiles-Crawford effect of the first kind with coherent light and dual Maxwellian sources.

The visual impact of light obliquely incident on the retina is diminished due to the Stiles-Crawford effect of the first kind. It is normally analyzed by scanning a small Maxwellian source across the eye pupil while making subjective visibility comparisons to a static reference field that enters the eye near the pupil center. Here, we propose an alternative characterization method with two coherent Maxwellian point sources located at opposing sides of the pupil. This produces interference fringes at the retina with an underlying phase gradient. Altering the power ratio of the two point sources makes tuning of the wavefront inclination at the retina feasible. Thus, the Stiles-Crawford effect of the first kind can be examined without scanning the incident light across the pupil. In this paper, a spatial light modulator with holographic phase maps has been used to generate two Maxwellian point sources at the pupil that project a given phase variation onto the retina. We found that the effective obliqueness of light at the retina is determined by the weighted center-of-mass of the field amplitude at the pupil. Alternative techniques to generate the two secondary point sources may improve the accuracy of the method.

Myopic aberrations: impact of centroiding noise in Hartmann Shack wavefront sensing.

PURPOSE: The presence of photon noise and readout noise can lead to centroiding errors in a Hartmann Shack wavefront sensor (HS) and hence limit the accuracy of wavefront reconstruction. The aim of this paper is to compare, via Monte Carlo simulations, the accuracy of various centroiding methods in detecting noisy focal spot patterns of the HS while sensing ocular aberrations of myopic eyes. METHODS: Myopic ocular aberrations were randomly simulated by using the modal statistics obtained from the measurements of 41 myopic subjects. HS spot patterns were simulated using a fast Fourier method where photon noise and readout noise were added using appropriate statistics. Adopting five different centroiding techniques: (1) centre of gravity, (2) weighted centre of gravity, (3) intensity weighted centroiding, (4) iteratively weighted centre of gravity and (5) matched filter based centroiding along with a zonal based wavefront sensing approach; the wavefronts were estimated and compared, by calculating the root mean square (RMS) wavefront error, with the initially simulated wavefront. The magnitude of readout noise was varied in terms of the maximum number of photons and electrons per subaperture per frame. The RMS error was calculated for each of the centroiding algorithms. RESULTS: For higher magnitude of readout noise and lesser number of photons per subaperture per frame (n), matched filter, iteratively weighted centre of gravity and intensity weighted centroiding outperform centre of gravity and weighted centre of gravity methods, for an appropriately chosen focal length and subaperture pitch. The plots of RMS error as a function of 'n' show that for lower amplitude of readout noise, computationally efficient centre of gravity and intensity weighted centroiding methods can be safely adopted to obtain high enough reconstruction accuracy. Also, even at greater readout noise levels, for a large enough 'n', intensity weighted centroiding is enough to sense the aberrations with high accuracy. It is shown that the wavefront sensing accuracy depends on the size of the spots and bit resolution of the camera. CONCLUSION: Five different centroid detection methods used in a HS in the presence of photon noise and readout noise were analysed in the context of sensing ocular aberrations of myopic subjects and identify cases under which each of these methods is appropriate.

Introduction to Visual and Physiological Optics feature issue of Biomedical Optics Express and JOSA A.

This feature issue collects articles presented at the tenth Visual and Physiological Optics meeting (VPO2022), held August 29-31, 2022, in Cambridge, UK. This joint feature issue between Biomedical Optics Express and Journal of the Optical Society of America A includes articles that cover the broad range of topics addressed at the meeting and examples of the current state of research in the field.

Wavefront sensing with an axicon.

The use of a large apex-angle axicon for common-path interferometric wavefront sensing is proposed. The approach is a variant of point-diffraction interferometry bearing similarities to pyramidal wavefront sensing. A theoretical basis for wavefront sensing with an axicon is developed, and the outcomes of numerical simulations are compared to experimental results obtained with spherical and cylindrical ophthalmic trial lenses. It is confirmed that the axicon can be used for wavefront sensing, although its refraction may ultimately complicate and limit its operational range.

Absence of an integrated Stiles-Crawford function for coherent light.

The Stiles-Crawford effect that relates visibility to pupil point is typically expressed by a Gaussian function at any given wavelength of illumination. The pupil location of the maximum and the width of this function refer, respectively, to the pointing and waveguide properties of individual cone photoreceptors. In vision simulations, the function is integrated across the pupil when estimating effective retinal images, but the validity of this approach has still not been unequivocally confirmed. Indeed, aberrations and coherence properties may significantly alter not only the amplitude but also the phase distribution of the light at the retina in a way that differs fundamentally from that of the Maxwellian illumination configuration used when characterizing the effect. Here, we report on an experimental comparison of the traditionally determined Stiles-Crawford function and the equivalent for annular and half-annular apertures using extended highly coherent and incoherent sources. We show that an integrated Stiles-Crawford function is absent for coherent light but remains valid for highly incoherent light at the pupil. The results are supported by numerical evidence for coherent light propagation and are in agreement with a light-coupling understanding of retina photoreceptor waveguides.

Geometrical scaling of the developing eye and photoreceptors and a possible relation to emmetropization and myopia.

In this study the role of vergence in relation to age-dependent scaling of eye and photoreceptor parameters is studied. The underlying hypothesis is that the size and packing of outer segments is matched to the pupil size outdoors in photopic conditions. Vergence is analysed in relation to the angular spectrum of waves being incident using age-dependent data from the literature for the actual geometry and density of photoreceptor cones and rods. This approach is used to derive simple relations for the angular confinement of light along outer segments. Only with a small photopic pupil can leakage and crosstalk for both central and peripheral photoreceptors be entirely ruled out due to the finite length of the outer segments. A limiting 3 mm pupil size is found for children in the school age. Larger pupils will increase the likelihood of leakage and crosstalk that may therefore impact on emmetropization. This study has introduced a new paradigm in myopia research by considering vergence across the 3-D retina as being matched to the angular spectrum of waves being incident from the eye pupil. Emmetropization suggests a delicate balance between photoreceptor outer segment length and density in relation to pupil size. Only when balanced will leakage and crosstalk between adjacent outer segments be effectively suppressed thereby ensuring the highest possible light capture efficiency by visual pigments in the outer segments whether an image is formed on the retina or not.

Subjective measurement of the Stiles-Crawford effect with different field sizes.

The Stiles-Crawford effect of the first kind (SCE) is the phenomenon in which light entering the eye near the center of the pupil appears brighter than light entering near the edge. Previous investigations have found an increase in the directionality (steepness) of the effect as the testing location moves from the center of the visual field to parafoveal positions, but the effect of central field size has not been considered. The influence of field size on the SCE was investigated using a uniaxial Maxwellian system in which stimulus presentation was controlled by an active-matrix liquid crystal display. SCE directionality increased as field size increased from 0.5° to 4.7° diameter, although this was noted in four mild myopes and not in two emmetropes. The change with field size was supported by a geometric optics absorption model.

Temporal wavefront stability of an ultrafast high-power laser beam.

We measured the temporal dynamics of wavefront aberrations in a beam produced by a commercial ultrafast high-power laser with a research-prototype real-time Hartmann-Shack wavefront sensor. Measurements were performed at two different temporal rates for a 7 mm diameter. Results showed that changes in the wavefront aberrations were always lower than 1%. The main contribution to the total root-mean-square (RMS) wavefront error was due to the effects of low order aberrations (defocus and astigmatism), which persisted even after cavity realignment. The potential improvement in the beam quality after correction of the different aberration modes was also shown. Real-time measurements of laser aberrations while modifying cavity parameters might be a useful tool to improve the beam quality.

Directional light-capture efficiency of the foveal and parafoveal photoreceptors at different luminance levels: an experimental and analytical study.

A gradual drop in visibility with obliquely incident light on retinal photoreceptors is namely described by the Stiles-Crawford effect of the first kind and characterized by a directionality parameter. Using a digital micromirror device in a uniaxial flicker system, here we report on variations of this effect with luminance levels, wavelengths within the visible and near-infrared spectrum and retinal regions ranging from the fovea to 7.5° parafoveal. Results show a consistent directionality in mesopic and photopic conditions. Higher directionality is measured for longer wavelengths, and a decrease with retinal eccentricity is observed. Results are discussed in relation to an absorption model for the visual pigments taking the outer-segment packing and thickness of the neural retina into account. Good correspondence is found without enforcing photoreceptor waveguiding.